Finite Group Databasebeta

← #35196938

Subgroups — #35196938

Order 20224.

7338 conjugacy classes of subgroups.

The subgroup lattice has 1538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777714C214yesmaximal, complemented
2#23777683C214yesmaximal, complemented
3#23777664C214yesmaximal, complemented
4#23777655C214yesmaximal, complemented
5#23777561C214yesmaximal, complemented
6#23777552C214yesmaximal, complemented
7#23777452C214yesmaximal, complemented
8#23777429C214yesmaximal, complemented
9#23777332C218yesmaximal, complemented
10#23777250C214yesmaximal, complemented
11#23777227C214yesmaximal, complemented
12#23777149C212yesmaximal, complemented
13#23777125C212yesmaximal, complemented
14#23777117C212yesmaximal, complemented
15#23777078C212yesmaximal, complemented
16#23777062C212yesmaximal, complemented
17#23777058C211yesmaximal, characteristic, complemented
18C2×#19099070C211yesmaximal, characteristic, complemented
19#525×D79C212yesmaximal, complemented
20C79×#3485C211yesmaximal, characteristic, complemented
21C2×#14579209C2211yescharacteristic, complemented
22C2×#41×D79C2212yescomplemented
23C23×C4×D79C2211yescharacteristic, complemented
24#19099316C2214yescomplemented
25#19099308C2218yescomplemented
26#19099306C2214yescomplemented
27#19099303C2214yescomplemented
28#19099302C2214yescomplemented
29#19099301C2218yescomplemented
30#19099297C2214yescomplemented
31#19099297C2218yescomplemented
32#19099284C2214yescomplemented
33#19099284C2214yescomplemented
34#19099283C2214yescomplemented
35#19099278C2214yescomplemented
36#19099278C2214yescomplemented
37#19099277C2214yescomplemented
38#19099271C2214yescomplemented
39#19099268C2218yescomplemented
40#19099263C2214yescomplemented
41#19099263C2214yescomplemented
42#19099261C2218yescomplemented
43#19099260C2214yescomplemented
44#19099260C2218yescomplemented
45#19099259C2214yescomplemented
46#19099258C2218yescomplemented
47#19099258C2218yescomplemented
48#19099255C2214yescomplemented
49#19099253C2214yescomplemented
50#19099250C2218yescomplemented
51#19099247C2214yescomplemented
52#19099247C2214yescomplemented
53#19099244C2214yescomplemented
54#19099241C2214yescomplemented
55#19099241C2218yescomplemented
56#19099239C2218yescomplemented
57#19099239C2218yescomplemented
58#19099236C2218yescomplemented
59#19099232C2214yescomplemented
60#19099232C2214yescomplemented
61#19099232C2214yescomplemented
62#19099228C2214yescomplemented
63#19099221C2214yescomplemented
64#19099220C2214yescomplemented
65#19099220C2214yescomplemented
66#19099220C2214yescomplemented
67#19099218C2214yescomplemented
68#19099216C2214yescomplemented
69#19099211C2218yescomplemented
70#19099210C2218yescomplemented
71#19099207C2218yescomplemented
72#19099207C2214yescomplemented
73#19099206C2214yescomplemented
74#19099205C2218yescomplemented
75#19099203C2218yescomplemented
76#19099203C2218yescomplemented
77D4×C22⋊D79C2218yescomplemented
78D4×C22⋊D79C2214yescomplemented
79#19099195C2214yescomplemented
80#19099191C2212yescomplemented
81#19099182C2214yescomplemented
82#19099181C2218yescomplemented
83#19099180C2218yescomplemented
84#19099178C2214yescomplemented
85#19099174C2214yescomplemented
86#19099165C2218yescomplemented
87#19099164C2214yescomplemented
88#19099163C2218yescomplemented
89#19099160C2218yescomplemented
90#19099156C2218yescomplemented
91#19099156C2218yescomplemented
92#19099151C2218yescomplemented
93#19099149C2218yescomplemented
94#19099149C2218yescomplemented
95#19099148C2218yescomplemented
96#19099148C2218yescomplemented
97#19099145C2218yescomplemented
98#19099143C2214yescomplemented
99#19099141C2212yescomplemented
100#19099141C2214yescomplemented
101#19099136C2214yescomplemented
102#19099130C2214yescomplemented
103#19099130C2212yescomplemented
104#19099130C2214yescomplemented
105#19099129C2218yescomplemented
106#19099123C2218yescomplemented
107#19099118C2214yescomplemented
108#19099110C2214yescomplemented
109#19099095C2214yescomplemented
110#19099092C2214yescomplemented
111#19099090C2218yescomplemented
112#19099076C2212yescomplemented
113#19099076C2212yescomplemented
114#19099076C2214yescomplemented
115#19099075C2212yescomplemented
116#19099074C2212yescomplemented
117#19099074C2214yescomplemented
118#19099073C2212yescomplemented
119#19099073C2212yescomplemented
120#19099072C2214yescomplemented
121#19099072C2214yescomplemented
122#19099071C2214yescomplemented
123#19099070C2212yes—
124#19099070C2214yescomplemented
125#19099070C2214yescomplemented
126#19099070C2214yescomplemented
127#19099070C2214yescomplemented
128#19099070C2214yescomplemented
129#19099069C2214yescomplemented
130C2×#14579142C2212yescomplemented
131#123×D79C2214yescomplemented
132C2×#14579137C2212yescomplemented
133C22⋊Q8×D79C2212yescomplemented
134C22⋊Q8×D79C2212yescomplemented
135C22⋊Q8×D79C2214yescomplemented
136C2×#14579132C2212yescomplemented
137C2×#14579132C2214yescomplemented
138#121×D79C2212yescomplemented
139#121×D79C2212yescomplemented
140C2×#14579129C2212yescomplemented
141#120×D79C2214yescomplemented
142#19099046C2212yescomplemented
143#19099044C2218yescomplemented
144#19099043C2212yescomplemented
145#19099041C2211yescharacteristic, complemented
146#19099036C2218yescomplemented
147C2×C4×C22⋊D79C2214yescomplemented
148C4×D4×D79C2214yescomplemented
149C4×D4×D79C2214yescomplemented
150C2×#14579120C2211yescharacteristic, complemented
151#117×D79C2212yescomplemented
152C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
153C22×#41×C79C2211yescharacteristic, complemented
154#547×C79C2214yescomplemented
155#547×C79C2214yescomplemented
156#546×C79C2214yescomplemented
157#546×C79C2214yescomplemented
158#536×C79C2212yescomplemented
159#534×C79C2214yescomplemented
160#525×C79C2212yescomplemented
161C2×#123×C79C2214yescomplemented
162#518×C79C2211yescharacteristic, complemented
163C24×D79C2311yescharacteristic
164#14579209—44no—
165C2×#11929625C2312yes—
166C2×#11929625C2314yescomplemented
167C2×#11929624C2312yes—
168C2×#11929624C2314yes—
169C2×#11929624C2314yes—
170C2×#11929624C2318yes—
171C2×#11929623C2314yes—
172C2×#11929623C2312yes—
173#41×D79—48no—
174C2×Q8×D79C2312yes—
175C2×Q8×D79C2314yescomplemented
176C22×C22⋊D79C2318yes—
177C22×C22⋊D79C2314yes—
178C2×D4×D79C2314yes—
179C2×D4×D79C2314yes—
180C2×D4×D79C2312yes—
181C2×D4×D79C2314yes—
182C23×Dic79C2311yescharacteristic
183C22×C4×D79—44no—
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186C22×C4×D79C2314yes—
187C22×C4×D79C2312yes—
188C22×C4×D79C2312yes—
189C22×C4×D79C2312yes—
190C22×C4×D79C2312yes—
191#14579161C2314yescomplemented
192#14579160C2318yescomplemented
193#14579160C2314yescomplemented
194#14579157C2314yes—
195#14579157C2318yes—
196#14579157C2314yes—
197#14579157C2314yescomplemented
198#14579156C2318yes—
199#14579156C2318yes—
200#14579156C2318yescomplemented
201#14579154C2318yes—
202#14579154C2318yes—
203#14579154C2318yescomplemented
204#14579154C2318yescomplemented
205#14579154C2318yescomplemented
206#14579154C2318yescomplemented
207#14579154C2318yescomplemented
208#14579153C2314yescomplemented
209#14579152C2318yescomplemented
210#14579152C2314yescomplemented
211#14579151C2318yescomplemented
212#14579151C2318yescomplemented
213#14579151C2318yescomplemented
214#14579148C2314yes—
215#14579148C2318yes—
216#14579148C2314yes—
217#14579148C2314yescomplemented
218#14579148C2318yescomplemented
219#14579147C2318yes—
220#14579147C2318yes—
221#14579147C2318yes—
222#14579147C2318yes—
223#14579147C2318yescomplemented
224#14579147C2318yescomplemented
225#14579146C2318yes—
226#14579146C2314yes—
227#14579146C2314yes—
228#14579146C2318yescomplemented
229#14579145C2318yes—
230#14579145C2314yes—
231#14579144C2318yes—
232#14579144C2314yes—
233#14579144C2318yescomplemented
234#14579143C2318yes—
235#14579143C2314yes—
236#14579143C2318yes—
237#14579143C2318yes—
238#14579143C2314yes—
239#14579143C2318yescomplemented
240#14579143C2318yescomplemented
241#14579142C2318yes—
242#14579142C2318yes—
243#14579142C2314yes—
244#14579142C2314yes—
245#14579142C2314yes—
246#14579142C2318yescomplemented
247#14579141C2312yes—
248#14579141C2318yes—
249#14579141C2312yes—
250#14579140C2312yes—
251#14579140C2312yes—
252#14579140C2314yescomplemented
253#14579140C2318yescomplemented
254#14579140C2318yescomplemented
255#14579140C2318yescomplemented
256#14579139C2318yes—
257#14579139C2314yes—
258#14579139C2314yes—
259#14579139C2318yescomplemented
260#14579138C2318yes—
261#14579138C2314yes—
262#14579138C2314yes—
263#14579138C2318yescomplemented
264#14579138C2318yescomplemented
265#14579137C2314yes—
266#14579137C2312yes—
267#14579137C2314yes—
268#14579137C2314yes—
269#14579137C2314yes—
270#14579137C2312yes—
271#14579137C2314yescomplemented
272#14579136C2312yes—
273#14579136C2318yes—
274#14579136C2312yes—
275#14579135C2318yes—
276#14579135C2318yes—
277#14579135C2312yes—
278#14579135C2312yes—
279#14579135C2314yescomplemented
280#14579135C2318yescomplemented
281#14579134C2318yes—
282#14579134C2318yes—
283#14579134C2314yes—
284#14579134C2318yes—
285#14579134C2314yes—
286#14579134C2318yescomplemented
287#14579133C2318yes—
288#14579133C2318yes—
289#14579133C2314yes—
290#14579133C2318yes—
291#14579133C2314yes—
292#14579133C2318yescomplemented
293#14579132C2314yes—
294#14579132C2318yes—
295#14579132C2318yes—
296#14579132C2318yes—
297#14579132C2318yes—
298#14579132C2312yes—
299#14579132C2314yes—
300#14579132C2314yes—
301#14579132C2312yes—
302#14579132C2314yes—
303#14579132C2314yescomplemented
304#14579132C2314yescomplemented
305#14579132C2318yescomplemented
306#14579132C2314yescomplemented
307#14579131C2314yes—
308#14579131C2318yes—
309#14579131C2314yes—
310#14579131C2314yes—
311#14579130C2314yes—
312#14579130C2318yes—
313#14579130C2318yes—
314#14579130C2318yescomplemented
315#14579129C2314yes—
316#14579129C2318yes—
317#14579129C2318yes—
318#14579129C2314yes—
319#14579129C2314yes—
320#14579129C2314yes—
321#14579129C2314yes—
322Q8×Dic79C2314yescomplemented
323Q8×Dic79C2314yescomplemented
324Q8×Dic79C2314yescomplemented
325C4×Dic158C2314yescomplemented
326#14579126C2318yescomplemented
327#14579126C2318yescomplemented
328C4×D316C2314yes—
329C4×D316C2314yes—
330C4×D316C2314yescomplemented
331D4×Dic79C2314yes—
332D4×Dic79C2318yes—
333D4×Dic79C2314yes—
334D4×Dic79C2314yescomplemented
335#14579123C2314yes—
336#14579123C2318yes—
337#14579123C2314yes—
338C4×C22⋊D79C2318yes—
339C4×C22⋊D79C2318yes—
340C4×C22⋊D79C2318yes—
341C4×C22⋊D79C2318yes—
342C4×C22⋊D79C2314yes—
343C4×C22⋊D79C2318yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2318yes—
348C4×C22⋊D79C2318yescomplemented
349C4×C22⋊D79C2318yescomplemented
350C4×C22⋊D79C2318yescomplemented
351C4×C22⋊D79C2318yescomplemented
352(C22⋊D79)⋊C4C2318yes—
353(C22⋊D79)⋊C4C2318yes—
354(C22⋊D79)⋊C4C2314yes—
355(C22⋊D79)⋊C4C2314yes—
356(C22⋊D79)⋊C4C2314yes—
357(C22⋊D79)⋊C4C2314yes—
358(C22⋊D79)⋊C4C2318yescomplemented
359(C22⋊D79)⋊C4C2318yescomplemented
360#14579120C2312yes—
361#14579120C2314yes—
362#14579120C2314yes—
363#14579120C2314yes—
364#14579120C2318yescomplemented
365#14579120C2314yescomplemented
366#14579119C2318yes—
367#14579119C2312yes—
368#14579119C2312yes—
369#14579119C2314yescomplemented
370#14579119C2318yescomplemented
371#14579118C2314yes—
372#14579117C2314yes—
373#14579117C2318yescomplemented
374#14579117C2318yescomplemented
375C2×C4⋊Dic79C2312yes—
376C2×C4⋊Dic79C2314yescomplemented
377C2×Dic79⋊C4C2314yes—
378C4⋊C4×D79C2314yes—
379C4⋊C4×D79C2312yes—
380C4⋊C4×D79C2314yes—
381C4⋊C4×D79C2312yes—
382C4⋊C4×D79C2314yescomplemented
383C4⋊C4×D79C2318yescomplemented
384C2×C22⋊Dic79C2312yes—
385C2×C22⋊Dic79C2314yes—
386C2×C22⋊Dic79C2318yescomplemented
387C2×(C2×D79)⋊C4C2314yes—
388C22⋊C4×D79C2314yes—
389C22⋊C4×D79C2314yes—
390C22⋊C4×D79C2314yes—
391C22⋊C4×D79C2314yes—
392C22⋊C4×D79C2318yes—
393C22⋊C4×D79C2314yes—
394C2×C4×Dic79C2312yes—
395C42×D79C2314yes—
396H(5,𝔽2)×C79—44no—
397C2×#41×C79—44no—
398C2×#41×C79C2312yes—
399C2×#41×C79C2314yes—
400C2×#41×C79C2314yes—
401C2×#41×C79C2314yescomplemented
402C22×Q8×C79C2311yescharacteristic
403C22×D4×C79C2311yescharacteristic
404C22×D4×C79C2314yes—
405C22×D4×C79C2312yes—
406C22×D4×C79C2314yescomplemented
407C23×C4×C79C2311yescharacteristic
408C23×C4×C79C2312yes—
409C4⋊Q8×C79C2314yescomplemented
410#124×C79C2314yescomplemented
411#123×C79C2314yes—
412#123×C79C2314yes—
413#123×C79C2318yes—
414#123×C79C2314yes—
415#123×C79C2318yescomplemented
416#123×C79C2318yescomplemented
417C22⋊Q8×C79C2312yes—
418C22⋊Q8×C79C2312yes—
419C22⋊Q8×C79C2314yescomplemented
420C22⋊Q8×C79C2314yescomplemented
421#121×C79C2318yes—
422#121×C79C2318yes—
423#121×C79C2312yes—
424#121×C79C2312yes—
425#120×C79C2314yes—
426#120×C79C2314yes—
427#120×C79C2314yes—
428C4×D4×C79C2314yes—
429C4×D4×C79C2314yes—
430C4×D4×C79C2314yescomplemented
431C4×D4×C79C2314yescomplemented
432#117×C79C2312yes—
433C2×C4⋊C4×C79C2318yescomplemented
434C2×C22⋊C4×C79C2314yes—
435C2×C22⋊C4×C79C2318yescomplemented
436C23×D79—44no—
437C23×D79—42no—
438C23×D79C2411yescharacteristic
439C23×D79C2412yes—
440C23×D79C2412yes—
441C23×D79C2414yes—
442C23×D79C2411yescharacteristic
443#11929625—44no—
444#11929625—48no—
445#11929624—28no—
446#11929624—48no—
447#11929624—416no—
448#11929624—48no—
449#11929623—48no—
450#11929623—44no—
451C2×Dic158C2412yes—
452C2×Dic158C2414yes—
453C2×Dic158C2414yes—
454C2×Dic158C2418yes—
455Q8×D79—44no—
456Q8×D79—48no—
457C2×D316C2414yes—
458C2×D316C2412yes—
459C2×D316C2414yes—
460C2×D316C2414yes—
461C2×D316C2414yes—
462C2×C22⋊D79—416no—
463C2×C22⋊D79—48no—
464C2×C22⋊D79C2414yes—
465C2×C22⋊D79C2418yes—
466C2×C22⋊D79C2414yes—
467C2×C22⋊D79C2414yes—
468C2×C22⋊D79C2414yes—
469C2×C22⋊D79C2418yes—
470C2×C22⋊D79C2414yes—
471C2×C22⋊D79C2414yes—
472C2×C22⋊D79C2414yes—
473C2×C22⋊D79C2418yes—
474C2×C22⋊D79C2418yes—
475C2×C22⋊D79C2418yes—
476D4×D79—48no—
477D4×D79—48no—
478D4×D79—44no—
479D4×D79—48no—
480C22×Dic79—42no—
481C22×Dic79C2412yes—
482C22×Dic79C2414yes—
483C22×Dic79C2414yes—
484C22×Dic79C2418yes—
485C22×Dic79C2411yescharacteristic
486C22×Dic79C2412yes—
487C22×Dic79C2411yescharacteristic
488C2×C4×D79—28no—
489C2×C4×D79—44no—
490C2×C4×D79—48no—
491C2×C4×D79—44no—
492C2×C4×D79—44no—
493C2×C4×D79—44no—
494C2×C4×D79—44no—
495C2×C4×D79C2412yes—
496C2×C4×D79C2414yes—
497C2×C4×D79C2412yes—
498C2×C4×D79C2414yes—
499C2×C4×D79C2412yes—
500C2×C4×D79C2412yes—
501C2×C4×D79C2414yes—
502C2×C4×D79C2418yes—
503C2×C4×D79C2414yes—
504C2×C4×D79C2418yes—
505C2×C4×D79C2414yes—
506C2×C4×D79C2412yes—
507C2×C4×D79C2412yes—
508C2×C4×D79C2412yes—
509C2×C4×D79C2412yes—
510C4⋊Dic79C2414yes—
511C4⋊Dic79C2412yes—
512C4⋊Dic79C2412yes—
513C4⋊Dic79C2414yes—
514C4⋊Dic79C2414yes—
515C4⋊Dic79C2414yes—
516C4⋊Dic79C2418yes—
517C4⋊Dic79C2418yes—
518C4⋊Dic79C2418yes—
519Dic79⋊C4C2414yes—
520Dic79⋊C4C2414yes—
521Dic79⋊C4C2414yes—
522Dic79⋊C4C2414yes—
523Dic79⋊C4C2414yes—
524Dic79⋊C4C2414yes—
525Dic79⋊C4C2418yes—
526Dic79⋊C4C2418yes—
527Dic79⋊C4C2418yes—
528Dic79⋊C4C2418yes—
529Dic79⋊C4C2418yes—
530Dic79⋊C4C2418yes—
531C22⋊Dic79C2414yes—
532C22⋊Dic79C2418yes—
533C22⋊Dic79C2414yes—
534C22⋊Dic79C2414yes—
535C22⋊Dic79C2414yes—
536C22⋊Dic79C2414yes—
537C22⋊Dic79C2418yes—
538C22⋊Dic79C2414yes—
539C22⋊Dic79C2414yes—
540C22⋊Dic79C2418yes—
541C22⋊Dic79C2418yes—
542C22⋊Dic79C2418yes—
543C22⋊Dic79C2418yes—
544(C2×D79)⋊C4C2414yes—
545(C2×D79)⋊C4C2418yes—
546(C2×D79)⋊C4C2414yes—
547(C2×D79)⋊C4C2414yes—
548(C2×D79)⋊C4C2414yes—
549(C2×D79)⋊C4C2414yes—
550(C2×D79)⋊C4C2414yes—
551(C2×D79)⋊C4C2414yes—
552(C2×D79)⋊C4C2414yes—
553(C2×D79)⋊C4C2414yes—
554(C2×D79)⋊C4C2414yes—
555(C2×D79)⋊C4C2418yes—
556(C2×D79)⋊C4C2418yes—
557(C2×D79)⋊C4C2418yes—
558C4×Dic79C2414yes—
559C4×Dic79C2414yes—
560C4×Dic79C2414yes—
561C4×Dic79C2418yes—
562C4×Dic79C2414yes—
563C4×Dic79C2418yes—
564C4×Dic79C2414yes—
565C4×Dic79C2418yes—
566C24×C79C2411yescharacteristic
567C24×C79C2412yes—
568C24×C79C2414yes—
569#41×C79—28no—
570#41×C79—48no—
571#41×C79—48no—
572#41×C79—48no—
573C2×Q8×C79—24no—
574C2×Q8×C79C2412yes—
575C2×Q8×C79C2414yes—
576C2×D4×C79—24no—
577C2×D4×C79—48no—
578C2×D4×C79—44no—
579C2×D4×C79—48no—
580C2×D4×C79C2414yes—
581C2×D4×C79C2412yes—
582C2×D4×C79C2414yes—
583C2×D4×C79C2414yes—
584C2×D4×C79C2414yes—
585C2×D4×C79C2414yes—
586C2×D4×C79C2414yes—
587C2×D4×C79C2418yes—
588C22×C4×C79—24no—
589C22×C4×C79—44no—
590C22×C4×C79C2412yes—
591C22×C4×C79C2414yes—
592C22×C4×C79C2412yes—
593C22×C4×C79C2412yes—
594C22×C4×C79C2411yescharacteristic
595C22×C4×C79C2418yes—
596C22×C4×C79C2418yes—
597C22×C4×C79C2414yes—
598C22×C4×C79C2411yescharacteristic
599C4⋊C4×C79C2414yes—
600C4⋊C4×C79C2414yes—
601C4⋊C4×C79C2418yes—
602C4⋊C4×C79C2418yes—
603C4⋊C4×C79C2412yes—
604C4⋊C4×C79C2412yes—
605C22⋊C4×C79C2414yes—
606C22⋊C4×C79C2414yes—
607C22⋊C4×C79C2414yes—
608C22⋊C4×C79C2414yes—
609C22⋊C4×C79C2414yes—
610C22⋊C4×C79C2418yes—
611C22⋊C4×C79C2418yes—
612C22⋊C4×C79C2414yes—
613C22⋊C4×C79C2414yes—
614C42×C79C2414yes—
615C23×C79—22no—
616C23×C79—24no—
617C23×C79—42no—
618C23×C79—44no—
619C23×C79—48no—
620C23×C79—44no—
621C23×C79C2511yescharacteristic
622C23×C79C2511yescharacteristic
623C23×C79C2514yes—
624C23×C79C2514yes—
625C23×C79C2511yescharacteristic
626C22×D79—24no—
627C22×D79—24no—
628C22×D79—24no—
629C22×D79—24no—
630C22×D79—28no—
631C22×D79—41no—
632C22×D79—42no—
633C22×D79—41no—
634C22×D79—42no—
635C22×D79—42no—
636C22×D79—42no—
637C22×D79—44no—
638C22×D79—44no—
639C22×D79—416no—
640C22×D79C2512yes—
641C22×D79C2514yes—
642C22×D79C2512yes—
643Q8×C79—28no—
644Q8×C79—24no—
645D4×C79—28no—
646D4×C79—24no—
647D4×C79—28no—
648D4×C79—44no—
649D4×C79—44no—
650D4×C79—48no—
651D4×C79—44no—
652D4×C79—44no—
653C2×C4×C79—22no—
654C2×C4×C79—24no—
655C2×C4×C79—24no—
656C2×C4×C79—24no—
657C2×C4×C79—28no—
658C2×C4×C79—48no—
659C2×C4×C79—48no—
660C2×C4×C79—44no—
661C2×C4×C79H(5,𝔽2)14yes—
662C2×C4×C79C2512yes—
663C2×C4×C79C2514yes—
664C2×C4×C79C2514yes—
665C2×C4×C79C2514yes—
666C2×C4×C79C2514yes—
667C2×C4×C79C2512yes—
668C22⋊D79—28no—
669C22⋊D79—28no—
670C22⋊D79—216no—
671C22⋊D79—44no—
672C22⋊D79—44no—
673C22⋊D79—44no—
674C22⋊D79—44no—
675C22⋊D79—44no—
676C22⋊D79—48no—
677C22⋊D79—48no—
678C22⋊D79—48no—
679C22⋊D79—48no—
680C2×Dic79—24no—
681C2×Dic79—41no—
682C2×Dic79—42no—
683C2×Dic79—41no—
684C2×Dic79—44no—
685C2×Dic79—48no—
686C2×Dic79—44no—
687C2×Dic79C2514yes—
688C2×Dic79C2518yes—
689C2×Dic79C2514yes—
690C2×Dic79C2512yes—
691C2×Dic79C2514yes—
692C2×Dic79C2512yes—
693D316—28no—
694D316—24no—
695D316—44no—
696D316—44no—
697D316—44no—
698C4×D79—28no—
699C4×D79—24no—
700C4×D79—24no—
701C4×D79—24no—
702C4×D79—24no—
703C4×D79—28no—
704C4×D79—42no—
705C4×D79—42no—
706C4×D79—42no—
707C4×D79—42no—
708C4×D79—44no—
709C4×D79—44no—
710C4×D79—44no—
711C4×D79—48no—
712C4×D79—48no—
713Dic158—24no—
714Dic158—44no—
715Dic158—44no—
716Dic158—48no—
717C22×C79—22no—
718C22×C79—24no—
719C22×C79—21no—
720C22×C79—21no—
721C22×C79—24no—
722C22×C79—28no—
723C22×C79—24no—
724C22×C79—22no—
725C22×C79—22no—
726C22×C79—24no—
727C22×C79—44no—
728C22×C79—84no—
729C22×C79—164no—
730C22×C79C2×H(5,𝔽2)12yes—
731C22×C79C2611yescharacteristic
732C2×D79—22no—
733C2×D79—22no—
734C2×D79—24no—
735C2×D79—22no—
736C2×D79—24no—
737C2×D79—22no—
738C2×D79—24no—
739C2×D79—22no—
740C2×D79—44no—
741C2×D79—48no—
742C2×D79—48no—
743C2×D79—44no—
744C2×D79—88no—
745C2×D79#58514yes—
746C4×C79—22no—
747C4×C79—24no—
748C4×C79—24no—
749C4×C79—24no—
750C4×C79—24no—
751C4×C79C2×H(5,𝔽2)14yes—
752Dic79—24no—
753Dic79—22no—
754Dic79—22no—
755Dic79—24no—
756Dic79—28no—
757Dic79—24no—
758#62821—791nomaximal, Sylow
759C2×C79—22no—
760C2×C79—41no—
761C2×C79—41no—
762C2×C79—44no—
763C2×C79—44no—
764C2×C79C22×H(5,𝔽2)11yescharacteristic
765C2×C79C2×#58512yes—
766D79—24no—
767D79—42no—
768D79—44no—
769#3542—794no—
770#3541—794no—
771#3540—794no—
772#3539—794no—
773#3533—794no—
774#3532—794no—
775#3520—794no—
776#3519—794no—
777#3513—798no—
778#3506—794no—
779#3505—794no—
780#3495—792no—
781#3494—792no—
782#3493—792no—
783#3489—792no—
784#3488—792no—
785#3487—791no—
786#3485D7911yescharacteristic, complemented
787C2×#525—791no—
788C2×#525—792no—
789C79#6282111yescharacteristic, complemented, Sylow
790C2×2−1+4—791no—
791C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
792C22×#41—792no—
793C22×#41C2×D7911yescharacteristic, complemented
794C24×C4—791no—
795#563—794no—
796#562—798no—
797H(3,𝔽4)—794no—
798#560—794no—
799#560—798no—
800#560—794no—
801#559—794no—
802#559—798no—
803#556—794no—
804#556—794no—
805#556—794no—
806#555—794no—
807#555—794no—
808#555—794no—
809#554—794no—
810#554—798no—
811#553—798no—
812#553—798no—
813#553—794no—
814#553—798no—
815#553—794no—
816#553—794no—
817#553—794no—
818#553—798no—
819#552—798no—
820#552—794no—
821#552—794no—
822#552—794no—
823#552—794no—
824#551—798no—
825#551—794no—
826#551—798no—
827#551—794no—
828#551—798no—
829#551—798no—
830#550—794no—
831#550—794no—
832#550—794no—
833D4×Q8—794no—
834#548—794no—
835#548—794no—
836#548—794no—
837#548—794no—
838#547—794no—
839#547—798no—
840#547—794no—
841#547C2×D7914yescomplemented
842#547C2×D7914yescomplemented
843#546—798no—
844#546—794no—
845#546—794no—
846#546—798no—
847#546—798no—
848#546—798no—
849#546—798no—
850#546C2×D7914yescomplemented
851#546C2×D7914yescomplemented
852D42—798no—
853D42—794no—
854D42—794no—
855#544—792no—
856#542—794no—
857#542—798no—
858#542—798no—
859#542—794no—
860#541—794no—
861#540—798no—
862#540—798no—
863#540—794no—
864#539—798no—
865#539—798no—
866#539—798no—
867#538—798no—
868#538—798no—
869#538—798no—
870#538—798no—
871#538—798no—
872#538—798no—
873#537—792no—
874#537—794no—
875#537—794no—
876#536—794no—
877#536C2×D7912yescomplemented
878#535—792no—
879#535—794no—
880#535—794no—
881#535—798no—
882#534—798no—
883#534C2×D7914yescomplemented
884#533—794no—
885#532—794no—
886#529—794no—
887#529—798no—
888#529—794no—
889#525—792no—
890#525—794no—
891#525—794no—
892#525—794no—
893#525—794no—
894#525—794no—
895#525—792no—
896#525—794no—
897#525—794no—
898#525—792no—
899#525—792no—
900#525—794no—
901#525—792no—
902#525—792no—
903#525—794no—
904#525—794no—
905#525—794no—
906#525—792no—
907#525C2×D7912yescomplemented
908C2×#123—792no—
909C2×#123—794no—
910C2×#123C2×D7914yescomplemented
911C2×C22⋊Q8—792no—
912C2×C22⋊Q8—792no—
913C2×C22⋊Q8—792no—
914C2×C22⋊Q8—794no—
915C2×#121—792no—
916C2×#121—794no—
917C2×#121—792no—
918C2×#121—792no—
919C2×#120—792no—
920C2×#120—794no—
921#520—792no—
922#520—792no—
923#520—798no—
924#519—791no—
925#518—798no—
926#518C2×D7911yescharacteristic, complemented
927C2×C4×D4—794no—
928C2×C4×D4—794no—
929C2×C4×D4—794no—
930C2×#117—791no—
931C2×#117—792no—
932C25—791no—
9332−1+4—3164no—
934H(5,𝔽2)—44no—
935C2×#41—44no—
936C2×#41—3168no—
937C2×#41—792no—
938C2×#41—794no—
939C2×#41—794no—
940C2×#41—792no—
941C2×#41—798no—
942C2×#41—794no—
943C2×#41—794no—
944C2×#41—792no—
945C2×#41C22×D7912yes—
946C2×#41C22×D7914yes—
947C2×#41C22×D7914yes—
948C2×#41C22×D7914yescomplemented
949C22×Q8—792no—
950C22×Q8—794no—
951C22×Q8C22×D7911yescharacteristic
952C22×D4—794no—
953C22×D4—798no—
954C22×D4—794no—
955C22×D4—794no—
956C22×D4—794no—
957C22×D4—792no—
958C22×D4C22×D7911yescharacteristic
959C22×D4C22×D7912yes—
960C22×D4C22×D7914yes—
961C22×D4C22×D7914yescomplemented
962C23×C4—3164no—
963C23×C4—791no—
964C23×C4—792no—
965C23×C4—794no—
966C23×C4—792no—
967C23×C4—792no—
968C23×C4—792no—
969C23×C4—792no—
970C23×C4—792no—
971C23×C4C22×D7911yescharacteristic
972C23×C4C22×D7912yes—
973C4⋊Q8—794no—
974C4⋊Q8—798no—
975C4⋊Q8—794no—
976C4⋊Q8C22×D7914yescomplemented
977#127—794no—
978#127—794no—
979#127—798no—
980#127—794no—
981#126—798no—
982#126—798no—
983#126—798no—
984#126—798no—
985#126—798no—
986#126—798no—
987#126—798no—
988#126—798no—
989#126—798no—
990#126—798no—
991#125—798no—
992#125—794no—
993#125—798no—
994#125—798no—
995#125—798no—
996#125—794no—
997#124—794no—
998#124—794no—
999#124—798no—
1000#124—794no—
1001#124—798no—
1002#124—798no—
1003#124—798no—
1004#124—798no—
1005#124—798no—
1006#124—798no—
1007#124—798no—
1008#124C22×D7914yescomplemented
1009#123—798no—
1010#123—794no—
1011#123—794no—
1012#123—794no—
1013#123—798no—
1014#123—798no—
1015#123—794no—
1016#123—798no—
1017#123—798no—
1018#123—794no—
1019#123—794no—
1020#123—798no—
1021#123—798no—
1022#123—794no—
1023#123—794no—
1024#123—794no—
1025#123—798no—
1026#123—798no—
1027#123—798no—
1028#123—798no—
1029#123—798no—
1030#123—798no—
1031#123C22×D7914yes—
1032#123C22×D7918yes—
1033#123C22×D7914yes—
1034#123C22×D7914yes—
1035#123C22×D7918yescomplemented
1036#123C22×D7918yescomplemented
1037C22⋊Q8—794no—
1038C22⋊Q8—792no—
1039C22⋊Q8—794no—
1040C22⋊Q8—792no—
1041C22⋊Q8—794no—
1042C22⋊Q8—794no—
1043C22⋊Q8—794no—
1044C22⋊Q8—792no—
1045C22⋊Q8—792no—
1046C22⋊Q8—794no—
1047C22⋊Q8—798no—
1048C22⋊Q8—798no—
1049C22⋊Q8—798no—
1050C22⋊Q8—792no—
1051C22⋊Q8—792no—
1052C22⋊Q8—794no—
1053C22⋊Q8—794no—
1054C22⋊Q8—798no—
1055C22⋊Q8—798no—
1056C22⋊Q8—798no—
1057C22⋊Q8—794no—
1058C22⋊Q8—794no—
1059C22⋊Q8—798no—
1060C22⋊Q8—798no—
1061C22⋊Q8—798no—
1062C22⋊Q8C22×D7912yes—
1063C22⋊Q8C22×D7912yes—
1064C22⋊Q8C22×D7914yescomplemented
1065C22⋊Q8C22×D7914yescomplemented
1066#121—792no—
1067#121—794no—
1068#121—792no—
1069#121—794no—
1070#121—794no—
1071#121—794no—
1072#121—794no—
1073#121—794no—
1074#121—794no—
1075#121—794no—
1076#121—798no—
1077#121—798no—
1078#121—794no—
1079#121—798no—
1080#121—798no—
1081#121—798no—
1082#121—798no—
1083#121—798no—
1084#121—798no—
1085#121—798no—
1086#121—792no—
1087#121—792no—
1088#121—794no—
1089#121—798no—
1090#121—798no—
1091#121—798no—
1092#121—792no—
1093#121—792no—
1094#121—798no—
1095#121—794no—
1096#121—794no—
1097#121—798no—
1098#121—798no—
1099#121—798no—
1100#121—798no—
1101#121C22×D7912yes—
1102#121C22×D7912yes—
1103#121C22×D7918yes—
1104#121C22×D7918yes—
1105#120—794no—
1106#120—798no—
1107#120—798no—
1108#120—798no—
1109#120—794no—
1110#120—798no—
1111#120—794no—
1112#120—794no—
1113#120—794no—
1114#120—794no—
1115#120—798no—
1116#120—794no—
1117#120—794no—
1118#120—794no—
1119#120—798no—
1120#120C22×D7914yes—
1121#120C22×D7914yes—
1122#120C22×D7914yes—
1123C4×Q8—794no—
1124C4×Q8—794no—
1125C4×Q8—794no—
1126C4×Q8—798no—
1127C4×Q8—798no—
1128C4×Q8—794no—
1129C4×D4—794no—
1130C4×D4—794no—
1131C4×D4—798no—
1132C4×D4—794no—
1133C4×D4—798no—
1134C4×D4—798no—
1135C4×D4—794no—
1136C4×D4—794no—
1137C4×D4—798no—
1138C4×D4—794no—
1139C4×D4—794no—
1140C4×D4—798no—
1141C4×D4—798no—
1142C4×D4—798no—
1143C4×D4—798no—
1144C4×D4—798no—
1145C4×D4—798no—
1146C4×D4—798no—
1147C4×D4—794no—
1148C4×D4—794no—
1149C4×D4—798no—
1150C4×D4—794no—
1151C4×D4—794no—
1152C4×D4—794no—
1153C4×D4—794no—
1154C4×D4—798no—
1155C4×D4—798no—
1156C4×D4—798no—
1157C4×D4—798no—
1158C4×D4—794no—
1159C4×D4—794no—
1160C4×D4—794no—
1161C4×D4C22×D7914yes—
1162C4×D4C22×D7914yes—
1163C4×D4C22×D7914yescomplemented
1164C4×D4C22×D7914yescomplemented
1165#117—792no—
1166#117—794no—
1167#117—794no—
1168#117—794no—
1169#117—794no—
1170#117—798no—
1171#117—792no—
1172#117—792no—
1173#117—794no—
1174#117—798no—
1175#117—798no—
1176#117—794no—
1177#117—798no—
1178#117—798no—
1179#117—794no—
1180#117C22×D7912yes—
1181C2×C4⋊C4—792no—
1182C2×C4⋊C4—794no—
1183C2×C4⋊C4—794no—
1184C2×C4⋊C4—792no—
1185C2×C4⋊C4—792no—
1186C2×C4⋊C4—794no—
1187C2×C4⋊C4—794no—
1188C2×C4⋊C4—794no—
1189C2×C4⋊C4—798no—
1190C2×C4⋊C4C22×D7918yescomplemented
1191C2×C22⋊C4—792no—
1192C2×C22⋊C4—794no—
1193C2×C22⋊C4—798no—
1194C2×C22⋊C4—794no—
1195C2×C22⋊C4—794no—
1196C2×C22⋊C4—794no—
1197C2×C22⋊C4—794no—
1198C2×C22⋊C4—794no—
1199C2×C22⋊C4—794no—
1200C2×C22⋊C4—798no—
1201C2×C22⋊C4C22×D7914yes—
1202C2×C22⋊C4C22×D7918yescomplemented
1203C2×C42—792no—
1204C2×C42—794no—
1205C24—3162no—
1206C24—3164no—
1207C24—791no—
1208C24—794no—
1209C24—792no—
1210C24—791no—
1211C24—792no—
1212C24C23×D7912yes—
1213C24C23×D7911yescharacteristic
1214C24C23×D7914yes—
1215#41—28no—
1216#41—48no—
1217#41—48no—
1218#41—48no—
1219#41—3168no—
1220#41—3168no—
1221#41—31616no—
1222#41—3164no—
1223#41—3168no—
1224#41—3164no—
1225#41—3168no—
1226#41—1588no—
1227C2×Q8—24no—
1228C2×Q8—3164no—
1229C2×Q8—3168no—
1230C2×Q8—798no—
1231C2×Q8—794no—
1232C2×Q8—794no—
1233C2×Q8—792no—
1234C2×Q8C23×D7912yes—
1235C2×Q8C23×D7914yes—
1236C2×D4—24no—
1237C2×D4—48no—
1238C2×D4—44no—
1239C2×D4—48no—
1240C2×D4—3168no—
1241C2×D4—3168no—
1242C2×D4—31616no—
1243C2×D4—3168no—
1244C2×D4—3164no—
1245C2×D4—3168no—
1246C2×D4—794no—
1247C2×D4—798no—
1248C2×D4—798no—
1249C2×D4—798no—
1250C2×D4—794no—
1251C2×D4—794no—
1252C2×D4—798no—
1253C2×D4—794no—
1254C2×D4—794no—
1255C2×D4—798no—
1256C2×D4—794no—
1257C2×D4—794no—
1258C2×D4—794no—
1259C2×D4—794no—
1260C2×D4—794no—
1261C2×D4—794no—
1262C2×D4—792no—
1263C2×D4C23×D7914yes—
1264C2×D4C23×D7912yes—
1265C2×D4C23×D7914yes—
1266C2×D4C23×D7914yes—
1267C2×D4C23×D7914yes—
1268C2×D4C23×D7914yes—
1269C2×D4C23×D7914yes—
1270C2×D4C23×D7918yes—
1271C22×C4—24no—
1272C22×C4—44no—
1273C22×C4—3164no—
1274C22×C4—3164no—
1275C22×C4—3164no—
1276C22×C4—3164no—
1277C22×C4—3164no—
1278C22×C4—3168no—
1279C22×C4—3162no—
1280C22×C4—794no—
1281C22×C4—794no—
1282C22×C4—798no—
1283C22×C4—791no—
1284C22×C4—792no—
1285C22×C4—791no—
1286C22×C4—794no—
1287C22×C4—792no—
1288C22×C4—792no—
1289C22×C4—794no—
1290C22×C4—798no—
1291C22×C4—798no—
1292C22×C4—794no—
1293C22×C4—792no—
1294C22×C4—792no—
1295C22×C4—792no—
1296C22×C4—792no—
1297C22×C4—794no—
1298C22×C4—792no—
1299C22×C4—794no—
1300C22×C4—792no—
1301C22×C4—792no—
1302C22×C4—1588no—
1303C22×C4C23×D7911yescharacteristic
1304C22×C4C23×D7912yes—
1305C22×C4C23×D7914yes—
1306C22×C4C23×D7912yes—
1307C22×C4C23×D7912yes—
1308C22×C4C23×D7918yes—
1309C22×C4C23×D7918yes—
1310C22×C4C23×D7914yes—
1311C22×C4C23×D7911yescharacteristic
1312C4⋊C4—798no—
1313C4⋊C4—794no—
1314C4⋊C4—794no—
1315C4⋊C4—794no—
1316C4⋊C4—794no—
1317C4⋊C4—794no—
1318C4⋊C4—794no—
1319C4⋊C4—798no—
1320C4⋊C4—798no—
1321C4⋊C4—798no—
1322C4⋊C4—798no—
1323C4⋊C4—798no—
1324C4⋊C4—794no—
1325C4⋊C4—792no—
1326C4⋊C4—794no—
1327C4⋊C4—794no—
1328C4⋊C4—792no—
1329C4⋊C4—794no—
1330C4⋊C4—798no—
1331C4⋊C4—798no—
1332C4⋊C4—798no—
1333C4⋊C4C23×D7912yes—
1334C4⋊C4C23×D7914yes—
1335C4⋊C4C23×D7914yes—
1336C4⋊C4C23×D7918yes—
1337C4⋊C4C23×D7912yes—
1338C4⋊C4C23×D7918yes—
1339C22⋊C4—794no—
1340C22⋊C4—798no—
1341C22⋊C4—798no—
1342C22⋊C4—794no—
1343C22⋊C4—794no—
1344C22⋊C4—794no—
1345C22⋊C4—794no—
1346C22⋊C4—794no—
1347C22⋊C4—794no—
1348C22⋊C4—798no—
1349C22⋊C4—798no—
1350C22⋊C4—798no—
1351C22⋊C4—798no—
1352C22⋊C4—794no—
1353C22⋊C4—798no—
1354C22⋊C4—794no—
1355C22⋊C4—794no—
1356C22⋊C4—794no—
1357C22⋊C4—794no—
1358C22⋊C4—794no—
1359C22⋊C4—794no—
1360C22⋊C4—794no—
1361C22⋊C4—798no—
1362C22⋊C4—794no—
1363C22⋊C4—794no—
1364C22⋊C4—798no—
1365C22⋊C4—798no—
1366C22⋊C4C23×D7914yes—
1367C22⋊C4C23×D7914yes—
1368C22⋊C4C23×D7914yes—
1369C22⋊C4C23×D7918yes—
1370C22⋊C4C23×D7914yes—
1371C22⋊C4C23×D7914yes—
1372C22⋊C4C23×D7914yes—
1373C22⋊C4C23×D7914yes—
1374C22⋊C4C23×D7918yes—
1375C42—794no—
1376C42—798no—
1377C42—794no—
1378C42—794no—
1379C42—798no—
1380C42—794no—
1381C42—798no—
1382C42—794no—
1383C42C23×D7914yes—
1384C23—22no—
1385C23—24no—
1386C23—42no—
1387C23—44no—
1388C23—44no—
1389C23—48no—
1390C23—3161no—
1391C23—3162no—
1392C23—3161no—
1393C23—3162no—
1394C23—3162no—
1395C23—3162no—
1396C23—3164no—
1397C23—3164no—
1398C23—31616no—
1399C23—792no—
1400C23—792no—
1401C23—794no—
1402C23—1584no—
1403C23—1584no—
1404C23—1584no—
1405C23—1588no—
1406C23—1584no—
1407C23C24×D7911yescharacteristic
1408C23C24×D7911yescharacteristic
1409C23C24×D7914yes—
1410C23C24×D7914yes—
1411C23C24×D7911yescharacteristic
1412Q8—28no—
1413Q8—24no—
1414Q8—3164no—
1415Q8—3164no—
1416Q8—3168no—
1417Q8—1584no—
1418D4—28no—
1419D4—28no—
1420D4—24no—
1421D4—48no—
1422D4—44no—
1423D4—44no—
1424D4—44no—
1425D4—44no—
1426D4—3164no—
1427D4—3164no—
1428D4—3164no—
1429D4—3168no—
1430D4—3164no—
1431D4—3168no—
1432D4—3168no—
1433D4—3164no—
1434D4—3164no—
1435D4—3164no—
1436D4—3164no—
1437D4—3168no—
1438D4—1588no—
1439D4—1588no—
1440D4—15816no—
1441D4—1588no—
1442D4—1584no—
1443C2×C4—22no—
1444C2×C4—24no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—28no—
1448C2×C4—48no—
1449C2×C4—44no—
1450C2×C4—48no—
1451C2×C4—3162no—
1452C2×C4—3162no—
1453C2×C4—3162no—
1454C2×C4—3162no—
1455C2×C4—3164no—
1456C2×C4—3164no—
1457C2×C4—3164no—
1458C2×C4—3168no—
1459C2×C4—3168no—
1460C2×C4—3161no—
1461C2×C4—3162no—
1462C2×C4—3161no—
1463C2×C4—3164no—
1464C2×C4—3168no—
1465C2×C4—3164no—
1466C2×C4—794no—
1467C2×C4—798no—
1468C2×C4—794no—
1469C2×C4—792no—
1470C2×C4—794no—
1471C2×C4—792no—
1472C2×C4—1588no—
1473C2×C4—1584no—
1474C2×C4—1584no—
1475C2×C4—1584no—
1476C2×C4—1584no—
1477C2×C4—1584no—
1478C2×C4—1588no—
1479C2×C4#1457920614yes—
1480C2×C4C24×D7912yes—
1481C2×C4C24×D7914yes—
1482C2×C4C24×D7914yes—
1483C2×C4C24×D7914yes—
1484C2×C4C24×D7914yes—
1485C2×C4C24×D7912yes—
1486C22—22no—
1487C22—21no—
1488C22—21no—
1489C22—24no—
1490C22—24no—
1491C22—28no—
1492C22—24no—
1493C22—22no—
1494C22—22no—
1495C22—24no—
1496C22—44no—
1497C22—84no—
1498C22—164no—
1499C22—3168no—
1500C22—3164no—
1501C22—3168no—
1502C22—3164no—
1503C22—794no—
1504C22—6328no—
1505C22—1584no—
1506C22—1582no—
1507C22—1584no—
1508C22—1584no—
1509C22—1582no—
1510C22—1582no—
1511C22—1582no—
1512C22—1582no—
1513C22C2×#1457920612yes—
1514C22C25×D7911yescharacteristic
1515C4—22no—
1516C4—24no—
1517C4—24no—
1518C4—24no—
1519C4—24no—
1520C4—1582no—
1521C4—1582no—
1522C4—1584no—
1523C4—1584no—
1524C4—1588no—
1525C4—1584no—
1526C4C2×#1457920614yes—
1527C2—22no—
1528C2—41no—
1529C2—41no—
1530C2—44no—
1531C2—44no—
1532C2—3162no—
1533C2—3164no—
1534C2—1584no—
1535C2C22×#1457920611yescharacteristic
1536C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3485C2
hypercenter#3485D79
hypocenterC79#62821
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #23777714C2semidirect
2. #23777683C2semidirect
3. #23777664C2semidirect
4. #23777655C2semidirect
5. #23777561C2semidirect
6. #23777552C2semidirect
7. #23777452C2semidirect
8. #23777429C2semidirect
9. #23777332C2semidirect
10. #23777250C2semidirect
11. #23777227C2semidirect
12. #23777149C2semidirect
13. #23777125C2semidirect
14. #23777117C2semidirect
15. #23777078C2semidirect
16. #23777062C2semidirect
17. #23777058C2semidirect
18. C2×#19099070C2semidirect
19. #525×D79C2semidirect
20. C79×#3485C2semidirect
21. C2×#14579209C22semidirect
22. C2×#41×D79C22semidirect
23. C23×C4×D79C22semidirect
24. #19099316C22semidirect
25. #19099308C22semidirect
26. #19099306C22semidirect
27. #19099303C22semidirect
28. #19099302C22semidirect
29. #19099301C22semidirect
30. #19099297C22semidirect
31. #19099297C22semidirect
32. #19099284C22semidirect
33. #19099284C22semidirect
34. #19099283C22semidirect
35. #19099278C22semidirect
36. #19099278C22semidirect
37. #19099277C22semidirect
38. #19099271C22semidirect
39. #19099268C22semidirect
40. #19099263C22semidirect
41. #19099263C22semidirect
42. #19099261C22semidirect
43. #19099260C22semidirect
44. #19099260C22semidirect
45. #19099259C22semidirect
46. #19099258C22semidirect
47. #19099258C22semidirect
48. #19099255C22semidirect
49. #19099253C22semidirect
50. #19099250C22semidirect
51. #19099247C22semidirect
52. #19099247C22semidirect
53. #19099244C22semidirect
54. #19099241C22semidirect
55. #19099241C22semidirect
56. #19099239C22semidirect
57. #19099239C22semidirect
58. #19099236C22semidirect
59. #19099232C22semidirect
60. #19099232C22semidirect
61. #19099232C22semidirect
62. #19099228C22semidirect
63. #19099221C22semidirect
64. #19099220C22semidirect
65. #19099220C22semidirect
66. #19099220C22semidirect
67. #19099218C22semidirect
68. #19099216C22semidirect
69. #19099211C22semidirect
70. #19099210C22semidirect
71. #19099207C22semidirect
72. #19099207C22semidirect
73. #19099206C22semidirect
74. #19099205C22semidirect
75. #19099203C22semidirect
76. #19099203C22semidirect
77. D4×C22⋊D79C22semidirect
78. D4×C22⋊D79C22semidirect
79. #19099195C22semidirect
80. #19099191C22semidirect
81. #19099182C22semidirect
82. #19099181C22semidirect
83. #19099180C22semidirect
84. #19099178C22semidirect
85. #19099174C22semidirect
86. #19099165C22semidirect
87. #19099164C22semidirect
88. #19099163C22semidirect
89. #19099160C22semidirect
90. #19099156C22semidirect
91. #19099156C22semidirect
92. #19099151C22semidirect
93. #19099149C22semidirect
94. #19099149C22semidirect
95. #19099148C22semidirect
96. #19099148C22semidirect
97. #19099145C22semidirect
98. #19099143C22semidirect
99. #19099141C22semidirect
100. #19099141C22semidirect
101. #19099136C22semidirect
102. #19099130C22semidirect
103. #19099130C22semidirect
104. #19099130C22semidirect
105. #19099129C22semidirect
106. #19099123C22semidirect
107. #19099118C22semidirect
108. #19099110C22semidirect
109. #19099095C22semidirect
110. #19099092C22semidirect
111. #19099090C22semidirect
112. #19099076C22semidirect
113. #19099076C22semidirect
114. #19099076C22semidirect
115. #19099075C22semidirect
116. #19099074C22semidirect
117. #19099074C22semidirect
118. #19099073C22semidirect
119. #19099073C22semidirect
120. #19099072C22semidirect
121. #19099072C22semidirect
122. #19099071C22semidirect
124. #19099070C22semidirect
125. #19099070C22semidirect
126. #19099070C22semidirect
127. #19099070C22semidirect
128. #19099070C22semidirect
129. #19099069C22semidirect
130. C2×#14579142C22semidirect
131. #123×D79C22semidirect
132. C2×#14579137C22semidirect
133. C22⋊Q8×D79C22semidirect
134. C22⋊Q8×D79C22semidirect
135. C22⋊Q8×D79C22semidirect
136. C2×#14579132C22semidirect
137. C2×#14579132C22semidirect
138. #121×D79C22semidirect
139. #121×D79C22semidirect
140. C2×#14579129C22semidirect
141. #120×D79C22semidirect
142. #19099046C22semidirect
143. #19099044C22semidirect
144. #19099043C22semidirect
145. #19099041C22semidirect
146. #19099036C22semidirect
147. C2×C4×C22⋊D79C22semidirect
148. C4×D4×D79C22semidirect
149. C4×D4×D79C22semidirect
150. C2×#14579120C22semidirect
151. #117×D79C22semidirect
152. C2×H(5,𝔽2)×C79C22semidirect
153. C22×#41×C79C22semidirect
154. #547×C79C22semidirect
155. #547×C79C22semidirect
156. #546×C79C22semidirect
157. #546×C79C22semidirect
158. #536×C79C22semidirect
159. #534×C79C22semidirect
160. #525×C79C22semidirect
161. C2×#123×C79C22semidirect
162. #518×C79C22semidirect
166. C2×#11929625C23semidirect
175. C2×Q8×D79C23semidirect
191. #14579161C23semidirect
192. #14579160C23semidirect
193. #14579160C23semidirect
197. #14579157C23semidirect
200. #14579156C23semidirect
203. #14579154C23semidirect
204. #14579154C23semidirect
205. #14579154C23semidirect
206. #14579154C23semidirect
207. #14579154C23semidirect
208. #14579153C23semidirect
209. #14579152C23semidirect
210. #14579152C23semidirect
211. #14579151C23semidirect
212. #14579151C23semidirect
213. #14579151C23semidirect
217. #14579148C23semidirect
218. #14579148C23semidirect
223. #14579147C23semidirect
224. #14579147C23semidirect
228. #14579146C23semidirect
233. #14579144C23semidirect
239. #14579143C23semidirect
240. #14579143C23semidirect
246. #14579142C23semidirect
252. #14579140C23semidirect
253. #14579140C23semidirect
254. #14579140C23semidirect
255. #14579140C23semidirect
259. #14579139C23semidirect
263. #14579138C23semidirect
264. #14579138C23semidirect
271. #14579137C23semidirect
279. #14579135C23semidirect
280. #14579135C23semidirect
286. #14579134C23semidirect
292. #14579133C23semidirect
303. #14579132C23semidirect
304. #14579132C23semidirect
305. #14579132C23semidirect
306. #14579132C23semidirect
314. #14579130C23semidirect
322. Q8×Dic79C23semidirect
323. Q8×Dic79C23semidirect
324. Q8×Dic79C23semidirect
325. C4×Dic158C23semidirect
326. #14579126C23semidirect
327. #14579126C23semidirect
330. C4×D316C23semidirect
334. D4×Dic79C23semidirect
348. C4×C22⋊D79C23semidirect
349. C4×C22⋊D79C23semidirect
350. C4×C22⋊D79C23semidirect
351. C4×C22⋊D79C23semidirect
358. (C22⋊D79)⋊C4C23semidirect
359. (C22⋊D79)⋊C4C23semidirect
364. #14579120C23semidirect
365. #14579120C23semidirect
369. #14579119C23semidirect
370. #14579119C23semidirect
373. #14579117C23semidirect
374. #14579117C23semidirect
376. C2×C4⋊Dic79C23semidirect
382. C4⋊C4×D79C23semidirect
383. C4⋊C4×D79C23semidirect
386. C2×C22⋊Dic79C23semidirect
401. C2×#41×C79C23semidirect
406. C22×D4×C79C23semidirect
409. C4⋊Q8×C79C23semidirect
410. #124×C79C23semidirect
415. #123×C79C23semidirect
416. #123×C79C23semidirect
419. C22⋊Q8×C79C23semidirect
420. C22⋊Q8×C79C23semidirect
430. C4×D4×C79C23semidirect
431. C4×D4×C79C23semidirect
433. C2×C4⋊C4×C79C23semidirect
435. C2×C22⋊C4×C79C23semidirect
786. #3485D79semidirect
789. C79#62821semidirect
791. C2×H(5,𝔽2)C2×D79semidirect
793. C22×#41C2×D79semidirect
841. #547C2×D79semidirect
842. #547C2×D79semidirect
850. #546C2×D79semidirect
851. #546C2×D79semidirect
877. #536C2×D79semidirect
883. #534C2×D79semidirect
907. #525C2×D79semidirect
910. C2×#123C2×D79semidirect
926. #518C2×D79semidirect
948. C2×#41C22×D79semidirect
961. C22×D4C22×D79semidirect
976. C4⋊Q8C22×D79semidirect
1008. #124C22×D79semidirect
1035. #123C22×D79semidirect
1036. #123C22×D79semidirect
1064. C22⋊Q8C22×D79semidirect
1065. C22⋊Q8C22×D79semidirect
1163. C4×D4C22×D79semidirect
1164. C4×D4C22×D79semidirect
1190. C2×C4⋊C4C22×D79semidirect
1202. C2×C22⋊C4C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237777142
#237776832
#237776642
#237776552
#237775612
#237775522
#237774522
#237774292
#237773322
#237772502
#237772272
#237771492
#237771252
#237771172
#237770782
#237770622
#237770582
C2×#190990702
#525×D792
C79×#34852
#6282179