Finite Group Databasebeta

← #35196889

Subgroups — #35196889

Order 20224.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777721C214yesmaximal, complemented
2#23777702C214yesmaximal, complemented
3#23777631C214yesmaximal, complemented
4#23777620C214yesmaximal, complemented
5#23777580C218yesmaximal, complemented
6#23777429C214yesmaximal, complemented
7#23777423C214yesmaximal, complemented
8#23777227C214yesmaximal, complemented
9#23777156C214yesmaximal, complemented
10#23777132C212yesmaximal, complemented
11#23777125C212yesmaximal, complemented
12#23777106C212yesmaximal, complemented
13#23777087C214yesmaximal, complemented
14#23777067C212yesmaximal, complemented
15#23777062C212yesmaximal, complemented
16#23777035C211yesmaximal, characteristic, complemented
17#23777029C214yesmaximal, complemented
18#525×D79C212yesmaximal, complemented
19C22×#14579132C211yesmaximal, characteristic, complemented
20C79×#3484C211yesmaximal, characteristic, complemented
21C2×#14579206C2214yescomplemented
22C2×#14579206C2211yescharacteristic, complemented
23C2×#41×D79C2212yescomplemented
24C23×C22⋊D79C2212yescomplemented
25C23×C4×D79C2211yescharacteristic, complemented
26#19099310C2218yescomplemented
27#19099308C2218yescomplemented
28#19099302C2218yescomplemented
29#19099301C2218yescomplemented
30#19099278C2214yescomplemented
31#19099277C2214yescomplemented
32#19099271C2214yescomplemented
33#19099270C2214yescomplemented
34#19099265C2214yescomplemented
35#19099265C2214yescomplemented
36#19099263C2214yescomplemented
37#19099263C2214yescomplemented
38#19099260C2218yescomplemented
39#19099260C2214yescomplemented
40#19099259C2214yescomplemented
41#19099258C2218yescomplemented
42#19099255C2214yescomplemented
43#19099253C2214yescomplemented
44#19099244C2218yescomplemented
45#19099244C2218yescomplemented
46#19099239C2218yescomplemented
47#19099239C2218yescomplemented
48#19099233C2214yescomplemented
49#19099232C2214yescomplemented
50#19099221C2214yescomplemented
51#19099220C2214yescomplemented
52#19099218C2214yescomplemented
53#19099217C2214yescomplemented
54#19099213C2214yescomplemented
55#19099213C2214yescomplemented
56#19099210C2218yescomplemented
57#19099207C2218yescomplemented
58#19099207C2218yescomplemented
59#19099207C2214yescomplemented
60#19099207C2214yescomplemented
61#19099207C2214yescomplemented
62#19099206C2214yescomplemented
63#19099203C2218yescomplemented
64#19099203C2218yescomplemented
65#19099200C2218yescomplemented
66#19099200C2218yescomplemented
67#19099200C2218yescomplemented
68#19099200C2218yescomplemented
69#19099200C2218yescomplemented
70#19099198C2214yescomplemented
71D4×C22⋊D79C2214yescomplemented
72D4×C22⋊D79C2214yescomplemented
73D4×C22⋊D79C2218yescomplemented
74D4×C22⋊D79C2218yescomplemented
75D4×C22⋊D79C2214yescomplemented
76#19099195C2218yescomplemented
77#19099195C2218yescomplemented
78#19099191C2212yescomplemented
79#19099189C2214yescomplemented
80#19099182C2214yescomplemented
81#19099178C2214yescomplemented
82#19099167C2214yescomplemented
83#19099166C2218yescomplemented
84#19099164C2214yescomplemented
85#19099163C2218yescomplemented
86#19099157C2218yescomplemented
87#19099156C2218yescomplemented
88#19099149C2218yescomplemented
89#19099148C2218yescomplemented
90#19099148C2218yescomplemented
91#19099148C2218yescomplemented
92#19099145C2218yescomplemented
93#19099142C2214yescomplemented
94#19099142C2218yescomplemented
95#19099141C2212yescomplemented
96#19099141C2214yescomplemented
97#19099130C2212yescomplemented
98#19099130C2214yescomplemented
99#19099129C2214yescomplemented
100#19099128C2218yescomplemented
101#19099125C2214yescomplemented
102#19099123C2218yescomplemented
103#19099123C2218yescomplemented
104#19099122C2214yescomplemented
105#19099122C2214yescomplemented
106#19099122C2214yescomplemented
107#19099111C2214yescomplemented
108#19099110C2214yescomplemented
109#19099095C2214yescomplemented
110#19099092C2214yescomplemented
111#19099076C2212yescomplemented
112#19099076C2212yescomplemented
113#19099075C2212yescomplemented
114#19099074C2212yescomplemented
115#19099073C2212yescomplemented
116#19099073C2212yescomplemented
117#19099073C2214yescomplemented
118#19099072C2214yescomplemented
119#19099072C2214yescomplemented
120#19099071C2214yescomplemented
121#19099070C2212yescomplemented
122#19099070C2214yescomplemented
123#19099069C2218yescomplemented
124#19099069C2214yescomplemented
125#123×D79C2214yescomplemented
126C22⋊Q8×D79C2212yescomplemented
127C22⋊Q8×D79C2212yescomplemented
128C2×#14579132C2212yescomplemented
129C2×#14579132C2212yescomplemented
130C2×#14579132C2214yescomplemented
131C2×#14579132C2214yescomplemented
132C2×#14579132C2214yescomplemented
133C2×#14579132C2214yescomplemented
134C2×#14579132C2214yescomplemented
135C2×#14579132C2214yescomplemented
136#121×D79C2212yescomplemented
137#121×D79C2212yescomplemented
138#121×D79C2214yescomplemented
139C2×#14579130C2214yescomplemented
140#120×D79C2214yescomplemented
141#19099046C2212yescomplemented
142#19099043C2212yescomplemented
143#19099038C2211yescharacteristic, complemented
144#19099038C2214yescomplemented
145#19099036C2214yescomplemented
146#19099036C2214yescomplemented
147C4×D4×D79C2214yescomplemented
148C4×D4×D79C2214yescomplemented
149#117×D79C2212yescomplemented
150C22×C4⋊Dic79C2211yescharacteristic, complemented
151C22×C22⋊Dic79C2212yescomplemented
152C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
153C23×D4×C79C2211yescharacteristic, complemented
154#546×C79C2214yescomplemented
155#546×C79C2214yescomplemented
156D42×C79C2214yescomplemented
157D42×C79C2214yescomplemented
158#535×C79C2212yescomplemented
159#534×C79C2214yescomplemented
160#525×C79C2212yescomplemented
161C2×#120×C79C2214yescomplemented
162#518×C79C2211yescharacteristic, complemented
163C24×D79C2311yescharacteristic
164#14579206—416no—
165#14579206—44no—
166C2×#11929625C2312yescomplemented
167C2×#11929624C2312yes—
168C2×#11929624C2318yescomplemented
169C2×#11929624C2314yescomplemented
170C2×#11929623C2318yes—
171C2×#11929623C2314yes—
172C2×#11929623C2318yescomplemented
173C2×#11929623C2314yescomplemented
174C2×#11929623C2312yescomplemented
175#41×D79—48no—
176C2×Q8×D79C2312yescomplemented
177C22×C22⋊D79—48no—
178C22×C22⋊D79C2314yes—
179C22×C22⋊D79C2314yes—
180C22×C22⋊D79C2314yes—
181C22×C22⋊D79C2314yes—
182C22×C22⋊D79C2314yes—
183C22×C22⋊D79C2318yes—
184C22×C22⋊D79C2314yes—
185C22×C22⋊D79C2314yes—
186C22×C22⋊D79C2318yescomplemented
187C2×D4×D79C2314yes—
188C2×D4×D79C2314yes—
189C2×D4×D79C2314yes—
190C2×D4×D79C2318yescomplemented
191C2×D4×D79C2314yescomplemented
192C2×D4×D79C2312yescomplemented
193C23×Dic79C2311yescharacteristic
194C23×Dic79C2312yes—
195C22×C4×D79—44no—
196C22×C4×D79C2312yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2312yes—
200C22×C4×D79C2312yes—
201C22×C4×D79C2312yes—
202C22×C4×D79C2314yescomplemented
203#14579161C2314yescomplemented
204#14579160C2314yescomplemented
205#14579157C2318yescomplemented
206#14579157C2314yescomplemented
207#14579157C2318yescomplemented
208#14579156C2318yescomplemented
209#14579154C2318yescomplemented
210#14579154C2318yescomplemented
211#14579154C2318yescomplemented
212#14579154C2318yescomplemented
213#14579154C2318yescomplemented
214#14579153C2314yescomplemented
215#14579152C2318yescomplemented
216#14579152C2314yescomplemented
217#14579151C2318yescomplemented
218#14579148C2318yescomplemented
219#14579148C2318yescomplemented
220#14579148C2314yescomplemented
221#14579147C2318yescomplemented
222#14579147C2318yescomplemented
223#14579147C2318yescomplemented
224#14579147C2318yescomplemented
225#14579146C2314yescomplemented
226#14579146C2314yescomplemented
227#14579145C2314yes—
228#14579145C2318yes—
229#14579145C2318yescomplemented
230#14579145C2318yescomplemented
231#14579144C2314yes—
232#14579144C2318yescomplemented
233#14579144C2318yescomplemented
234#14579143C2314yescomplemented
235#14579143C2318yescomplemented
236#14579143C2318yescomplemented
237#14579143C2318yescomplemented
238#14579143C2318yescomplemented
239#14579143C2318yescomplemented
240#14579143C2314yescomplemented
241#14579142C2314yes—
242#14579142C2318yes—
243#14579142C2318yescomplemented
244#14579142C2318yescomplemented
245#14579142C2318yescomplemented
246#14579142C2318yescomplemented
247#14579141C2312yescomplemented
248#14579141C2318yescomplemented
249#14579141C2312yescomplemented
250#14579140C2312yes—
251#14579140C2312yes—
252#14579140C2314yescomplemented
253#14579140C2318yescomplemented
254#14579140C2318yescomplemented
255#14579139C2314yescomplemented
256#14579139C2314yescomplemented
257#14579138C2314yes—
258#14579138C2318yes—
259#14579138C2318yes—
260#14579138C2314yes—
261#14579138C2318yescomplemented
262#14579138C2318yescomplemented
263#14579138C2318yescomplemented
264#14579137C2312yescomplemented
265#14579137C2314yescomplemented
266#14579137C2312yescomplemented
267#14579136C2312yescomplemented
268#14579136C2312yescomplemented
269#14579135C2312yes—
270#14579135C2312yes—
271#14579135C2318yescomplemented
272#14579135C2314yescomplemented
273#14579135C2318yescomplemented
274#14579134C2314yescomplemented
275#14579134C2318yescomplemented
276#14579134C2318yescomplemented
277#14579134C2318yescomplemented
278#14579134C2318yescomplemented
279#14579134C2314yescomplemented
280#14579133C2318yes—
281#14579133C2314yes—
282#14579133C2318yes—
283#14579133C2314yes—
284#14579133C2318yescomplemented
285#14579133C2318yescomplemented
286#14579133C2318yescomplemented
287#14579133C2318yescomplemented
288#14579133C2318yescomplemented
289#14579133C2318yescomplemented
290#14579133C2318yescomplemented
291#14579133C2318yescomplemented
292#14579132C2314yes—
293#14579132C2318yes—
294#14579132C2314yes—
295#14579132C2318yes—
296#14579132C2314yes—
297#14579132C2314yes—
298#14579132C2318yes—
299#14579132C2314yes—
300#14579132C2314yes—
301#14579132C2318yes—
302#14579132C2314yes—
303#14579132C2314yes—
304#14579132C2314yescomplemented
305#14579132C2314yescomplemented
306#14579132C2318yescomplemented
307#14579132C2318yescomplemented
308#14579132C2318yescomplemented
309#14579132C2312yescomplemented
310#14579132C2318yescomplemented
311#14579132C2314yescomplemented
312#14579132C2312yescomplemented
313#14579131C2314yes—
314#14579131C2314yes—
315#14579131C2314yes—
316#14579131C2318yescomplemented
317#14579130C2318yes—
318#14579130C2318yes—
319#14579130C2318yes—
320#14579130C2314yes—
321#14579130C2318yescomplemented
322#14579130C2318yescomplemented
323#14579129C2314yes—
324#14579129C2314yes—
325#14579129C2314yes—
326#14579129C2318yescomplemented
327#14579129C2318yescomplemented
328#14579129C2318yescomplemented
329#14579129C2318yescomplemented
330Q8×Dic79C2314yescomplemented
331C4×Dic158C2314yescomplemented
332C4×D316C2314yescomplemented
333C4×D316C2314yescomplemented
334C4×D316C2314yescomplemented
335D4×Dic79C2314yes—
336D4×Dic79C2318yes—
337D4×Dic79C2318yes—
338D4×Dic79C2314yes—
339D4×Dic79C2318yescomplemented
340D4×Dic79C2318yescomplemented
341D4×Dic79C2314yescomplemented
342D4×Dic79C2314yescomplemented
343D4×Dic79C2314yescomplemented
344#14579123C2314yescomplemented
345#14579123C2314yescomplemented
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348C4×C22⋊D79C2318yescomplemented
349C4×C22⋊D79C2318yescomplemented
350C4×C22⋊D79C2318yescomplemented
351C4×C22⋊D79C2318yescomplemented
352C4×C22⋊D79C2314yescomplemented
353C4×C22⋊D79C2314yescomplemented
354(C22⋊D79)⋊C4C2314yes—
355(C22⋊D79)⋊C4C2318yes—
356(C22⋊D79)⋊C4C2318yes—
357(C22⋊D79)⋊C4C2314yes—
358(C22⋊D79)⋊C4C2318yescomplemented
359(C22⋊D79)⋊C4C2314yescomplemented
360(C22⋊D79)⋊C4C2318yescomplemented
361(C22⋊D79)⋊C4C2314yescomplemented
362#14579120C2312yes—
363#14579120C2318yescomplemented
364#14579120C2314yescomplemented
365#14579119C2314yescomplemented
366#14579119C2312yescomplemented
367#14579119C2312yescomplemented
368#14579118C2314yescomplemented
369#14579117C2314yes—
370#14579117C2318yes—
371#14579117C2318yescomplemented
372C2×C4⋊Dic79C2312yes—
373C2×C4⋊Dic79C2312yes—
374C2×C4⋊Dic79C2314yes—
375C2×C4⋊Dic79C2314yes—
376C2×C4⋊Dic79C2314yescomplemented
377C4⋊C4×D79C2314yescomplemented
378C4⋊C4×D79C2314yescomplemented
379C4⋊C4×D79C2312yescomplemented
380C4⋊C4×D79C2314yescomplemented
381C4⋊C4×D79C2312yescomplemented
382C2×C22⋊Dic79C2314yes—
383C2×C22⋊Dic79C2314yes—
384C2×C22⋊Dic79C2314yes—
385C2×C22⋊Dic79C2314yes—
386C2×C22⋊Dic79C2314yes—
387C2×C22⋊Dic79C2318yes—
388C2×C22⋊Dic79C2314yes—
389C2×C22⋊Dic79C2314yes—
390C2×C22⋊Dic79C2318yescomplemented
391C22⋊C4×D79C2314yes—
392C22⋊C4×D79C2314yes—
393C22⋊C4×D79C2314yes—
394C22⋊C4×D79C2314yescomplemented
395C22⋊C4×D79C2318yescomplemented
396C22⋊C4×D79C2314yescomplemented
397C42×D79C2314yescomplemented
398C25×C79C2312yes—
399H(5,𝔽2)×C79—44no—
400C2×#41×C79C2312yes—
401C2×#41×C79C2314yescomplemented
402C22×D4×C79—44no—
403C22×D4×C79C2311yescharacteristic
404C22×D4×C79C2311yescharacteristic
405C22×D4×C79C2314yes—
406C22×D4×C79C2314yes—
407C22×D4×C79C2314yes—
408C22×D4×C79C2314yes—
409C22×D4×C79C2314yes—
410C22×D4×C79C2312yes—
411C22×D4×C79C2314yescomplemented
412C23×C4×C79C2311yescharacteristic
413#127×C79C2314yescomplemented
414#124×C79C2314yescomplemented
415#123×C79C2314yes—
416#123×C79C2318yescomplemented
417C22⋊Q8×C79C2312yes—
418C22⋊Q8×C79C2312yes—
419#121×C79C2312yes—
420#121×C79C2312yes—
421#121×C79C2318yescomplemented
422#121×C79C2314yescomplemented
423#121×C79C2318yescomplemented
424#121×C79C2314yescomplemented
425#120×C79C2318yes—
426#120×C79C2318yes—
427#120×C79C2318yes—
428#120×C79C2314yes—
429#120×C79C2318yescomplemented
430C4×D4×C79C2314yes—
431C4×D4×C79C2314yes—
432C4×D4×C79C2314yescomplemented
433C4×D4×C79C2314yescomplemented
434#117×C79C2312yes—
435C2×C22⋊C4×C79C2314yes—
436C2×C22⋊C4×C79C2314yes—
437C2×C22⋊C4×C79C2314yes—
438C23×D79—24no—
439C23×D79—42no—
440C23×D79—42no—
441C23×D79C2412yes—
442C23×D79C2412yes—
443C23×D79C2411yescharacteristic
444C23×D79C2414yes—
445C23×D79C2414yes—
446C23×D79C2411yescharacteristic
447#11929625—44no—
448#11929624—28no—
449#11929624—416no—
450#11929624—48no—
451#11929623—416no—
452#11929623—48no—
453#11929623—416no—
454#11929623—44no—
455#11929623—48no—
456C2×Dic158C2412yes—
457C2×Dic158C2414yes—
458C2×Dic158C2418yes—
459Q8×D79—44no—
460C2×D316C2412yes—
461C2×D316C2414yes—
462C2×D316C2414yes—
463C2×D316C2414yes—
464C2×C22⋊D79—216no—
465C2×C22⋊D79—416no—
466C2×C22⋊D79—48no—
467C2×C22⋊D79—416no—
468C2×C22⋊D79—48no—
469C2×C22⋊D79—48no—
470C2×C22⋊D79—48no—
471C2×C22⋊D79—48no—
472C2×C22⋊D79—48no—
473C2×C22⋊D79C2414yes—
474C2×C22⋊D79C2414yes—
475C2×C22⋊D79C2414yes—
476C2×C22⋊D79C2418yes—
477C2×C22⋊D79C2418yes—
478C2×C22⋊D79C2414yes—
479C2×C22⋊D79C2414yes—
480C2×C22⋊D79C2418yes—
481C2×C22⋊D79C2414yes—
482C2×C22⋊D79C2418yes—
483C2×C22⋊D79C2418yes—
484C2×C22⋊D79C2414yes—
485C2×C22⋊D79C2418yes—
486C2×C22⋊D79C2418yes—
487C2×C22⋊D79C2418yes—
488D4×D79—216no—
489D4×D79—48no—
490D4×D79—48no—
491D4×D79—416no—
492D4×D79—44no—
493D4×D79—48no—
494C22×Dic79—42no—
495C22×Dic79—44no—
496C22×Dic79C2412yes—
497C22×Dic79C2414yes—
498C22×Dic79C2414yes—
499C22×Dic79C2418yes—
500C22×Dic79C2414yes—
501C22×Dic79C2414yes—
502C22×Dic79C2411yescharacteristic
503C22×Dic79C2412yes—
504C22×Dic79C2411yescharacteristic
505C22×Dic79C2414yes—
506C22×Dic79C2414yes—
507C22×Dic79C2414yes—
508C2×C4×D79—28no—
509C2×C4×D79—44no—
510C2×C4×D79—48no—
511C2×C4×D79—44no—
512C2×C4×D79—44no—
513C2×C4×D79—44no—
514C2×C4×D79—44no—
515C2×C4×D79C2412yes—
516C2×C4×D79C2414yes—
517C2×C4×D79C2414yes—
518C2×C4×D79C2412yes—
519C2×C4×D79C2412yes—
520C2×C4×D79C2412yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2418yes—
523C2×C4×D79C2414yes—
524C2×C4×D79C2414yes—
525C2×C4×D79C2412yes—
526C2×C4×D79C2412yes—
527C2×C4×D79C2412yes—
528C2×C4×D79C2412yes—
529C4⋊Dic79C2414yes—
530C4⋊Dic79C2412yes—
531C4⋊Dic79C2412yes—
532C4⋊Dic79C2414yes—
533C4⋊Dic79C2414yes—
534C4⋊Dic79C2414yes—
535C4⋊Dic79C2418yes—
536C4⋊Dic79C2418yes—
537C4⋊Dic79C2418yes—
538Dic79⋊C4C2414yes—
539Dic79⋊C4C2414yes—
540Dic79⋊C4C2414yes—
541Dic79⋊C4C2414yes—
542Dic79⋊C4C2418yes—
543Dic79⋊C4C2414yes—
544Dic79⋊C4C2414yes—
545Dic79⋊C4C2418yes—
546Dic79⋊C4C2418yes—
547Dic79⋊C4C2418yes—
548C22⋊Dic79C2414yes—
549C22⋊Dic79C2414yes—
550C22⋊Dic79C2414yes—
551C22⋊Dic79C2418yes—
552C22⋊Dic79C2414yes—
553C22⋊Dic79C2414yes—
554C22⋊Dic79C2418yes—
555C22⋊Dic79C2418yes—
556C22⋊Dic79C2418yes—
557C22⋊Dic79C2418yes—
558C22⋊Dic79C2418yes—
559C22⋊Dic79C2418yes—
560C22⋊Dic79C2418yes—
561C22⋊Dic79C2418yes—
562(C2×D79)⋊C4C2414yes—
563(C2×D79)⋊C4C2414yes—
564(C2×D79)⋊C4C2414yes—
565(C2×D79)⋊C4C2414yes—
566(C2×D79)⋊C4C2414yes—
567(C2×D79)⋊C4C2414yes—
568(C2×D79)⋊C4C2414yes—
569(C2×D79)⋊C4C2418yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2414yes—
572(C2×D79)⋊C4C2414yes—
573(C2×D79)⋊C4C2418yes—
574C4×Dic79C2414yes—
575C4×Dic79C2414yes—
576C4×Dic79C2414yes—
577C4×Dic79C2418yes—
578C4×Dic79C2418yes—
579C24×C79—44no—
580C24×C79—44no—
581C24×C79—44no—
582C24×C79C2411yescharacteristic
583C24×C79C2412yes—
584C24×C79C2414yes—
585C24×C79C2414yes—
586C24×C79C2412yes—
587C24×C79C2414yes—
588#41×C79—28no—
589#41×C79—48no—
590C2×Q8×C79C2412yes—
591C2×D4×C79—24no—
592C2×D4×C79—24no—
593C2×D4×C79—48no—
594C2×D4×C79—48no—
595C2×D4×C79—48no—
596C2×D4×C79—44no—
597C2×D4×C79—48no—
598C2×D4×C79—48no—
599C2×D4×C79—48no—
600C2×D4×C79C2414yes—
601C2×D4×C79C2414yes—
602C2×D4×C79C2412yes—
603C2×D4×C79C2414yes—
604C2×D4×C79C2414yes—
605C2×D4×C79C2414yes—
606C2×D4×C79C2418yes—
607C2×D4×C79C2418yes—
608C2×D4×C79C2418yes—
609C2×D4×C79C2418yes—
610C22×C4×C79—24no—
611C22×C4×C79C2414yes—
612C22×C4×C79C2412yes—
613C22×C4×C79C2412yes—
614C22×C4×C79C2411yescharacteristic
615C22×C4×C79C2414yes—
616C22×C4×C79C2414yes—
617C22×C4×C79C2414yes—
618C22×C4×C79C2411yescharacteristic
619C4⋊C4×C79C2412yes—
620C4⋊C4×C79C2412yes—
621C4⋊C4×C79C2414yes—
622C4⋊C4×C79C2414yes—
623C22⋊C4×C79C2414yes—
624C22⋊C4×C79C2414yes—
625C22⋊C4×C79C2414yes—
626C22⋊C4×C79C2418yes—
627C22⋊C4×C79C2418yes—
628C22⋊C4×C79C2418yes—
629C22⋊C4×C79C2414yes—
630C22⋊C4×C79C2414yes—
631C42×C79C2414yes—
632C23×C79—22no—
633C23×C79—22no—
634C23×C79—22no—
635C23×C79—28no—
636C23×C79—24no—
637C23×C79—24no—
638C23×C79—28no—
639C23×C79—42no—
640C23×C79—44no—
641C23×C79—42no—
642C23×C79—44no—
643C23×C79—44no—
644C23×C79—42no—
645C23×C79—44no—
646C23×C79—42no—
647C23×C79—44no—
648C23×C79—44no—
649C23×C79—44no—
650C23×C79—816no—
651C23×C79C2514yes—
652C23×C79C2514yes—
653C23×C79C2514yes—
654C23×C79C2511yescharacteristic
655C23×C79C2511yescharacteristic
656C23×C79C2511yescharacteristic
657C22×D79—24no—
658C22×D79—22no—
659C22×D79—24no—
660C22×D79—24no—
661C22×D79—24no—
662C22×D79—28no—
663C22×D79—41no—
664C22×D79—42no—
665C22×D79—41no—
666C22×D79—41no—
667C22×D79—42no—
668C22×D79—41no—
669C22×D79—44no—
670C22×D79—44no—
671C22×D79—44no—
672C22×D79—44no—
673C22×D79—44no—
674C22×D79—416no—
675C22×D79H(5,𝔽2)14yescomplemented
676C22×D79C2514yes—
677C22×D79C2512yes—
678C22×D79C2512yes—
679Q8×C79—24no—
680D4×C79—28no—
681D4×C79—28no—
682D4×C79—28no—
683D4×C79—28no—
684D4×C79—24no—
685D4×C79—28no—
686D4×C79—48no—
687D4×C79—48no—
688D4×C79—48no—
689D4×C79—48no—
690C2×C4×C79—22no—
691C2×C4×C79—24no—
692C2×C4×C79—24no—
693C2×C4×C79—28no—
694C2×C4×C79—44no—
695C2×C4×C79—44no—
696C2×C4×C79—44no—
697C2×C4×C79H(5,𝔽2)14yescomplemented
698C2×C4×C79C2514yes—
699C2×C4×C79C2514yes—
700C2×C4×C79C2514yes—
701C2×C4×C79C2512yes—
702C2×C4×C79C2512yes—
703C22⋊D79—28no—
704C22⋊D79—28no—
705C22⋊D79—28no—
706C22⋊D79—28no—
707C22⋊D79—216no—
708C22⋊D79—216no—
709C22⋊D79—48no—
710C22⋊D79—48no—
711C22⋊D79—44no—
712C22⋊D79—44no—
713C22⋊D79—44no—
714C22⋊D79—48no—
715C22⋊D79—48no—
716C22⋊D79—48no—
717C22⋊D79—48no—
718C2×Dic79—24no—
719C2×Dic79—28no—
720C2×Dic79—41no—
721C2×Dic79—42no—
722C2×Dic79—41no—
723C2×Dic79—44no—
724C2×Dic79—44no—
725C2×Dic79—44no—
726C2×Dic79—44no—
727C2×Dic79—48no—
728C2×Dic79—44no—
729C2×Dic79—44no—
730C2×Dic79C2514yes—
731C2×Dic79C2512yes—
732C2×Dic79C2514yes—
733C2×Dic79C2514yes—
734C2×Dic79C2518yes—
735C2×Dic79C2512yes—
736D316—28no—
737D316—24no—
738D316—44no—
739D316—44no—
740C4×D79—28no—
741C4×D79—24no—
742C4×D79—24no—
743C4×D79—24no—
744C4×D79—24no—
745C4×D79—28no—
746C4×D79—42no—
747C4×D79—42no—
748C4×D79—42no—
749C4×D79—42no—
750C4×D79—44no—
751C4×D79—44no—
752C4×D79—44no—
753C4×D79—48no—
754Dic158—24no—
755Dic158—44no—
756Dic158—48no—
757C22×C79—28no—
758C22×C79—21no—
759C22×C79—21no—
760C22×C79—21no—
761C22×C79—21no—
762C22×C79—21no—
763C22×C79—21no—
764C22×C79—24no—
765C22×C79—24no—
766C22×C79—24no—
767C22×C79—24no—
768C22×C79—24no—
769C22×C79—24no—
770C22×C79—24no—
771C22×C79—24no—
772C22×C79—24no—
773C22×C79—84no—
774C22×C79—88no—
775C22×C79—84no—
776C22×C79—88no—
777C22×C79—164no—
778C22×C79C2×H(5,𝔽2)12yes—
779C22×C79C2×H(5,𝔽2)12yes—
780C22×C79#58512yes—
781C22×C79C2611yescharacteristic
782C2×D79—22no—
783C2×D79—22no—
784C2×D79—24no—
785C2×D79—24no—
786C2×D79—22no—
787C2×D79—22no—
788C2×D79—24no—
789C2×D79—22no—
790C2×D79—44no—
791C2×D79—48no—
792C2×D79—48no—
793C2×D79—44no—
794C2×D79—88no—
795C2×D79—164no—
796C2×D79C2×H(5,𝔽2)14yes—
797C4×C79—22no—
798C4×C79—24no—
799C4×C79—24no—
800C4×C79—24no—
801C4×C79C2×H(5,𝔽2)14yes—
802Dic79—28no—
803Dic79—24no—
804Dic79—24no—
805Dic79—22no—
806Dic79—22no—
807Dic79—24no—
808#62818—791nomaximal, Sylow
809C2×C79—22no—
810C2×C79—22no—
811C2×C79—22no—
812C2×C79—44no—
813C2×C79—44no—
814C2×C79—44no—
815C2×C79C22×H(5,𝔽2)11yescharacteristic
816C2×C79C22×H(5,𝔽2)11yescharacteristic
817C2×C79C2×#58511yescharacteristic
818D79—24no—
819D79—42no—
820D79—44no—
821#3542—794no—
822#3542—794no—
823#3537—794no—
824#3536—794no—
825#3534—798no—
826#3519—794no—
827#3519—794no—
828#3505—794no—
829#3496—794no—
830#3494—792no—
831#3494—792no—
832#3492—792no—
833#3490—794no—
834#3488—792no—
835#3488—792no—
836#3484—791no—
837#3484—794no—
838#3484D7911yescharacteristic, complemented
839C2×#525—792no—
840C22×#121—791no—
841C79#6281811yescharacteristic, complemented, Sylow
842C2×H(5,𝔽2)—791no—
843C2×H(5,𝔽2)—794no—
844C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
845C22×#41—792no—
846C23×D4—792no—
847C23×D4C2×D7911yescharacteristic, complemented
848C24×C4—791no—
849#562—798no—
850#562—798no—
851#560—798no—
852#560—798no—
853#555—794no—
854#555—794no—
855#554—794no—
856#554—794no—
857#553—798no—
858#553—794no—
859#553—794no—
860#553—798no—
861#553—794no—
862#553—794no—
863#553—794no—
864#553—794no—
865#552—794no—
866#552—794no—
867#551—798no—
868#551—798no—
869#551—798no—
870#551—798no—
871#550—794no—
872#550—794no—
873#548—794no—
874#548—794no—
875#547—794no—
876#547—794no—
877#547—794no—
878#547—794no—
879#546—794no—
880#546—794no—
881#546—798no—
882#546—798no—
883#546—794no—
884#546—794no—
885#546—798no—
886#546—798no—
887#546—798no—
888#546—798no—
889#546—798no—
890#546—798no—
891#546—798no—
892#546—798no—
893#546C2×D7914yescomplemented
894#546C2×D7914yescomplemented
895D42—798no—
896D42—794no—
897D42—798no—
898D42—794no—
899D42—794no—
900D42—794no—
901D42—798no—
902D42—798no—
903D42C2×D7914yescomplemented
904D42C2×D7914yescomplemented
905#544—792no—
906#543—794no—
907#542—794no—
908#542—794no—
909#540—794no—
910#540—798no—
911#540—798no—
912#540—794no—
913#539—798no—
914#539—798no—
915#538—798no—
916#538—798no—
917#538—798no—
918#538—798no—
919#538—798no—
920#537—792no—
921#537—794no—
922#537—794no—
923#537—798no—
924#535—792no—
925#535—794no—
926#535—794no—
927#535—798no—
928#535C2×D7912yescomplemented
929#534—794no—
930#534—794no—
931#534—794no—
932#534—798no—
933#534—798no—
934#534—794no—
935#534C2×D7914yescomplemented
936#532—794no—
937#532—794no—
938#529—794no—
939#529—794no—
940#525—792no—
941#525—794no—
942#525—792no—
943#525—794no—
944#525—792no—
945#525—792no—
946#525—792no—
947#525—792no—
948#525—794no—
949#525—794no—
950#525—798no—
951#525—794no—
952#525—794no—
953#525—792no—
954#525C2×D7912yescomplemented
955C2×#123—794no—
956C2×C22⋊Q8—792no—
957C2×C22⋊Q8—792no—
958C2×#121—792no—
959C2×#121—792no—
960C2×#121—794no—
961C2×#121—794no—
962C2×#121—794no—
963C2×#121—794no—
964C2×#121—794no—
965C2×#121—794no—
966C2×#121—792no—
967C2×#121—792no—
968C2×#121—794no—
969C2×#120—794no—
970C2×#120—794no—
971C2×#120C2×D7914yescomplemented
972#520—792no—
973#520—792no—
974#518—791no—
975#518—794no—
976#518—794no—
977#518—794no—
978#518C2×D7911yescharacteristic, complemented
979C2×C4×D4—794no—
980C2×C4×D4—794no—
981C2×#117—792no—
982C22×C4⋊C4—791no—
983C22×C22⋊C4—792no—
984C25—791no—
985C25C22×D7912yes—
986H(5,𝔽2)—44no—
987H(5,𝔽2)—3164no—
988H(5,𝔽2)—31616no—
989C2×#41—3168no—
990C2×#41—792no—
991C2×#41—794no—
992C2×#41—798no—
993C2×#41—792no—
994C2×#41—794no—
995C2×#41—798no—
996C2×#41—794no—
997C2×#41—798no—
998C2×#41—792no—
999C2×#41C22×D7912yes—
1000C2×#41C22×D7914yescomplemented
1001C22×Q8—792no—
1002C22×D4—44no—
1003C22×D4—3168no—
1004C22×D4—794no—
1005C22×D4—794no—
1006C22×D4—794no—
1007C22×D4—794no—
1008C22×D4—794no—
1009C22×D4—798no—
1010C22×D4—794no—
1011C22×D4—798no—
1012C22×D4—794no—
1013C22×D4—794no—
1014C22×D4—792no—
1015C22×D4—798no—
1016C22×D4—794no—
1017C22×D4—794no—
1018C22×D4—794no—
1019C22×D4C22×D7911yescharacteristic
1020C22×D4C22×D7911yescharacteristic
1021C22×D4C22×D7914yes—
1022C22×D4C22×D7914yes—
1023C22×D4C22×D7914yes—
1024C22×D4C22×D7912yes—
1025C22×D4C22×D7914yes—
1026C22×D4C22×D7914yes—
1027C22×D4C22×D7914yescomplemented
1028C23×C4—3164no—
1029C23×C4—791no—
1030C23×C4—792no—
1031C23×C4—792no—
1032C23×C4—792no—
1033C23×C4—794no—
1034C23×C4—792no—
1035C23×C4—792no—
1036C23×C4—792no—
1037C23×C4—792no—
1038C23×C4C22×D7911yescharacteristic
1039C4⋊Q8—794no—
1040C4⋊Q8—794no—
1041#127—794no—
1042#127—798no—
1043#127—798no—
1044#127C22×D7914yescomplemented
1045#126—798no—
1046#126—798no—
1047#126—798no—
1048#126—798no—
1049#126—798no—
1050#126—798no—
1051#125—794no—
1052#125—798no—
1053#125—798no—
1054#125—794no—
1055#124—794no—
1056#124—798no—
1057#124—798no—
1058#124—798no—
1059#124—798no—
1060#124—798no—
1061#124—798no—
1062#124C22×D7914yescomplemented
1063#123—794no—
1064#123—798no—
1065#123—798no—
1066#123—798no—
1067#123—798no—
1068#123—798no—
1069#123—794no—
1070#123—798no—
1071#123—798no—
1072#123—794no—
1073#123—794no—
1074#123—794no—
1075#123—794no—
1076#123—794no—
1077#123—798no—
1078#123—798no—
1079#123—798no—
1080#123—798no—
1081#123—798no—
1082#123—798no—
1083#123—798no—
1084#123—798no—
1085#123C22×D7914yes—
1086#123C22×D7918yescomplemented
1087C22⋊Q8—792no—
1088C22⋊Q8—792no—
1089C22⋊Q8—794no—
1090C22⋊Q8—792no—
1091C22⋊Q8—792no—
1092C22⋊Q8—794no—
1093C22⋊Q8—798no—
1094C22⋊Q8—798no—
1095C22⋊Q8—792no—
1096C22⋊Q8—792no—
1097C22⋊Q8—794no—
1098C22⋊Q8—794no—
1099C22⋊Q8—798no—
1100C22⋊Q8—794no—
1101C22⋊Q8—794no—
1102C22⋊Q8—798no—
1103C22⋊Q8—798no—
1104C22⋊Q8—798no—
1105C22⋊Q8—798no—
1106C22⋊Q8—798no—
1107C22⋊Q8C22×D7912yes—
1108C22⋊Q8C22×D7912yes—
1109#121—794no—
1110#121—794no—
1111#121—792no—
1112#121—798no—
1113#121—794no—
1114#121—794no—
1115#121—798no—
1116#121—794no—
1117#121—794no—
1118#121—798no—
1119#121—794no—
1120#121—794no—
1121#121—798no—
1122#121—794no—
1123#121—792no—
1124#121—794no—
1125#121—798no—
1126#121—794no—
1127#121—794no—
1128#121—798no—
1129#121—798no—
1130#121—798no—
1131#121—794no—
1132#121—798no—
1133#121—798no—
1134#121—798no—
1135#121—798no—
1136#121—798no—
1137#121—798no—
1138#121—798no—
1139#121—798no—
1140#121—798no—
1141#121—798no—
1142#121—792no—
1143#121—792no—
1144#121—794no—
1145#121—798no—
1146#121—798no—
1147#121—792no—
1148#121—792no—
1149#121—794no—
1150#121—794no—
1151#121—798no—
1152#121—798no—
1153#121—798no—
1154#121—798no—
1155#121C22×D7912yes—
1156#121C22×D7912yes—
1157#121C22×D7914yescomplemented
1158#121C22×D7914yescomplemented
1159#121C22×D7918yescomplemented
1160#121C22×D7918yescomplemented
1161#120—794no—
1162#120—798no—
1163#120—798no—
1164#120—798no—
1165#120—798no—
1166#120—798no—
1167#120—794no—
1168#120—794no—
1169#120—794no—
1170#120—798no—
1171#120—798no—
1172#120—798no—
1173#120—798no—
1174#120—794no—
1175#120—794no—
1176#120—794no—
1177#120—798no—
1178#120C22×D7914yes—
1179#120C22×D7918yes—
1180#120C22×D7918yes—
1181#120C22×D7918yes—
1182#120C22×D7918yescomplemented
1183C4×Q8—794no—
1184C4×Q8—794no—
1185C4×D4—794no—
1186C4×D4—794no—
1187C4×D4—798no—
1188C4×D4—798no—
1189C4×D4—794no—
1190C4×D4—798no—
1191C4×D4—794no—
1192C4×D4—798no—
1193C4×D4—794no—
1194C4×D4—794no—
1195C4×D4—794no—
1196C4×D4—794no—
1197C4×D4—794no—
1198C4×D4—798no—
1199C4×D4—798no—
1200C4×D4—798no—
1201C4×D4—798no—
1202C4×D4—794no—
1203C4×D4—794no—
1204C4×D4—794no—
1205C4×D4—794no—
1206C4×D4—794no—
1207C4×D4—794no—
1208C4×D4—798no—
1209C4×D4—798no—
1210C4×D4—798no—
1211C4×D4—798no—
1212C4×D4—794no—
1213C4×D4—794no—
1214C4×D4—794no—
1215C4×D4C22×D7914yes—
1216C4×D4C22×D7914yes—
1217C4×D4C22×D7914yescomplemented
1218C4×D4C22×D7914yescomplemented
1219#117—792no—
1220#117—798no—
1221#117—794no—
1222#117—792no—
1223#117—792no—
1224#117—794no—
1225#117—794no—
1226#117—798no—
1227#117—798no—
1228#117—794no—
1229#117C22×D7912yes—
1230C2×C4⋊C4—792no—
1231C2×C4⋊C4—792no—
1232C2×C4⋊C4—794no—
1233C2×C4⋊C4—794no—
1234C2×C4⋊C4—794no—
1235C2×C4⋊C4—792no—
1236C2×C4⋊C4—792no—
1237C2×C4⋊C4—794no—
1238C2×C4⋊C4—794no—
1239C2×C4⋊C4—794no—
1240C2×C22⋊C4—794no—
1241C2×C22⋊C4—794no—
1242C2×C22⋊C4—798no—
1243C2×C22⋊C4—794no—
1244C2×C22⋊C4—794no—
1245C2×C22⋊C4—794no—
1246C2×C22⋊C4—794no—
1247C2×C22⋊C4—794no—
1248C2×C22⋊C4—798no—
1249C2×C22⋊C4—794no—
1250C2×C22⋊C4—794no—
1251C2×C22⋊C4—794no—
1252C2×C22⋊C4—794no—
1253C2×C22⋊C4—794no—
1254C2×C22⋊C4—798no—
1255C2×C22⋊C4C22×D7914yes—
1256C2×C22⋊C4C22×D7914yes—
1257C2×C22⋊C4C22×D7914yes—
1258C2×C42—794no—
1259C24—44no—
1260C24—44no—
1261C24—44no—
1262C24—3162no—
1263C24—3162no—
1264C24—794no—
1265C24—791no—
1266C24—794no—
1267C24—791no—
1268C24—792no—
1269C24—792no—
1270C24—1584no—
1271C24C23×D7911yescharacteristic
1272C24C23×D7912yes—
1273C24C23×D7914yes—
1274C24C23×D7914yes—
1275C24C23×D7912yes—
1276C24C23×D7914yes—
1277#41—28no—
1278#41—48no—
1279#41—3168no—
1280#41—31616no—
1281#41—3164no—
1282#41—3168no—
1283#41—3168no—
1284#41—31616no—
1285#41—31616no—
1286#41—3164no—
1287#41—1588no—
1288C2×Q8—3164no—
1289C2×Q8—794no—
1290C2×Q8—798no—
1291C2×Q8—792no—
1292C2×Q8C23×D7912yes—
1293C2×D4—24no—
1294C2×D4—24no—
1295C2×D4—48no—
1296C2×D4—48no—
1297C2×D4—48no—
1298C2×D4—44no—
1299C2×D4—48no—
1300C2×D4—48no—
1301C2×D4—48no—
1302C2×D4—3168no—
1303C2×D4—3168no—
1304C2×D4—31616no—
1305C2×D4—3168no—
1306C2×D4—3168no—
1307C2×D4—3168no—
1308C2×D4—3168no—
1309C2×D4—31616no—
1310C2×D4—3168no—
1311C2×D4—31616no—
1312C2×D4—3164no—
1313C2×D4—3168no—
1314C2×D4—3168no—
1315C2×D4—798no—
1316C2×D4—794no—
1317C2×D4—794no—
1318C2×D4—794no—
1319C2×D4—798no—
1320C2×D4—798no—
1321C2×D4—798no—
1322C2×D4—798no—
1323C2×D4—798no—
1324C2×D4—794no—
1325C2×D4—794no—
1326C2×D4—794no—
1327C2×D4—794no—
1328C2×D4—798no—
1329C2×D4—798no—
1330C2×D4—794no—
1331C2×D4—794no—
1332C2×D4—794no—
1333C2×D4—792no—
1334C2×D4—15816no—
1335C2×D4—15816no—
1336C2×D4C23×D7914yes—
1337C2×D4C23×D7914yes—
1338C2×D4C23×D7912yes—
1339C2×D4C23×D7914yes—
1340C2×D4C23×D7914yes—
1341C2×D4C23×D7914yes—
1342C2×D4C23×D7918yes—
1343C2×D4C23×D7918yes—
1344C2×D4C23×D7918yes—
1345C2×D4C23×D7918yes—
1346C22×C4—24no—
1347C22×C4—3164no—
1348C22×C4—3164no—
1349C22×C4—3164no—
1350C22×C4—3164no—
1351C22×C4—3164no—
1352C22×C4—3168no—
1353C22×C4—3162no—
1354C22×C4—3164no—
1355C22×C4—791no—
1356C22×C4—792no—
1357C22×C4—791no—
1358C22×C4—794no—
1359C22×C4—794no—
1360C22×C4—794no—
1361C22×C4—794no—
1362C22×C4—794no—
1363C22×C4—794no—
1364C22×C4—798no—
1365C22×C4—794no—
1366C22×C4—792no—
1367C22×C4—794no—
1368C22×C4—792no—
1369C22×C4—794no—
1370C22×C4—798no—
1371C22×C4—792no—
1372C22×C4—792no—
1373C22×C4—792no—
1374C22×C4—794no—
1375C22×C4—792no—
1376C22×C4—794no—
1377C22×C4—792no—
1378C22×C4—794no—
1379C22×C4—792no—
1380C22×C4—792no—
1381C22×C4—1588no—
1382C22×C4C23×D7912yes—
1383C22×C4C23×D7912yes—
1384C22×C4C23×D7911yescharacteristic
1385C22×C4C23×D7914yes—
1386C22×C4C23×D7914yes—
1387C22×C4C23×D7914yes—
1388C22×C4C23×D7914yes—
1389C22×C4C23×D7911yescharacteristic
1390C4⋊C4—794no—
1391C4⋊C4—794no—
1392C4⋊C4—794no—
1393C4⋊C4—794no—
1394C4⋊C4—794no—
1395C4⋊C4—794no—
1396C4⋊C4—798no—
1397C4⋊C4—798no—
1398C4⋊C4—798no—
1399C4⋊C4—798no—
1400C4⋊C4—794no—
1401C4⋊C4—794no—
1402C4⋊C4—792no—
1403C4⋊C4—798no—
1404C4⋊C4—792no—
1405C4⋊C4—794no—
1406C4⋊C4—794no—
1407C4⋊C4—798no—
1408C4⋊C4—798no—
1409C4⋊C4C23×D7912yes—
1410C4⋊C4C23×D7912yes—
1411C4⋊C4C23×D7914yes—
1412C4⋊C4C23×D7914yes—
1413C22⋊C4—798no—
1414C22⋊C4—798no—
1415C22⋊C4—794no—
1416C22⋊C4—794no—
1417C22⋊C4—794no—
1418C22⋊C4—794no—
1419C22⋊C4—798no—
1420C22⋊C4—798no—
1421C22⋊C4—798no—
1422C22⋊C4—798no—
1423C22⋊C4—798no—
1424C22⋊C4—798no—
1425C22⋊C4—794no—
1426C22⋊C4—798no—
1427C22⋊C4—794no—
1428C22⋊C4—794no—
1429C22⋊C4—794no—
1430C22⋊C4—794no—
1431C22⋊C4—794no—
1432C22⋊C4—798no—
1433C22⋊C4—794no—
1434C22⋊C4—794no—
1435C22⋊C4—794no—
1436C22⋊C4—794no—
1437C22⋊C4—794no—
1438C22⋊C4—798no—
1439C22⋊C4C23×D7914yes—
1440C22⋊C4C23×D7914yes—
1441C22⋊C4C23×D7914yes—
1442C22⋊C4C23×D7918yes—
1443C22⋊C4C23×D7914yes—
1444C22⋊C4C23×D7914yes—
1445C22⋊C4C23×D7918yes—
1446C22⋊C4C23×D7918yes—
1447C42—794no—
1448C42—794no—
1449C42—794no—
1450C42—798no—
1451C42—798no—
1452C42C23×D7914yes—
1453C23—22no—
1454C23—22no—
1455C23—22no—
1456C23—28no—
1457C23—24no—
1458C23—24no—
1459C23—28no—
1460C23—44no—
1461C23—44no—
1462C23—42no—
1463C23—44no—
1464C23—42no—
1465C23—42no—
1466C23—44no—
1467C23—42no—
1468C23—44no—
1469C23—44no—
1470C23—44no—
1471C23—816no—
1472C23—31616no—
1473C23—3161no—
1474C23—3162no—
1475C23—3161no—
1476C23—3161no—
1477C23—3162no—
1478C23—3161no—
1479C23—3164no—
1480C23—3164no—
1481C23—3164no—
1482C23—3164no—
1483C23—3164no—
1484C23—794no—
1485C23—792no—
1486C23—794no—
1487C23—792no—
1488C23—1584no—
1489C23—1584no—
1490C23—1588no—
1491C23—1582no—
1492C23—1584no—
1493C23—1584no—
1494C23C24×D7914yes—
1495C23C24×D7914yes—
1496C23C24×D7914yes—
1497C23C24×D7911yescharacteristic
1498C23C24×D7911yescharacteristic
1499C23C24×D7911yescharacteristic
1500Q8—24no—
1501Q8—3164no—
1502Q8—3168no—
1503Q8—1584no—
1504D4—28no—
1505D4—28no—
1506D4—28no—
1507D4—28no—
1508D4—28no—
1509D4—24no—
1510D4—48no—
1511D4—48no—
1512D4—48no—
1513D4—48no—
1514D4—3164no—
1515D4—3164no—
1516D4—3168no—
1517D4—3168no—
1518D4—3168no—
1519D4—3168no—
1520D4—3168no—
1521D4—3168no—
1522D4—3164no—
1523D4—3164no—
1524D4—3164no—
1525D4—1588no—
1526D4—15816no—
1527D4—15816no—
1528D4—1588no—
1529D4—1588no—
1530D4—1588no—
1531D4—1588no—
1532D4—1584no—
1533C2×C4—22no—
1534C2×C4—24no—
1535C2×C4—24no—
1536C2×C4—28no—
1537C2×C4—44no—
1538C2×C4—44no—
1539C2×C4—44no—
1540C2×C4—3162no—
1541C2×C4—3162no—
1542C2×C4—3162no—
1543C2×C4—3162no—
1544C2×C4—3164no—
1545C2×C4—3164no—
1546C2×C4—3168no—
1547C2×C4—3164no—
1548C2×C4—3161no—
1549C2×C4—3162no—
1550C2×C4—3161no—
1551C2×C4—3164no—
1552C2×C4—3164no—
1553C2×C4—3164no—
1554C2×C4—3168no—
1555C2×C4—3164no—
1556C2×C4—3164no—
1557C2×C4—3164no—
1558C2×C4—794no—
1559C2×C4—792no—
1560C2×C4—794no—
1561C2×C4—794no—
1562C2×C4—798no—
1563C2×C4—792no—
1564C2×C4—1588no—
1565C2×C4—1588no—
1566C2×C4—1584no—
1567C2×C4—1584no—
1568C2×C4—1584no—
1569C2×C4—1584no—
1570C2×C4—1584no—
1571C2×C4—1588no—
1572C2×C4#1457920614yescomplemented
1573C2×C4C24×D7914yes—
1574C2×C4C24×D7914yes—
1575C2×C4C24×D7914yes—
1576C2×C4C24×D7912yes—
1577C2×C4C24×D7912yes—
1578C22—28no—
1579C22—21no—
1580C22—21no—
1581C22—21no—
1582C22—21no—
1583C22—21no—
1584C22—21no—
1585C22—24no—
1586C22—24no—
1587C22—24no—
1588C22—24no—
1589C22—24no—
1590C22—24no—
1591C22—24no—
1592C22—24no—
1593C22—24no—
1594C22—88no—
1595C22—84no—
1596C22—84no—
1597C22—88no—
1598C22—164no—
1599C22—3164no—
1600C22—3168no—
1601C22—3168no—
1602C22—3164no—
1603C22—794no—
1604C22—6328no—
1605C22—1584no—
1606C22—1582no—
1607C22—1582no—
1608C22—1584no—
1609C22—1582no—
1610C22—1584no—
1611C22—1582no—
1612C22—1582no—
1613C22—12644no—
1614C22H(5,𝔽2)×D7912yes—
1615C22C2×#1457920612yes—
1616C22#1909939812yes—
1617C22C25×D7911yescharacteristic
1618C4—24no—
1619C4—22no—
1620C4—24no—
1621C4—24no—
1622C4—1588no—
1623C4—1584no—
1624C4—1582no—
1625C4—1582no—
1626C4—1584no—
1627C4—1584no—
1628C4C2×#1457920614yes—
1629C2—22no—
1630C2—22no—
1631C2—22no—
1632C2—44no—
1633C2—44no—
1634C2—44no—
1635C2—3162no—
1636C2—3164no—
1637C2—1584no—
1638C2C2×H(5,𝔽2)×D7911yescharacteristic
1639C2C22×#1457920611yescharacteristic
1640C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3484C2
hypercenter#3484D79
hypocenterC79#62818
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777721C2semidirect
2. #23777702C2semidirect
3. #23777631C2semidirect
4. #23777620C2semidirect
5. #23777580C2semidirect
6. #23777429C2semidirect
7. #23777423C2semidirect
8. #23777227C2semidirect
9. #23777156C2semidirect
10. #23777132C2semidirect
11. #23777125C2semidirect
12. #23777106C2semidirect
13. #23777087C2semidirect
14. #23777067C2semidirect
15. #23777062C2semidirect
16. #23777035C2semidirect
17. #23777029C2semidirect
18. #525×D79C2semidirect
19. C22×#14579132C2semidirect
20. C79×#3484C2semidirect
21. C2×#14579206C22semidirect
22. C2×#14579206C22semidirect
23. C2×#41×D79C22semidirect
24. C23×C22⋊D79C22semidirect
25. C23×C4×D79C22semidirect
26. #19099310C22semidirect
27. #19099308C22semidirect
28. #19099302C22semidirect
29. #19099301C22semidirect
30. #19099278C22semidirect
31. #19099277C22semidirect
32. #19099271C22semidirect
33. #19099270C22semidirect
34. #19099265C22semidirect
35. #19099265C22semidirect
36. #19099263C22semidirect
37. #19099263C22semidirect
38. #19099260C22semidirect
39. #19099260C22semidirect
40. #19099259C22semidirect
41. #19099258C22semidirect
42. #19099255C22semidirect
43. #19099253C22semidirect
44. #19099244C22semidirect
45. #19099244C22semidirect
46. #19099239C22semidirect
47. #19099239C22semidirect
48. #19099233C22semidirect
49. #19099232C22semidirect
50. #19099221C22semidirect
51. #19099220C22semidirect
52. #19099218C22semidirect
53. #19099217C22semidirect
54. #19099213C22semidirect
55. #19099213C22semidirect
56. #19099210C22semidirect
57. #19099207C22semidirect
58. #19099207C22semidirect
59. #19099207C22semidirect
60. #19099207C22semidirect
61. #19099207C22semidirect
62. #19099206C22semidirect
63. #19099203C22semidirect
64. #19099203C22semidirect
65. #19099200C22semidirect
66. #19099200C22semidirect
67. #19099200C22semidirect
68. #19099200C22semidirect
69. #19099200C22semidirect
70. #19099198C22semidirect
71. D4×C22⋊D79C22semidirect
72. D4×C22⋊D79C22semidirect
73. D4×C22⋊D79C22semidirect
74. D4×C22⋊D79C22semidirect
75. D4×C22⋊D79C22semidirect
76. #19099195C22semidirect
77. #19099195C22semidirect
78. #19099191C22semidirect
79. #19099189C22semidirect
80. #19099182C22semidirect
81. #19099178C22semidirect
82. #19099167C22semidirect
83. #19099166C22semidirect
84. #19099164C22semidirect
85. #19099163C22semidirect
86. #19099157C22semidirect
87. #19099156C22semidirect
88. #19099149C22semidirect
89. #19099148C22semidirect
90. #19099148C22semidirect
91. #19099148C22semidirect
92. #19099145C22semidirect
93. #19099142C22semidirect
94. #19099142C22semidirect
95. #19099141C22semidirect
96. #19099141C22semidirect
97. #19099130C22semidirect
98. #19099130C22semidirect
99. #19099129C22semidirect
100. #19099128C22semidirect
101. #19099125C22semidirect
102. #19099123C22semidirect
103. #19099123C22semidirect
104. #19099122C22semidirect
105. #19099122C22semidirect
106. #19099122C22semidirect
107. #19099111C22semidirect
108. #19099110C22semidirect
109. #19099095C22semidirect
110. #19099092C22semidirect
111. #19099076C22semidirect
112. #19099076C22semidirect
113. #19099075C22semidirect
114. #19099074C22semidirect
115. #19099073C22semidirect
116. #19099073C22semidirect
117. #19099073C22semidirect
118. #19099072C22semidirect
119. #19099072C22semidirect
120. #19099071C22semidirect
121. #19099070C22semidirect
122. #19099070C22semidirect
123. #19099069C22semidirect
124. #19099069C22semidirect
125. #123×D79C22semidirect
126. C22⋊Q8×D79C22semidirect
127. C22⋊Q8×D79C22semidirect
128. C2×#14579132C22semidirect
129. C2×#14579132C22semidirect
130. C2×#14579132C22semidirect
131. C2×#14579132C22semidirect
132. C2×#14579132C22semidirect
133. C2×#14579132C22semidirect
134. C2×#14579132C22semidirect
135. C2×#14579132C22semidirect
136. #121×D79C22semidirect
137. #121×D79C22semidirect
138. #121×D79C22semidirect
139. C2×#14579130C22semidirect
140. #120×D79C22semidirect
141. #19099046C22semidirect
142. #19099043C22semidirect
143. #19099038C22semidirect
144. #19099038C22semidirect
145. #19099036C22semidirect
146. #19099036C22semidirect
147. C4×D4×D79C22semidirect
148. C4×D4×D79C22semidirect
149. #117×D79C22semidirect
150. C22×C4⋊Dic79C22semidirect
151. C22×C22⋊Dic79C22semidirect
152. C2×H(5,𝔽2)×C79C22semidirect
153. C23×D4×C79C22semidirect
154. #546×C79C22semidirect
155. #546×C79C22semidirect
156. D42×C79C22semidirect
157. D42×C79C22semidirect
158. #535×C79C22semidirect
159. #534×C79C22semidirect
160. #525×C79C22semidirect
161. C2×#120×C79C22semidirect
162. #518×C79C22semidirect
166. C2×#11929625C23semidirect
168. C2×#11929624C23semidirect
169. C2×#11929624C23semidirect
172. C2×#11929623C23semidirect
173. C2×#11929623C23semidirect
174. C2×#11929623C23semidirect
176. C2×Q8×D79C23semidirect
186. C22×C22⋊D79C23semidirect
190. C2×D4×D79C23semidirect
191. C2×D4×D79C23semidirect
192. C2×D4×D79C23semidirect
202. C22×C4×D79C23semidirect
203. #14579161C23semidirect
204. #14579160C23semidirect
205. #14579157C23semidirect
206. #14579157C23semidirect
207. #14579157C23semidirect
208. #14579156C23semidirect
209. #14579154C23semidirect
210. #14579154C23semidirect
211. #14579154C23semidirect
212. #14579154C23semidirect
213. #14579154C23semidirect
214. #14579153C23semidirect
215. #14579152C23semidirect
216. #14579152C23semidirect
217. #14579151C23semidirect
218. #14579148C23semidirect
219. #14579148C23semidirect
220. #14579148C23semidirect
221. #14579147C23semidirect
222. #14579147C23semidirect
223. #14579147C23semidirect
224. #14579147C23semidirect
225. #14579146C23semidirect
226. #14579146C23semidirect
229. #14579145C23semidirect
230. #14579145C23semidirect
232. #14579144C23semidirect
233. #14579144C23semidirect
234. #14579143C23semidirect
235. #14579143C23semidirect
236. #14579143C23semidirect
237. #14579143C23semidirect
238. #14579143C23semidirect
239. #14579143C23semidirect
240. #14579143C23semidirect
243. #14579142C23semidirect
244. #14579142C23semidirect
245. #14579142C23semidirect
246. #14579142C23semidirect
247. #14579141C23semidirect
248. #14579141C23semidirect
249. #14579141C23semidirect
252. #14579140C23semidirect
253. #14579140C23semidirect
254. #14579140C23semidirect
255. #14579139C23semidirect
256. #14579139C23semidirect
261. #14579138C23semidirect
262. #14579138C23semidirect
263. #14579138C23semidirect
264. #14579137C23semidirect
265. #14579137C23semidirect
266. #14579137C23semidirect
267. #14579136C23semidirect
268. #14579136C23semidirect
271. #14579135C23semidirect
272. #14579135C23semidirect
273. #14579135C23semidirect
274. #14579134C23semidirect
275. #14579134C23semidirect
276. #14579134C23semidirect
277. #14579134C23semidirect
278. #14579134C23semidirect
279. #14579134C23semidirect
284. #14579133C23semidirect
285. #14579133C23semidirect
286. #14579133C23semidirect
287. #14579133C23semidirect
288. #14579133C23semidirect
289. #14579133C23semidirect
290. #14579133C23semidirect
291. #14579133C23semidirect
304. #14579132C23semidirect
305. #14579132C23semidirect
306. #14579132C23semidirect
307. #14579132C23semidirect
308. #14579132C23semidirect
309. #14579132C23semidirect
310. #14579132C23semidirect
311. #14579132C23semidirect
312. #14579132C23semidirect
316. #14579131C23semidirect
321. #14579130C23semidirect
322. #14579130C23semidirect
326. #14579129C23semidirect
327. #14579129C23semidirect
328. #14579129C23semidirect
329. #14579129C23semidirect
330. Q8×Dic79C23semidirect
331. C4×Dic158C23semidirect
332. C4×D316C23semidirect
333. C4×D316C23semidirect
334. C4×D316C23semidirect
339. D4×Dic79C23semidirect
340. D4×Dic79C23semidirect
341. D4×Dic79C23semidirect
342. D4×Dic79C23semidirect
343. D4×Dic79C23semidirect
344. #14579123C23semidirect
345. #14579123C23semidirect
348. C4×C22⋊D79C23semidirect
349. C4×C22⋊D79C23semidirect
350. C4×C22⋊D79C23semidirect
351. C4×C22⋊D79C23semidirect
352. C4×C22⋊D79C23semidirect
353. C4×C22⋊D79C23semidirect
358. (C22⋊D79)⋊C4C23semidirect
359. (C22⋊D79)⋊C4C23semidirect
360. (C22⋊D79)⋊C4C23semidirect
361. (C22⋊D79)⋊C4C23semidirect
363. #14579120C23semidirect
364. #14579120C23semidirect
365. #14579119C23semidirect
366. #14579119C23semidirect
367. #14579119C23semidirect
368. #14579118C23semidirect
371. #14579117C23semidirect
376. C2×C4⋊Dic79C23semidirect
377. C4⋊C4×D79C23semidirect
378. C4⋊C4×D79C23semidirect
379. C4⋊C4×D79C23semidirect
380. C4⋊C4×D79C23semidirect
381. C4⋊C4×D79C23semidirect
390. C2×C22⋊Dic79C23semidirect
394. C22⋊C4×D79C23semidirect
395. C22⋊C4×D79C23semidirect
396. C22⋊C4×D79C23semidirect
397. C42×D79C23semidirect
401. C2×#41×C79C23semidirect
411. C22×D4×C79C23semidirect
413. #127×C79C23semidirect
414. #124×C79C23semidirect
416. #123×C79C23semidirect
421. #121×C79C23semidirect
422. #121×C79C23semidirect
423. #121×C79C23semidirect
424. #121×C79C23semidirect
429. #120×C79C23semidirect
432. C4×D4×C79C23semidirect
433. C4×D4×C79C23semidirect
675. C22×D79H(5,𝔽2)semidirect
697. C2×C4×C79H(5,𝔽2)semidirect
838. #3484D79semidirect
841. C79#62818semidirect
844. C2×H(5,𝔽2)C2×D79semidirect
847. C23×D4C2×D79semidirect
893. #546C2×D79semidirect
894. #546C2×D79semidirect
903. D42C2×D79semidirect
904. D42C2×D79semidirect
928. #535C2×D79semidirect
935. #534C2×D79semidirect
954. #525C2×D79semidirect
971. C2×#120C2×D79semidirect
978. #518C2×D79semidirect
1000. C2×#41C22×D79semidirect
1027. C22×D4C22×D79semidirect
1044. #127C22×D79semidirect
1062. #124C22×D79semidirect
1086. #123C22×D79semidirect
1157. #121C22×D79semidirect
1158. #121C22×D79semidirect
1159. #121C22×D79semidirect
1160. #121C22×D79semidirect
1182. #120C22×D79semidirect
1217. C4×D4C22×D79semidirect
1218. C4×D4C22×D79semidirect
1572. C2×C4#14579206semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237777212
#237777022
#237776312
#237776202
#237775802
#237774292
#237774232
#237772272
#237771562
#237771322
#237771252
#237771062
#237770872
#237770672
#237770622
#237770352
#237770292
#525×D792
C22×#145791322
C79×#34842
#6281879