Finite Group Databasebeta

← #35196721

Subgroups — #35196721

Order 20224.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777496C211yesmaximal, characteristic, complemented
2#23777451C213yesmaximal, complemented
3#23777444C213yesmaximal, complemented
4#23777411C212yesmaximal, complemented
5#23777376C216yesmaximal, complemented
6#23777304C213yesmaximal, complemented
7#23777283C213yesmaximal, complemented
8#23777217C211yesmaximal, characteristic, complemented
9#23777184C211yesmaximal, characteristic, complemented
10#23777141C216yesmaximal, complemented
11#23777077C212yesmaximal, complemented
12#23777021C211yesmaximal, characteristic, complemented
13#23777020C213yesmaximal, complemented
14#23777020C211yesmaximal, characteristic, complemented
15#23777019C213yesmaximal, complemented
16Q8×#11929623C212yesmaximal, complemented
17#23776965C216yesmaximal, complemented
18#23776832C216yesmaximal, complemented
19#23776694C213yesmaximal, complemented
20#533×D79C213yesmaximal, complemented
21#23776609C212yesmaximal, complemented
22C2×C4×#11929625C211yesmaximal, characteristic, complemented
23C79×#3523C211yesmaximal, characteristic, complemented
24C2×#14579209C2212yes—
25C22×#11929625C2211yescharacteristic
26Q8×Dic158C2212yescomplemented
27#19099292C2211yescharacteristic, complemented
28#19099291C2213yescomplemented
29#19099288C2216yescomplemented
30#19099287C2213yescomplemented
31#19099286C2213yescomplemented
32#19099286C2213yescomplemented
33#19099286C2216yescomplemented
34#19099285C2216yescomplemented
35#19099281C2216yescomplemented
36#19099276C2216yescomplemented
37#19099271C2216yes—
38#19099271C2216yescomplemented
39#19099270C2216yes—
40#19099269C2216yescomplemented
41#19099264C22112yescomplemented
42#19099255C2216yescomplemented
43#19099254C2216yescomplemented
44#19099251C2216yescomplemented
45#19099251C22112yescomplemented
46#19099251C2216yescomplemented
47#19099249C22112yescomplemented
48#19099248C2216yes—
49#19099245C22112yescomplemented
50#19099237C22112yes—
51#19099236C22112yes—
52Q8×D316C2211yescharacteristic, complemented
53Q8×D316C2213yescomplemented
54#19099228C2213yescomplemented
55Q8×C22⋊D79C2212yes—
56Q8×C22⋊D79C2212yescomplemented
57#19099225C2212yes—
58#19099225C2216yescomplemented
59#19099224C2212yes—
60#19099221C2216yescomplemented
61#19099218C2213yescomplemented
62#19099217C2213yescomplemented
63#19099216C2216yes—
64#19099216C2213yescomplemented
65#19099216C2213yescomplemented
66#19099215C2216yes—
67#19099215C2216yescomplemented
68#19099209C2216yes—
69#19099204C2216yes—
70#19099193C2216yescomplemented
71#19099185C2216yescomplemented
72#19099184C2216yescomplemented
73#19099179C22112yescomplemented
74#19099172C22112yescomplemented
75#19099171C2216yescomplemented
76#19099161C22112yescomplemented
77#19099154C22112yescomplemented
78#19099143C2216yes—
79#19099138C2216yes—
80#19099136C2216yescomplemented
81#19099120C2213yes—
82#19099119C2213yescomplemented
83#19099119C2216yescomplemented
84#19099118C2216yescomplemented
85#19099118C2213yescomplemented
86#19099118C2213yescomplemented
87#19099117C2216yescomplemented
88#19099117C2213yescomplemented
89#19099117C2216yescomplemented
90#19099116C2216yes—
91#19099115C2213yes—
92#19099115C2216yes—
93#19099115C2216yescomplemented
94#19099112C2213yescomplemented
95#19099110C2213yescomplemented
96#19099108C2211yescharacteristic
97C4⋊Q8×D79C2213yescomplemented
98C4⋊Q8×D79C2213yescomplemented
99#19099099C2216yescomplemented
100#19099098C22112yescomplemented
101#19099098C2216yescomplemented
102#19099098C2213yescomplemented
103#19099097C2213yes—
104#19099096C2216yescomplemented
105#19099096C22112yescomplemented
106#19099096C2216yescomplemented
107#19099092C2213yescomplemented
108#19099091C2216yescomplemented
109#19099090C2216yes—
110#125×D79C2216yescomplemented
111#19099076C2213yes—
112#19099073C2213yes—
113#19099072C2216yes—
114#19099071C2216yes—
115C22⋊Q8×D79C2216yes—
116C22⋊Q8×D79C2216yes—
117#19099045C2212yes—
118#19099045C2216yescomplemented
119#19099043C2216yescomplemented
120#19099043C2216yescomplemented
121#19099039C2216yescomplemented
122#19099039C2212yescomplemented
123C4×#11929625C2213yes—
124C4×#11929625C2213yes—
125C4×#11929625C2213yes—
126C4×#11929625C2211yescharacteristic
127C4×#11929625C2211yescharacteristic
128C4×#11929625C2211yescharacteristic
129C4×#11929625C2213yes—
130C4×#11929625C2211yescharacteristic
131C4×#11929625C2216yescomplemented
132C4×#11929625C2213yescomplemented
133#19099031C2216yescomplemented
134#19099031C2216yescomplemented
135C4×#11929623C2216yes—
136C4×#11929623C2213yescomplemented
137C2×Q8×Dic79C2211yescharacteristic
138C2×Q8×Dic79C2212yescomplemented
139C4×Q8×D79C2216yescomplemented
140C4×Q8×D79C2212yescomplemented
141C4×Q8×D79C2216yescomplemented
142C2×C4×D316C2213yes—
143C2×#14579123C2213yes—
144C2×#14579119C2213yes—
145#117×D79C2216yes—
146C2×C42×D79C2213yes—
147#557×C79C2213yescomplemented
148#557×C79C2211yescharacteristic, complemented
149#556×C79C2213yescomplemented
150#552×C79C2216yes—
151D4×Q8×C79C2212yes—
152D4×Q8×C79C2211yescharacteristic, complemented
153#541×C79C2216yescomplemented
154#533×C79C2213yes—
155#529×C79C2213yes—
156#519×C79C2212yescomplemented
157C2×C4×Q8×C79C2211yescharacteristic
158#14579209—216no—
159C2×#11929625—28no—
160C2×#11929625C2313yes—
161C2×#11929625C2316yes—
162C2×#11929625C2313yes—
163C2×#11929625C2311yescharacteristic
164C2×#11929625C2313yes—
165C2×#11929625C2311yescharacteristic
166C2×#11929624C2316yes—
167C2×#11929624C2316yes—
168C2×#11929623C2312yes—
169C2×#11929623C2313yes—
170C2×Q8×D79C2316yes—
171C2×Q8×D79C2312yes—
172C2×Q8×D79C2316yes—
173C22×D316C2313yes—
174C22×C4×D79C2313yes—
175C22×C4×D79C2313yes—
176C22×C4×D79C2313yes—
177#14579161C2316yes—
178#14579161C2313yes—
179#14579161C2313yes—
180#14579160C2316yes—
181#14579160C2316yes—
182#14579160C2316yes—
183#14579160C2316yes—
184#14579160C2313yes—
185#14579160C2311yescharacteristic
186#14579159C2316yes—
187#14579159C2316yes—
188#14579159C2313yes—
189#14579157C2311yescharacteristic
190#14579156C23112yes—
191#14579156C23112yes—
192#14579156C23112yes—
193#14579156C23112yes—
194#14579156C2316yes—
195#14579155C2316yes—
196#14579155C23112yes—
197#14579154C2316yes—
198#14579153C2316yes—
199#14579153C2313yes—
200#14579152C23112yes—
201#14579152C2316yes—
202#14579152C2316yes—
203#14579152C2316yes—
204#14579151C23112yes—
205#14579151C23112yes—
206#14579151C2316yes—
207#14579151C23112yes—
208#14579151C2316yes—
209#14579150C2316yes—
210#14579149C2316yes—
211#14579149C23112yes—
212#14579149C2313yes—
213#14579147C2316yes—
214#14579147C23112yes—
215#14579147C2312yes—
216#14579146C23112yes—
217#14579146C23112yes—
218#14579146C23112yes—
219#14579146C2316yes—
220#14579146C23112yes—
221#14579146C2316yes—
222#14579145C23112yes—
223#14579144C2316yes—
224#14579143C23112yes—
225#14579143C2316yes—
226#14579143C2316yes—
227#14579141C2316yes—
228#14579141C23112yes—
229#14579141C23112yes—
230#14579141C2316yes—
231#14579141C2316yes—
232#14579141C2313yes—
233#14579140C2316yes—
234#14579140C2316yes—
235#14579140C2313yes—
236#14579139C2316yes—
237#14579139C23112yes—
238#14579139C23112yes—
239#14579139C23112yes—
240#14579139C2316yes—
241#14579139C2316yes—
242#14579138C23112yes—
243#14579138C23112yes—
244#14579138C2316yes—
245#14579137C2316yes—
246#14579137C2316yes—
247#14579137C2316yes—
248#14579137C2316yes—
249#14579137C2313yes—
250#14579136C23112yes—
251#14579136C2316yes—
252#14579136C2313yes—
253#14579135C2316yes—
254#14579135C2311yescharacteristic
255#14579134C2316yes—
256#14579134C23112yes—
257#14579134C2316yes—
258#14579134C2316yes—
259#14579133C2312yes—
260#14579132C2313yes—
261#14579131C2316yes—
262#14579129C2316yes—
263Q8×Dic79C2312yes—
264Q8×Dic79C2311yescharacteristic
265Q8×Dic79C2316yes—
266Q8×Dic79C2313yes—
267Q8×Dic79C2311yescharacteristic
268Q8×Dic79C2313yes—
269Q8×Dic79C2316yes—
270Q8×Dic79C2313yes—
271C4×Dic158C2316yes—
272C4×Dic158C23112yes—
273C4×Dic158C2316yes—
274C4×Dic158C2313yes—
275C4×Dic158C23112yes—
276C4×Dic158C2316yes—
277C4×Dic158C2316yes—
278#14579126C2316yes—
279#14579126C2316yes—
280#14579126C2316yes—
281#14579126C2313yes—
282#14579126C2316yes—
283#14579126C2316yes—
284#14579126C23112yes—
285C4×D316C2316yes—
286C4×D316C2313yes—
287C4×D316C2316yes—
288C4×D316C2316yes—
289C4×D316C2313yes—
290C4×D316C2313yes—
291C4×D316C2313yes—
292C4×D316C2316yes—
293C4×D316C23112yes—
294C4×D316C2313yes—
295D4×Dic79C2316yes—
296D4×Dic79C2311yescharacteristic
297#14579123C2316yes—
298#14579123C2316yes—
299#14579123C2313yes—
300#14579123C2316yes—
301#14579123C2313yes—
302#14579123C2313yes—
303#14579123C2316yes—
304#14579123C2313yes—
305#14579123C2316yes—
306#14579123C2311yescharacteristic
307#14579123C2316yes—
308C4×C22⋊D79C2316yes—
309C4×C22⋊D79C2316yes—
310C4×C22⋊D79C2316yes—
311(C22⋊D79)⋊C4C2316yes—
312(C22⋊D79)⋊C4C2316yes—
313(C22⋊D79)⋊C4C23112yes—
314(C22⋊D79)⋊C4C2316yes—
315(C22⋊D79)⋊C4C2316yes—
316(C22⋊D79)⋊C4C2316yes—
317(C22⋊D79)⋊C4C2316yes—
318(C22⋊D79)⋊C4C2312yes—
319#14579120C2316yes—
320#14579119C2313yes—
321#14579119C2316yes—
322#14579119C23112yes—
323#14579119C2316yes—
324#14579119C2316yes—
325#14579119C2316yes—
326#14579119C2313yes—
327#14579119C2313yes—
328#14579119C2313yes—
329#14579119C2316yes—
330#14579119C2316yes—
331#14579119C2313yes—
332#14579119C2313yes—
333#14579119C2316yes—
334#14579118C2316yes—
335#14579118C2316yes—
336#14579118C23112yes—
337#14579118C23112yes—
338#14579117C2316yes—
339#14579117C2316yes—
340#14579117C2316yes—
341C2×C4⋊Dic79C2316yes—
342C2×C4⋊Dic79C2313yes—
343C4⋊C4×D79C2316yes—
344C4⋊C4×D79C23112yes—
345C4⋊C4×D79C23112yes—
346C4⋊C4×D79C2316yes—
347C4⋊C4×D79C2316yes—
348C4⋊C4×D79C2316yes—
349C4⋊C4×D79C2316yes—
350C2×(C2×D79)⋊C4C2316yes—
351C22⋊C4×D79C23112yes—
352C2×C4×Dic79C2311yescharacteristic
353C2×C4×Dic79C2313yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2316yes—
356C42×D79C2313yes—
357C42×D79C2313yes—
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C23112yes—
365C42×D79C2316yes—
366C22×Q8×C79C2312yes—
367C22×Q8×C79C2311yescharacteristic
368C4⋊Q8×C79C2316yes—
369C4⋊Q8×C79C2313yes—
370C4⋊Q8×C79C2313yes—
371#126×C79C2316yes—
372#126×C79C23112yes—
373#125×C79C2316yes—
374#125×C79C23112yes—
375#125×C79C2316yes—
376#125×C79C2313yes—
377#124×C79C2313yes—
378#123×C79C2316yes—
379C22⋊Q8×C79C2316yes—
380C22⋊Q8×C79C2316yes—
381C22⋊Q8×C79C2316yes—
382C22⋊Q8×C79C2313yes—
383#121×C79C2311yescharacteristic
384C4×Q8×C79C2313yes—
385C4×Q8×C79C2316yes—
386C4×Q8×C79C2312yes—
387C4×Q8×C79C2316yes—
388C4×Q8×C79C2311yescharacteristic
389C4×Q8×C79C2313yes—
390C4×Q8×C79C2311yescharacteristic
391C4×Q8×C79C2313yes—
392C4×Q8×C79C2316yes—
393C4×D4×C79C2316yes—
394C4×D4×C79C2313yes—
395#117×C79C2316yes—
396#117×C79C2316yes—
397#117×C79C2316yes—
398C2×C4⋊C4×C79C2313yes—
399C2×C42×C79C2313yes—
400C23×D79C2413yes—
401#11929625—212no—
402#11929625—224no—
403#11929625—212no—
404#11929625—24no—
405#11929625—46no—
406#11929625#4118yescomplemented
407#11929624—224no—
408#11929624—224no—
409#11929623—28no—
410#11929623—46no—
411C2×Dic158C2413yes—
412C2×Dic158C2416yes—
413C2×Dic158C2416yes—
414C2×Dic158C2412yes—
415C2×Dic158C24112yes—
416Q8×D79—224no—
417Q8×D79—28no—
418Q8×D79—412no—
419C2×D316—212no—
420C2×D316C2416yes—
421C2×D316C2411yescharacteristic
422C2×D316C2416yes—
423C2×D316C2413yes—
424C2×D316C2416yes—
425C2×D316C2413yes—
426C2×C22⋊D79C2412yes—
427C2×C22⋊D79C2412yes—
428C2×C22⋊D79C2416yes—
429C2×C22⋊D79C2412yes—
430C2×C22⋊D79C2416yes—
431C22×Dic79C2412yes—
432C22×Dic79C2411yescharacteristic
433C22×Dic79C2416yes—
434C22×Dic79C2413yes—
435C22×Dic79C2411yescharacteristic
436C2×C4×D79—212no—
437C2×C4×D79—212no—
438C2×C4×D79—46no—
439C2×C4×D79C2413yes—
440C2×C4×D79C24112yes—
441C2×C4×D79C2416yes—
442C2×C4×D79C2413yes—
443C2×C4×D79C2412yes—
444C2×C4×D79C2413yes—
445C2×C4×D79C2413yes—
446C2×C4×D79C2413yes—
447C2×C4×D79C2413yes—
448C2×C4×D79C2413yes—
449C2×C4×D79C2413yes—
450C2×C4×D79C2413yes—
451C2×C4×D79C24112yes—
452C2×C4×D79C2416yes—
453C2×C4×D79C2413yes—
454C2×C4×D79C2413yes—
455C2×C4×D79C2413yes—
456C4⋊Dic79C2413yes—
457C4⋊Dic79C2413yes—
458C4⋊Dic79C2416yes—
459C4⋊Dic79C2416yes—
460C4⋊Dic79C24112yes—
461C4⋊Dic79C2416yes—
462C4⋊Dic79C2416yes—
463C4⋊Dic79C2413yes—
464C4⋊Dic79C2416yes—
465C4⋊Dic79C2411yescharacteristic
466C4⋊Dic79C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C2416yes—
470Dic79⋊C4C2416yes—
471Dic79⋊C4C24112yes—
472Dic79⋊C4C2416yes—
473Dic79⋊C4C24112yes—
474Dic79⋊C4C24112yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2416yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2412yes—
479Dic79⋊C4C2416yes—
480C22⋊Dic79C2416yes—
481C22⋊Dic79C2412yes—
482C22⋊Dic79C2416yes—
483(C2×D79)⋊C4C24112yes—
484(C2×D79)⋊C4C24112yes—
485(C2×D79)⋊C4C2416yes—
486(C2×D79)⋊C4C2416yes—
487(C2×D79)⋊C4C2416yes—
488(C2×D79)⋊C4C2416yes—
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C2412yes—
491(C2×D79)⋊C4C2416yes—
492(C2×D79)⋊C4C2416yes—
493(C2×D79)⋊C4C2412yes—
494(C2×D79)⋊C4C2416yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498(C2×D79)⋊C4C2416yes—
499C4×Dic79C2411yescharacteristic
500C4×Dic79C2411yescharacteristic
501C4×Dic79C2411yescharacteristic
502C4×Dic79C2411yescharacteristic
503C4×Dic79C2413yes—
504C4×Dic79C2416yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2416yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C2413yes—
513C4×Dic79C24112yes—
514C4×Dic79C2416yes—
515C4×Dic79C2416yes—
516C4×Dic79C2416yes—
517C2×Q8×C79—24no—
518C2×Q8×C79—28no—
519C2×Q8×C79C2413yes—
520C2×Q8×C79C2416yes—
521C2×Q8×C79C2413yes—
522C2×Q8×C79C2411yescharacteristic
523C2×D4×C79C2411yescharacteristic
524C2×D4×C79C2412yes—
525C22×C4×C79C2416yes—
526C22×C4×C79C2411yescharacteristic
527C22×C4×C79C2413yes—
528C22×C4×C79C2413yes—
529C4⋊C4×C79C2413yes—
530C4⋊C4×C79C2413yes—
531C4⋊C4×C79C2416yes—
532C4⋊C4×C79C2416yes—
533C4⋊C4×C79C2416yes—
534C4⋊C4×C79C2416yes—
535C4⋊C4×C79C2416yes—
536C4⋊C4×C79C2416yes—
537C4⋊C4×C79C2413yes—
538C4⋊C4×C79C2416yes—
539C4⋊C4×C79C2411yescharacteristic
540C4⋊C4×C79C24112yes—
541C4⋊C4×C79C2416yes—
542C22⋊C4×C79C2412yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2416yes—
545C22⋊C4×C79C2416yes—
546C22⋊C4×C79C2416yes—
547C42×C79C2413yes—
548C42×C79C2413yes—
549C42×C79C2413yes—
550C42×C79C2413yes—
551C42×C79C24112yes—
552C42×C79C2416yes—
553C23×C79C2512yes—
554C23×C79C2511yescharacteristic
555C22×D79—26no—
556C22×D79—26no—
557C22×D79—43no—
558C22×D79C2513yes—
559C22×D79C2512yes—
560C22×D79C2513yes—
561Q8×C79—212no—
562Q8×C79—26no—
563Q8×C79—26no—
564Q8×C79C2×#4114yes—
565D4×C79—24no—
566D4×C79—22no—
567C2×C4×C79—26no—
568C2×C4×C79—26no—
569C2×C4×C79—212no—
570C2×C4×C79—22no—
571C2×C4×C79C2513yes—
572C2×C4×C79C2512yes—
573C2×C4×C79C2513yes—
574C2×C4×C79C2516yes—
575C2×C4×C79C2513yes—
576C2×C4×C79C2511yescharacteristic
577C2×C4×C79C2516yes—
578C2×C4×C79C2513yes—
579C2×C4×C79C2511yescharacteristic
580C22⋊D79—24no—
581C22⋊D79—212no—
582C22⋊D79—24no—
583C22⋊D79—24no—
584C22⋊D79—46no—
585C2×Dic79—22no—
586C2×Dic79—24no—
587C2×Dic79—43no—
588C2×Dic79—46no—
589C2×Dic792−1+414yescomplemented
590C2×Dic79C2513yes—
591C2×Dic79C2511yescharacteristic
592C2×Dic79C2512yes—
593C2×Dic79C2513yes—
594C2×Dic79C2516yes—
595C2×Dic79C2516yes—
596C2×Dic79C2511yescharacteristic
597C2×Dic79C2511yescharacteristic
598C2×Dic79C2511yescharacteristic
599D316—212no—
600D316—212no—
601D316—26no—
602D316—22no—
603D316—46no—
604D316C2×#41112yes—
605C4×D79—26no—
606C4×D79—224no—
607C4×D79—26no—
608C4×D79—212no—
609C4×D79—26no—
610C4×D79—26no—
611C4×D79—26no—
612C4×D79—26no—
613C4×D79—26no—
614C4×D79—26no—
615C4×D79—26no—
616C4×D79—24no—
617C4×D79—43no—
618C4×D79—43no—
619C4×D79—412no—
620C4×D79—46no—
621C4×D79C2×#41112yes—
622Dic158—212no—
623Dic158—26no—
624Dic158—212no—
625Dic158—24no—
626Dic158—412no—
627C22×C79—21no—
628C22×C79—21no—
629C22×C79—22no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79C2×2−1+412yes—
633C22×C79C2611yescharacteristic
634C2×D79—23no—
635C2×D79—23no—
636C2×D79—22no—
637C2×D79—23no—
638C2×D79—22no—
639C2×D79—23no—
640C2×D79—23no—
641C2×D79—22no—
642C2×D79—412no—
643C2×D79C22×#4116yes—
644C4×C79—26no—
645C4×C79—23no—
646C4×C79—23no—
647C4×C79—23no—
648C4×C79—22no—
649C4×C79—21no—
650C4×C79—26no—
651C4×C79C22×#4116yes—
652C4×C79#58512yes—
653Dic79—26no—
654Dic79—21no—
655Dic79—22no—
656Dic79—26no—
657Dic79—23no—
658Dic79—23no—
659Dic79C22×#4112yes—
660Dic79C2×2−1+412yes—
661Dic79C2×2−1+412yes—
662#62805—791nomaximal, Sylow
663C2×C79—22no—
664C2×C79—42no—
665C2×C79C23×#4111yescharacteristic
666C2×C79C22×2−1+411yescharacteristic
667C2×C79C2×#58511yescharacteristic
668D79—26no—
669D79—42no—
670D79—43no—
671#3523—791no—
672#3523D7911yescharacteristic, complemented
673#3520—793no—
674#3520—793no—
675#3518—792no—
676#3515—796no—
677#3511—793no—
678#3509—793no—
679#3503—791no—
680#3499—791no—
681#3495—796no—
682#3489—792no—
683#3482—791no—
684#3482—793no—
685#3482—793no—
686#3482—791no—
687Q8×#41—792no—
688#3475—796no—
689#3461—796no—
690#3444—793no—
691C2×#533—793no—
692C4×2−1+4—792no—
693C2×C4×#41—791no—
694C79#6280511yescharacteristic, complemented, Sylow
695C2×2−1+4—792no—
696C22×#41—791no—
697Q82—792no—
698#557—796no—
699#557—793no—
700#557—791no—
701#557C2×D7911yescharacteristic, complemented
702#557C2×D7913yescomplemented
703#556—793no—
704#556—796no—
705#556—796no—
706#556—793no—
707#556—793no—
708#556—796no—
709#556C2×D7913yescomplemented
710#555—796no—
711#554—796no—
712#554—796no—
713#554—796no—
714#554—796no—
715#553—7912no—
716#552—7912no—
717#552—7912no—
718#552—796no—
719#552—7912no—
720#552—796no—
721#552—796no—
722#552—796no—
723#552—796no—
724#552C2×D7916yes—
725#551—7912no—
726#551—7912no—
727D4×Q8—792no—
728D4×Q8—792no—
729D4×Q8—793no—
730D4×Q8—791no—
731D4×Q8—793no—
732D4×Q8C2×D7912yes—
733D4×Q8C2×D7911yescharacteristic, complemented
734#548—792no—
735#548—796no—
736#548—792no—
737#548—796no—
738#547—796no—
739#547—793no—
740#547—793no—
741#547—796no—
742#547—796no—
743#547—793no—
744#547—793no—
745#546—796no—
746#546—796no—
747#544—796no—
748#542—7912no—
749#542—796no—
750#542—796no—
751#541—7912no—
752#541—796no—
753#541C2×D7916yescomplemented
754#539—7912no—
755#539—7912no—
756#537—796no—
757#536—796no—
758#536—796no—
759#533—793no—
760#533—793no—
761#533—796no—
762#533—796no—
763#533—793no—
764#533—793no—
765#533—796no—
766#533—796no—
767#533—796no—
768#533—796no—
769#533—793no—
770#533—796no—
771#533—793no—
772#533C2×D7913yes—
773#532—793no—
774#532—791no—
775#532—793no—
776C2×C4⋊Q8—793no—
777C2×C4⋊Q8—793no—
778#529—796no—
779#529—796no—
780#529—7912no—
781#529—793no—
782#529—7912no—
783#529—796no—
784#529—793no—
785#529—796no—
786#529—796no—
787#529—796no—
788#529—793no—
789#529C2×D7913yes—
790C2×#125—796no—
791#525—796no—
792#525—793no—
793#525—793no—
794#525—796no—
795C2×C22⋊Q8—796no—
796C2×C22⋊Q8—796no—
797#520—792no—
798#520—796no—
799#520—796no—
800#520—796no—
801#519—796no—
802#519—792no—
803#519C2×D7912yescomplemented
804C4×#41—791no—
805C4×#41—793no—
806C4×#41—793no—
807C4×#41—791no—
808C4×#41—791no—
809C4×#41—793no—
810C4×#41—793no—
811C4×#41—791no—
812C4×#41—796no—
813C4×#41—793no—
814C4×#41—796no—
815C4×#41—793no—
816C4×#41—796no—
817C4×#41—796no—
818C2×C4×Q8—791no—
819C2×C4×Q8—792no—
820C2×C4×Q8—796no—
821C2×C4×Q8—792no—
822C2×C4×Q8—796no—
823C2×C4×Q8C2×D7911yescharacteristic
824C2×C4×D4—793no—
825C2×C4×D4—793no—
826C2×#117—796no—
827C2×#117—793no—
828C22×C42—793no—
8292−1+4—15816no—
830C2×#41—793no—
831C2×#41—791no—
832C2×#41—793no—
833C2×#41—793no—
834C2×#41—791no—
835C2×#41—796no—
836C2×#41—793no—
837C2×#41—792no—
838C2×#41—796no—
839C2×#41—796no—
840C2×#41—1588no—
841C22×Q8—796no—
842C22×Q8—796no—
843C22×Q8—792no—
844C22×Q8C22×D7911yescharacteristic
845C22×Q8C22×D7912yes—
846C22×D4—793no—
847C23×C4—793no—
848C23×C4—793no—
849C23×C4—793no—
850C4⋊Q8—793no—
851C4⋊Q8—796no—
852C4⋊Q8—796no—
853C4⋊Q8—793no—
854C4⋊Q8—796no—
855C4⋊Q8—796no—
856C4⋊Q8—796no—
857C4⋊Q8—791no—
858C4⋊Q8—796no—
859C4⋊Q8—793no—
860C4⋊Q8—793no—
861C4⋊Q8—796no—
862C4⋊Q8C22×D7913yes—
863C4⋊Q8C22×D7913yes—
864C4⋊Q8C22×D7916yes—
865#127—791no—
866#126—796no—
867#126—7912no—
868#126—7912no—
869#126—7912no—
870#126—7912no—
871#126—796no—
872#126—796no—
873#126—7912no—
874#126C22×D7916yes—
875#126C22×D79112yes—
876#125—796no—
877#125—796no—
878#125—796no—
879#125—7912no—
880#125—796no—
881#125—7912no—
882#125—796no—
883#125—7912no—
884#125—7912no—
885#125—796no—
886#125—793no—
887#125C22×D7916yes—
888#125C22×D7913yes—
889#125C22×D79112yes—
890#125C22×D7916yes—
891#124—796no—
892#124—792no—
893#124—796no—
894#124—7912no—
895#124—793no—
896#124—796no—
897#124—7912no—
898#124C22×D7913yes—
899#123—796no—
900#123—796no—
901#123—796no—
902#123—7912no—
903#123—7912no—
904#123—7912no—
905#123—7912no—
906#123—796no—
907#123—796no—
908#123—7912no—
909#123—7912no—
910#123C22×D7916yes—
911C22⋊Q8—796no—
912C22⋊Q8—796no—
913C22⋊Q8—793no—
914C22⋊Q8—796no—
915C22⋊Q8—796no—
916C22⋊Q8—793no—
917C22⋊Q8—796no—
918C22⋊Q8—796no—
919C22⋊Q8—7912no—
920C22⋊Q8—7912no—
921C22⋊Q8—796no—
922C22⋊Q8—796no—
923C22⋊Q8—796no—
924C22⋊Q8—793no—
925C22⋊Q8—796no—
926C22⋊Q8—796no—
927C22⋊Q8—796no—
928C22⋊Q8—7912no—
929C22⋊Q8—7912no—
930C22⋊Q8—7912no—
931C22⋊Q8—796no—
932C22⋊Q8—7912no—
933C22⋊Q8—7912no—
934C22⋊Q8C22×D7913yes—
935C22⋊Q8C22×D7916yes—
936C22⋊Q8C22×D7916yes—
937C22⋊Q8C22×D7916yes—
938#121—792no—
939#121—793no—
940#121—791no—
941#121—796no—
942#121—793no—
943#121—7912no—
944#121—796no—
945#121—796no—
946#121—796no—
947#121—796no—
948#121—7912no—
949#121C22×D7911yescharacteristic
950#120—796no—
951#120—796no—
952C4×Q8—791no—
953C4×Q8—796no—
954C4×Q8—793no—
955C4×Q8—793no—
956C4×Q8—791no—
957C4×Q8—793no—
958C4×Q8—792no—
959C4×Q8—796no—
960C4×Q8—796no—
961C4×Q8—793no—
962C4×Q8—796no—
963C4×Q8—7912no—
964C4×Q8—796no—
965C4×Q8—796no—
966C4×Q8—796no—
967C4×Q8—7912no—
968C4×Q8—796no—
969C4×Q8—796no—
970C4×Q8—796no—
971C4×Q8—7912no—
972C4×Q8—793no—
973C4×Q8—796no—
974C4×Q8C22×D7916yes—
975C4×Q8C22×D7912yes—
976C4×Q8C22×D7916yes—
977C4×Q8C22×D7911yescharacteristic
978C4×Q8C22×D7913yes—
979C4×Q8C22×D7911yescharacteristic
980C4×Q8C22×D7913yes—
981C4×Q8C22×D7916yes—
982C4×Q8C22×D7913yes—
983C4×D4—791no—
984C4×D4—796no—
985C4×D4—796no—
986C4×D4—796no—
987C4×D4—796no—
988C4×D4—793no—
989C4×D4—793no—
990C4×D4—796no—
991C4×D4—793no—
992C4×D4—796no—
993C4×D4—793no—
994C4×D4—796no—
995C4×D4—791no—
996C4×D4—796no—
997C4×D4—796no—
998C4×D4—796no—
999C4×D4—796no—
1000C4×D4—792no—
1001C4×D4—796no—
1002C4×D4—796no—
1003C4×D4—7912no—
1004C4×D4—796no—
1005C4×D4—796no—
1006C4×D4—796no—
1007C4×D4—793no—
1008C4×D4—796no—
1009C4×D4—793no—
1010C4×D4—793no—
1011C4×D4—793no—
1012C4×D4—796no—
1013C4×D4—796no—
1014C4×D4—7912no—
1015C4×D4—796no—
1016C4×D4—793no—
1017C4×D4C22×D7916yes—
1018C4×D4C22×D7913yes—
1019#117—796no—
1020#117—793no—
1021#117—793no—
1022#117—796no—
1023#117—793no—
1024#117—796no—
1025#117—793no—
1026#117—796no—
1027#117—796no—
1028#117—7912no—
1029#117—796no—
1030#117—793no—
1031#117—793no—
1032#117—796no—
1033#117—796no—
1034#117—796no—
1035#117—796no—
1036#117—796no—
1037#117—7912no—
1038#117—796no—
1039#117—796no—
1040#117—7912no—
1041#117C22×D7916yes—
1042#117C22×D7916yes—
1043#117C22×D7916yes—
1044C2×C4⋊C4—793no—
1045C2×C4⋊C4—796no—
1046C2×C4⋊C4—796no—
1047C2×C4⋊C4—796no—
1048C2×C4⋊C4—7912no—
1049C2×C4⋊C4—796no—
1050C2×C4⋊C4—796no—
1051C2×C4⋊C4—7912no—
1052C2×C4⋊C4—796no—
1053C2×C4⋊C4C22×D7913yes—
1054C2×C22⋊C4—796no—
1055C2×C22⋊C4—7912no—
1056C2×C42—793no—
1057C2×C42—793no—
1058C2×C42—796no—
1059C2×C42—791no—
1060C2×C42—7912no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—796no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—793no—
1067C2×C42—793no—
1068C2×C42—793no—
1069C2×C42—793no—
1070C2×C42C22×D7913yes—
1071C24—793no—
1072#41—3166no—
1073#41—3166no—
1074#41—798no—
1075#41—15824no—
1076#41—15824no—
1077#41—1588no—
1078#41—15812no—
1079#41—15812no—
1080#41—15824no—
1081#41—1584no—
1082C2×Q8—24no—
1083C2×Q8—28no—
1084C2×Q8—31612no—
1085C2×Q8—7912no—
1086C2×Q8—792no—
1087C2×Q8—796no—
1088C2×Q8—793no—
1089C2×Q8—796no—
1090C2×Q8—15824no—
1091C2×Q8—1588no—
1092C2×Q8C23×D7916yes—
1093C2×Q8C23×D7913yes—
1094C2×Q8C23×D7913yes—
1095C2×Q8C23×D7911yescharacteristic
1096C2×D4—796no—
1097C2×D4—792no—
1098C2×D4—792no—
1099C2×D4—796no—
1100C2×D4—792no—
1101C2×D4—796no—
1102C2×D4—793no—
1103C2×D4—796no—
1104C2×D4—796no—
1105C2×D4—793no—
1106C2×D4—791no—
1107C2×D4—15812no—
1108C2×D4C23×D7912yes—
1109C2×D4C23×D7911yescharacteristic
1110C22×C4—3166no—
1111C22×C4—793no—
1112C22×C4—796no—
1113C22×C4—793no—
1114C22×C4—793no—
1115C22×C4—7912no—
1116C22×C4—796no—
1117C22×C4—791no—
1118C22×C4—793no—
1119C22×C4—791no—
1120C22×C4—792no—
1121C22×C4—793no—
1122C22×C4—792no—
1123C22×C4—793no—
1124C22×C4—793no—
1125C22×C4—793no—
1126C22×C4—793no—
1127C22×C4—793no—
1128C22×C4—793no—
1129C22×C4—793no—
1130C22×C4—793no—
1131C22×C4—7912no—
1132C22×C4—796no—
1133C22×C4—15812no—
1134C22×C4—15812no—
1135C22×C4C23×D7911yescharacteristic
1136C22×C4C23×D7913yes—
1137C22×C4C23×D7913yes—
1138C22×C4C23×D7916yes—
1139C4⋊C4—796no—
1140C4⋊C4—796no—
1141C4⋊C4—796no—
1142C4⋊C4—796no—
1143C4⋊C4—7912no—
1144C4⋊C4—796no—
1145C4⋊C4—7912no—
1146C4⋊C4—7912no—
1147C4⋊C4—792no—
1148C4⋊C4—796no—
1149C4⋊C4—796no—
1150C4⋊C4—796no—
1151C4⋊C4—796no—
1152C4⋊C4—793no—
1153C4⋊C4—793no—
1154C4⋊C4—796no—
1155C4⋊C4—7912no—
1156C4⋊C4—796no—
1157C4⋊C4—796no—
1158C4⋊C4—793no—
1159C4⋊C4—796no—
1160C4⋊C4—796no—
1161C4⋊C4—791no—
1162C4⋊C4—796no—
1163C4⋊C4C23×D7913yes—
1164C4⋊C4C23×D7916yes—
1165C4⋊C4C23×D7916yes—
1166C4⋊C4C23×D7916yes—
1167C4⋊C4C23×D7916yes—
1168C4⋊C4C23×D79112yes—
1169C4⋊C4C23×D7913yes—
1170C4⋊C4C23×D7913yes—
1171C4⋊C4C23×D7916yes—
1172C4⋊C4C23×D7911yescharacteristic
1173C4⋊C4C23×D7916yes—
1174C4⋊C4C23×D7916yes—
1175C4⋊C4C23×D7916yes—
1176C22⋊C4—796no—
1177C22⋊C4—792no—
1178C22⋊C4—796no—
1179C22⋊C4—796no—
1180C22⋊C4—796no—
1181C22⋊C4—796no—
1182C22⋊C4—796no—
1183C22⋊C4—7912no—
1184C22⋊C4—7912no—
1185C22⋊C4—796no—
1186C22⋊C4—796no—
1187C22⋊C4—792no—
1188C22⋊C4—792no—
1189C22⋊C4—796no—
1190C22⋊C4—796no—
1191C22⋊C4—796no—
1192C22⋊C4—796no—
1193C22⋊C4—796no—
1194C22⋊C4—796no—
1195C22⋊C4C23×D7916yes—
1196C22⋊C4C23×D7916yes—
1197C22⋊C4C23×D7916yes—
1198C22⋊C4C23×D7916yes—
1199C22⋊C4C23×D7912yes—
1200C42—791no—
1201C42—791no—
1202C42—793no—
1203C42—791no—
1204C42—791no—
1205C42—793no—
1206C42—793no—
1207C42—796no—
1208C42—796no—
1209C42—793no—
1210C42—793no—
1211C42—793no—
1212C42—793no—
1213C42—793no—
1214C42—796no—
1215C42—796no—
1216C42—7912no—
1217C42—796no—
1218C42C23×D7913yes—
1219C42C23×D7913yes—
1220C42C23×D7913yes—
1221C42C23×D7913yes—
1222C42C23×D79112yes—
1223C42C23×D7916yes—
1224C23—3163no—
1225C23—793no—
1226C23—793no—
1227C23—792no—
1228C23—1586no—
1229C23—1586no—
1230C23C24×D7912yes—
1231C23C24×D7911yescharacteristic
1232Q8—26no—
1233Q8—212no—
1234Q8—26no—
1235Q8—31612no—
1236Q8—15812no—
1237Q8—1584no—
1238Q8—1586no—
1239Q8—15812no—
1240Q8#41×D7914yes—
1241D4—24no—
1242D4—22no—
1243D4—3166no—
1244D4—3166no—
1245D4—7912no—
1246D4—15812no—
1247D4—15812no—
1248D4—1584no—
1249D4—1584no—
1250D4—15812no—
1251D4—1584no—
1252D4—1582no—
1253D4—1586no—
1254C2×C4—26no—
1255C2×C4—22no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—3163no—
1259C2×C4—3163no—
1260C2×C4—31612no—
1261C2×C4—3166no—
1262C2×C4—3163no—
1263C2×C4—3166no—
1264C2×C4—794no—
1265C2×C4—791no—
1266C2×C4—791no—
1267C2×C4—791no—
1268C2×C4—7912no—
1269C2×C4—791no—
1270C2×C4—793no—
1271C2×C4—792no—
1272C2×C4—793no—
1273C2×C4—796no—
1274C2×C4—796no—
1275C2×C4—1586no—
1276C2×C4—1586no—
1277C2×C4—1586no—
1278C2×C4—1586no—
1279C2×C4—1586no—
1280C2×C4—1584no—
1281C2×C4—1586no—
1282C2×C4—15824no—
1283C2×C4—1582no—
1284C2×C4—1584no—
1285C2×C4—1586no—
1286C2×C4—1586no—
1287C2×C4—1586no—
1288C2×C4—15812no—
1289C2×C4C24×D7913yes—
1290C2×C4C24×D7912yes—
1291C2×C4C24×D7911yescharacteristic
1292C2×C4C24×D7913yes—
1293C2×C4C24×D7916yes—
1294C2×C4C24×D7913yes—
1295C2×C4C24×D7916yes—
1296C2×C4C24×D7911yescharacteristic
1297C2×C4C24×D7913yes—
1298C22—21no—
1299C22—21no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—31612no—
1304C22—796no—
1305C22—1582no—
1306C22—1583no—
1307C22—1583no—
1308C22—1582no—
1309C22—1582no—
1310C22—1583no—
1311C22—1583no—
1312C22—1583no—
1313C222−1+4×D7912yes—
1314C22C25×D7911yescharacteristic
1315C4—23no—
1316C4—26no—
1317C4—23no—
1318C4—23no—
1319C4—22no—
1320C4—21no—
1321C4—26no—
1322C4—792no—
1323C4—792no—
1324C4—792no—
1325C4—1581no—
1326C4—1586no—
1327C4—1582no—
1328C4—1583no—
1329C4—1586no—
1330C4—1583no—
1331C4C2×#41×D7916yes—
1332C4#1909940012yes—
1333C2—22no—
1334C2—42no—
1335C2—3163no—
1336C2—3162no—
1337C2—1586no—
1338C2C22×#41×D7911yescharacteristic
1339C2C2×2−1+4×D7911yescharacteristic
1340C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3523C2
hypercenter#3523D79
hypocenterC79#62805
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #23777496C2semidirect
2. #23777451C2semidirect
3. #23777444C2semidirect
4. #23777411C2semidirect
5. #23777376C2semidirect
6. #23777304C2semidirect
7. #23777283C2semidirect
8. #23777217C2semidirect
9. #23777184C2semidirect
10. #23777141C2semidirect
11. #23777077C2semidirect
12. #23777021C2semidirect
13. #23777020C2semidirect
14. #23777020C2semidirect
15. #23777019C2semidirect
16. Q8×#11929623C2semidirect
17. #23776965C2semidirect
18. #23776832C2semidirect
19. #23776694C2semidirect
20. #533×D79C2semidirect
21. #23776609C2semidirect
22. C2×C4×#11929625C2semidirect
23. C79×#3523C2semidirect
26. Q8×Dic158C22semidirect
27. #19099292C22semidirect
28. #19099291C22semidirect
29. #19099288C22semidirect
30. #19099287C22semidirect
31. #19099286C22semidirect
32. #19099286C22semidirect
33. #19099286C22semidirect
34. #19099285C22semidirect
35. #19099281C22semidirect
36. #19099276C22semidirect
38. #19099271C22semidirect
40. #19099269C22semidirect
41. #19099264C22semidirect
42. #19099255C22semidirect
43. #19099254C22semidirect
44. #19099251C22semidirect
45. #19099251C22semidirect
46. #19099251C22semidirect
47. #19099249C22semidirect
49. #19099245C22semidirect
52. Q8×D316C22semidirect
53. Q8×D316C22semidirect
54. #19099228C22semidirect
56. Q8×C22⋊D79C22semidirect
58. #19099225C22semidirect
60. #19099221C22semidirect
61. #19099218C22semidirect
62. #19099217C22semidirect
64. #19099216C22semidirect
65. #19099216C22semidirect
67. #19099215C22semidirect
70. #19099193C22semidirect
71. #19099185C22semidirect
72. #19099184C22semidirect
73. #19099179C22semidirect
74. #19099172C22semidirect
75. #19099171C22semidirect
76. #19099161C22semidirect
77. #19099154C22semidirect
80. #19099136C22semidirect
82. #19099119C22semidirect
83. #19099119C22semidirect
84. #19099118C22semidirect
85. #19099118C22semidirect
86. #19099118C22semidirect
87. #19099117C22semidirect
88. #19099117C22semidirect
89. #19099117C22semidirect
93. #19099115C22semidirect
94. #19099112C22semidirect
95. #19099110C22semidirect
97. C4⋊Q8×D79C22semidirect
98. C4⋊Q8×D79C22semidirect
99. #19099099C22semidirect
100. #19099098C22semidirect
101. #19099098C22semidirect
102. #19099098C22semidirect
104. #19099096C22semidirect
105. #19099096C22semidirect
106. #19099096C22semidirect
107. #19099092C22semidirect
108. #19099091C22semidirect
110. #125×D79C22semidirect
118. #19099045C22semidirect
119. #19099043C22semidirect
120. #19099043C22semidirect
121. #19099039C22semidirect
122. #19099039C22semidirect
131. C4×#11929625C22semidirect
132. C4×#11929625C22semidirect
133. #19099031C22semidirect
134. #19099031C22semidirect
136. C4×#11929623C22semidirect
138. C2×Q8×Dic79C22semidirect
139. C4×Q8×D79C22semidirect
140. C4×Q8×D79C22semidirect
141. C4×Q8×D79C22semidirect
147. #557×C79C22semidirect
148. #557×C79C22semidirect
149. #556×C79C22semidirect
152. D4×Q8×C79C22semidirect
153. #541×C79C22semidirect
156. #519×C79C22semidirect
406. #11929625#41semidirect
589. C2×Dic792−1+4semidirect
672. #3523D79semidirect
694. C79#62805semidirect
701. #557C2×D79semidirect
702. #557C2×D79semidirect
709. #556C2×D79semidirect
733. D4×Q8C2×D79semidirect
753. #541C2×D79semidirect
803. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237774962
#237774512
#237774442
#237774112
#237773762
#237773042
#237772832
#237772172
#237771842
#237771412
#237770772
#237770212
#237770202
#237770192
Q8×#119296232
#237769652
#237768322
#237766942
#533×D792
#237766092
C2×C4×#119296252
C79×#35232
#6280579