Finite Group Databasebeta

← #35197269

Subgroups — #35197269

Order 20224.

6624 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778097C213yesmaximal, complemented
2#23778096C213yesmaximal, complemented
3#23778094C211yesmaximal, characteristic, complemented
4#23777810C213yesmaximal, complemented
5#23777804C211yesmaximal, characteristic, complemented
6#23777671C216yesmaximal, complemented
7#23777665C216yesmaximal, complemented
8#23777413C216yesmaximal, complemented
9#23777410C216yesmaximal, complemented
10#23777353C216yesmaximal, complemented
11#23777350C216yesmaximal, complemented
12#23777290C216yesmaximal, complemented
13#23777288C216yesmaximal, complemented
14#23776694C213yesmaximal, complemented
15C79×#3568C211yesmaximal, characteristic, complemented
16#19099317C2213yescomplemented
17#19099317C2213yescomplemented
18#19099313C2213yescomplemented
19#19099306C2212yescomplemented
20#19099305C2213yescomplemented
21#19099305C2216yescomplemented
22#19099304C2212yescomplemented
23#19099301C2216yescomplemented
24#19099298C2216yescomplemented
25#19099297C2216yescomplemented
26#19099297C2216yescomplemented
27#19099296C2216yescomplemented
28#19099295C2216yescomplemented
29#19099293C2216yescomplemented
30#19099287C2216yescomplemented
31#19099285C2216yescomplemented
32#19099285C2216yescomplemented
33#19099284C2216yescomplemented
34#19099282C2216yescomplemented
35#19099282C2216yescomplemented
36#19099281C2216yescomplemented
37#19099280C2216yescomplemented
38#19099280C2216yescomplemented
39#19099280C2216yescomplemented
40#19099280C2216yescomplemented
41#19099280C2216yescomplemented
42#19099280C2216yescomplemented
43#19099277C2216yescomplemented
44#19099276C2216yescomplemented
45#19099275C2216yescomplemented
46#19099275C2216yescomplemented
47#19099275C2216yescomplemented
48#19099244C2216yescomplemented
49#19099242C2216yescomplemented
50#19099240C2216yescomplemented
51#19099240C2216yescomplemented
52#19099239C2216yescomplemented
53#19099238C2216yescomplemented
54#19099238C2216yescomplemented
55#19099238C2216yescomplemented
56#19099237C2216yescomplemented
57#19099237C2216yescomplemented
58#19099236C2216yescomplemented
59#19099226C2216yescomplemented
60#19099226C2216yescomplemented
61#19099223C2216yescomplemented
62#19099222C2216yescomplemented
63#19099221C2216yescomplemented
64#19099219C2216yescomplemented
65#19099205C2216yescomplemented
66#19099203C2216yescomplemented
67#19099202C2216yescomplemented
68#19099200C2216yescomplemented
69#19099195C2216yescomplemented
70#19099187C2216yescomplemented
71#19099186C2216yescomplemented
72#19099183C2216yescomplemented
73#19099183C2216yescomplemented
74#19099183C2216yescomplemented
75#19099183C2216yescomplemented
76#19099181C2216yescomplemented
77#19099181C2216yescomplemented
78#19099179C2216yescomplemented
79#19099179C2216yescomplemented
80#19099179C2216yescomplemented
81#19099179C2216yescomplemented
82#19099178C2216yescomplemented
83#19099177C2216yescomplemented
84#19099177C2216yescomplemented
85#19099153C2216yescomplemented
86#19099152C2216yescomplemented
87#19099149C2216yescomplemented
88#19099149C2216yescomplemented
89#19099148C2216yescomplemented
90#19099146C2216yescomplemented
91#19099145C2216yescomplemented
92#19099138C2216yescomplemented
93#19099135C2216yescomplemented
94#19099131C2216yes—
95#19099128C2216yes—
96#19099119C2213yescomplemented
97#19099117C2216yescomplemented
98#19099117C2213yescomplemented
99#19099115C2216yescomplemented
100#19099115C2213yescomplemented
101#19099112C2213yes—
102#19099110C2213yes—
103#19099108C2213yes—
104#19099098C2213yescomplemented
105#19099097C2213yescomplemented
106#19099096C2216yescomplemented
107#19099096C2216yescomplemented
108#19099096C2216yescomplemented
109#19099093C2216yescomplemented
110#19099092C2213yescomplemented
111#19099091C2216yescomplemented
112#19099091C2216yescomplemented
113#19099090C2216yescomplemented
114#19099090C2216yescomplemented
115C2×#14579147C2216yescomplemented
116#124×D79C2216yescomplemented
117#19099076C2213yescomplemented
118#19099073C2213yescomplemented
119#19099072C2216yescomplemented
120#19099071C2216yescomplemented
121#19099040C2216yescomplemented
122#19099039C2216yescomplemented
123#19099036C2216yescomplemented
124#19099035C2216yescomplemented
125C4×#11929625C2213yescomplemented
126#19099031C2216yescomplemented
127C4×#11929623C2213yescomplemented
128C4×#11929623C2216yescomplemented
129C2×C42×D79C2211yescharacteristic, complemented
130#563×C79C2213yescomplemented
131H(3,𝔽4)×C79C2211yescharacteristic, complemented
132#556×C79C2216yescomplemented
133#551×C79C2216yescomplemented
134#542×C79C2216yescomplemented
135#538×C79C2216yescomplemented
136#529×C79C2213yescomplemented
137C2×#11929625C2313yes—
138C2×#11929624C2316yes—
139C2×#11929623C2316yes—
140C2×#11929623C2313yes—
141C22×Dic158C2316yes—
142C2×Q8×D79C2316yes—
143C22×C22⋊D79C2316yes—
144C2×D4×D79C2316yes—
145C22×C4×D79C2313yes—
146#14579160C2316yes—
147#14579160C2316yes—
148#14579160C2316yes—
149#14579160C2316yes—
150#14579160C2313yes—
151#14579160C2313yes—
152#14579159C2316yes—
153#14579159C2316yes—
154#14579159C2316yes—
155#14579159C2313yes—
156#14579158C2312yes—
157#14579157C2313yes—
158#14579157C2316yes—
159#14579156C2316yes—
160#14579156C2316yes—
161#14579156C2316yes—
162#14579156C2316yes—
163#14579156C2316yes—
164#14579156C2316yes—
165#14579156C2316yes—
166#14579156C2316yes—
167#14579156C2316yes—
168#14579155C2316yes—
169#14579155C2312yes—
170#14579155C2316yes—
171#14579154C2316yes—
172#14579154C2316yes—
173#14579154C2316yes—
174#14579154C2316yes—
175#14579154C2316yes—
176#14579154C2316yes—
177#14579154C2316yes—
178#14579153C2313yes—
179#14579151C2316yes—
180#14579151C2316yes—
181#14579150C2316yes—
182#14579150C2316yes—
183#14579150C2316yes—
184#14579150C2316yes—
185#14579149C2316yes—
186#14579149C2316yes—
187#14579149C2316yes—
188#14579149C2313yes—
189#14579148C2316yes—
190#14579148C2316yes—
191#14579147C2316yes—
192#14579147C2316yes—
193#14579147C2316yes—
194#14579147C2316yes—
195#14579147C2316yes—
196#14579147C2316yes—
197#14579147C2316yes—
198#14579147C2316yes—
199#14579147C2316yes—
200#14579147C2316yes—
201#14579147C2316yes—
202#14579147C2316yes—
203#14579147C2316yes—
204#14579147C2316yes—
205#14579147C2316yes—
206#14579147C2316yes—
207#14579147C2316yes—
208#14579147C2316yes—
209#14579146C2316yes—
210#14579146C2316yes—
211#14579146C2316yes—
212#14579146C2316yes—
213#14579146C2316yes—
214#14579146C2316yes—
215#14579146C2316yes—
216#14579146C2316yes—
217#14579145C2316yes—
218#14579145C2316yes—
219#14579144C2316yes—
220#14579144C2316yes—
221#14579144C2316yes—
222#14579143C2316yes—
223#14579143C2316yes—
224#14579143C2316yes—
225#14579143C2316yes—
226#14579142C2316yes—
227#14579142C2316yes—
228#14579141C2316yes—
229#14579141C2316yes—
230#14579141C2313yes—
231#14579141C2316yes—
232#14579140C2313yes—
233#14579140C2316yes—
234#14579139C2316yes—
235#14579139C2316yes—
236#14579139C2316yes—
237#14579139C2316yes—
238#14579139C2316yes—
239#14579139C2316yes—
240#14579139C2316yes—
241#14579139C2316yes—
242#14579139C2316yes—
243#14579138C2316yes—
244#14579138C2316yes—
245#14579138C2316yes—
246#14579138C2316yes—
247#14579138C2316yes—
248#14579138C2316yes—
249#14579138C2316yes—
250#14579137C2313yes—
251#14579137C2316yes—
252#14579136C2313yes—
253#14579136C2316yes—
254#14579135C2313yes—
255#14579135C2316yes—
256#14579134C2316yes—
257#14579134C2316yes—
258#14579134C2316yes—
259#14579134C2316yes—
260#14579134C2316yes—
261#14579134C2316yes—
262#14579134C2316yes—
263#14579133C2316yes—
264#14579133C2316yes—
265#14579133C2316yes—
266#14579133C2316yes—
267#14579133C2316yes—
268#14579132C2316yes—
269#14579132C2313yes—
270#14579131C2316yes—
271#14579131C2316yes—
272#14579131C2316yes—
273#14579131C2316yes—
274#14579131C2316yes—
275#14579130C2312yes—
276#14579130C2312yes—
277#14579129C2316yes—
278#14579129C2316yes—
279#14579129C2316yes—
280Q8×Dic79C2316yes—
281Q8×Dic79C2313yes—
282C4×Dic158C2316yes—
283C4×Dic158C2316yes—
284C4×Dic158C2316yes—
285C4×Dic158C2316yes—
286C4×Dic158C2316yes—
287C4×Dic158C2316yes—
288C4×Dic158C2313yes—
289#14579126C2316yes—
290#14579126C2316yes—
291#14579126C2316yes—
292#14579126C2316yes—
293#14579126C2316yes—
294#14579126C2316yes—
295#14579126C2316yes—
296#14579126C2316yes—
297#14579126C2313yes—
298C4×D316C2316yes—
299C4×D316C2313yes—
300C4×D316C2316yes—
301D4×Dic79C2316yes—
302D4×Dic79C2316yes—
303D4×Dic79C2313yes—
304#14579123C2316yes—
305#14579123C2316yes—
306#14579123C2316yes—
307#14579123C2313yes—
308#14579123C2316yes—
309C4×C22⋊D79C2316yes—
310C4×C22⋊D79C2316yes—
311C4×C22⋊D79C2316yes—
312C4×C22⋊D79C2316yes—
313C4×C22⋊D79C2316yes—
314C4×C22⋊D79C2316yes—
315C4×C22⋊D79C2316yes—
316(C22⋊D79)⋊C4C2316yes—
317(C22⋊D79)⋊C4C2316yes—
318(C22⋊D79)⋊C4C2316yes—
319(C22⋊D79)⋊C4C2316yes—
320(C22⋊D79)⋊C4C2316yes—
321(C22⋊D79)⋊C4C2316yes—
322(C22⋊D79)⋊C4C2316yes—
323(C22⋊D79)⋊C4C2316yes—
324(C22⋊D79)⋊C4C2316yes—
325(C22⋊D79)⋊C4C2316yes—
326(C22⋊D79)⋊C4C2316yes—
327#14579120C2316yes—
328#14579119C2313yes—
329#14579119C2313yes—
330#14579119C2316yes—
331#14579119C2316yes—
332#14579119C2316yes—
333#14579119C2316yes—
334#14579118C2316yes—
335#14579118C2316yes—
336#14579118C2316yes—
337#14579118C2316yes—
338#14579118C2316yes—
339#14579118C2316yes—
340#14579117C2316yes—
341#14579117C2316yes—
342#14579117C2316yes—
343#14579117C2316yes—
344#14579117C2316yes—
345#14579117C2316yes—
346#14579117C2316yes—
347C2×C22⋊Dic79C2316yes—
348C2×(C2×D79)⋊C4C2316yes—
349C2×(C2×D79)⋊C4C2316yes—
350C22⋊C4×D79C2316yes—
351C22⋊C4×D79C2316yes—
352C22⋊C4×D79C2316yes—
353C22⋊C4×D79C2316yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2316yes—
356C42×D79C2313yes—
357C42×D79C2313yes—
358C42×D79C2311yescharacteristic
359C42×D79C2311yescharacteristic
360C42×D79C2316yes—
361C4⋊Q8×C79C2316yes—
362#126×C79C2316yes—
363#126×C79C2316yes—
364#126×C79C2316yes—
365#126×C79C2316yes—
366#126×C79C2312yes—
367#125×C79C2313yes—
368#124×C79C2316yes—
369#124×C79C2316yes—
370#124×C79C2316yes—
371#124×C79C2313yes—
372#123×C79C2316yes—
373#123×C79C2316yes—
374#123×C79C2316yes—
375C22⋊Q8×C79C2316yes—
376C22⋊Q8×C79C2313yes—
377C22⋊Q8×C79C2316yes—
378C22⋊Q8×C79C2316yes—
379#121×C79C2313yes—
380#121×C79C2316yes—
381#120×C79C2316yes—
382#120×C79C2312yes—
383C4×Q8×C79C2313yes—
384C4×Q8×C79C2316yes—
385C4×D4×C79C2316yes—
386C4×D4×C79C2316yes—
387C4×D4×C79C2313yes—
388#117×C79C2316yes—
389#117×C79C2316yes—
390C2×C22⋊C4×C79C2316yes—
391C2×C42×C79C2311yescharacteristic
392C23×D79C2416yes—
393C23×D79C2411yescharacteristic
394#11929625—46no—
395#11929624—412no—
396#11929623—412no—
397#11929623—46no—
398C2×Dic158—412no—
399C2×Dic158C2416yes—
400C2×Dic158C2416yes—
401C2×Dic158C2416yes—
402C2×Dic158C2416yes—
403C2×Dic158C2416yes—
404C2×Dic158C2413yes—
405Q8×D79—412no—
406C2×D316C2416yes—
407C2×D316C2413yes—
408C2×D316C2416yes—
409C2×D316C2416yes—
410C2×C22⋊D79—412no—
411C2×C22⋊D79C2416yes—
412C2×C22⋊D79C2416yes—
413C2×C22⋊D79C2416yes—
414C2×C22⋊D79C2416yes—
415C2×C22⋊D79C2416yes—
416C2×C22⋊D79C2416yes—
417C2×C22⋊D79C2416yes—
418D4×D79—412no—
419C22×Dic79C2416yes—
420C22×Dic79C2413yes—
421C22×Dic79C2416yes—
422C22×Dic79C2416yes—
423C2×C4×D79—46no—
424C2×C4×D79C2416yes—
425C2×C4×D79C2413yes—
426C2×C4×D79C2413yes—
427C2×C4×D79C2416yes—
428C2×C4×D79C2416yes—
429C2×C4×D79C2416yes—
430C2×C4×D79C2416yes—
431C2×C4×D79C2413yes—
432C2×C4×D79C2413yes—
433C4⋊Dic79C2416yes—
434C4⋊Dic79C2416yes—
435C4⋊Dic79C2413yes—
436C4⋊Dic79C2413yes—
437C4⋊Dic79C2416yes—
438C4⋊Dic79C2416yes—
439Dic79⋊C4C2416yes—
440Dic79⋊C4C2416yes—
441Dic79⋊C4C2416yes—
442Dic79⋊C4C2416yes—
443Dic79⋊C4C2416yes—
444Dic79⋊C4C2416yes—
445Dic79⋊C4C2416yes—
446Dic79⋊C4C2416yes—
447Dic79⋊C4C2416yes—
448Dic79⋊C4C2416yes—
449Dic79⋊C4C2416yes—
450Dic79⋊C4C2416yes—
451Dic79⋊C4C2416yes—
452Dic79⋊C4C2416yes—
453C22⋊Dic79C2416yes—
454C22⋊Dic79C2416yes—
455C22⋊Dic79C2416yes—
456C22⋊Dic79C2416yes—
457C22⋊Dic79C2416yes—
458C22⋊Dic79C2416yes—
459C22⋊Dic79C2416yes—
460(C2×D79)⋊C4C2416yes—
461(C2×D79)⋊C4C2416yes—
462(C2×D79)⋊C4C2416yes—
463(C2×D79)⋊C4C2416yes—
464(C2×D79)⋊C4C2416yes—
465(C2×D79)⋊C4C2416yes—
466(C2×D79)⋊C4C2416yes—
467(C2×D79)⋊C4C2416yes—
468(C2×D79)⋊C4C2416yes—
469(C2×D79)⋊C4C2416yes—
470(C2×D79)⋊C4C2416yes—
471(C2×D79)⋊C4C2416yes—
472(C2×D79)⋊C4C2416yes—
473(C2×D79)⋊C4C2416yes—
474(C2×D79)⋊C4C2416yes—
475(C2×D79)⋊C4C2416yes—
476(C2×D79)⋊C4C2416yes—
477(C2×D79)⋊C4C2416yes—
478C4×Dic79C2413yes—
479C4×Dic79C2413yes—
480C4×Dic79C2413yes—
481C4×Dic79C2413yes—
482C4×Dic79C2416yes—
483C4×Dic79C2416yes—
484C4×Dic79C2416yes—
485C4×Dic79C2416yes—
486C4×Dic79C2416yes—
487C4×Dic79C2416yes—
488C4×Dic79C2416yes—
489C4×Dic79C2416yes—
490C4×Dic79C2416yes—
491C24×C79C2412yes—
492C2×Q8×C79C2416yes—
493C2×Q8×C79C2413yes—
494C2×D4×C79C2413yes—
495C2×D4×C79C2416yes—
496C2×D4×C79C2416yes—
497C22×C4×C79C2416yes—
498C22×C4×C79C2416yes—
499C22×C4×C79C2413yes—
500C4⋊C4×C79C2416yes—
501C4⋊C4×C79C2416yes—
502C4⋊C4×C79C2416yes—
503C4⋊C4×C79C2416yes—
504C4⋊C4×C79C2413yes—
505C4⋊C4×C79C2416yes—
506C4⋊C4×C79C2413yes—
507C4⋊C4×C79C2416yes—
508C22⋊C4×C79C2416yes—
509C22⋊C4×C79C2416yes—
510C22⋊C4×C79C2416yes—
511C22⋊C4×C79C2416yes—
512C22⋊C4×C79C2416yes—
513C22⋊C4×C79C2416yes—
514C22⋊C4×C79C2416yes—
515C22⋊C4×C79C2416yes—
516C22⋊C4×C79C2416yes—
517C42×C79C2413yes—
518C42×C79C2411yescharacteristic
519C42×C79C2416yes—
520C42×C79C2416yes—
521C42×C79C2412yes—
522C23×C79—46no—
523C23×C79C2516yes—
524C23×C79C2511yescharacteristic
525C22×D79—43no—
526C22×D79—46no—
527C22×D79—46no—
528C22×D79—46no—
529C22×D79C2516yes—
530C22×D79C2511yescharacteristic
531C22×D79C2511yescharacteristic
532Q8×C79—46no—
533Q8×C79—43no—
534D4×C79—46no—
535D4×C79—46no—
536D4×C79—43no—
537C2×C4×C79—43no—
538C2×C4×C79—46no—
539C2×C4×C79—46no—
540C2×C4×C79C2513yes—
541C2×C4×C79C2516yes—
542C2×C4×C79C2516yes—
543C2×C4×C79C2516yes—
544C2×C4×C79C2513yes—
545C22⋊D79—212no—
546C22⋊D79—212no—
547C22⋊D79—46no—
548C22⋊D79—46no—
549C22⋊D79—46no—
550C22⋊D79—46no—
551C22⋊D79—46no—
552C2×Dic79—26no—
553C2×Dic79—212no—
554C2×Dic79—46no—
555C2×Dic79—46no—
556C2×Dic79C2513yes—
557C2×Dic79C2516yes—
558C2×Dic79C2516yes—
559C2×Dic79C2516yes—
560C2×Dic79C2513yes—
561D316—46no—
562D316—46no—
563D316—43no—
564D316—46no—
565C4×D79—26no—
566C4×D79—26no—
567C4×D79—212no—
568C4×D79—43no—
569C4×D79—43no—
570C4×D79—46no—
571C4×D79—46no—
572C4×D79—46no—
573C4×D79—46no—
574Dic158—212no—
575Dic158—212no—
576Dic158—46no—
577Dic158—46no—
578Dic158—46no—
579Dic158—43no—
580C22×C79—26no—
581C22×C79—26no—
582C22×C79—23no—
583C22×C79—26no—
584C22×C79—162no—
585C22×C79C2611yescharacteristic
586C2×D79—26no—
587C2×D79—26no—
588C2×D79—23no—
589C2×D79—23no—
590C2×D79—26no—
591C2×D79—44no—
592C2×D79—166no—
593C4×C79—23no—
594C4×C79—26no—
595C4×C79—26no—
596C4×C79—23no—
597C4×C79—26no—
598Dic79—26no—
599Dic79—26no—
600Dic79—26no—
601Dic79—23no—
602Dic79#58516yes—
603#62841—791nomaximal, Sylow
604C2×C79—41no—
605C2×C79—46no—
606C2×C79C2×#58513yes—
607D79—41no—
608D79—41no—
609D79—46no—
610#3568—793no—
611#3568—791no—
612#3568—793no—
613#3568D7911yescharacteristic, complemented
614#3550—793no—
615#3549—791no—
616#3540—796no—
617#3540—796no—
618#3518—796no—
619#3518—796no—
620#3514—796no—
621#3514—796no—
622#3510—796no—
623#3510—796no—
624#3444—793no—
625C79#6284111yescharacteristic, complemented, Sylow
626#563—793no—
627#563—793no—
628#563—793no—
629#563C2×D7913yescomplemented
630H(3,𝔽4)—796no—
631H(3,𝔽4)—793no—
632H(3,𝔽4)—792no—
633H(3,𝔽4)C2×D7911yescharacteristic, complemented
634#560—792no—
635#560—796no—
636#559—796no—
637#559—796no—
638#559—796no—
639#559—796no—
640#559—796no—
641Q82—796no—
642#556—796no—
643#556—796no—
644#556—796no—
645#556—796no—
646#556—796no—
647#556—796no—
648#556—796no—
649#556—796no—
650#556—796no—
651#556—796no—
652#556—796no—
653#556—796no—
654#556—796no—
655#556C2×D7916yescomplemented
656#555—796no—
657#555—796no—
658#555—796no—
659#555—796no—
660#555—796no—
661#551—796no—
662#551—796no—
663#551—796no—
664#551—796no—
665#551—796no—
666#551—796no—
667#551—796no—
668#551—796no—
669#551—796no—
670#551—796no—
671#551—796no—
672#551C2×D7916yescomplemented
673D4×Q8—796no—
674D4×Q8—796no—
675#548—796no—
676#548—796no—
677#548—796no—
678#548—796no—
679#546—796no—
680#546—796no—
681#546—796no—
682#546—796no—
683D42—796no—
684#542—796no—
685#542—796no—
686#542—796no—
687#542—796no—
688#542—796no—
689#542—796no—
690#542—796no—
691#542—796no—
692#542—796no—
693#542—796no—
694#542—796no—
695#542—796no—
696#542—796no—
697#542—796no—
698#542—796no—
699#542C2×D7916yescomplemented
700#538—796no—
701#538—796no—
702#538—796no—
703#538—796no—
704#538—796no—
705#538—796no—
706#538—796no—
707#538C2×D7916yescomplemented
708#536—796no—
709#536—796no—
710#535—796no—
711#535—796no—
712#533—793no—
713#533—793no—
714#533—796no—
715#533—793no—
716#533—796no—
717#532—793no—
718#532—793no—
719#532—793no—
720#529—796no—
721#529—796no—
722#529—796no—
723#529—793no—
724#529—793no—
725#529—796no—
726#529—796no—
727#529—796no—
728#529—796no—
729#529—796no—
730#529—793no—
731#529C2×D7913yescomplemented
732C2×#124—796no—
733C2×#124—796no—
734#525—796no—
735#525—793no—
736#525—793no—
737#525—796no—
738#519—796no—
739#519—796no—
740#518—796no—
741#518—796no—
742C4×#41—793no—
743C4×#41—793no—
744C4×#41—796no—
745C4×#41—796no—
746C22×C42—791no—
747C2×#41—793no—
748C2×#41—793no—
749C2×#41—796no—
750C2×#41—796no—
751C22×Q8—796no—
752C22×Q8—796no—
753C22×D4—796no—
754C22×D4—796no—
755C23×C4—793no—
756C4⋊Q8—793no—
757C4⋊Q8—796no—
758C4⋊Q8—796no—
759C4⋊Q8—796no—
760C4⋊Q8—793no—
761C4⋊Q8—793no—
762C4⋊Q8—796no—
763C4⋊Q8—796no—
764C4⋊Q8—796no—
765C4⋊Q8—796no—
766C4⋊Q8C22×D7916yes—
767#127—793no—
768#127—796no—
769#127—792no—
770#126—796no—
771#126—796no—
772#126—796no—
773#126—796no—
774#126—796no—
775#126—796no—
776#126—796no—
777#126—796no—
778#126—796no—
779#126—796no—
780#126—796no—
781#126—796no—
782#126—796no—
783#126—796no—
784#126—796no—
785#126—796no—
786#126—796no—
787#126—796no—
788#126—792no—
789#126C22×D7916yes—
790#126C22×D7916yes—
791#126C22×D7916yes—
792#126C22×D7916yes—
793#126C22×D7912yes—
794#125—796no—
795#125—796no—
796#125—793no—
797#125C22×D7913yes—
798#124—796no—
799#124—796no—
800#124—796no—
801#124—796no—
802#124—796no—
803#124—796no—
804#124—796no—
805#124—796no—
806#124—796no—
807#124—796no—
808#124—796no—
809#124—796no—
810#124—796no—
811#124—796no—
812#124—796no—
813#124—796no—
814#124—796no—
815#124—796no—
816#124—796no—
817#124—796no—
818#124—796no—
819#124—796no—
820#124—796no—
821#124—796no—
822#124—796no—
823#124—793no—
824#124—796no—
825#124—796no—
826#124C22×D7916yes—
827#124C22×D7913yes—
828#124C22×D7916yes—
829#124C22×D7916yes—
830#123—796no—
831#123—796no—
832#123—796no—
833#123—796no—
834#123—796no—
835#123—796no—
836#123—796no—
837#123—796no—
838#123—796no—
839#123—796no—
840#123—796no—
841#123—796no—
842#123—796no—
843#123—796no—
844#123—796no—
845#123—796no—
846#123—796no—
847#123—796no—
848#123—796no—
849#123C22×D7916yes—
850#123C22×D7916yes—
851#123C22×D7916yes—
852C22⋊Q8—793no—
853C22⋊Q8—796no—
854C22⋊Q8—793no—
855C22⋊Q8—796no—
856C22⋊Q8—796no—
857C22⋊Q8—796no—
858C22⋊Q8—793no—
859C22⋊Q8—796no—
860C22⋊Q8—796no—
861C22⋊Q8—796no—
862C22⋊Q8—796no—
863C22⋊Q8—796no—
864C22⋊Q8—796no—
865C22⋊Q8—796no—
866C22⋊Q8—796no—
867C22⋊Q8—796no—
868C22⋊Q8—796no—
869C22⋊Q8—796no—
870C22⋊Q8—796no—
871C22⋊Q8—796no—
872C22⋊Q8—796no—
873C22⋊Q8—796no—
874C22⋊Q8—796no—
875C22⋊Q8—796no—
876C22⋊Q8C22×D7913yes—
877C22⋊Q8C22×D7916yes—
878C22⋊Q8C22×D7916yes—
879C22⋊Q8C22×D7916yes—
880#121—793no—
881#121—796no—
882#121—796no—
883#121—796no—
884#121—796no—
885#121—796no—
886#121—796no—
887#121—793no—
888#121—796no—
889#121—793no—
890#121—796no—
891#121—796no—
892#121—796no—
893#121—796no—
894#121—796no—
895#121—796no—
896#121—796no—
897#121—796no—
898#121C22×D7913yes—
899#121C22×D7916yes—
900#120—792no—
901#120—792no—
902#120—796no—
903#120—796no—
904#120—796no—
905#120—796no—
906#120—796no—
907#120—796no—
908#120—796no—
909#120—796no—
910#120C22×D7916yes—
911#120C22×D7912yes—
912C4×Q8—793no—
913C4×Q8—796no—
914C4×Q8—796no—
915C4×Q8—796no—
916C4×Q8—796no—
917C4×Q8—793no—
918C4×Q8—796no—
919C4×Q8—796no—
920C4×Q8—796no—
921C4×Q8—796no—
922C4×Q8—796no—
923C4×Q8—796no—
924C4×Q8—793no—
925C4×Q8—796no—
926C4×Q8—796no—
927C4×Q8—796no—
928C4×Q8—796no—
929C4×Q8—796no—
930C4×Q8C22×D7913yes—
931C4×Q8C22×D7916yes—
932C4×D4—796no—
933C4×D4—793no—
934C4×D4—796no—
935C4×D4—796no—
936C4×D4—796no—
937C4×D4—796no—
938C4×D4—796no—
939C4×D4—796no—
940C4×D4—796no—
941C4×D4—796no—
942C4×D4—796no—
943C4×D4—796no—
944C4×D4—796no—
945C4×D4—793no—
946C4×D4—796no—
947C4×D4—796no—
948C4×D4—796no—
949C4×D4—796no—
950C4×D4—796no—
951C4×D4—796no—
952C4×D4—796no—
953C4×D4—796no—
954C4×D4—796no—
955C4×D4—796no—
956C4×D4—796no—
957C4×D4—796no—
958C4×D4—796no—
959C4×D4—793no—
960C4×D4—796no—
961C4×D4C22×D7916yes—
962C4×D4C22×D7913yes—
963C4×D4C22×D7916yes—
964#117—796no—
965#117—796no—
966#117—793no—
967#117—793no—
968#117—796no—
969#117—796no—
970#117—796no—
971#117—796no—
972#117—796no—
973#117—796no—
974#117—796no—
975#117—796no—
976#117—796no—
977#117—796no—
978#117—796no—
979#117—796no—
980#117—796no—
981#117—796no—
982#117—796no—
983#117—796no—
984#117C22×D7916yes—
985#117C22×D7916yes—
986C2×C22⋊C4—796no—
987C2×C22⋊C4—796no—
988C2×C22⋊C4—796no—
989C2×C22⋊C4—796no—
990C2×C22⋊C4—796no—
991C2×C22⋊C4—796no—
992C2×C22⋊C4—796no—
993C2×C22⋊C4C22×D7916yes—
994C2×C42—796no—
995C2×C42—793no—
996C2×C42—796no—
997C2×C42—793no—
998C2×C42—793no—
999C2×C42—791no—
1000C2×C42—791no—
1001C2×C42C22×D7911yescharacteristic
1002C24—796no—
1003C24—791no—
1004C24C23×D7912yes—
1005#41—31612no—
1006#41—31612no—
1007#41—3166no—
1008#41—3166no—
1009C2×Q8—31612no—
1010C2×Q8—31612no—
1011C2×Q8—796no—
1012C2×Q8—796no—
1013C2×Q8—796no—
1014C2×Q8—793no—
1015C2×Q8—796no—
1016C2×Q8—796no—
1017C2×Q8C23×D7916yes—
1018C2×Q8C23×D7913yes—
1019C2×D4—31612no—
1020C2×D4—31612no—
1021C2×D4—796no—
1022C2×D4—796no—
1023C2×D4—796no—
1024C2×D4—796no—
1025C2×D4—796no—
1026C2×D4—796no—
1027C2×D4—796no—
1028C2×D4—793no—
1029C2×D4—796no—
1030C2×D4—796no—
1031C2×D4—796no—
1032C2×D4C23×D7913yes—
1033C2×D4C23×D7916yes—
1034C2×D4C23×D7916yes—
1035C22×C4—3166no—
1036C22×C4—796no—
1037C22×C4—796no—
1038C22×C4—793no—
1039C22×C4—793no—
1040C22×C4—796no—
1041C22×C4—796no—
1042C22×C4—796no—
1043C22×C4—796no—
1044C22×C4—793no—
1045C22×C4—796no—
1046C22×C4—793no—
1047C22×C4—793no—
1048C22×C4—796no—
1049C22×C4C23×D7913yes—
1050C22×C4C23×D7916yes—
1051C22×C4C23×D7916yes—
1052C4⋊C4—796no—
1053C4⋊C4—796no—
1054C4⋊C4—796no—
1055C4⋊C4—796no—
1056C4⋊C4—796no—
1057C4⋊C4—796no—
1058C4⋊C4—796no—
1059C4⋊C4—796no—
1060C4⋊C4—796no—
1061C4⋊C4—796no—
1062C4⋊C4—796no—
1063C4⋊C4—796no—
1064C4⋊C4—796no—
1065C4⋊C4—796no—
1066C4⋊C4—796no—
1067C4⋊C4—796no—
1068C4⋊C4—793no—
1069C4⋊C4—793no—
1070C4⋊C4—796no—
1071C4⋊C4—796no—
1072C4⋊C4C23×D7916yes—
1073C4⋊C4C23×D7916yes—
1074C4⋊C4C23×D7913yes—
1075C4⋊C4C23×D7913yes—
1076C4⋊C4C23×D7916yes—
1077C4⋊C4C23×D7916yes—
1078C4⋊C4C23×D7916yes—
1079C4⋊C4C23×D7916yes—
1080C22⋊C4—796no—
1081C22⋊C4—796no—
1082C22⋊C4—796no—
1083C22⋊C4—796no—
1084C22⋊C4—796no—
1085C22⋊C4—796no—
1086C22⋊C4—796no—
1087C22⋊C4—796no—
1088C22⋊C4—796no—
1089C22⋊C4—796no—
1090C22⋊C4—796no—
1091C22⋊C4—796no—
1092C22⋊C4—796no—
1093C22⋊C4—796no—
1094C22⋊C4—796no—
1095C22⋊C4—796no—
1096C22⋊C4—796no—
1097C22⋊C4—796no—
1098C22⋊C4—796no—
1099C22⋊C4—796no—
1100C22⋊C4—796no—
1101C22⋊C4—796no—
1102C22⋊C4—796no—
1103C22⋊C4—796no—
1104C22⋊C4—796no—
1105C22⋊C4C23×D7916yes—
1106C22⋊C4C23×D7916yes—
1107C22⋊C4C23×D7916yes—
1108C22⋊C4C23×D7916yes—
1109C22⋊C4C23×D7916yes—
1110C22⋊C4C23×D7916yes—
1111C22⋊C4C23×D7916yes—
1112C22⋊C4C23×D7916yes—
1113C22⋊C4C23×D7916yes—
1114C42—793no—
1115C42—793no—
1116C42—793no—
1117C42—793no—
1118C42—796no—
1119C42—796no—
1120C42—796no—
1121C42—796no—
1122C42—796no—
1123C42—796no—
1124C42—796no—
1125C42—796no—
1126C42—796no—
1127C42C23×D7913yes—
1128C42C23×D7911yescharacteristic
1129C42C23×D7916yes—
1130C42C23×D7912yes—
1131C42C23×D7916yes—
1132C23—46no—
1133C23—3163no—
1134C23—3166no—
1135C23—3166no—
1136C23—3166no—
1137C23—796no—
1138C23—791no—
1139C23—791no—
1140C23C24×D7916yes—
1141C23C24×D7911yescharacteristic
1142Q8—46no—
1143Q8—43no—
1144Q8—3166no—
1145Q8—3166no—
1146Q8—3166no—
1147Q8—3163no—
1148Q8—15812no—
1149Q8—15812no—
1150D4—46no—
1151D4—46no—
1152D4—43no—
1153D4—3166no—
1154D4—3166no—
1155D4—3163no—
1156D4—3166no—
1157D4—3166no—
1158D4—3166no—
1159D4—3166no—
1160D4—3166no—
1161D4—3166no—
1162D4—15812no—
1163D4—15812no—
1164C2×C4—43no—
1165C2×C4—46no—
1166C2×C4—46no—
1167C2×C4—3163no—
1168C2×C4—3163no—
1169C2×C4—3166no—
1170C2×C4—3166no—
1171C2×C4—3166no—
1172C2×C4—3166no—
1173C2×C4—3166no—
1174C2×C4—3166no—
1175C2×C4—793no—
1176C2×C4—793no—
1177C2×C4—796no—
1178C2×C4—796no—
1179C2×C4—796no—
1180C2×C4—1586no—
1181C2×C4—1586no—
1182C2×C4—15812no—
1183C2×C4—1586no—
1184C2×C4—15812no—
1185C2×C4C24×D7913yes—
1186C2×C4C24×D7916yes—
1187C2×C4C24×D7916yes—
1188C2×C4C24×D7916yes—
1189C2×C4C24×D7913yes—
1190C22—26no—
1191C22—23no—
1192C22—26no—
1193C22—26no—
1194C22—162no—
1195C22—3164no—
1196C22—1586no—
1197C22—1583no—
1198C22—1583no—
1199C22—1586no—
1200C22—1586no—
1201C22—12646no—
1202C22C25×D7911yescharacteristic
1203C4—23no—
1204C4—26no—
1205C4—26no—
1206C4—23no—
1207C4—26no—
1208C4—796no—
1209C4—1583no—
1210C4—1586no—
1211C4—1586no—
1212C4—1586no—
1213C2—46no—
1214C2—41no—
1215C2—3161no—
1216C2—3161no—
1217C2—3166no—
1218C2#585×D7913yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3568C2
hypercenter#3568D79
hypocenterC79#62841
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3568

Complements

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

NH ≅ G/Ntype
1. #23778097C2semidirect
2. #23778096C2semidirect
3. #23778094C2semidirect
4. #23777810C2semidirect
5. #23777804C2semidirect
6. #23777671C2semidirect
7. #23777665C2semidirect
8. #23777413C2semidirect
9. #23777410C2semidirect
10. #23777353C2semidirect
11. #23777350C2semidirect
12. #23777290C2semidirect
13. #23777288C2semidirect
14. #23776694C2semidirect
15. C79×#3568C2semidirect
16. #19099317C22semidirect
17. #19099317C22semidirect
18. #19099313C22semidirect
19. #19099306C22semidirect
20. #19099305C22semidirect
21. #19099305C22semidirect
22. #19099304C22semidirect
23. #19099301C22semidirect
24. #19099298C22semidirect
25. #19099297C22semidirect
26. #19099297C22semidirect
27. #19099296C22semidirect
28. #19099295C22semidirect
29. #19099293C22semidirect
30. #19099287C22semidirect
31. #19099285C22semidirect
32. #19099285C22semidirect
33. #19099284C22semidirect
34. #19099282C22semidirect
35. #19099282C22semidirect
36. #19099281C22semidirect
37. #19099280C22semidirect
38. #19099280C22semidirect
39. #19099280C22semidirect
40. #19099280C22semidirect
41. #19099280C22semidirect
42. #19099280C22semidirect
43. #19099277C22semidirect
44. #19099276C22semidirect
45. #19099275C22semidirect
46. #19099275C22semidirect
47. #19099275C22semidirect
48. #19099244C22semidirect
49. #19099242C22semidirect
50. #19099240C22semidirect
51. #19099240C22semidirect
52. #19099239C22semidirect
53. #19099238C22semidirect
54. #19099238C22semidirect
55. #19099238C22semidirect
56. #19099237C22semidirect
57. #19099237C22semidirect
58. #19099236C22semidirect
59. #19099226C22semidirect
60. #19099226C22semidirect
61. #19099223C22semidirect
62. #19099222C22semidirect
63. #19099221C22semidirect
64. #19099219C22semidirect
65. #19099205C22semidirect
66. #19099203C22semidirect
67. #19099202C22semidirect
68. #19099200C22semidirect
69. #19099195C22semidirect
70. #19099187C22semidirect
71. #19099186C22semidirect
72. #19099183C22semidirect
73. #19099183C22semidirect
74. #19099183C22semidirect
75. #19099183C22semidirect
76. #19099181C22semidirect
77. #19099181C22semidirect
78. #19099179C22semidirect
79. #19099179C22semidirect
80. #19099179C22semidirect
81. #19099179C22semidirect
82. #19099178C22semidirect
83. #19099177C22semidirect
84. #19099177C22semidirect
85. #19099153C22semidirect
86. #19099152C22semidirect
87. #19099149C22semidirect
88. #19099149C22semidirect
89. #19099148C22semidirect
90. #19099146C22semidirect
91. #19099145C22semidirect
92. #19099138C22semidirect
93. #19099135C22semidirect
96. #19099119C22semidirect
97. #19099117C22semidirect
98. #19099117C22semidirect
99. #19099115C22semidirect
100. #19099115C22semidirect
104. #19099098C22semidirect
105. #19099097C22semidirect
106. #19099096C22semidirect
107. #19099096C22semidirect
108. #19099096C22semidirect
109. #19099093C22semidirect
110. #19099092C22semidirect
111. #19099091C22semidirect
112. #19099091C22semidirect
113. #19099090C22semidirect
114. #19099090C22semidirect
115. C2×#14579147C22semidirect
116. #124×D79C22semidirect
117. #19099076C22semidirect
118. #19099073C22semidirect
119. #19099072C22semidirect
120. #19099071C22semidirect
121. #19099040C22semidirect
122. #19099039C22semidirect
123. #19099036C22semidirect
124. #19099035C22semidirect
125. C4×#11929625C22semidirect
126. #19099031C22semidirect
127. C4×#11929623C22semidirect
128. C4×#11929623C22semidirect
129. C2×C42×D79C22semidirect
130. #563×C79C22semidirect
131. H(3,𝔽4)×C79C22semidirect
132. #556×C79C22semidirect
133. #551×C79C22semidirect
134. #542×C79C22semidirect
135. #538×C79C22semidirect
136. #529×C79C22semidirect
613. #3568D79semidirect
625. C79#62841semidirect
629. #563C2×D79semidirect
633. H(3,𝔽4)C2×D79semidirect
655. #556C2×D79semidirect
672. #551C2×D79semidirect
699. #542C2×D79semidirect
707. #538C2×D79semidirect
731. #529C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780972
#237780962
#237780942
#237778102
#237778042
#237776712
#237776652
#237774132
#237774102
#237773532
#237773502
#237772902
#237772882
#237766942
C79×#35682
#6284179