Finite Group Databasebeta

← #35197146

Subgroups — #35197146

Order 20224.

8650 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777733C211yesmaximal, characteristic, complemented
2#23777730C212yesmaximal, complemented
3#23777729C214yesmaximal, complemented
4#23777728C218yesmaximal, complemented
5#23777727C214yesmaximal, complemented
6#23777726C214yesmaximal, complemented
7#23777273C212yesmaximal, complemented
8#23777272C214yesmaximal, complemented
9#23777270C212yesmaximal, complemented
10#23777268C214yesmaximal, complemented
11#23777177C212yesmaximal, complemented
12#23777175C214yesmaximal, complemented
13#23777172C214yesmaximal, complemented
14#23777172C212yesmaximal, complemented
15#23777032C214yesmaximal, complemented
16#23777030C214yesmaximal, complemented
17#23777028C214yesmaximal, complemented
18#23776694C212yesmaximal, complemented
19C2×#127×D79C211yesmaximal, characteristic, complemented
20C79×#3543C211yesmaximal, characteristic, complemented
21C2×#14579207C2214yescomplemented
22C2×#14579206C2214yescomplemented
23C2×#14579206C2214yescomplemented
24C22×D4×D79C2214yescomplemented
25C22×D4×D79C2212yescomplemented
26#19099304C2218yescomplemented
27#19099303C2214yescomplemented
28#19099302C2214yescomplemented
29#19099301C2218yescomplemented
30#19099300C2214yescomplemented
31#19099299C2211yescharacteristic, complemented
32#19099298C2212yescomplemented
33#19099297C2214yescomplemented
34#19099297C2218yescomplemented
35#19099296C2214yescomplemented
36#19099295C2214yescomplemented
37#19099235C2212yescomplemented
38#19099234C2214yescomplemented
39#19099234C2212yescomplemented
40#19099233C2212yescomplemented
41#19099233C2214yescomplemented
42#19099232C2214yescomplemented
43#19099231C2218yescomplemented
44#19099231C2214yescomplemented
45#19099231C2218yescomplemented
46#19099231C2218yescomplemented
47#19099210C2214yescomplemented
48#19099209C2214yescomplemented
49#19099208C2214yescomplemented
50#19099207C2214yescomplemented
51#19099206C2214yescomplemented
52#19099205C2218yescomplemented
53#19099205C2218yescomplemented
54#19099205C2218yescomplemented
55#19099204C2214yescomplemented
56#19099203C2218yescomplemented
57#19099202C2218yescomplemented
58#19099202C2218yescomplemented
59#19099202C2218yescomplemented
60#19099201C2214yescomplemented
61#19099200C2218yescomplemented
62D4×D316C2214yescomplemented
63D4×D316C2214yescomplemented
64D4×D316C2212yescomplemented
65#19099198C2211yescharacteristic, complemented
66#19099198C2214yescomplemented
67#19099197C2214yescomplemented
68#19099197C2214yescomplemented
69#19099197C2218yescomplemented
70#19099197C2218yescomplemented
71#19099197C2218yescomplemented
72#19099197C2214yescomplemented
73D4×C22⋊D79C2214yescomplemented
74D4×C22⋊D79C2218yescomplemented
75D4×C22⋊D79C2214yescomplemented
76D4×C22⋊D79C2214yescomplemented
77#19099195C2218yescomplemented
78#19099195C2218yescomplemented
79#19099195C2218yescomplemented
80#19099195C2218yescomplemented
81#19099195C2218yescomplemented
82#19099195C2214yescomplemented
83#19099169C2214yescomplemented
84#19099168C2214yescomplemented
85#19099167C2214yescomplemented
86#19099165C2218yescomplemented
87#19099165C2218yescomplemented
88#19099163C2218yescomplemented
89#19099163C2218yescomplemented
90#19099132C2214yescomplemented
91#19099131C2214yescomplemented
92#19099131C2214yescomplemented
93#19099129C2214yescomplemented
94#19099129C2214yescomplemented
95#19099129C2218yescomplemented
96#19099129C2218yescomplemented
97#19099128C2218yescomplemented
98#19099128C2218yescomplemented
99#19099128C2218yescomplemented
100#19099126C2214yescomplemented
101#19099126C2214yescomplemented
102#19099124C2218yescomplemented
103#19099124C2218yescomplemented
104#19099123C2218yescomplemented
105#19099122C2214yescomplemented
106#19099121C2218yescomplemented
107#19099121C2218yescomplemented
108#19099119C2212yescomplemented
109#19099117C2212yescomplemented
110#19099115C2212yescomplemented
111#19099112C2212yescomplemented
112#19099112C2214yescomplemented
113#19099110C2212yescomplemented
114#19099110C2214yescomplemented
115#19099110C2214yescomplemented
116#19099109C2214yescomplemented
117#19099108C2212yescomplemented
118#19099108C2214yescomplemented
119#19099108C2214yescomplemented
120C2×#14579158C2211yescharacteristic, complemented
121C2×#14579157C2214yescomplemented
122C2×#14579157C2212yescomplemented
123C2×#14579157C2214yescomplemented
124#127×D79C2212yescomplemented
125#127×D79C2214yescomplemented
126#127×D79C2212yescomplemented
127#127×D79C2214yescomplemented
128#127×D79C2214yescomplemented
129#127×D79C2214yescomplemented
130#19099098C2212yescomplemented
131#19099097C2212yescomplemented
132#19099096C2214yescomplemented
133#19099096C2214yescomplemented
134#19099092C2212yescomplemented
135#19099091C2214yescomplemented
136#19099090C2214yescomplemented
137#19099076C2212yescomplemented
138#19099073C2212yescomplemented
139#19099072C2214yescomplemented
140#19099071C2214yescomplemented
141C2×#14579131C2214yescomplemented
142C2×#14579129C2214yescomplemented
143#120×D79C2218yescomplemented
144#19099036C2214yescomplemented
145#19099035C2214yescomplemented
146#19099035C2214yescomplemented
147C4×#11929625C2212yescomplemented
148#19099031C2214yescomplemented
149C4×#11929623C2214yescomplemented
150C4×#11929623C2212yescomplemented
151C2×C42×D79C2211yescharacteristic, complemented
152#560×C79C2214yescomplemented
153#559×C79C2211yescharacteristic, complemented
154#550×C79C2212yescomplemented
155#546×C79C2214yescomplemented
156D42×C79C2214yescomplemented
157D42×C79C2211yescharacteristic, complemented
158#540×C79C2214yescomplemented
159#535×C79C2214yescomplemented
160#534×C79C2214yescomplemented
161C2×#127×C79C2211yescharacteristic, complemented
162#529×C79C2212yescomplemented
163C24×D79C2314yes—
164#14579207—416no—
165#14579206—416no—
166#14579206—416no—
167C2×#11929625C2312yes—
168C2×#11929625C2314yescomplemented
169C2×#11929624C2314yes—
170C2×#11929624C2318yescomplemented
171C2×#11929624C2314yescomplemented
172C2×#11929624C2318yescomplemented
173C2×#11929623C2314yes—
174C2×#11929623C2312yes—
175C2×#11929623C2318yescomplemented
176C2×#11929623C2318yescomplemented
177C2×#11929623C2314yescomplemented
178C22×D316C2318yes—
179C22×D316C2314yes—
180C22×D316C2312yes—
181C22×D316C2314yescomplemented
182C22×C22⋊D79C2314yes—
183C22×C22⋊D79C2318yes—
184C22×C22⋊D79C2314yes—
185C22×C22⋊D79C2318yes—
186C22×C22⋊D79C2318yescomplemented
187C22×C22⋊D79C2318yescomplemented
188C2×D4×D79—416no—
189C2×D4×D79—48no—
190C2×D4×D79C2314yes—
191C2×D4×D79C2314yes—
192C2×D4×D79C2318yes—
193C2×D4×D79C2318yes—
194C2×D4×D79C2318yes—
195C2×D4×D79C2314yes—
196C2×D4×D79C2318yes—
197C2×D4×D79C2318yes—
198C2×D4×D79C2314yes—
199C2×D4×D79C2314yes—
200C2×D4×D79C2314yes—
201C2×D4×D79C2318yes—
202C2×D4×D79C2318yescomplemented
203C2×D4×D79C2314yescomplemented
204C2×D4×D79C2318yescomplemented
205C2×D4×D79C2314yescomplemented
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2312yes—
208#14579160C2312yescomplemented
209#14579160C2312yescomplemented
210#14579159C2312yescomplemented
211#14579158C2314yes—
212#14579158C2312yes—
213#14579158C2312yes—
214#14579158C2314yescomplemented
215#14579157C2314yes—
216#14579157C2318yes—
217#14579157C2314yes—
218#14579157C2314yes—
219#14579157C2318yes—
220#14579157C2314yes—
221#14579157C2314yes—
222#14579157C2314yes—
223#14579157C2314yes—
224#14579157C2314yes—
225#14579157C2318yescomplemented
226#14579157C2318yescomplemented
227#14579157C2318yescomplemented
228#14579157C2318yescomplemented
229#14579157C2314yescomplemented
230#14579157C2314yescomplemented
231#14579157C2312yescomplemented
232#14579156C2314yescomplemented
233#14579155C2314yescomplemented
234#14579154C2314yescomplemented
235#14579153C2312yescomplemented
236#14579151C2314yescomplemented
237#14579151C2314yescomplemented
238#14579150C2314yescomplemented
239#14579149C2314yescomplemented
240#14579149C2312yescomplemented
241#14579148C2314yescomplemented
242#14579147C2318yescomplemented
243#14579147C2318yescomplemented
244#14579147C2318yescomplemented
245#14579147C2318yescomplemented
246#14579147C2314yescomplemented
247#14579147C2314yescomplemented
248#14579146C2314yes—
249#14579146C2314yes—
250#14579146C2318yescomplemented
251#14579146C2318yescomplemented
252#14579146C2318yescomplemented
253#14579146C2318yescomplemented
254#14579145C2318yescomplemented
255#14579144C2314yes—
256#14579144C2318yescomplemented
257#14579143C2314yes—
258#14579143C2314yes—
259#14579143C2318yescomplemented
260#14579143C2318yescomplemented
261#14579142C2314yescomplemented
262#14579142C2318yescomplemented
263#14579142C2314yescomplemented
264#14579141C2312yes—
265#14579140C2312yes—
266#14579139C2314yes—
267#14579139C2314yes—
268#14579139C2314yes—
269#14579138C2314yes—
270#14579137C2312yes—
271#14579136C2312yes—
272#14579136C2318yescomplemented
273#14579136C2318yescomplemented
274#14579136C2314yescomplemented
275#14579136C2318yescomplemented
276#14579136C2314yescomplemented
277#14579136C2318yescomplemented
278#14579135C2312yes—
279#14579135C2318yescomplemented
280#14579135C2318yescomplemented
281#14579135C2314yescomplemented
282#14579135C2314yescomplemented
283#14579134C2314yes—
284#14579134C2314yes—
285#14579134C2314yes—
286#14579134C2318yescomplemented
287#14579134C2318yescomplemented
288#14579134C2318yescomplemented
289#14579134C2318yescomplemented
290#14579134C2318yescomplemented
291#14579134C2318yescomplemented
292#14579134C2318yescomplemented
293#14579134C2318yescomplemented
294#14579134C2318yescomplemented
295#14579134C2318yescomplemented
296#14579133C2314yes—
297#14579133C2318yescomplemented
298#14579133C2318yescomplemented
299#14579133C2318yescomplemented
300#14579133C2318yescomplemented
301#14579133C2318yescomplemented
302#14579133C2318yescomplemented
303#14579133C2318yescomplemented
304#14579133C2318yescomplemented
305#14579133C2318yescomplemented
306#14579133C2318yescomplemented
307#14579132C2312yes—
308#14579132C2318yescomplemented
309#14579132C2318yescomplemented
310#14579132C2314yescomplemented
311#14579132C2314yescomplemented
312#14579131C2318yes—
313#14579131C2318yes—
314#14579131C2318yes—
315#14579131C2318yes—
316#14579131C2318yes—
317#14579131C2314yes—
318#14579131C2318yescomplemented
319#14579131C2318yescomplemented
320#14579131C2318yescomplemented
321#14579131C2318yescomplemented
322#14579131C2318yescomplemented
323#14579130C2318yes—
324#14579130C2318yescomplemented
325#14579129C2318yes—
326#14579129C2318yes—
327#14579129C2318yes—
328#14579129C2318yes—
329#14579129C2318yes—
330#14579129C2314yes—
331#14579129C2318yescomplemented
332#14579129C2318yescomplemented
333#14579129C2314yescomplemented
334#14579129C2318yescomplemented
335#14579129C2314yescomplemented
336Q8×Dic79C2312yescomplemented
337C4×Dic158C2314yescomplemented
338C4×Dic158C2312yescomplemented
339#14579126C2312yescomplemented
340#14579126C2314yescomplemented
341#14579126C2314yescomplemented
342#14579126C2314yescomplemented
343C4×D316C2314yes—
344C4×D316C2314yescomplemented
345C4×D316C2314yescomplemented
346C4×D316C2312yescomplemented
347D4×Dic79C2314yes—
348D4×Dic79C2314yescomplemented
349D4×Dic79C2314yescomplemented
350D4×Dic79C2312yescomplemented
351#14579123C2314yes—
352#14579123C2314yes—
353#14579123C2314yes—
354#14579123C2314yescomplemented
355#14579123C2314yescomplemented
356#14579123C2312yescomplemented
357C4×C22⋊D79C2314yes—
358C4×C22⋊D79C2314yes—
359C4×C22⋊D79C2318yescomplemented
360C4×C22⋊D79C2318yescomplemented
361C4×C22⋊D79C2318yescomplemented
362C4×C22⋊D79C2318yescomplemented
363C4×C22⋊D79C2314yescomplemented
364(C22⋊D79)⋊C4C2314yes—
365(C22⋊D79)⋊C4C2314yes—
366(C22⋊D79)⋊C4C2314yes—
367(C22⋊D79)⋊C4C2314yes—
368(C22⋊D79)⋊C4C2318yescomplemented
369(C22⋊D79)⋊C4C2318yescomplemented
370(C22⋊D79)⋊C4C2318yescomplemented
371(C22⋊D79)⋊C4C2318yescomplemented
372(C22⋊D79)⋊C4C2314yescomplemented
373(C22⋊D79)⋊C4C2314yescomplemented
374(C22⋊D79)⋊C4C2314yescomplemented
375#14579119C2312yes—
376#14579119C2312yes—
377#14579119C2314yescomplemented
378#14579119C2314yescomplemented
379#14579118C2314yes—
380#14579118C2314yescomplemented
381#14579117C2314yes—
382#14579117C2314yescomplemented
383#14579117C2314yescomplemented
384C2×C22⋊Dic79C2314yes—
385C2×(C2×D79)⋊C4C2318yes—
386C2×(C2×D79)⋊C4C2318yes—
387C22⋊C4×D79C2318yes—
388C22⋊C4×D79C2318yes—
389C22⋊C4×D79C2318yes—
390C2×C4×Dic79C2312yes—
391C2×C4×Dic79C2311yescharacteristic
392C2×C4×Dic79C2314yescomplemented
393C42×D79C2312yes—
394C42×D79C2312yes—
395C42×D79C2312yes—
396C42×D79C2312yes—
397C42×D79C2314yescomplemented
398C2×#41×C79C2314yescomplemented
399C22×D4×C79C2314yes—
400C22×D4×C79C2314yes—
401C22×D4×C79C2312yes—
402C22×D4×C79C2314yescomplemented
403#127×C79C2314yes—
404#127×C79C2311yescharacteristic
405#127×C79C2311yescharacteristic
406#127×C79C2312yes—
407#127×C79C2314yescomplemented
408#126×C79C2314yescomplemented
409#125×C79C2312yescomplemented
410#124×C79C2314yescomplemented
411#124×C79C2312yescomplemented
412#123×C79C2314yes—
413#123×C79C2314yescomplemented
414#123×C79C2318yescomplemented
415#123×C79C2314yescomplemented
416C22⋊Q8×C79C2312yes—
417#121×C79C2312yes—
418#121×C79C2318yescomplemented
419#121×C79C2318yescomplemented
420#121×C79C2318yescomplemented
421#121×C79C2314yescomplemented
422#121×C79C2314yescomplemented
423#121×C79C2318yescomplemented
424#120×C79C2318yes—
425#120×C79C2314yescomplemented
426#120×C79C2314yescomplemented
427#120×C79C2318yescomplemented
428C4×Q8×C79C2312yescomplemented
429C4×D4×C79C2314yes—
430C4×D4×C79C2312yescomplemented
431C4×D4×C79C2314yescomplemented
432C4×D4×C79C2314yescomplemented
433#117×C79C2314yescomplemented
434C2×C22⋊C4×C79C2314yes—
435C2×C42×C79C2311yescharacteristic
436C23×D79—416no—
437C23×D79—48no—
438C23×D79C2411yescharacteristic
439C23×D79C2414yes—
440C23×D79C2418yes—
441C23×D79C2418yes—
442C23×D79C2414yes—
443C23×D79C2418yes—
444#11929625—28no—
445#11929625—48no—
446#11929624—216no—
447#11929624—416no—
448#11929624—416no—
449#11929624—48no—
450#11929623—216no—
451#11929623—28no—
452#11929623—416no—
453#11929623—416no—
454#11929623—48no—
455C2×Dic158C2414yes—
456C2×Dic158C2412yes—
457C2×Dic158C2414yes—
458C2×D316—44no—
459C2×D316—48no—
460C2×D316—48no—
461C2×D316—416no—
462C2×D316C2414yes—
463C2×D316C2414yes—
464C2×D316C2414yes—
465C2×D316C2412yes—
466C2×D316C2414yes—
467C2×D316C2418yes—
468C2×D316C2418yes—
469C2×D316C2418yes—
470C2×D316C2414yes—
471C2×D316C2418yes—
472C2×D316C2414yes—
473C2×C22⋊D79—216no—
474C2×C22⋊D79—416no—
475C2×C22⋊D79—48no—
476C2×C22⋊D79—416no—
477C2×C22⋊D79—416no—
478C2×C22⋊D79—416no—
479C2×C22⋊D79C2414yes—
480C2×C22⋊D79C2414yes—
481C2×C22⋊D79C2414yes—
482C2×C22⋊D79C2418yes—
483C2×C22⋊D79C2418yes—
484C2×C22⋊D79C2414yes—
485C2×C22⋊D79C2414yes—
486C2×C22⋊D79C2418yes—
487C2×C22⋊D79C2418yes—
488C2×C22⋊D79C2418yes—
489C2×C22⋊D79C2418yes—
490C2×C22⋊D79C2418yes—
491C2×C22⋊D79C2418yes—
492C2×C22⋊D79C2418yes—
493C2×C22⋊D79C2418yes—
494C2×C22⋊D79C2418yes—
495C2×C22⋊D79C2418yes—
496D4×D79—216no—
497D4×D79—216no—
498D4×D79—416no—
499D4×D79—416no—
500D4×D79—416no—
501D4×D79—48no—
502D4×D79—416no—
503D4×D79—48no—
504D4×D79—416no—
505D4×D79—416no—
506D4×D79—416no—
507D4×D79—48no—
508D4×D79—48no—
509D4×D79—48no—
510D4×D79—48no—
511D4×D79—416no—
512C22×Dic79C2414yes—
513C22×Dic79C2414yes—
514C22×Dic79C2412yes—
515C22×Dic79C2414yes—
516C22×Dic79C2418yes—
517C22×Dic79C2411yescharacteristic
518C2×C4×D79—24no—
519C2×C4×D79—28no—
520C2×C4×D79C2414yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2414yes—
523C2×C4×D79C2412yes—
524C2×C4×D79C2412yes—
525C2×C4×D79C2412yes—
526C2×C4×D79C2412yes—
527C2×C4×D79C2412yes—
528C2×C4×D79C2418yes—
529C2×C4×D79C2418yes—
530C2×C4×D79C2418yes—
531C2×C4×D79C2412yes—
532C4⋊Dic79C2412yes—
533C4⋊Dic79C2412yes—
534C4⋊Dic79C2414yes—
535C4⋊Dic79C2414yes—
536Dic79⋊C4C2414yes—
537Dic79⋊C4C2414yes—
538Dic79⋊C4C2414yes—
539Dic79⋊C4C2414yes—
540Dic79⋊C4C2414yes—
541Dic79⋊C4C2414yes—
542Dic79⋊C4C2414yes—
543Dic79⋊C4C2414yes—
544Dic79⋊C4C2414yes—
545Dic79⋊C4C2414yes—
546C22⋊Dic79C2414yes—
547C22⋊Dic79C2418yes—
548C22⋊Dic79C2418yes—
549C22⋊Dic79C2414yes—
550C22⋊Dic79C2414yes—
551C22⋊Dic79C2414yes—
552C22⋊Dic79C2414yes—
553(C2×D79)⋊C4C2414yes—
554(C2×D79)⋊C4C2414yes—
555(C2×D79)⋊C4C2414yes—
556(C2×D79)⋊C4C2414yes—
557(C2×D79)⋊C4C2418yes—
558(C2×D79)⋊C4C2418yes—
559(C2×D79)⋊C4C2418yes—
560(C2×D79)⋊C4C2418yes—
561(C2×D79)⋊C4C2418yes—
562(C2×D79)⋊C4C2418yes—
563(C2×D79)⋊C4C2414yes—
564(C2×D79)⋊C4C2414yes—
565(C2×D79)⋊C4C2414yes—
566(C2×D79)⋊C4C2414yes—
567(C2×D79)⋊C4C2414yes—
568(C2×D79)⋊C4C2414yes—
569C4×Dic79C2412yes—
570C4×Dic79C2412yes—
571C4×Dic79C2412yes—
572C4×Dic79C2411yescharacteristic
573C4×Dic79C2412yes—
574C4×Dic79C2412yes—
575C4×Dic79C2411yescharacteristic
576C4×Dic79C2414yes—
577C4×Dic79C2414yes—
578C4×Dic79C2414yes—
579C4×Dic79C2414yes—
580C4×Dic79C2414yes—
581C24×C79C2414yes—
582C24×C79C2414yes—
583#41×C79—48no—
584C2×Q8×C79C2412yes—
585C2×D4×C79—48no—
586C2×D4×C79—48no—
587C2×D4×C79—44no—
588C2×D4×C79—48no—
589C2×D4×C79C2414yes—
590C2×D4×C79C2412yes—
591C2×D4×C79C2414yes—
592C2×D4×C79C2414yes—
593C2×D4×C79C2418yes—
594C2×D4×C79C2418yes—
595C2×D4×C79C2418yes—
596C2×D4×C79C2412yes—
597C2×D4×C79C2414yes—
598C2×D4×C79C2418yes—
599C2×D4×C79C2412yes—
600C22×C4×C79C2414yes—
601C22×C4×C79C2412yes—
602C22×C4×C79C2411yescharacteristic
603C22×C4×C79C2414yes—
604C22×C4×C79C2418yes—
605C4⋊C4×C79C2414yes—
606C4⋊C4×C79C2414yes—
607C4⋊C4×C79C2414yes—
608C4⋊C4×C79C2412yes—
609C4⋊C4×C79C2412yes—
610C4⋊C4×C79C2414yes—
611C22⋊C4×C79C2414yes—
612C22⋊C4×C79C2414yes—
613C22⋊C4×C79C2414yes—
614C22⋊C4×C79C2414yes—
615C22⋊C4×C79C2414yes—
616C22⋊C4×C79C2414yes—
617C22⋊C4×C79C2418yes—
618C22⋊C4×C79C2418yes—
619C22⋊C4×C79C2414yes—
620C42×C79C2412yes—
621C42×C79C2411yescharacteristic
622C42×C79C2411yescharacteristic
623C42×C79C2414yes—
624C23×C79—28no—
625C23×C79—48no—
626C23×C79—48no—
627C23×C79—44no—
628C23×C79C2514yes—
629C23×C79C2514yes—
630C23×C79C2514yes—
631C23×C79C2511yescharacteristic
632C22×D79—22no—
633C22×D79—24no—
634C22×D79—28no—
635C22×D79—216no—
636C22×D79—216no—
637C22×D79—48no—
638C22×D79—48no—
639C22×D79—48no—
640C22×D79—48no—
641C22×D79—48no—
642C22×D79—44no—
643C22×D79—48no—
644C22×D79—48no—
645C22×D79—48no—
646C22×D79—48no—
647C22×D79—832no—
648C22×D79C2514yes—
649C22×D79C2518yes—
650C22×D79C2512yes—
651Q8×C79—24no—
652D4×C79—28no—
653D4×C79—28no—
654D4×C79—28no—
655D4×C79—24no—
656D4×C79—42no—
657D4×C79—44no—
658D4×C79—42no—
659D4×C79—48no—
660D4×C79—48no—
661D4×C79—48no—
662D4×C79—48no—
663C2×C4×C79—22no—
664C2×C4×C79—24no—
665C2×C4×C79—28no—
666C2×C4×C79—48no—
667C2×C4×C79—44no—
668C2×C4×C79C2514yes—
669C2×C4×C79C2511yescharacteristic
670C2×C4×C79C2512yes—
671C2×C4×C79C2511yescharacteristic
672C2×C4×C79C2514yes—
673C2×C4×C79C2514yes—
674C2×C4×C79C2512yes—
675C22⋊D79—28no—
676C22⋊D79—28no—
677C22⋊D79—28no—
678C22⋊D79—216no—
679C22⋊D79—216no—
680C22⋊D79—216no—
681C22⋊D79—216no—
682C22⋊D79—28no—
683C22⋊D79—28no—
684C22⋊D79—48no—
685C22⋊D79—48no—
686C22⋊D79—48no—
687C22⋊D79—48no—
688C22⋊D79—48no—
689C22⋊D79—48no—
690C22⋊D79—48no—
691C22⋊D79—48no—
692C2×Dic79—24no—
693C2×Dic79—28no—
694C2×Dic79—28no—
695C2×Dic79—48no—
696C2×Dic79—44no—
697C2×Dic79H(5,𝔽2)14yescomplemented
698C2×Dic79C2512yes—
699C2×Dic79C2514yes—
700C2×Dic79C2514yes—
701C2×Dic79C2514yes—
702C2×Dic79C2512yes—
703C2×Dic79C2512yes—
704D316—28no—
705D316—28no—
706D316—28no—
707D316—28no—
708D316—24no—
709D316—44no—
710D316—44no—
711D316—48no—
712D316—48no—
713D316—48no—
714D316—48no—
715C4×D79—24no—
716C4×D79—24no—
717C4×D79—28no—
718C4×D79—24no—
719C4×D79—24no—
720C4×D79—24no—
721C4×D79—28no—
722C4×D79—28no—
723C4×D79—48no—
724C4×D79—48no—
725C4×D79—48no—
726C4×D79H(5,𝔽2)18yescomplemented
727Dic158—24no—
728Dic158—28no—
729Dic158—28no—
730C22×C79—22no—
731C22×C79—24no—
732C22×C79—24no—
733C22×C79—24no—
734C22×C79—28no—
735C22×C79—28no—
736C22×C79—24no—
737C22×C79—24no—
738C22×C79—88no—
739C22×C79—164no—
740C22×C79C2×H(5,𝔽2)12yes—
741C22×C79C2611yescharacteristic
742C2×D79—28no—
743C2×D79—22no—
744C2×D79—22no—
745C2×D79—24no—
746C2×D79—28no—
747C2×D79—28no—
748C2×D79—24no—
749C2×D79—28no—
750C2×D79—24no—
751C2×D79—816no—
752C2×D79—816no—
753C2×D79—88no—
754C2×D79—168no—
755C2×D79—164no—
756C2×D79C2×H(5,𝔽2)14yes—
757C4×C79—24no—
758C4×C79—22no—
759C4×C79—21no—
760C4×C79—21no—
761C4×C79—24no—
762C4×C79—24no—
763C4×C79C2×H(5,𝔽2)14yes—
764Dic79—24no—
765Dic79—24no—
766Dic79—24no—
767Dic79—22no—
768Dic79C2×H(5,𝔽2)14yes—
769Dic79C2×H(5,𝔽2)14yes—
770#62832—791nomaximal, Sylow
771C2×C79—22no—
772C2×C79—44no—
773C2×C79—44no—
774C2×C79—44no—
775C2×C79C22×H(5,𝔽2)12yes—
776C2×C79C22×H(5,𝔽2)11yescharacteristic
777D79—24no—
778D79—48no—
779D79—44no—
780#3543—798no—
781#3543—794no—
782#3543—794no—
783#3543—794no—
784#3543—791no—
785#3543—792no—
786#3543D7911yescharacteristic, complemented
787#3508—792no—
788#3508—792no—
789#3508—794no—
790#3508—794no—
791#3498—792no—
792#3498—794no—
793#3498—792no—
794#3498—794no—
795#3484—794no—
796#3484—794no—
797#3484—794no—
798#3444—792no—
799C22×#127—791no—
800C79#6283211yescharacteristic, complemented, Sylow
801C2×H(5,𝔽2)—794no—
802C2×H(5,𝔽2)—794no—
803C2×H(5,𝔽2)—794no—
804C23×D4—794no—
805C23×D4—792no—
806#560—794no—
807#560—798no—
808#560—794no—
809#560—798no—
810#560—794no—
811#560C2×D7914yescomplemented
812#559—791no—
813#559—794no—
814#559—798no—
815#559—794no—
816#559—792no—
817#559—794no—
818#559C2×D7911yescharacteristic, complemented
819#550—794no—
820#550—792no—
821#550—794no—
822#550—794no—
823#550—798no—
824#550—798no—
825#550—798no—
826#550—792no—
827#550—794no—
828#550—792no—
829#550C2×D7912yescomplemented
830#546—794no—
831#546—794no—
832#546—794no—
833#546—798no—
834#546—798no—
835#546—798no—
836#546—794no—
837#546—798no—
838#546—798no—
839#546—798no—
840#546—794no—
841#546—798no—
842#546—794no—
843#546—794no—
844#546—798no—
845#546C2×D7914yescomplemented
846D42—798no—
847D42—794no—
848D42—794no—
849D42—794no—
850D42—791no—
851D42—794no—
852D42—794no—
853D42—794no—
854D42—798no—
855D42—798no—
856D42—798no—
857D42—794no—
858D42—798no—
859D42—798no—
860D42—798no—
861D42—798no—
862D42—798no—
863D42—794no—
864D42—794no—
865D42—794no—
866D42—792no—
867D42C2×D7914yescomplemented
868D42C2×D7911yescharacteristic, complemented
869#540—794no—
870#540—794no—
871#540—798no—
872#540—798no—
873#540—798no—
874#540—798no—
875#540—794no—
876#540C2×D7914yescomplemented
877#535—794no—
878#535—794no—
879#535—794no—
880#535—794no—
881#535—794no—
882#535—794no—
883#535—798no—
884#535—798no—
885#535—798no—
886#535—798no—
887#535—798no—
888#535—794no—
889#535C2×D7914yescomplemented
890#534—794no—
891#534—798no—
892#534—798no—
893#534—798no—
894#534—798no—
895#534—798no—
896#534C2×D7914yescomplemented
897#533—792no—
898#533—792no—
899#533—792no—
900#532—794no—
901#532—792no—
902#532—794no—
903#532—792no—
904#532—794no—
905#532—794no—
906#532—792no—
907#532—794no—
908#532—794no—
909C2×#127—794no—
910C2×#127—792no—
911C2×#127—794no—
912C2×#127—792no—
913C2×#127—792no—
914C2×#127—794no—
915C2×#127—794no—
916C2×#127—794no—
917C2×#127—794no—
918C2×#127—791no—
919C2×#127C2×D7911yescharacteristic, complemented
920#529—794no—
921#529—794no—
922#529—792no—
923#529—792no—
924#529—794no—
925#529—794no—
926#529—792no—
927#529C2×D7912yescomplemented
928#525—794no—
929#525—792no—
930#525—792no—
931#525—794no—
932C2×#120—794no—
933C2×#120—798no—
934C2×#120—794no—
935#518—794no—
936#518—794no—
937#518—794no—
938C4×#41—792no—
939C4×#41—794no—
940C4×#41—792no—
941C4×#41—794no—
942C22×C42—791no—
943C25—794no—
944H(5,𝔽2)—31616no—
945H(5,𝔽2)—31616no—
946H(5,𝔽2)—31616no—
947C2×#41—794no—
948C2×#41—792no—
949C2×#41—794no—
950C2×#41—798no—
951C2×#41—798no—
952C2×#41—794no—
953C2×#41—792no—
954C2×#41—794no—
955C2×#41—798no—
956C2×#41—798no—
957C2×#41—794no—
958C2×#41C22×D7914yescomplemented
959C22×D4—31616no—
960C22×D4—3168no—
961C22×D4—794no—
962C22×D4—798no—
963C22×D4—798no—
964C22×D4—798no—
965C22×D4—798no—
966C22×D4—798no—
967C22×D4—798no—
968C22×D4—798no—
969C22×D4—798no—
970C22×D4—794no—
971C22×D4—794no—
972C22×D4—794no—
973C22×D4—798no—
974C22×D4—798no—
975C22×D4—794no—
976C22×D4—794no—
977C22×D4—794no—
978C22×D4—798no—
979C22×D4—798no—
980C22×D4—794no—
981C22×D4—794no—
982C22×D4—794no—
983C22×D4—798no—
984C22×D4—792no—
985C22×D4—794no—
986C22×D4—794no—
987C22×D4C22×D7914yes—
988C22×D4C22×D7912yes—
989C22×D4C22×D7914yes—
990C22×D4C22×D7914yescomplemented
991C23×C4—791no—
992C23×C4—792no—
993C4⋊Q8—792no—
994C4⋊Q8—792no—
995C4⋊Q8—792no—
996#127—794no—
997#127—794no—
998#127—792no—
999#127—794no—
1000#127—798no—
1001#127—794no—
1002#127—794no—
1003#127—794no—
1004#127—798no—
1005#127—794no—
1006#127—794no—
1007#127—794no—
1008#127—794no—
1009#127—798no—
1010#127—798no—
1011#127—798no—
1012#127—798no—
1013#127—794no—
1014#127—792no—
1015#127—792no—
1016#127—794no—
1017#127C22×D7914yes—
1018#127C22×D7911yescharacteristic
1019#127C22×D7911yescharacteristic
1020#127C22×D7912yes—
1021#127C22×D7914yescomplemented
1022#126—794no—
1023#126—794no—
1024#126—794no—
1025#126C22×D7914yescomplemented
1026#125—794no—
1027#125—794no—
1028#125—792no—
1029#125C22×D7912yescomplemented
1030#124—794no—
1031#124—794no—
1032#124—794no—
1033#124—794no—
1034#124—798no—
1035#124—798no—
1036#124—798no—
1037#124—798no—
1038#124—792no—
1039#124—794no—
1040#124C22×D7912yescomplemented
1041#124C22×D7914yescomplemented
1042#123—794no—
1043#123—794no—
1044#123—798no—
1045#123—794no—
1046#123—798no—
1047#123—794no—
1048#123—794no—
1049#123—798no—
1050#123—798no—
1051#123—798no—
1052#123—798no—
1053#123—794no—
1054#123—794no—
1055#123—798no—
1056#123—798no—
1057#123—798no—
1058#123C22×D7914yes—
1059#123C22×D7918yescomplemented
1060#123C22×D7914yescomplemented
1061#123C22×D7914yescomplemented
1062C22⋊Q8—792no—
1063C22⋊Q8—792no—
1064C22⋊Q8—794no—
1065C22⋊Q8—794no—
1066C22⋊Q8—794no—
1067C22⋊Q8—792no—
1068C22⋊Q8—794no—
1069C22⋊Q8C22×D7912yes—
1070#121—792no—
1071#121—794no—
1072#121—794no—
1073#121—794no—
1074#121—798no—
1075#121—798no—
1076#121—798no—
1077#121—798no—
1078#121—798no—
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—794no—
1088#121—794no—
1089#121—798no—
1090#121—798no—
1091#121—792no—
1092#121—794no—
1093#121—794no—
1094#121—798no—
1095#121—798no—
1096#121—798no—
1097#121—798no—
1098#121—794no—
1099#121—794no—
1100#121—794no—
1101#121—798no—
1102#121—798no—
1103#121—798no—
1104#121—798no—
1105#121—798no—
1106#121—798no—
1107#121—798no—
1108#121—798no—
1109#121—798no—
1110#121—798no—
1111#121C22×D7912yes—
1112#121C22×D7914yescomplemented
1113#121C22×D7914yescomplemented
1114#121C22×D7918yescomplemented
1115#121C22×D7918yescomplemented
1116#121C22×D7918yescomplemented
1117#121C22×D7918yescomplemented
1118#120—798no—
1119#120—798no—
1120#120—794no—
1121#120—798no—
1122#120—798no—
1123#120—798no—
1124#120—798no—
1125#120—798no—
1126#120—794no—
1127#120—794no—
1128#120—798no—
1129#120—798no—
1130#120—798no—
1131#120—794no—
1132#120—798no—
1133#120—798no—
1134#120—798no—
1135#120—798no—
1136#120—798no—
1137#120—798no—
1138#120—798no—
1139#120—798no—
1140#120—798no—
1141#120—798no—
1142#120C22×D7918yes—
1143#120C22×D7918yescomplemented
1144#120C22×D7914yescomplemented
1145#120C22×D7914yescomplemented
1146C4×Q8—792no—
1147C4×Q8—794no—
1148C4×Q8—794no—
1149C4×Q8—794no—
1150C4×Q8—792no—
1151C4×Q8—794no—
1152C4×Q8—792no—
1153C4×Q8C22×D7912yescomplemented
1154C4×D4—794no—
1155C4×D4—792no—
1156C4×D4—794no—
1157C4×D4—794no—
1158C4×D4—794no—
1159C4×D4—794no—
1160C4×D4—794no—
1161C4×D4—798no—
1162C4×D4—798no—
1163C4×D4—798no—
1164C4×D4—798no—
1165C4×D4—794no—
1166C4×D4—794no—
1167C4×D4—794no—
1168C4×D4—792no—
1169C4×D4—794no—
1170C4×D4—794no—
1171C4×D4—794no—
1172C4×D4—794no—
1173C4×D4—794no—
1174C4×D4—794no—
1175C4×D4—794no—
1176C4×D4—794no—
1177C4×D4—794no—
1178C4×D4—798no—
1179C4×D4—798no—
1180C4×D4—798no—
1181C4×D4—798no—
1182C4×D4—794no—
1183C4×D4—792no—
1184C4×D4—794no—
1185C4×D4—794no—
1186C4×D4C22×D7914yes—
1187C4×D4C22×D7912yescomplemented
1188C4×D4C22×D7914yescomplemented
1189C4×D4C22×D7914yescomplemented
1190#117—792no—
1191#117—792no—
1192#117—794no—
1193#117—794no—
1194#117—794no—
1195#117—794no—
1196#117—794no—
1197#117—794no—
1198#117—794no—
1199#117C22×D7914yescomplemented
1200C2×C22⋊C4—794no—
1201C2×C22⋊C4—798no—
1202C2×C22⋊C4—798no—
1203C2×C22⋊C4—798no—
1204C2×C22⋊C4—798no—
1205C2×C22⋊C4—798no—
1206C2×C22⋊C4C22×D7914yes—
1207C2×C42—794no—
1208C2×C42—792no—
1209C2×C42—791no—
1210C2×C42—794no—
1211C2×C42—792no—
1212C2×C42—792no—
1213C2×C42—792no—
1214C2×C42—792no—
1215C2×C42C22×D7911yescharacteristic
1216C24—3168no—
1217C24—31616no—
1218C24—794no—
1219C24—798no—
1220C24—798no—
1221C24—798no—
1222C24—794no—
1223C24—791no—
1224C24C23×D7914yes—
1225C24C23×D7914yes—
1226#41—48no—
1227#41—3168no—
1228#41—31616no—
1229#41—31616no—
1230#41—3168no—
1231#41—31616no—
1232#41—31616no—
1233#41—3168no—
1234#41—15816no—
1235#41—15816no—
1236#41—1588no—
1237#41—1588no—
1238C2×Q8—794no—
1239C2×Q8—794no—
1240C2×Q8—792no—
1241C2×Q8C23×D7912yes—
1242C2×D4—48no—
1243C2×D4—48no—
1244C2×D4—44no—
1245C2×D4—48no—
1246C2×D4—3164no—
1247C2×D4—3168no—
1248C2×D4—3168no—
1249C2×D4—31616no—
1250C2×D4—31616no—
1251C2×D4—31616no—
1252C2×D4—31616no—
1253C2×D4—3168no—
1254C2×D4—31616no—
1255C2×D4—3168no—
1256C2×D4—3168no—
1257C2×D4—3168no—
1258C2×D4—3168no—
1259C2×D4—31616no—
1260C2×D4—31616no—
1261C2×D4—3168no—
1262C2×D4—31616no—
1263C2×D4—3168no—
1264C2×D4—31616no—
1265C2×D4—31616no—
1266C2×D4—31616no—
1267C2×D4—31616no—
1268C2×D4—31616no—
1269C2×D4—798no—
1270C2×D4—798no—
1271C2×D4—798no—
1272C2×D4—798no—
1273C2×D4—798no—
1274C2×D4—798no—
1275C2×D4—798no—
1276C2×D4—798no—
1277C2×D4—794no—
1278C2×D4—794no—
1279C2×D4—794no—
1280C2×D4—794no—
1281C2×D4—794no—
1282C2×D4—798no—
1283C2×D4—798no—
1284C2×D4—798no—
1285C2×D4—798no—
1286C2×D4—798no—
1287C2×D4—798no—
1288C2×D4—798no—
1289C2×D4—794no—
1290C2×D4—798no—
1291C2×D4—794no—
1292C2×D4—794no—
1293C2×D4—794no—
1294C2×D4—792no—
1295C2×D4—794no—
1296C2×D4—794no—
1297C2×D4—15816no—
1298C2×D4—15816no—
1299C2×D4—15816no—
1300C2×D4C23×D7914yes—
1301C2×D4C23×D7912yes—
1302C2×D4C23×D7914yes—
1303C2×D4C23×D7914yes—
1304C2×D4C23×D7918yes—
1305C2×D4C23×D7918yes—
1306C2×D4C23×D7912yes—
1307C2×D4C23×D7918yes—
1308C2×D4C23×D7918yes—
1309C2×D4C23×D7914yes—
1310C2×D4C23×D7912yes—
1311C22×C4—794no—
1312C22×C4—798no—
1313C22×C4—798no—
1314C22×C4—798no—
1315C22×C4—798no—
1316C22×C4—791no—
1317C22×C4—792no—
1318C22×C4—792no—
1319C22×C4—794no—
1320C22×C4—794no—
1321C22×C4—792no—
1322C22×C4—792no—
1323C22×C4—792no—
1324C22×C4—792no—
1325C22×C4—792no—
1326C22×C4—794no—
1327C22×C4—794no—
1328C22×C4—794no—
1329C22×C4—1584no—
1330C22×C4—1588no—
1331C22×C4C23×D7912yes—
1332C22×C4C23×D7911yescharacteristic
1333C22×C4C23×D7914yes—
1334C22×C4C23×D7914yes—
1335C22×C4C23×D7918yes—
1336C4⋊C4—794no—
1337C4⋊C4—794no—
1338C4⋊C4—794no—
1339C4⋊C4—794no—
1340C4⋊C4—794no—
1341C4⋊C4—794no—
1342C4⋊C4—794no—
1343C4⋊C4—794no—
1344C4⋊C4—794no—
1345C4⋊C4—794no—
1346C4⋊C4—792no—
1347C4⋊C4—792no—
1348C4⋊C4—794no—
1349C4⋊C4—794no—
1350C4⋊C4C23×D7912yes—
1351C4⋊C4C23×D7912yes—
1352C4⋊C4C23×D7914yes—
1353C4⋊C4C23×D7914yes—
1354C4⋊C4C23×D7914yes—
1355C4⋊C4C23×D7914yes—
1356C22⋊C4—794no—
1357C22⋊C4—798no—
1358C22⋊C4—794no—
1359C22⋊C4—794no—
1360C22⋊C4—798no—
1361C22⋊C4—794no—
1362C22⋊C4—794no—
1363C22⋊C4—794no—
1364C22⋊C4—794no—
1365C22⋊C4—794no—
1366C22⋊C4—794no—
1367C22⋊C4—798no—
1368C22⋊C4—798no—
1369C22⋊C4—798no—
1370C22⋊C4—798no—
1371C22⋊C4—798no—
1372C22⋊C4—798no—
1373C22⋊C4—794no—
1374C22⋊C4—794no—
1375C22⋊C4—794no—
1376C22⋊C4—794no—
1377C22⋊C4—794no—
1378C22⋊C4—794no—
1379C22⋊C4C23×D7914yes—
1380C22⋊C4C23×D7918yes—
1381C22⋊C4C23×D7918yes—
1382C22⋊C4C23×D7914yes—
1383C22⋊C4C23×D7914yes—
1384C22⋊C4C23×D7914yes—
1385C22⋊C4C23×D7914yes—
1386C22⋊C4C23×D7914yes—
1387C22⋊C4C23×D7914yes—
1388C42—792no—
1389C42—792no—
1390C42—792no—
1391C42—792no—
1392C42—791no—
1393C42—792no—
1394C42—791no—
1395C42—794no—
1396C42—794no—
1397C42—794no—
1398C42—794no—
1399C42—794no—
1400C42C23×D7912yes—
1401C42C23×D7911yescharacteristic
1402C42C23×D7911yescharacteristic
1403C42C23×D7914yes—
1404C23—28no—
1405C23—48no—
1406C23—48no—
1407C23—44no—
1408C23—3168no—
1409C23—3168no—
1410C23—3168no—
1411C23—3168no—
1412C23—3168no—
1413C23—3168no—
1414C23—3168no—
1415C23—3164no—
1416C23—3168no—
1417C23—3168no—
1418C23—792no—
1419C23—798no—
1420C23—794no—
1421C23—63232no—
1422C23—15816no—
1423C23—15816no—
1424C23—1584no—
1425C23—1588no—
1426C23—1582no—
1427C23C24×D7914yes—
1428C23C24×D7914yes—
1429C23C24×D7914yes—
1430C23C24×D7911yescharacteristic
1431Q8—24no—
1432Q8—1588no—
1433Q8—1588no—
1434Q8—1584no—
1435D4—28no—
1436D4—24no—
1437D4—28no—
1438D4—28no—
1439D4—48no—
1440D4—42no—
1441D4—44no—
1442D4—42no—
1443D4—48no—
1444D4—48no—
1445D4—48no—
1446D4—3164no—
1447D4—3164no—
1448D4—3168no—
1449D4—3168no—
1450D4—3168no—
1451D4—3168no—
1452D4—3168no—
1453D4—3168no—
1454D4—3168no—
1455D4—3168no—
1456D4—3168no—
1457D4—3168no—
1458D4—3168no—
1459D4—3168no—
1460D4—1588no—
1461D4—1588no—
1462D4—1588no—
1463D4—1588no—
1464D4—15816no—
1465D4—15816no—
1466D4—15816no—
1467D4—15816no—
1468D4—1588no—
1469D4—1588no—
1470D4—1588no—
1471D4—1584no—
1472D4—1588no—
1473D4—1588no—
1474C2×C4—22no—
1475C2×C4—24no—
1476C2×C4—28no—
1477C2×C4—44no—
1478C2×C4—48no—
1479C2×C4—3168no—
1480C2×C4—3168no—
1481C2×C4—3168no—
1482C2×C4—3168no—
1483C2×C4—3164no—
1484C2×C4—794no—
1485C2×C4—792no—
1486C2×C4—792no—
1487C2×C4—798no—
1488C2×C4—792no—
1489C2×C4—794no—
1490C2×C4—794no—
1491C2×C4—794no—
1492C2×C4—1584no—
1493C2×C4—1584no—
1494C2×C4—1584no—
1495C2×C4—1588no—
1496C2×C4—1588no—
1497C2×C4—1584no—
1498C2×C4—1584no—
1499C2×C4—1588no—
1500C2×C4—1588no—
1501C2×C4—1584no—
1502C2×C4—1588no—
1503C2×C4C24×D7911yescharacteristic
1504C2×C4C24×D7912yes—
1505C2×C4C24×D7911yescharacteristic
1506C2×C4C24×D7914yes—
1507C2×C4C24×D7914yes—
1508C2×C4C24×D7914yes—
1509C2×C4C24×D7912yes—
1510C22—22no—
1511C22—24no—
1512C22—28no—
1513C22—24no—
1514C22—28no—
1515C22—24no—
1516C22—24no—
1517C22—24no—
1518C22—88no—
1519C22—164no—
1520C22—794no—
1521C22—6328no—
1522C22—63216no—
1523C22—63216no—
1524C22—1588no—
1525C22—1588no—
1526C22—1588no—
1527C22—1588no—
1528C22—1584no—
1529C22—1584no—
1530C22—1584no—
1531C22—1582no—
1532C22—1582no—
1533C22—12644no—
1534C22—12648no—
1535C22H(5,𝔽2)×D7912yes—
1536C22C25×D7911yescharacteristic
1537C4—24no—
1538C4—21no—
1539C4—21no—
1540C4—22no—
1541C4—24no—
1542C4—24no—
1543C4—794no—
1544C4—794no—
1545C4—1584no—
1546C4—1584no—
1547C4—1584no—
1548C4—1582no—
1549C4H(5,𝔽2)×D7914yes—
1550C2—22no—
1551C2—44no—
1552C2—44no—
1553C2—44no—
1554C2—3168no—
1555C2—3164no—
1556C2—1584no—
1557C2C2×H(5,𝔽2)×D7911yescharacteristic
1558C2C2×H(5,𝔽2)×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3543C2
hypercenter#3543D79
hypocenterC79#62832
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3543

Complements

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

NH ≅ G/Ntype
1. #23777733C2semidirect
2. #23777730C2semidirect
3. #23777729C2semidirect
4. #23777728C2semidirect
5. #23777727C2semidirect
6. #23777726C2semidirect
7. #23777273C2semidirect
8. #23777272C2semidirect
9. #23777270C2semidirect
10. #23777268C2semidirect
11. #23777177C2semidirect
12. #23777175C2semidirect
13. #23777172C2semidirect
14. #23777172C2semidirect
15. #23777032C2semidirect
16. #23777030C2semidirect
17. #23777028C2semidirect
18. #23776694C2semidirect
19. C2×#127×D79C2semidirect
20. C79×#3543C2semidirect
21. C2×#14579207C22semidirect
22. C2×#14579206C22semidirect
23. C2×#14579206C22semidirect
24. C22×D4×D79C22semidirect
25. C22×D4×D79C22semidirect
26. #19099304C22semidirect
27. #19099303C22semidirect
28. #19099302C22semidirect
29. #19099301C22semidirect
30. #19099300C22semidirect
31. #19099299C22semidirect
32. #19099298C22semidirect
33. #19099297C22semidirect
34. #19099297C22semidirect
35. #19099296C22semidirect
36. #19099295C22semidirect
37. #19099235C22semidirect
38. #19099234C22semidirect
39. #19099234C22semidirect
40. #19099233C22semidirect
41. #19099233C22semidirect
42. #19099232C22semidirect
43. #19099231C22semidirect
44. #19099231C22semidirect
45. #19099231C22semidirect
46. #19099231C22semidirect
47. #19099210C22semidirect
48. #19099209C22semidirect
49. #19099208C22semidirect
50. #19099207C22semidirect
51. #19099206C22semidirect
52. #19099205C22semidirect
53. #19099205C22semidirect
54. #19099205C22semidirect
55. #19099204C22semidirect
56. #19099203C22semidirect
57. #19099202C22semidirect
58. #19099202C22semidirect
59. #19099202C22semidirect
60. #19099201C22semidirect
61. #19099200C22semidirect
62. D4×D316C22semidirect
63. D4×D316C22semidirect
64. D4×D316C22semidirect
65. #19099198C22semidirect
66. #19099198C22semidirect
67. #19099197C22semidirect
68. #19099197C22semidirect
69. #19099197C22semidirect
70. #19099197C22semidirect
71. #19099197C22semidirect
72. #19099197C22semidirect
73. D4×C22⋊D79C22semidirect
74. D4×C22⋊D79C22semidirect
75. D4×C22⋊D79C22semidirect
76. D4×C22⋊D79C22semidirect
77. #19099195C22semidirect
78. #19099195C22semidirect
79. #19099195C22semidirect
80. #19099195C22semidirect
81. #19099195C22semidirect
82. #19099195C22semidirect
83. #19099169C22semidirect
84. #19099168C22semidirect
85. #19099167C22semidirect
86. #19099165C22semidirect
87. #19099165C22semidirect
88. #19099163C22semidirect
89. #19099163C22semidirect
90. #19099132C22semidirect
91. #19099131C22semidirect
92. #19099131C22semidirect
93. #19099129C22semidirect
94. #19099129C22semidirect
95. #19099129C22semidirect
96. #19099129C22semidirect
97. #19099128C22semidirect
98. #19099128C22semidirect
99. #19099128C22semidirect
100. #19099126C22semidirect
101. #19099126C22semidirect
102. #19099124C22semidirect
103. #19099124C22semidirect
104. #19099123C22semidirect
105. #19099122C22semidirect
106. #19099121C22semidirect
107. #19099121C22semidirect
108. #19099119C22semidirect
109. #19099117C22semidirect
110. #19099115C22semidirect
111. #19099112C22semidirect
112. #19099112C22semidirect
113. #19099110C22semidirect
114. #19099110C22semidirect
115. #19099110C22semidirect
116. #19099109C22semidirect
117. #19099108C22semidirect
118. #19099108C22semidirect
119. #19099108C22semidirect
120. C2×#14579158C22semidirect
121. C2×#14579157C22semidirect
122. C2×#14579157C22semidirect
123. C2×#14579157C22semidirect
124. #127×D79C22semidirect
125. #127×D79C22semidirect
126. #127×D79C22semidirect
127. #127×D79C22semidirect
128. #127×D79C22semidirect
129. #127×D79C22semidirect
130. #19099098C22semidirect
131. #19099097C22semidirect
132. #19099096C22semidirect
133. #19099096C22semidirect
134. #19099092C22semidirect
135. #19099091C22semidirect
136. #19099090C22semidirect
137. #19099076C22semidirect
138. #19099073C22semidirect
139. #19099072C22semidirect
140. #19099071C22semidirect
141. C2×#14579131C22semidirect
142. C2×#14579129C22semidirect
143. #120×D79C22semidirect
144. #19099036C22semidirect
145. #19099035C22semidirect
146. #19099035C22semidirect
147. C4×#11929625C22semidirect
148. #19099031C22semidirect
149. C4×#11929623C22semidirect
150. C4×#11929623C22semidirect
151. C2×C42×D79C22semidirect
152. #560×C79C22semidirect
153. #559×C79C22semidirect
154. #550×C79C22semidirect
155. #546×C79C22semidirect
156. D42×C79C22semidirect
157. D42×C79C22semidirect
158. #540×C79C22semidirect
159. #535×C79C22semidirect
160. #534×C79C22semidirect
161. C2×#127×C79C22semidirect
162. #529×C79C22semidirect
168. C2×#11929625C23semidirect
170. C2×#11929624C23semidirect
171. C2×#11929624C23semidirect
172. C2×#11929624C23semidirect
175. C2×#11929623C23semidirect
176. C2×#11929623C23semidirect
177. C2×#11929623C23semidirect
181. C22×D316C23semidirect
186. C22×C22⋊D79C23semidirect
187. C22×C22⋊D79C23semidirect
202. C2×D4×D79C23semidirect
203. C2×D4×D79C23semidirect
204. C2×D4×D79C23semidirect
205. C2×D4×D79C23semidirect
208. #14579160C23semidirect
209. #14579160C23semidirect
210. #14579159C23semidirect
214. #14579158C23semidirect
225. #14579157C23semidirect
226. #14579157C23semidirect
227. #14579157C23semidirect
228. #14579157C23semidirect
229. #14579157C23semidirect
230. #14579157C23semidirect
231. #14579157C23semidirect
232. #14579156C23semidirect
233. #14579155C23semidirect
234. #14579154C23semidirect
235. #14579153C23semidirect
236. #14579151C23semidirect
237. #14579151C23semidirect
238. #14579150C23semidirect
239. #14579149C23semidirect
240. #14579149C23semidirect
241. #14579148C23semidirect
242. #14579147C23semidirect
243. #14579147C23semidirect
244. #14579147C23semidirect
245. #14579147C23semidirect
246. #14579147C23semidirect
247. #14579147C23semidirect
250. #14579146C23semidirect
251. #14579146C23semidirect
252. #14579146C23semidirect
253. #14579146C23semidirect
254. #14579145C23semidirect
256. #14579144C23semidirect
259. #14579143C23semidirect
260. #14579143C23semidirect
261. #14579142C23semidirect
262. #14579142C23semidirect
263. #14579142C23semidirect
272. #14579136C23semidirect
273. #14579136C23semidirect
274. #14579136C23semidirect
275. #14579136C23semidirect
276. #14579136C23semidirect
277. #14579136C23semidirect
279. #14579135C23semidirect
280. #14579135C23semidirect
281. #14579135C23semidirect
282. #14579135C23semidirect
286. #14579134C23semidirect
287. #14579134C23semidirect
288. #14579134C23semidirect
289. #14579134C23semidirect
290. #14579134C23semidirect
291. #14579134C23semidirect
292. #14579134C23semidirect
293. #14579134C23semidirect
294. #14579134C23semidirect
295. #14579134C23semidirect
297. #14579133C23semidirect
298. #14579133C23semidirect
299. #14579133C23semidirect
300. #14579133C23semidirect
301. #14579133C23semidirect
302. #14579133C23semidirect
303. #14579133C23semidirect
304. #14579133C23semidirect
305. #14579133C23semidirect
306. #14579133C23semidirect
308. #14579132C23semidirect
309. #14579132C23semidirect
310. #14579132C23semidirect
311. #14579132C23semidirect
318. #14579131C23semidirect
319. #14579131C23semidirect
320. #14579131C23semidirect
321. #14579131C23semidirect
322. #14579131C23semidirect
324. #14579130C23semidirect
331. #14579129C23semidirect
332. #14579129C23semidirect
333. #14579129C23semidirect
334. #14579129C23semidirect
335. #14579129C23semidirect
336. Q8×Dic79C23semidirect
337. C4×Dic158C23semidirect
338. C4×Dic158C23semidirect
339. #14579126C23semidirect
340. #14579126C23semidirect
341. #14579126C23semidirect
342. #14579126C23semidirect
344. C4×D316C23semidirect
345. C4×D316C23semidirect
346. C4×D316C23semidirect
348. D4×Dic79C23semidirect
349. D4×Dic79C23semidirect
350. D4×Dic79C23semidirect
354. #14579123C23semidirect
355. #14579123C23semidirect
356. #14579123C23semidirect
359. C4×C22⋊D79C23semidirect
360. C4×C22⋊D79C23semidirect
361. C4×C22⋊D79C23semidirect
362. C4×C22⋊D79C23semidirect
363. C4×C22⋊D79C23semidirect
368. (C22⋊D79)⋊C4C23semidirect
369. (C22⋊D79)⋊C4C23semidirect
370. (C22⋊D79)⋊C4C23semidirect
371. (C22⋊D79)⋊C4C23semidirect
372. (C22⋊D79)⋊C4C23semidirect
373. (C22⋊D79)⋊C4C23semidirect
374. (C22⋊D79)⋊C4C23semidirect
377. #14579119C23semidirect
378. #14579119C23semidirect
380. #14579118C23semidirect
382. #14579117C23semidirect
383. #14579117C23semidirect
392. C2×C4×Dic79C23semidirect
397. C42×D79C23semidirect
398. C2×#41×C79C23semidirect
402. C22×D4×C79C23semidirect
407. #127×C79C23semidirect
408. #126×C79C23semidirect
409. #125×C79C23semidirect
410. #124×C79C23semidirect
411. #124×C79C23semidirect
413. #123×C79C23semidirect
414. #123×C79C23semidirect
415. #123×C79C23semidirect
418. #121×C79C23semidirect
419. #121×C79C23semidirect
420. #121×C79C23semidirect
421. #121×C79C23semidirect
422. #121×C79C23semidirect
423. #121×C79C23semidirect
425. #120×C79C23semidirect
426. #120×C79C23semidirect
427. #120×C79C23semidirect
428. C4×Q8×C79C23semidirect
430. C4×D4×C79C23semidirect
431. C4×D4×C79C23semidirect
432. C4×D4×C79C23semidirect
433. #117×C79C23semidirect
697. C2×Dic79H(5,𝔽2)semidirect
726. C4×D79H(5,𝔽2)semidirect
786. #3543D79semidirect
800. C79#62832semidirect
811. #560C2×D79semidirect
818. #559C2×D79semidirect
829. #550C2×D79semidirect
845. #546C2×D79semidirect
867. D42C2×D79semidirect
868. D42C2×D79semidirect
876. #540C2×D79semidirect
889. #535C2×D79semidirect
896. #534C2×D79semidirect
919. C2×#127C2×D79semidirect
927. #529C2×D79semidirect
958. C2×#41C22×D79semidirect
990. C22×D4C22×D79semidirect
1021. #127C22×D79semidirect
1025. #126C22×D79semidirect
1029. #125C22×D79semidirect
1040. #124C22×D79semidirect
1041. #124C22×D79semidirect
1059. #123C22×D79semidirect
1060. #123C22×D79semidirect
1061. #123C22×D79semidirect
1112. #121C22×D79semidirect
1113. #121C22×D79semidirect
1114. #121C22×D79semidirect
1115. #121C22×D79semidirect
1116. #121C22×D79semidirect
1117. #121C22×D79semidirect
1143. #120C22×D79semidirect
1144. #120C22×D79semidirect
1145. #120C22×D79semidirect
1153. C4×Q8C22×D79semidirect
1187. C4×D4C22×D79semidirect
1188. C4×D4C22×D79semidirect
1189. C4×D4C22×D79semidirect
1199. #117C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237777332
#237777302
#237777292
#237777282
#237777272
#237777262
#237772732
#237772722
#237772702
#237772682
#237771772
#237771752
#237771722
#237770322
#237770302
#237770282
#237766942
C2×#127×D792
C79×#35432
#6283279