Finite Group Databasebeta

← #35197166

Subgroups — #35197166

Order 20224.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777920C214yesmaximal, complemented
2#23777909C214yesmaximal, complemented
3#23777803C212yesmaximal, complemented
4#23777794C212yesmaximal, complemented
5#23777767C214yesmaximal, complemented
6#23777759C214yesmaximal, complemented
7#23777638C212yesmaximal, complemented
8#23777633C212yesmaximal, complemented
9#23777430C214yesmaximal, complemented
10#23777422C214yesmaximal, complemented
11#23777312C212yesmaximal, complemented
12#23777301C212yesmaximal, complemented
13#23777276C211yesmaximal, characteristic, complemented
14#23777269C212yesmaximal, complemented
15#23777248C214yesmaximal, complemented
16#23777176C212yesmaximal, complemented
17#23777173C212yesmaximal, complemented
18#23777160C214yesmaximal, complemented
19#23777068C214yesmaximal, complemented
20#23777063C214yesmaximal, complemented
21#23776693C211yesmaximal, characteristic, complemented
22#532×D79C212yesmaximal, complemented
23C79×#3508C211yesmaximal, characteristic, complemented
24C2×#14579207C2214yescomplemented
25C2×#14579206C2214yescomplemented
26C2×#41×D79C2214yescomplemented
27#19099310C2218yescomplemented
28#19099306C2214yescomplemented
29#19099305C2214yescomplemented
30#19099302C2214yescomplemented
31#19099301C2218yescomplemented
32#19099300C2214yescomplemented
33#19099298C2214yescomplemented
34#19099296C2214yescomplemented
35#19099295C2214yescomplemented
36#19099285C2214yescomplemented
37#19099282C2214yescomplemented
38#19099277C2214yescomplemented
39#19099276C2214yescomplemented
40#19099275C2214yescomplemented
41#19099272C2214yescomplemented
42#19099269C2214yescomplemented
43#19099266C2214yescomplemented
44#19099263C2214yescomplemented
45#19099262C2218yescomplemented
46#19099260C2214yescomplemented
47#19099258C2218yescomplemented
48#19099257C2214yescomplemented
49#19099234C2214yescomplemented
50#19099234C2214yescomplemented
51#19099234C2214yescomplemented
52#19099233C2214yescomplemented
53#19099233C2214yescomplemented
54#19099232C2214yescomplemented
55#19099231C2214yescomplemented
56#19099225C2214yescomplemented
57#19099223C2214yescomplemented
58#19099221C2214yescomplemented
59#19099220C2214yescomplemented
60#19099215C2214yescomplemented
61#19099212C2214yescomplemented
62#19099211C2218yescomplemented
63#19099210C2218yescomplemented
64#19099210C2214yescomplemented
65#19099209C2218yescomplemented
66#19099209C2214yescomplemented
67#19099209C2214yescomplemented
68#19099208C2214yescomplemented
69#19099206C2214yescomplemented
70#19099205C2218yescomplemented
71#19099203C2218yescomplemented
72#19099203C2218yescomplemented
73#19099202C2218yescomplemented
74#19099201C2214yescomplemented
75D4×D316C2214yescomplemented
76D4×D316C2214yescomplemented
77#19099198C2214yescomplemented
78#19099198C2214yescomplemented
79#19099198C2214yescomplemented
80#19099197C2214yescomplemented
81#19099197C2218yescomplemented
82#19099197C2214yescomplemented
83#19099197C2214yescomplemented
84#19099197C2214yescomplemented
85D4×C22⋊D79C2214yescomplemented
86D4×C22⋊D79C2214yescomplemented
87D4×C22⋊D79C2214yescomplemented
88D4×C22⋊D79C2214yescomplemented
89#19099195C2214yescomplemented
90#19099195C2214yescomplemented
91#19099186C2214yescomplemented
92#19099185C2214yescomplemented
93#19099180C2214yescomplemented
94#19099178C2214yescomplemented
95#19099168C2212yescomplemented
96#19099168C2212yescomplemented
97#19099166C2214yescomplemented
98#19099164C2214yescomplemented
99#19099151C2218yescomplemented
100#19099149C2218yescomplemented
101#19099149C2218yescomplemented
102#19099147C2218yescomplemented
103#19099146C2218yescomplemented
104#19099145C2218yescomplemented
105#19099143C2214yescomplemented
106#19099142C2218yescomplemented
107#19099142C2214yescomplemented
108#19099140C2218yescomplemented
109#19099131C2214yescomplemented
110#19099131C2214yescomplemented
111#19099130C2214yescomplemented
112#19099129C2214yescomplemented
113#19099128C2218yescomplemented
114#19099127C2212yescomplemented
115#19099127C2214yescomplemented
116#19099126C2218yescomplemented
117#19099126C2214yescomplemented
118#19099126C2214yescomplemented
119#19099124C2218yescomplemented
120#19099123C2218yescomplemented
121#19099120C2211yescharacteristic, complemented
122#19099118C2212yescomplemented
123#19099117C2212yescomplemented
124#19099116C2211yescharacteristic, complemented
125#19099114C2212yescomplemented
126#19099114C2212yescomplemented
127#19099113C2212yescomplemented
128#19099113C2212yescomplemented
129#19099112C2214yescomplemented
130#19099111C2212yescomplemented
131#19099111C2212yescomplemented
132#19099110C2214yescomplemented
133#19099110C2212yescomplemented
134#19099110C2214yescomplemented
135#19099109C2211yescharacteristic, complemented
136#19099109C2214yescomplemented
137#19099108C2214yescomplemented
138#19099108C2214yescomplemented
139C4⋊Q8×D79C2212yescomplemented
140C2×#14579158C2211yescharacteristic, complemented
141#127×D79C2212yescomplemented
142#127×D79C2212yescomplemented
143#19099100C2212yescomplemented
144#19099095C2212yescomplemented
145#19099093C2212yescomplemented
146#19099093C2212yescomplemented
147#19099091C2212yescomplemented
148#19099091C2212yescomplemented
149#124×D79C2214yescomplemented
150#19099075C2211yescharacteristic, complemented
151#19099072C2212yescomplemented
152#19099072C2212yescomplemented
153#19099072C2218yescomplemented
154#19099071C2218yescomplemented
155#19099070C2211yescharacteristic, complemented
156C2×#14579134C2218yescomplemented
157#121×D79C2214yescomplemented
158#121×D79C2218yescomplemented
159#121×D79C2214yescomplemented
160#19099045C2214yescomplemented
161#19099042C2214yescomplemented
162#19099037C2212yescomplemented
163#19099035C2214yescomplemented
164C4×#11929624C2212yescomplemented
165C4×#11929624C2212yescomplemented
166C4×#11929624C2211yescharacteristic, complemented
167C4×D4×D79C2214yescomplemented
168C4×D4×D79C2214yescomplemented
169C2×C42×D79C2211yescharacteristic, complemented
170#559×C79C2214yescomplemented
171#550×C79C2214yescomplemented
172#546×C79C2214yescomplemented
173#546×C79C2214yescomplemented
174#540×C79C2212yescomplemented
175#540×C79C2212yescomplemented
176#535×C79C2212yescomplemented
177#533×C79C2211yescharacteristic, complemented
178#532×C79C2212yescomplemented
179#532×C79C2212yescomplemented
180C2×#127×C79C2211yescharacteristic, complemented
181#518×C79C2212yescomplemented
182C4×#41×C79C2211yescharacteristic, complemented
183#14579207—416no—
184#14579206—416no—
185C2×#11929625C2314yes—
186C2×#11929625C2314yes—
187C2×#11929624C2312yes—
188C2×#11929624C2312yes—
189C2×#11929624C2314yes—
190C2×#11929624C2318yes—
191C2×#11929624C2318yes—
192C2×#11929624C2314yes—
193C2×#11929624C2311yescharacteristic
194C2×#11929623C2314yes—
195C2×#11929623C2318yes—
196C2×#11929623C2314yes—
197C2×#11929623C2318yes—
198#41×D79—416no—
199C2×Q8×D79C2314yes—
200C22×D316C2314yes—
201C22×D316C2318yes—
202C22×D316C2312yes—
203C22×C22⋊D79C2318yes—
204C22×C22⋊D79C2318yes—
205C2×D4×D79C2314yes—
206C2×D4×D79C2318yes—
207C2×D4×D79C2314yes—
208C2×D4×D79C2318yes—
209C2×D4×D79C2314yes—
210C2×D4×D79C2318yes—
211C2×D4×D79C2318yes—
212C2×D4×D79C2314yes—
213C2×D4×D79C2314yes—
214C2×D4×D79C2314yes—
215C22×C4×D79C2312yes—
216C22×C4×D79C2311yescharacteristic
217C22×C4×D79C2318yes—
218#14579161C2312yes—
219#14579160C2314yes—
220#14579160C2312yes—
221#14579160C2314yes—
222#14579159C2314yes—
223#14579159C2311yescharacteristic
224#14579158C2312yes—
225#14579158C2314yes—
226#14579158C2312yes—
227#14579157C2314yes—
228#14579157C2311yescharacteristic
229#14579157C2314yes—
230#14579157C2314yes—
231#14579157C2314yes—
232#14579157C2314yes—
233#14579157C2318yes—
234#14579157C2314yes—
235#14579157C2314yes—
236#14579156C2318yes—
237#14579156C2312yes—
238#14579156C2312yes—
239#14579155C2318yes—
240#14579154C2312yes—
241#14579154C2318yes—
242#14579154C2318yes—
243#14579154C2312yes—
244#14579153C2312yes—
245#14579152C2314yes—
246#14579152C2312yes—
247#14579151C2312yes—
248#14579151C2312yes—
249#14579150C2314yes—
250#14579150C2314yes—
251#14579150C2314yes—
252#14579150C2311yescharacteristic
253#14579149C2318yes—
254#14579149C2314yes—
255#14579149C2314yes—
256#14579148C2318yes—
257#14579148C2314yes—
258#14579148C2314yes—
259#14579148C2311yescharacteristic
260#14579147C2318yes—
261#14579147C2318yes—
262#14579147C2318yes—
263#14579147C2318yes—
264#14579147C2312yes—
265#14579147C2312yes—
266#14579147C2318yes—
267#14579146C2318yes—
268#14579146C2318yes—
269#14579146C2318yes—
270#14579146C2312yes—
271#14579146C2312yes—
272#14579145C2318yes—
273#14579145C2312yes—
274#14579144C2318yes—
275#14579144C2318yes—
276#14579143C2318yes—
277#14579143C2318yes—
278#14579143C2318yes—
279#14579143C2312yes—
280#14579143C2312yes—
281#14579142C2318yes—
282#14579142C2311yescharacteristic
283#14579142C2311yescharacteristic
284#14579141C2318yes—
285#14579141C2314yes—
286#14579141C2312yes—
287#14579140C2318yes—
288#14579140C2314yes—
289#14579139C2318yes—
290#14579139C2318yes—
291#14579139C2312yes—
292#14579139C2312yes—
293#14579138C2312yes—
294#14579138C2318yes—
295#14579138C2312yes—
296#14579138C2318yes—
297#14579137C2314yes—
298#14579137C2312yes—
299#14579136C2314yes—
300#14579136C2318yes—
301#14579136C2314yes—
302#14579136C2314yes—
303#14579136C2314yes—
304#14579136C2312yes—
305#14579135C2318yes—
306#14579135C2314yes—
307#14579135C2318yes—
308#14579135C2318yes—
309#14579135C2314yes—
310#14579135C2314yes—
311#14579135C2314yes—
312#14579134C2318yes—
313#14579134C2318yes—
314#14579134C2318yes—
315#14579134C2318yes—
316#14579134C2318yes—
317#14579134C2318yes—
318#14579134C2318yes—
319#14579134C2318yes—
320#14579134C2318yes—
321#14579134C2318yes—
322#14579134C2318yes—
323#14579134C2312yes—
324#14579134C2318yes—
325#14579134C2312yes—
326#14579133C2318yes—
327#14579133C2318yes—
328#14579133C2318yes—
329#14579133C2318yes—
330#14579133C2318yes—
331#14579133C2318yes—
332#14579133C2318yes—
333#14579133C2318yes—
334#14579133C2312yes—
335#14579133C2312yes—
336#14579132C2318yes—
337#14579132C2318yes—
338#14579132C2314yes—
339#14579132C2318yes—
340#14579132C2318yes—
341#14579132C2314yes—
342#14579132C2314yes—
343#14579132C2314yes—
344#14579132C2312yes—
345#14579131C2318yes—
346#14579131C2318yes—
347#14579131C2318yes—
348#14579131C2318yes—
349#14579131C2318yes—
350#14579131C2312yes—
351#14579130C2318yes—
352#14579130C2318yes—
353#14579129C2318yes—
354#14579129C2318yes—
355#14579129C2318yes—
356#14579129C2318yes—
357#14579129C2318yes—
358#14579129C2318yes—
359#14579129C2311yescharacteristic
360#14579129C2314yes—
361#14579129C2318yes—
362#14579129C2311yescharacteristic
363#14579129C2314yes—
364Q8×Dic79C2314yes—
365C4×Dic158C2314yes—
366C4×Dic158C2312yes—
367C4×Dic158C2312yes—
368C4×Dic158C2312yes—
369C4×Dic158C2312yes—
370C4×Dic158C2312yes—
371#14579126C2314yes—
372C4×D316C2318yes—
373C4×D316C2314yes—
374C4×D316C2314yes—
375C4×D316C2314yes—
376C4×D316C2312yes—
377C4×D316C2312yes—
378C4×D316C2312yes—
379C4×D316C2312yes—
380C4×D316C2312yes—
381C4×D316C2314yes—
382D4×Dic79C2314yes—
383D4×Dic79C2314yes—
384D4×Dic79C2314yes—
385D4×Dic79C2314yes—
386#14579123C2318yes—
387#14579123C2318yes—
388#14579123C2314yes—
389#14579123C2314yes—
390#14579123C2314yes—
391#14579123C2314yes—
392C4×C22⋊D79C2318yes—
393C4×C22⋊D79C2318yes—
394C4×C22⋊D79C2318yes—
395C4×C22⋊D79C2312yes—
396C4×C22⋊D79C2312yes—
397C4×C22⋊D79C2312yes—
398C4×C22⋊D79C2312yes—
399C4×C22⋊D79C2312yes—
400C4×C22⋊D79C2312yes—
401C4×C22⋊D79C2312yes—
402C4×C22⋊D79C2312yes—
403C4×C22⋊D79C2312yes—
404C4×C22⋊D79C2318yes—
405C4×C22⋊D79C2312yes—
406(C22⋊D79)⋊C4C2318yes—
407(C22⋊D79)⋊C4C2318yes—
408(C22⋊D79)⋊C4C2318yes—
409(C22⋊D79)⋊C4C2318yes—
410#14579120C2311yescharacteristic
411#14579120C2312yes—
412#14579120C2312yes—
413#14579120C2312yes—
414#14579119C2314yes—
415#14579118C2312yes—
416#14579118C2312yes—
417#14579118C2312yes—
418#14579118C2318yes—
419#14579118C2312yes—
420#14579118C2312yes—
421#14579117C2318yes—
422C2×Dic79⋊C4C2318yes—
423C4⋊C4×D79C2314yes—
424C4⋊C4×D79C2318yes—
425C4⋊C4×D79C2314yes—
426C2×(C2×D79)⋊C4C2318yes—
427C22⋊C4×D79C2318yes—
428C22⋊C4×D79C2318yes—
429C22⋊C4×D79C2318yes—
430C22⋊C4×D79C2318yes—
431C2×C4×Dic79C2312yes—
432C2×C4×Dic79C2311yescharacteristic
433C42×D79C2312yes—
434C42×D79C2312yes—
435C42×D79C2312yes—
436C42×D79C2312yes—
437C42×D79C2312yes—
438C2×#41×C79C2314yes—
439C2×#41×C79C2314yes—
440C2×#41×C79C2311yescharacteristic
441C22×D4×C79C2314yes—
442C22×D4×C79C2312yes—
443C4⋊Q8×C79C2312yes—
444#127×C79C2312yes—
445#127×C79C2314yes—
446#127×C79C2314yes—
447#127×C79C2312yes—
448#125×C79C2312yes—
449#124×C79C2314yes—
450#124×C79C2314yes—
451#124×C79C2314yes—
452#123×C79C2318yes—
453#123×C79C2318yes—
454C22⋊Q8×C79C2314yes—
455#121×C79C2318yes—
456#121×C79C2314yes—
457#121×C79C2318yes—
458#121×C79C2314yes—
459#121×C79C2314yes—
460#121×C79C2314yes—
461#120×C79C2314yes—
462#120×C79C2314yes—
463C4×Q8×C79C2314yes—
464C4×Q8×C79C2312yes—
465C4×D4×C79C2318yes—
466C4×D4×C79C2314yes—
467C4×D4×C79C2314yes—
468C4×D4×C79C2314yes—
469C4×D4×C79C2314yes—
470C4×D4×C79C2312yes—
471C4×D4×C79C2312yes—
472C4×D4×C79C2312yes—
473#117×C79C2311yescharacteristic
474#117×C79C2311yescharacteristic
475#117×C79C2311yescharacteristic
476#117×C79C2312yes—
477C2×C22⋊C4×C79C2318yes—
478C2×C42×C79C2311yescharacteristic
479C2×C42×C79C2311yescharacteristic
480C2×C42×C79C2311yescharacteristic
481C23×D79C2411yescharacteristic
482C23×D79C2418yes—
483C23×D79C2414yes—
484C23×D79C2418yes—
485#11929625—216no—
486#11929625—48no—
487#11929624—28no—
488#11929624—28no—
489#11929624—416no—
490#11929624—416no—
491#11929624—48no—
492#11929624—48no—
493#11929624—42no—
494#11929623—216no—
495#11929623—416no—
496#11929623—48no—
497#11929623—416no—
498C2×Dic158C2414yes—
499C2×Dic158C2412yes—
500C2×Dic158C2412yes—
501C2×Dic158C2418yes—
502C2×Dic158C2411yescharacteristic
503Q8×D79—48no—
504C2×D316—48no—
505C2×D316—44no—
506C2×D316—416no—
507C2×D316C2418yes—
508C2×D316C2414yes—
509C2×D316C2414yes—
510C2×D316C2412yes—
511C2×D316C2412yes—
512C2×D316C2414yes—
513C2×D316C2411yescharacteristic
514C2×D316C2418yes—
515C2×D316C2418yes—
516C2×D316C2414yes—
517C2×C22⋊D79—416no—
518C2×C22⋊D79—416no—
519C2×C22⋊D79C2418yes—
520C2×C22⋊D79C2418yes—
521C2×C22⋊D79C2412yes—
522C2×C22⋊D79C2412yes—
523C2×C22⋊D79C2412yes—
524C2×C22⋊D79C2412yes—
525C2×C22⋊D79C2418yes—
526C2×C22⋊D79C2418yes—
527C2×C22⋊D79C2418yes—
528C2×C22⋊D79C2418yes—
529C2×C22⋊D79C2412yes—
530C2×C22⋊D79C2418yes—
531C2×C22⋊D79C2418yes—
532C2×C22⋊D79C2418yes—
533C2×C22⋊D79C2418yes—
534D4×D79—216no—
535D4×D79—416no—
536D4×D79—416no—
537D4×D79—416no—
538D4×D79—416no—
539D4×D79—48no—
540D4×D79—48no—
541D4×D79—48no—
542D4×D79—48no—
543D4×D79—48no—
544C22×Dic79C2412yes—
545C22×Dic79C2418yes—
546C22×Dic79C2418yes—
547C22×Dic79C2411yescharacteristic
548C2×C4×D79—28no—
549C2×C4×D79—42no—
550C2×C4×D79—416no—
551C2×C4×D79C2412yes—
552C2×C4×D79C2412yes—
553C2×C4×D79C2418yes—
554C2×C4×D79C2412yes—
555C2×C4×D79C2412yes—
556C2×C4×D79C2412yes—
557C2×C4×D79C2412yes—
558C2×C4×D79C2412yes—
559C2×C4×D79C2418yes—
560C2×C4×D79C2418yes—
561C2×C4×D79C2418yes—
562C2×C4×D79C2418yes—
563C2×C4×D79C2412yes—
564C2×C4×D79C2412yes—
565C4⋊Dic79C2414yes—
566C4⋊Dic79C2414yes—
567C4⋊Dic79C2418yes—
568C4⋊Dic79C2412yes—
569C4⋊Dic79C2412yes—
570C4⋊Dic79C2412yes—
571C4⋊Dic79C2412yes—
572C4⋊Dic79C2412yes—
573Dic79⋊C4C2412yes—
574Dic79⋊C4C2418yes—
575Dic79⋊C4C2418yes—
576Dic79⋊C4C2412yes—
577Dic79⋊C4C2418yes—
578Dic79⋊C4C2418yes—
579Dic79⋊C4C2412yes—
580Dic79⋊C4C2412yes—
581Dic79⋊C4C2412yes—
582Dic79⋊C4C2412yes—
583Dic79⋊C4C2412yes—
584Dic79⋊C4C2412yes—
585Dic79⋊C4C2412yes—
586Dic79⋊C4C2412yes—
587C22⋊Dic79C2414yes—
588C22⋊Dic79C2418yes—
589C22⋊Dic79C2418yes—
590C22⋊Dic79C2418yes—
591C22⋊Dic79C2418yes—
592C22⋊Dic79C2412yes—
593C22⋊Dic79C2412yes—
594C22⋊Dic79C2411yescharacteristic
595C22⋊Dic79C2411yescharacteristic
596C22⋊Dic79C2412yes—
597C22⋊Dic79C2412yes—
598(C2×D79)⋊C4C2412yes—
599(C2×D79)⋊C4C2418yes—
600(C2×D79)⋊C4C2418yes—
601(C2×D79)⋊C4C2418yes—
602(C2×D79)⋊C4C2418yes—
603(C2×D79)⋊C4C2418yes—
604(C2×D79)⋊C4C2418yes—
605(C2×D79)⋊C4C2412yes—
606(C2×D79)⋊C4C2418yes—
607(C2×D79)⋊C4C2412yes—
608(C2×D79)⋊C4C2412yes—
609(C2×D79)⋊C4C2412yes—
610(C2×D79)⋊C4C2412yes—
611(C2×D79)⋊C4C2412yes—
612(C2×D79)⋊C4C2412yes—
613(C2×D79)⋊C4C2412yes—
614(C2×D79)⋊C4C2412yes—
615(C2×D79)⋊C4C2418yes—
616(C2×D79)⋊C4C2418yes—
617C4×Dic79C2412yes—
618C4×Dic79C2411yescharacteristic
619C4×Dic79C2412yes—
620C4×Dic79C2412yes—
621C4×Dic79C2412yes—
622C4×Dic79C2412yes—
623C4×Dic79C2411yescharacteristic
624C4×Dic79C2412yes—
625C4×Dic79C2412yes—
626C4×Dic79C2412yes—
627C4×Dic79C2414yes—
628C4×Dic79C2418yes—
629C24×C79C2414yes—
630#41×C79—42no—
631#41×C79—48no—
632#41×C79—48no—
633C2×Q8×C79C2414yes—
634C2×Q8×C79C2411yescharacteristic
635C2×D4×C79—48no—
636C2×D4×C79—44no—
637C2×D4×C79C2414yes—
638C2×D4×C79C2414yes—
639C2×D4×C79C2414yes—
640C2×D4×C79C2418yes—
641C2×D4×C79C2418yes—
642C2×D4×C79C2411yescharacteristic
643C2×D4×C79C2411yescharacteristic
644C2×D4×C79C2414yes—
645C2×D4×C79C2411yescharacteristic
646C2×D4×C79C2418yes—
647C22×C4×C79C2412yes—
648C22×C4×C79C2412yes—
649C22×C4×C79C2411yescharacteristic
650C22×C4×C79C2412yes—
651C22×C4×C79C2411yescharacteristic
652C22×C4×C79C2411yescharacteristic
653C22×C4×C79C2418yes—
654C22×C4×C79C2418yes—
655C4⋊C4×C79C2412yes—
656C4⋊C4×C79C2414yes—
657C4⋊C4×C79C2412yes—
658C4⋊C4×C79C2412yes—
659C4⋊C4×C79C2414yes—
660C4⋊C4×C79C2418yes—
661C22⋊C4×C79C2412yes—
662C22⋊C4×C79C2414yes—
663C22⋊C4×C79C2418yes—
664C22⋊C4×C79C2418yes—
665C22⋊C4×C79C2412yes—
666C22⋊C4×C79C2412yes—
667C22⋊C4×C79C2418yes—
668C22⋊C4×C79C2418yes—
669C42×C79C2411yescharacteristic
670C42×C79C2411yescharacteristic
671C42×C79C2411yescharacteristic
672C42×C79C2411yescharacteristic
673C42×C79C2412yes—
674C42×C79C2412yes—
675C42×C79C2412yes—
676C42×C79C2414yes—
677C23×C79—48no—
678C23×C79—44no—
679C23×C79C2511yescharacteristic
680C23×C79C2518yes—
681C23×C79C2511yescharacteristic
682C23×C79C2511yescharacteristic
683C22×D79—24no—
684C22×D79—216no—
685C22×D79—41no—
686C22×D79—48no—
687C22×D79—48no—
688C22×D79—48no—
689C22×D79—48no—
690C22×D79—48no—
691C22×D79—48no—
692C22×D79—44no—
693C22×D79C2512yes—
694C22×D79C2518yes—
695C22×D79C2512yes—
696Q8×C79—28no—
697Q8×C79—41no—
698D4×C79—28no—
699D4×C79—28no—
700D4×C79—28no—
701D4×C79—48no—
702D4×C79—48no—
703D4×C79—48no—
704D4×C79—44no—
705D4×C79—41no—
706D4×C79—41no—
707D4×C79—41no—
708C2×C4×C79—24no—
709C2×C4×C79—24no—
710C2×C4×C79—24no—
711C2×C4×C79—22no—
712C2×C4×C79—22no—
713C2×C4×C79—22no—
714C2×C4×C79—48no—
715C2×C4×C79—48no—
716C2×C4×C79C2511yescharacteristic
717C2×C4×C79C2511yescharacteristic
718C2×C4×C79C2512yes—
719C2×C4×C79C2518yes—
720C2×C4×C79C2511yescharacteristic
721C2×C4×C79C2512yes—
722C2×C4×C79C2512yes—
723C2×C4×C79C2512yes—
724C2×C4×C79C2511yescharacteristic
725C22⋊D79—24no—
726C22⋊D79—216no—
727C22⋊D79—24no—
728C22⋊D79—216no—
729C22⋊D79—24no—
730C22⋊D79—24no—
731C22⋊D79—48no—
732C22⋊D79—48no—
733C22⋊D79—48no—
734C22⋊D79—48no—
735C22⋊D79—48no—
736C22⋊D79—48no—
737C22⋊D79—48no—
738C22⋊D79—48no—
739C22⋊D79—42no—
740C2×Dic79—24no—
741C2×Dic79—216no—
742C2×Dic79—41no—
743C2×Dic79—48no—
744C2×Dic79C2512yes—
745C2×Dic79C2512yes—
746C2×Dic79C2512yes—
747C2×Dic79C2512yes—
748C2×Dic79C2518yes—
749C2×Dic79C2512yes—
750C2×Dic79C2512yes—
751D316—24no—
752D316—216no—
753D316—24no—
754D316—28no—
755D316—28no—
756D316—28no—
757D316—48no—
758D316—48no—
759D316—44no—
760D316—41no—
761C4×D79—24no—
762C4×D79—24no—
763C4×D79—24no—
764C4×D79—24no—
765C4×D79—24no—
766C4×D79—24no—
767C4×D79—24no—
768C4×D79—216no—
769C4×D79—42no—
770C4×D79—48no—
771C4×D79—48no—
772C4×D79—48no—
773C4×D79—48no—
774C4×D79H(5,𝔽2)18yescomplemented
775Dic158—28no—
776Dic158—24no—
777Dic158—24no—
778Dic158—48no—
779Dic158—41no—
780C22×C79—22no—
781C22×C79—22no—
782C22×C79—28no—
783C22×C79—28no—
784C22×C79—22no—
785C22×C79—21no—
786C22×C79—28no—
787C22×C79—21no—
788C22×C79—21no—
789C22×C79—164no—
790C22×C79C2611yescharacteristic
791C2×D79—22no—
792C2×D79—22no—
793C2×D79—22no—
794C2×D79—28no—
795C2×D79—22no—
796C2×D79—28no—
797C2×D79—28no—
798C2×D79—22no—
799C2×D79—44no—
800C2×D79—816no—
801C2×D79—164no—
802C2×D79—168no—
803C2×D79C2×H(5,𝔽2)14yes—
804C4×C79—22no—
805C4×C79—22no—
806C4×C79—22no—
807C4×C79—28no—
808C4×C79—21no—
809C4×C79—21no—
810C4×C79—21no—
811C4×C79C2×H(5,𝔽2)14yes—
812C4×C79#58512yes—
813Dic79—22no—
814Dic79—22no—
815Dic79—28no—
816Dic79—22no—
817Dic79—22no—
818Dic79—22no—
819Dic79C2×H(5,𝔽2)14yes—
820#62834—791nomaximal, Sylow
821C2×C79—41no—
822C2×C79—48no—
823C2×C79—41no—
824C2×C79—41no—
825C2×C79C22×H(5,𝔽2)12yes—
826C2×C79C2×#58511yescharacteristic
827D79—24no—
828D79—48no—
829D79—42no—
830#3558—794no—
831#3558—794no—
832#3549—792no—
833#3548—792no—
834#3546—794no—
835#3546—794no—
836#3537—792no—
837#3537—792no—
838#3519—794no—
839#3519—794no—
840#3511—792no—
841#3511—792no—
842#3508—792no—
843#3508—791no—
844#3508D7911yescharacteristic, complemented
845#3506—794no—
846#3498—792no—
847#3498—792no—
848#3496—794no—
849#3488—794no—
850#3488—794no—
851#3444—791no—
852C2×#532—792no—
853C79#6283411yescharacteristic, complemented, Sylow
854C2×H(5,𝔽2)—794no—
855C2×H(5,𝔽2)—794no—
856C22×#41—794no—
857#562—798no—
858H(3,𝔽4)—794no—
859H(3,𝔽4)—794no—
860#560—794no—
861#560—798no—
862#560—794no—
863#559—794no—
864#559—794no—
865#559—794no—
866#559C2×D7914yescomplemented
867#556—794no—
868#556—794no—
869#555—794no—
870#555—794no—
871#555—794no—
872#554—794no—
873#554—794no—
874#553—794no—
875#553—798no—
876#553—794no—
877#553—798no—
878#553—794no—
879#553—794no—
880#550—794no—
881#550—794no—
882#550—794no—
883#550—794no—
884#550—794no—
885#550—794no—
886#550—794no—
887#550C2×D7914yescomplemented
888#548—794no—
889#548—794no—
890#548—794no—
891#548—794no—
892#547—794no—
893#547—798no—
894#547—794no—
895#546—794no—
896#546—794no—
897#546—798no—
898#546—798no—
899#546—794no—
900#546—798no—
901#546—794no—
902#546—794no—
903#546—798no—
904#546—794no—
905#546—798no—
906#546—798no—
907#546C2×D7914yescomplemented
908#546C2×D7914yescomplemented
909D42—794no—
910D42—794no—
911D42—794no—
912D42—794no—
913D42—794no—
914D42—794no—
915D42—794no—
916D42—798no—
917D42—794no—
918D42—794no—
919D42—794no—
920D42—794no—
921D42—794no—
922D42—794no—
923D42—794no—
924D42—794no—
925#542—794no—
926#542—794no—
927#542—794no—
928#542—794no—
929#540—794no—
930#540—794no—
931#540—792no—
932#540—792no—
933#540C2×D7912yescomplemented
934#540C2×D7912yescomplemented
935#538—798no—
936#538—798no—
937#538—798no—
938#538—798no—
939#538—798no—
940#538—798no—
941#537—794no—
942#537—798no—
943#537—794no—
944#537—798no—
945#535—794no—
946#535—792no—
947#535—794no—
948#535—794no—
949#535—798no—
950#535—794no—
951#535—794no—
952#535—794no—
953#535—794no—
954#535—798no—
955#535C2×D7912yescomplemented
956#534—798no—
957#534—798no—
958#533—792no—
959#533—792no—
960#533—791no—
961#533—791no—
962#533C2×D7911yescharacteristic, complemented
963#532—794no—
964#532—791no—
965#532—792no—
966#532—792no—
967#532—792no—
968#532—792no—
969#532—794no—
970#532—794no—
971#532—794no—
972#532—794no—
973#532—794no—
974#532—792no—
975#532—792no—
976#532—792no—
977#532C2×D7912yescomplemented
978#532C2×D7912yescomplemented
979C2×C4⋊Q8—792no—
980C2×#127—792no—
981C2×#127—792no—
982C2×#127—791no—
983C2×#127C2×D7911yescharacteristic, complemented
984#529—792no—
985#529—792no—
986#529—792no—
987#529—792no—
988#529—792no—
989#529—792no—
990C2×#124—794no—
991#525—791no—
992#525—798no—
993#525—792no—
994#525—792no—
995#525—798no—
996#525—791no—
997C2×#121—794no—
998C2×#121—794no—
999C2×#121—798no—
1000C2×#121—798no—
1001#520—794no—
1002#520—794no—
1003#518—794no—
1004#518—792no—
1005#518C2×D7912yescomplemented
1006C4×#41—792no—
1007C4×#41—792no—
1008C4×#41—791no—
1009C4×#41C2×D7911yescharacteristic, complemented
1010C2×C4×D4—794no—
1011C2×C4×D4—794no—
1012C22×C42—791no—
1013H(5,𝔽2)—31616no—
1014H(5,𝔽2)—31616no—
1015C2×#41—31616no—
1016C2×#41—794no—
1017C2×#41—794no—
1018C2×#41—798no—
1019C2×#41—798no—
1020C2×#41—794no—
1021C2×#41—794no—
1022C2×#41—791no—
1023C2×#41—798no—
1024C2×#41—798no—
1025C2×#41—794no—
1026C2×#41—794no—
1027C2×#41—792no—
1028C2×#41—792no—
1029C2×#41C22×D7911yescharacteristic
1030C2×#41C22×D7914yes—
1031C2×#41C22×D7914yes—
1032C22×Q8—794no—
1033C22×D4—798no—
1034C22×D4—798no—
1035C22×D4—794no—
1036C22×D4—794no—
1037C22×D4—798no—
1038C22×D4—798no—
1039C22×D4—798no—
1040C22×D4—798no—
1041C22×D4—794no—
1042C22×D4—794no—
1043C22×D4—794no—
1044C22×D4—794no—
1045C22×D4—792no—
1046C22×D4—798no—
1047C22×D4—794no—
1048C22×D4C22×D7912yes—
1049C22×D4C22×D7914yes—
1050C23×C4—798no—
1051C23×C4—791no—
1052C23×C4—792no—
1053C4⋊Q8—794no—
1054C4⋊Q8—791no—
1055C4⋊Q8—794no—
1056C4⋊Q8—794no—
1057C4⋊Q8—792no—
1058C4⋊Q8—792no—
1059C4⋊Q8C22×D7912yes—
1060#127—794no—
1061#127—794no—
1062#127—794no—
1063#127—794no—
1064#127—794no—
1065#127—794no—
1066#127—791no—
1067#127—798no—
1068#127—794no—
1069#127—792no—
1070#127—794no—
1071#127—792no—
1072#127C22×D7912yes—
1073#127C22×D7914yes—
1074#127C22×D7912yes—
1075#127C22×D7914yes—
1076#126—792no—
1077#126—792no—
1078#126—798no—
1079#126—792no—
1080#126—792no—
1081#126—798no—
1082#126—798no—
1083#126—798no—
1084#125—792no—
1085#125—792no—
1086#125—792no—
1087#125—794no—
1088#125—792no—
1089#125C22×D7912yes—
1090#124—794no—
1091#124—791no—
1092#124—794no—
1093#124—794no—
1094#124—794no—
1095#124—791no—
1096#124—794no—
1097#124—798no—
1098#124—798no—
1099#124—798no—
1100#124—792no—
1101#124—792no—
1102#124—798no—
1103#124—798no—
1104#124—798no—
1105#124—794no—
1106#124—794no—
1107#124—798no—
1108#124C22×D7914yes—
1109#124C22×D7914yes—
1110#124C22×D7914yes—
1111#123—791no—
1112#123—791no—
1113#123—798no—
1114#123—798no—
1115#123—798no—
1116#123—792no—
1117#123—792no—
1118#123—798no—
1119#123—798no—
1120#123—798no—
1121#123—792no—
1122#123—792no—
1123#123—792no—
1124#123—798no—
1125#123—798no—
1126#123—798no—
1127#123—798no—
1128#123C22×D7918yes—
1129#123C22×D7918yes—
1130C22⋊Q8—792no—
1131C22⋊Q8—794no—
1132C22⋊Q8—794no—
1133C22⋊Q8—798no—
1134C22⋊Q8—792no—
1135C22⋊Q8—792no—
1136C22⋊Q8—792no—
1137C22⋊Q8—798no—
1138C22⋊Q8—794no—
1139C22⋊Q8—798no—
1140C22⋊Q8—798no—
1141C22⋊Q8—792no—
1142C22⋊Q8—792no—
1143C22⋊Q8—798no—
1144C22⋊Q8—798no—
1145C22⋊Q8C22×D7914yes—
1146#121—798no—
1147#121—794no—
1148#121—794no—
1149#121—798no—
1150#121—798no—
1151#121—798no—
1152#121—798no—
1153#121—792no—
1154#121—792no—
1155#121—792no—
1156#121—798no—
1157#121—794no—
1158#121—794no—
1159#121—798no—
1160#121—798no—
1161#121—798no—
1162#121—798no—
1163#121—798no—
1164#121—798no—
1165#121—794no—
1166#121—794no—
1167#121—798no—
1168#121—794no—
1169#121—794no—
1170#121—798no—
1171#121—798no—
1172#121—794no—
1173#121—794no—
1174#121—798no—
1175#121—792no—
1176#121—794no—
1177#121—794no—
1178#121—792no—
1179#121—792no—
1180#121—798no—
1181#121—798no—
1182#121—798no—
1183#121—798no—
1184#121—798no—
1185#121—798no—
1186#121—798no—
1187#121—798no—
1188#121—798no—
1189#121—798no—
1190#121—798no—
1191#121—798no—
1192#121C22×D7914yes—
1193#121C22×D7914yes—
1194#121C22×D7918yes—
1195#121C22×D7914yes—
1196#121C22×D7914yes—
1197#121C22×D7918yes—
1198#120—798no—
1199#120—798no—
1200#120—791no—
1201#120—791no—
1202#120—798no—
1203#120—798no—
1204#120—794no—
1205#120—798no—
1206#120—798no—
1207#120—794no—
1208#120—798no—
1209#120—798no—
1210#120—798no—
1211#120—792no—
1212#120—798no—
1213#120—798no—
1214#120—798no—
1215#120—798no—
1216#120—798no—
1217#120C22×D7914yes—
1218#120C22×D7914yes—
1219C4×Q8—794no—
1220C4×Q8—794no—
1221C4×Q8—792no—
1222C4×Q8—792no—
1223C4×Q8—792no—
1224C4×Q8—792no—
1225C4×Q8—792no—
1226C4×Q8—794no—
1227C4×Q8C22×D7912yes—
1228C4×Q8C22×D7914yes—
1229C4×D4—794no—
1230C4×D4—794no—
1231C4×D4—794no—
1232C4×D4—794no—
1233C4×D4—798no—
1234C4×D4—798no—
1235C4×D4—792no—
1236C4×D4—792no—
1237C4×D4—792no—
1238C4×D4—792no—
1239C4×D4—792no—
1240C4×D4—792no—
1241C4×D4—792no—
1242C4×D4—792no—
1243C4×D4—792no—
1244C4×D4—792no—
1245C4×D4—798no—
1246C4×D4—798no—
1247C4×D4—794no—
1248C4×D4—794no—
1249C4×D4—798no—
1250C4×D4—794no—
1251C4×D4—798no—
1252C4×D4—794no—
1253C4×D4—798no—
1254C4×D4—798no—
1255C4×D4—798no—
1256C4×D4—798no—
1257C4×D4—794no—
1258C4×D4—794no—
1259C4×D4—792no—
1260C4×D4—792no—
1261C4×D4—792no—
1262C4×D4—792no—
1263C4×D4—792no—
1264C4×D4—794no—
1265C4×D4—798no—
1266C4×D4—794no—
1267C4×D4C22×D7914yes—
1268C4×D4C22×D7914yes—
1269C4×D4C22×D7912yes—
1270C4×D4C22×D7912yes—
1271C4×D4C22×D7912yes—
1272C4×D4C22×D7918yes—
1273C4×D4C22×D7914yes—
1274C4×D4C22×D7914yes—
1275#117—791no—
1276#117—792no—
1277#117—792no—
1278#117—792no—
1279#117—794no—
1280#117—798no—
1281#117—792no—
1282#117—792no—
1283#117—792no—
1284#117—792no—
1285#117—792no—
1286#117—798no—
1287#117C22×D7911yescharacteristic
1288#117C22×D7911yescharacteristic
1289#117C22×D7911yescharacteristic
1290#117C22×D7912yes—
1291C2×C4⋊C4—798no—
1292C2×C4⋊C4—794no—
1293C2×C4⋊C4—794no—
1294C2×C4⋊C4—798no—
1295C2×C22⋊C4—798no—
1296C2×C22⋊C4—798no—
1297C2×C22⋊C4—798no—
1298C2×C22⋊C4—798no—
1299C2×C22⋊C4—798no—
1300C2×C22⋊C4C22×D7918yes—
1301C2×C42—792no—
1302C2×C42—791no—
1303C2×C42—792no—
1304C2×C42—792no—
1305C2×C42—792no—
1306C2×C42—792no—
1307C2×C42—792no—
1308C2×C42C22×D7911yescharacteristic
1309C2×C42C22×D7911yescharacteristic
1310C2×C42C22×D7911yescharacteristic
1311C24—798no—
1312C24—794no—
1313C24—798no—
1314C24—791no—
1315C24C23×D7914yes—
1316#41—42no—
1317#41—48no—
1318#41—48no—
1319#41—3168no—
1320#41—3168no—
1321#41—3162no—
1322#41—31616no—
1323#41—31616no—
1324#41—3168no—
1325#41—31616no—
1326#41—3168no—
1327#41—31616no—
1328#41—1588no—
1329#41—1588no—
1330#41—15816no—
1331#41—15816no—
1332C2×Q8—3168no—
1333C2×Q8—791no—
1334C2×Q8—798no—
1335C2×Q8—792no—
1336C2×Q8—792no—
1337C2×Q8—794no—
1338C2×Q8C23×D7914yes—
1339C2×Q8C23×D7911yescharacteristic
1340C2×D4—48no—
1341C2×D4—44no—
1342C2×D4—3164no—
1343C2×D4—3168no—
1344C2×D4—31616no—
1345C2×D4—31616no—
1346C2×D4—31616no—
1347C2×D4—31616no—
1348C2×D4—31616no—
1349C2×D4—3168no—
1350C2×D4—3168no—
1351C2×D4—3168no—
1352C2×D4—3168no—
1353C2×D4—3168no—
1354C2×D4—31616no—
1355C2×D4—31616no—
1356C2×D4—792no—
1357C2×D4—798no—
1358C2×D4—798no—
1359C2×D4—798no—
1360C2×D4—798no—
1361C2×D4—798no—
1362C2×D4—798no—
1363C2×D4—798no—
1364C2×D4—798no—
1365C2×D4—798no—
1366C2×D4—792no—
1367C2×D4—792no—
1368C2×D4—792no—
1369C2×D4—792no—
1370C2×D4—798no—
1371C2×D4—791no—
1372C2×D4—794no—
1373C2×D4—798no—
1374C2×D4—798no—
1375C2×D4—794no—
1376C2×D4—798no—
1377C2×D4—792no—
1378C2×D4—792no—
1379C2×D4—794no—
1380C2×D4—794no—
1381C2×D4—15816no—
1382C2×D4C23×D7914yes—
1383C2×D4C23×D7914yes—
1384C2×D4C23×D7914yes—
1385C2×D4C23×D7911yescharacteristic
1386C2×D4C23×D7911yescharacteristic
1387C2×D4C23×D7914yes—
1388C2×D4C23×D7911yescharacteristic
1389C2×D4C23×D7918yes—
1390C2×D4C23×D7918yes—
1391C2×D4C23×D7918yes—
1392C22×C4—3162no—
1393C22×C4—31616no—
1394C22×C4—791no—
1395C22×C4—798no—
1396C22×C4—792no—
1397C22×C4—798no—
1398C22×C4—798no—
1399C22×C4—798no—
1400C22×C4—798no—
1401C22×C4—792no—
1402C22×C4—792no—
1403C22×C4—798no—
1404C22×C4—792no—
1405C22×C4—792no—
1406C22×C4—792no—
1407C22×C4—792no—
1408C22×C4—792no—
1409C22×C4—792no—
1410C22×C4—792no—
1411C22×C4—798no—
1412C22×C4—1588no—
1413C22×C4C23×D7911yescharacteristic
1414C22×C4C23×D7912yes—
1415C22×C4C23×D7911yescharacteristic
1416C22×C4C23×D7912yes—
1417C22×C4C23×D7912yes—
1418C22×C4C23×D7911yescharacteristic
1419C22×C4C23×D7918yes—
1420C22×C4C23×D7918yes—
1421C4⋊C4—792no—
1422C4⋊C4—792no—
1423C4⋊C4—798no—
1424C4⋊C4—798no—
1425C4⋊C4—798no—
1426C4⋊C4—798no—
1427C4⋊C4—792no—
1428C4⋊C4—792no—
1429C4⋊C4—792no—
1430C4⋊C4—792no—
1431C4⋊C4—792no—
1432C4⋊C4—792no—
1433C4⋊C4—792no—
1434C4⋊C4—792no—
1435C4⋊C4—794no—
1436C4⋊C4—794no—
1437C4⋊C4—798no—
1438C4⋊C4—792no—
1439C4⋊C4—792no—
1440C4⋊C4—792no—
1441C4⋊C4—792no—
1442C4⋊C4—792no—
1443C4⋊C4C23×D7914yes—
1444C4⋊C4C23×D7914yes—
1445C4⋊C4C23×D7918yes—
1446C4⋊C4C23×D7912yes—
1447C4⋊C4C23×D7912yes—
1448C4⋊C4C23×D7912yes—
1449C22⋊C4—794no—
1450C22⋊C4—798no—
1451C22⋊C4—798no—
1452C22⋊C4—798no—
1453C22⋊C4—792no—
1454C22⋊C4—792no—
1455C22⋊C4—792no—
1456C22⋊C4—792no—
1457C22⋊C4—798no—
1458C22⋊C4—791no—
1459C22⋊C4—791no—
1460C22⋊C4—792no—
1461C22⋊C4—792no—
1462C22⋊C4—798no—
1463C22⋊C4—798no—
1464C22⋊C4—798no—
1465C22⋊C4—798no—
1466C22⋊C4—798no—
1467C22⋊C4—798no—
1468C22⋊C4—798no—
1469C22⋊C4—792no—
1470C22⋊C4—792no—
1471C22⋊C4—792no—
1472C22⋊C4—792no—
1473C22⋊C4—792no—
1474C22⋊C4—792no—
1475C22⋊C4—792no—
1476C22⋊C4—792no—
1477C22⋊C4—798no—
1478C22⋊C4—798no—
1479C22⋊C4C23×D7912yes—
1480C22⋊C4C23×D7918yes—
1481C22⋊C4C23×D7918yes—
1482C22⋊C4C23×D7912yes—
1483C22⋊C4C23×D7914yes—
1484C22⋊C4C23×D7918yes—
1485C22⋊C4C23×D7918yes—
1486C22⋊C4C23×D7912yes—
1487C42—792no—
1488C42—792no—
1489C42—791no—
1490C42—792no—
1491C42—792no—
1492C42—792no—
1493C42—791no—
1494C42—792no—
1495C42—792no—
1496C42—792no—
1497C42—798no—
1498C42—794no—
1499C42C23×D7911yescharacteristic
1500C42C23×D7911yescharacteristic
1501C42C23×D7912yes—
1502C42C23×D7912yes—
1503C42C23×D7912yes—
1504C42C23×D7911yescharacteristic
1505C42C23×D7911yescharacteristic
1506C42C23×D7914yes—
1507C23—48no—
1508C23—44no—
1509C23—3161no—
1510C23—3168no—
1511C23—3168no—
1512C23—3168no—
1513C23—3168no—
1514C23—3168no—
1515C23—3164no—
1516C23—3168no—
1517C23—792no—
1518C23—792no—
1519C23—798no—
1520C23—1584no—
1521C23—15816no—
1522C23C24×D7911yescharacteristic
1523C23C24×D7911yescharacteristic
1524C23C24×D7918yes—
1525C23C24×D7911yescharacteristic
1526Q8—28no—
1527Q8—41no—
1528Q8—3168no—
1529Q8—3161no—
1530Q8—1584no—
1531Q8—1584no—
1532Q8—1588no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—48no—
1537D4—44no—
1538D4—48no—
1539D4—48no—
1540D4—41no—
1541D4—41no—
1542D4—41no—
1543D4—3168no—
1544D4—3168no—
1545D4—3164no—
1546D4—3161no—
1547D4—3168no—
1548D4—3168no—
1549D4—3168no—
1550D4—3168no—
1551D4—3168no—
1552D4—3168no—
1553D4—3168no—
1554D4—3168no—
1555D4—3162no—
1556D4—1584no—
1557D4—1584no—
1558D4—15816no—
1559D4—1584no—
1560D4—1584no—
1561D4—15816no—
1562D4—1584no—
1563D4—1584no—
1564D4—15816no—
1565D4—1588no—
1566D4—1588no—
1567D4—1588no—
1568C2×C4—24no—
1569C2×C4—24no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—48no—
1575C2×C4—48no—
1576C2×C4—3168no—
1577C2×C4—3168no—
1578C2×C4—3162no—
1579C2×C4—3168no—
1580C2×C4—3168no—
1581C2×C4—3161no—
1582C2×C4—3168no—
1583C2×C4—792no—
1584C2×C4—798no—
1585C2×C4—792no—
1586C2×C4—792no—
1587C2×C4—792no—
1588C2×C4—798no—
1589C2×C4—792no—
1590C2×C4—792no—
1591C2×C4—1584no—
1592C2×C4—15816no—
1593C2×C4—1584no—
1594C2×C4—15816no—
1595C2×C4—1584no—
1596C2×C4—1584no—
1597C2×C4—1584no—
1598C2×C4—1584no—
1599C2×C4—1584no—
1600C2×C4—1584no—
1601C2×C4C24×D7911yescharacteristic
1602C2×C4C24×D7911yescharacteristic
1603C2×C4C24×D7912yes—
1604C2×C4C24×D7918yes—
1605C2×C4C24×D7911yescharacteristic
1606C2×C4C24×D7912yes—
1607C2×C4C24×D7912yes—
1608C2×C4C24×D7912yes—
1609C2×C4C24×D7911yescharacteristic
1610C22—22no—
1611C22—22no—
1612C22—22no—
1613C22—28no—
1614C22—28no—
1615C22—21no—
1616C22—21no—
1617C22—21no—
1618C22—28no—
1619C22—164no—
1620C22—3164no—
1621C22—794no—
1622C22—63216no—
1623C22—1588no—
1624C22—1588no—
1625C22—1582no—
1626C22—1582no—
1627C22—1582no—
1628C22—1588no—
1629C22—1582no—
1630C22—1582no—
1631C22—12648no—
1632C22—12644no—
1633C22C25×D7911yescharacteristic
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—28no—
1638C4—21no—
1639C4—21no—
1640C4—21no—
1641C4—794no—
1642C4—1582no—
1643C4—1582no—
1644C4—1588no—
1645C4—1582no—
1646C4—1582no—
1647C4—1582no—
1648C4H(5,𝔽2)×D7914yes—
1649C4#1909939912yes—
1650C2—41no—
1651C2—48no—
1652C2—41no—
1653C2—41no—
1654C2—3168no—
1655C2—3162no—
1656C2—1584no—
1657C2C2×H(5,𝔽2)×D7912yes—
1658C2C2×#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3508C2
hypercenter#3508D79
hypocenterC79#62834
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #23777920C2semidirect
2. #23777909C2semidirect
3. #23777803C2semidirect
4. #23777794C2semidirect
5. #23777767C2semidirect
6. #23777759C2semidirect
7. #23777638C2semidirect
8. #23777633C2semidirect
9. #23777430C2semidirect
10. #23777422C2semidirect
11. #23777312C2semidirect
12. #23777301C2semidirect
13. #23777276C2semidirect
14. #23777269C2semidirect
15. #23777248C2semidirect
16. #23777176C2semidirect
17. #23777173C2semidirect
18. #23777160C2semidirect
19. #23777068C2semidirect
20. #23777063C2semidirect
21. #23776693C2semidirect
22. #532×D79C2semidirect
23. C79×#3508C2semidirect
24. C2×#14579207C22semidirect
25. C2×#14579206C22semidirect
26. C2×#41×D79C22semidirect
27. #19099310C22semidirect
28. #19099306C22semidirect
29. #19099305C22semidirect
30. #19099302C22semidirect
31. #19099301C22semidirect
32. #19099300C22semidirect
33. #19099298C22semidirect
34. #19099296C22semidirect
35. #19099295C22semidirect
36. #19099285C22semidirect
37. #19099282C22semidirect
38. #19099277C22semidirect
39. #19099276C22semidirect
40. #19099275C22semidirect
41. #19099272C22semidirect
42. #19099269C22semidirect
43. #19099266C22semidirect
44. #19099263C22semidirect
45. #19099262C22semidirect
46. #19099260C22semidirect
47. #19099258C22semidirect
48. #19099257C22semidirect
49. #19099234C22semidirect
50. #19099234C22semidirect
51. #19099234C22semidirect
52. #19099233C22semidirect
53. #19099233C22semidirect
54. #19099232C22semidirect
55. #19099231C22semidirect
56. #19099225C22semidirect
57. #19099223C22semidirect
58. #19099221C22semidirect
59. #19099220C22semidirect
60. #19099215C22semidirect
61. #19099212C22semidirect
62. #19099211C22semidirect
63. #19099210C22semidirect
64. #19099210C22semidirect
65. #19099209C22semidirect
66. #19099209C22semidirect
67. #19099209C22semidirect
68. #19099208C22semidirect
69. #19099206C22semidirect
70. #19099205C22semidirect
71. #19099203C22semidirect
72. #19099203C22semidirect
73. #19099202C22semidirect
74. #19099201C22semidirect
75. D4×D316C22semidirect
76. D4×D316C22semidirect
77. #19099198C22semidirect
78. #19099198C22semidirect
79. #19099198C22semidirect
80. #19099197C22semidirect
81. #19099197C22semidirect
82. #19099197C22semidirect
83. #19099197C22semidirect
84. #19099197C22semidirect
85. D4×C22⋊D79C22semidirect
86. D4×C22⋊D79C22semidirect
87. D4×C22⋊D79C22semidirect
88. D4×C22⋊D79C22semidirect
89. #19099195C22semidirect
90. #19099195C22semidirect
91. #19099186C22semidirect
92. #19099185C22semidirect
93. #19099180C22semidirect
94. #19099178C22semidirect
95. #19099168C22semidirect
96. #19099168C22semidirect
97. #19099166C22semidirect
98. #19099164C22semidirect
99. #19099151C22semidirect
100. #19099149C22semidirect
101. #19099149C22semidirect
102. #19099147C22semidirect
103. #19099146C22semidirect
104. #19099145C22semidirect
105. #19099143C22semidirect
106. #19099142C22semidirect
107. #19099142C22semidirect
108. #19099140C22semidirect
109. #19099131C22semidirect
110. #19099131C22semidirect
111. #19099130C22semidirect
112. #19099129C22semidirect
113. #19099128C22semidirect
114. #19099127C22semidirect
115. #19099127C22semidirect
116. #19099126C22semidirect
117. #19099126C22semidirect
118. #19099126C22semidirect
119. #19099124C22semidirect
120. #19099123C22semidirect
121. #19099120C22semidirect
122. #19099118C22semidirect
123. #19099117C22semidirect
124. #19099116C22semidirect
125. #19099114C22semidirect
126. #19099114C22semidirect
127. #19099113C22semidirect
128. #19099113C22semidirect
129. #19099112C22semidirect
130. #19099111C22semidirect
131. #19099111C22semidirect
132. #19099110C22semidirect
133. #19099110C22semidirect
134. #19099110C22semidirect
135. #19099109C22semidirect
136. #19099109C22semidirect
137. #19099108C22semidirect
138. #19099108C22semidirect
139. C4⋊Q8×D79C22semidirect
140. C2×#14579158C22semidirect
141. #127×D79C22semidirect
142. #127×D79C22semidirect
143. #19099100C22semidirect
144. #19099095C22semidirect
145. #19099093C22semidirect
146. #19099093C22semidirect
147. #19099091C22semidirect
148. #19099091C22semidirect
149. #124×D79C22semidirect
150. #19099075C22semidirect
151. #19099072C22semidirect
152. #19099072C22semidirect
153. #19099072C22semidirect
154. #19099071C22semidirect
155. #19099070C22semidirect
156. C2×#14579134C22semidirect
157. #121×D79C22semidirect
158. #121×D79C22semidirect
159. #121×D79C22semidirect
160. #19099045C22semidirect
161. #19099042C22semidirect
162. #19099037C22semidirect
163. #19099035C22semidirect
164. C4×#11929624C22semidirect
165. C4×#11929624C22semidirect
166. C4×#11929624C22semidirect
167. C4×D4×D79C22semidirect
168. C4×D4×D79C22semidirect
169. C2×C42×D79C22semidirect
170. #559×C79C22semidirect
171. #550×C79C22semidirect
172. #546×C79C22semidirect
173. #546×C79C22semidirect
174. #540×C79C22semidirect
175. #540×C79C22semidirect
176. #535×C79C22semidirect
177. #533×C79C22semidirect
178. #532×C79C22semidirect
179. #532×C79C22semidirect
180. C2×#127×C79C22semidirect
181. #518×C79C22semidirect
182. C4×#41×C79C22semidirect
774. C4×D79H(5,𝔽2)semidirect
844. #3508D79semidirect
853. C79#62834semidirect
866. #559C2×D79semidirect
887. #550C2×D79semidirect
907. #546C2×D79semidirect
908. #546C2×D79semidirect
933. #540C2×D79semidirect
934. #540C2×D79semidirect
955. #535C2×D79semidirect
962. #533C2×D79semidirect
977. #532C2×D79semidirect
978. #532C2×D79semidirect
983. C2×#127C2×D79semidirect
1005. #518C2×D79semidirect
1009. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779202
#237779092
#237778032
#237777942
#237777672
#237777592
#237776382
#237776332
#237774302
#237774222
#237773122
#237773012
#237772762
#237772692
#237772482
#237771762
#237771732
#237771602
#237770682
#237770632
#237766932
#532×D792
C79×#35082
#6283479