Finite Group Databasebeta

← #35201985

Subgroups — #35201985

Order 20224.

7352 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777917C216yesmaximal, complemented
2#23777816C216yesmaximal, complemented
3#23777803C213yesmaximal, complemented
4#23777726C216yesmaximal, complemented
5#23777724C216yesmaximal, complemented
6#23777708C216yesmaximal, complemented
7#23777706C216yesmaximal, complemented
8#23777639C213yesmaximal, complemented
9#23777633C213yesmaximal, complemented
10#23777538C213yesmaximal, complemented
11#23777511C212yesmaximal, complemented
12#23777502C212yesmaximal, complemented
13#23777397C212yesmaximal, complemented
14#23777194C211yesmaximal, characteristic, complemented
15#23777177C212yesmaximal, complemented
16#23777069C212yesmaximal, complemented
17#23777066C212yesmaximal, complemented
18#23777055C211yesmaximal, characteristic, complemented
19C79×#3487C211yesmaximal, characteristic, complemented
20C2×#14579207C2212yescomplemented
21C2×#14579207C2211yescharacteristic, complemented
22C22×#11929625C2211yescharacteristic, complemented
23#19099316C2211yescharacteristic, complemented
24#19099314C2216yescomplemented
25#19099310C2216yescomplemented
26#19099309C2216yescomplemented
27#19099308C2216yescomplemented
28#19099306C2213yescomplemented
29#19099305C2216yescomplemented
30#19099303C2213yescomplemented
31#19099303C2216yescomplemented
32#19099302C2213yescomplemented
33#19099302C2216yescomplemented
34#19099301C2216yescomplemented
35#19099301C22112yescomplemented
36#19099300C2216yescomplemented
37#19099298C2216yescomplemented
38#19099295C2216yescomplemented
39#19099289C2212yescomplemented
40#19099277C2216yescomplemented
41#19099276C2216yescomplemented
42#19099275C2216yescomplemented
43#19099260C2216yescomplemented
44#19099259C2216yescomplemented
45#19099259C2216yescomplemented
46#19099257C2216yescomplemented
47#19099255C2216yescomplemented
48#19099254C2216yescomplemented
49#19099242C22112yescomplemented
50#19099235C2212yescomplemented
51#19099233C2216yescomplemented
52#19099232C2212yescomplemented
53#19099232C2216yescomplemented
54#19099232C2212yescomplemented
55#19099232C2212yescomplemented
56#19099224C2216yescomplemented
57#19099224C2212yescomplemented
58#19099224C2212yescomplemented
59#19099224C2212yescomplemented
60#19099213C2216yescomplemented
61#19099208C22112yescomplemented
62#19099206C2216yescomplemented
63#19099204C2216yescomplemented
64#19099202C22112yescomplemented
65#19099201C2216yescomplemented
66#19099201C2216yescomplemented
67#19099201C2216yescomplemented
68#19099201C2216yescomplemented
69D4×D316C2216yescomplemented
70D4×D316C2216yescomplemented
71#19099198C2216yescomplemented
72#19099198C2216yescomplemented
73#19099197C2216yescomplemented
74#19099197C2216yescomplemented
75#19099197C2216yescomplemented
76D4×C22⋊D79C2216yescomplemented
77D4×C22⋊D79C2216yescomplemented
78#19099195C2216yescomplemented
79#19099195C2216yescomplemented
80#19099186C2216yescomplemented
81#19099185C2216yescomplemented
82#19099168C2216yescomplemented
83#19099167C2216yescomplemented
84#19099166C2216yescomplemented
85#19099166C2216yescomplemented
86#19099164C22112yescomplemented
87#19099163C22112yescomplemented
88#19099153C22112yescomplemented
89#19099147C22112yescomplemented
90#19099146C22112yescomplemented
91#19099143C2216yescomplemented
92#19099141C2216yescomplemented
93#19099137C2213yescomplemented
94#19099131C2216yescomplemented
95#19099129C2216yescomplemented
96#19099129C2216yescomplemented
97#19099128C22112yescomplemented
98#19099127C2213yescomplemented
99#19099127C2213yescomplemented
100#19099127C2216yescomplemented
101#19099127C2213yescomplemented
102#19099126C22112yescomplemented
103#19099123C22112yescomplemented
104#19099121C22112yescomplemented
105#19099121C22112yescomplemented
106#19099110C2216yescomplemented
107#19099109C2213yescomplemented
108#19099108C2216yescomplemented
109#127×D79C2216yescomplemented
110#19099100C2216yescomplemented
111#19099095C2216yescomplemented
112#19099093C2216yescomplemented
113#19099092C2216yescomplemented
114#19099091C2216yescomplemented
115C2×#14579150C2213yescomplemented
116#19099074C2216yescomplemented
117#19099072C2216yescomplemented
118#19099070C2213yescomplemented
119#19099070C2213yescomplemented
120C2×#14579135C2216yescomplemented
121#121×D79C2216yescomplemented
122#19099046C2212yescomplemented
123#19099045C2212yescomplemented
124#19099041C2211yescharacteristic, complemented
125#41×Dic79C2211yescharacteristic, complemented
126C4×#11929625C2212yescomplemented
127C2×2−1+4×C79C2211yescharacteristic, complemented
128C22×#41×C79C2211yescharacteristic, complemented
129#550×C79C2212yescomplemented
130#550×C79C2216yescomplemented
131#548×C79C2216yescomplemented
132#548×C79C2212yescomplemented
133#535×C79C2213yescomplemented
134#535×C79C2213yescomplemented
135#525×C79C2213yescomplemented
136#525×C79C2213yescomplemented
137#519×C79C2211yescharacteristic, complemented
138#14579207—48no—
139#14579207—44no—
140C2×#11929625—44no—
141C2×#11929625C2312yes—
142C2×#11929625C2312yes—
143C2×#11929625C2316yes—
144C2×#11929624C2313yes—
145C2×#11929624C2316yes—
146C2×#11929623C23112yes—
147C22×D316C2313yes—
148C22×D316C2316yes—
149C22×D316C2313yes—
150C22×C22⋊D79C23112yes—
151C2×D4×D79C2316yes—
152C2×D4×D79C2316yes—
153C2×D4×D79C2316yes—
154C2×D4×D79C23112yes—
155C2×D4×D79C23112yes—
156C2×D4×D79C23112yes—
157C22×C4×D79C2313yes—
158#14579160C2316yes—
159#14579160C2312yes—
160#14579159C2313yes—
161#14579158C2316yes—
162#14579157C23112yes—
163#14579157C2316yes—
164#14579157C2316yes—
165#14579157C2313yes—
166#14579157C2316yes—
167#14579157C2316yes—
168#14579157C2316yes—
169#14579156C23112yes—
170#14579156C2316yes—
171#14579156C2316yes—
172#14579155C23112yes—
173#14579154C2316yes—
174#14579154C2312yes—
175#14579154C2316yes—
176#14579154C2312yes—
177#14579153C2316yes—
178#14579152C2316yes—
179#14579152C2316yes—
180#14579151C2316yes—
181#14579151C2312yes—
182#14579150C2316yes—
183#14579150C2316yes—
184#14579150C2316yes—
185#14579150C2316yes—
186#14579150C2316yes—
187#14579150C2313yes—
188#14579149C23112yes—
189#14579148C2316yes—
190#14579148C2311yescharacteristic
191#14579147C23112yes—
192#14579147C2316yes—
193#14579147C2316yes—
194#14579147C2316yes—
195#14579147C2316yes—
196#14579146C2316yes—
197#14579146C23112yes—
198#14579146C23112yes—
199#14579146C2316yes—
200#14579145C23112yes—
201#14579145C2316yes—
202#14579144C23112yes—
203#14579144C2316yes—
204#14579144C2316yes—
205#14579143C23112yes—
206#14579143C2316yes—
207#14579143C23112yes—
208#14579143C2316yes—
209#14579143C2316yes—
210#14579143C2316yes—
211#14579142C23112yes—
212#14579142C2316yes—
213#14579142C2313yes—
214#14579142C2311yescharacteristic
215#14579141C2316yes—
216#14579140C2316yes—
217#14579140C2312yes—
218#14579139C2316yes—
219#14579139C2316yes—
220#14579138C2316yes—
221#14579138C2312yes—
222#14579137C2316yes—
223#14579137C2316yes—
224#14579137C2316yes—
225#14579137C2316yes—
226#14579136C23112yes—
227#14579136C2316yes—
228#14579136C2316yes—
229#14579136C2316yes—
230#14579135C23112yes—
231#14579135C2316yes—
232#14579135C23112yes—
233#14579135C2316yes—
234#14579135C2316yes—
235#14579135C2316yes—
236#14579135C2316yes—
237#14579135C2316yes—
238#14579135C2316yes—
239#14579135C2316yes—
240#14579134C23112yes—
241#14579134C23112yes—
242#14579134C2316yes—
243#14579134C2316yes—
244#14579134C2316yes—
245#14579134C23112yes—
246#14579134C2316yes—
247#14579133C23112yes—
248#14579133C23112yes—
249#14579133C23112yes—
250#14579133C23112yes—
251#14579133C23112yes—
252#14579133C2316yes—
253#14579133C2316yes—
254#14579133C2316yes—
255#14579133C2316yes—
256#14579132C2316yes—
257#14579132C2316yes—
258#14579132C2316yes—
259#14579132C23112yes—
260#14579132C2316yes—
261#14579132C2316yes—
262#14579132C2316yes—
263#14579131C23112yes—
264#14579131C23112yes—
265#14579131C23112yes—
266#14579131C23112yes—
267#14579131C2316yes—
268#14579130C2316yes—
269#14579130C2316yes—
270#14579129C23112yes—
271#14579129C23112yes—
272#14579129C2313yes—
273#14579129C2316yes—
274#14579129C23112yes—
275#14579129C2316yes—
276#14579129C23112yes—
277#14579129C2313yes—
278#14579129C2316yes—
279#14579129C2316yes—
280Q8×Dic79C2316yes—
281Q8×Dic79C2312yes—
282Q8×Dic79C2312yes—
283C4×Dic158C2316yes—
284C4×D316C23112yes—
285C4×D316C2316yes—
286C4×D316C2316yes—
287C4×D316C2316yes—
288D4×Dic79C2316yes—
289D4×Dic79C2316yes—
290D4×Dic79C2316yes—
291#14579123C2316yes—
292#14579123C2316yes—
293C4×C22⋊D79C23112yes—
294C4×C22⋊D79C2316yes—
295C4×C22⋊D79C2316yes—
296C4×C22⋊D79C2316yes—
297C4×C22⋊D79C2316yes—
298C4×C22⋊D79C2316yes—
299C4×C22⋊D79C2316yes—
300(C22⋊D79)⋊C4C23112yes—
301(C22⋊D79)⋊C4C23112yes—
302#14579120C2313yes—
303#14579120C2313yes—
304#14579120C2316yes—
305#14579120C2313yes—
306#14579119C2316yes—
307#14579118C23112yes—
308#14579118C2316yes—
309#14579117C23112yes—
310C2×C4⋊Dic79C2316yes—
311C4⋊C4×D79C2316yes—
312C2×(C2×D79)⋊C4C23112yes—
313C2×(C2×D79)⋊C4C23112yes—
314C22⋊C4×D79C23112yes—
315C2×C4×Dic79C2313yes—
316C42×D79C2316yes—
3172−1+4×C79—44no—
318C2×#41×C79—44no—
319C2×#41×C79C2312yes—
320C2×#41×C79C2311yescharacteristic
321C2×#41×C79C2316yes—
322C2×#41×C79C2313yes—
323C2×#41×C79C2313yes—
324C2×#41×C79C2313yes—
325C22×Q8×C79C2311yescharacteristic
326C22×Q8×C79C2311yescharacteristic
327C22×Q8×C79C2313yes—
328C22×D4×C79C2313yes—
329C23×C4×C79C2313yes—
330#127×C79C2316yes—
331#127×C79C2316yes—
332#124×C79C2316yes—
333#124×C79C2316yes—
334#123×C79C2311yescharacteristic
335#123×C79C2313yes—
336C22⋊Q8×C79C2316yes—
337C22⋊Q8×C79C2316yes—
338#121×C79C23112yes—
339#121×C79C2316yes—
340#121×C79C2316yes—
341#121×C79C2316yes—
342#121×C79C2316yes—
343#120×C79C2313yes—
344#120×C79C2313yes—
345#120×C79C2316yes—
346C4×Q8×C79C2316yes—
347C4×Q8×C79C2312yes—
348C4×D4×C79C23112yes—
349C4×D4×C79C2316yes—
350C4×D4×C79C2316yes—
351#117×C79C2313yes—
352#117×C79C2313yes—
353C23×D79C24112yes—
354C23×D79C2416yes—
355C23×D79C2413yes—
356#11929625—28no—
357#11929625—28no—
358#11929625—412no—
359#11929624—412no—
360#11929624—46no—
361#11929623—812no—
362C2×Dic158C2416yes—
363C2×Dic158C2412yes—
364C2×Dic158C2411yescharacteristic
365C2×D316—46no—
366C2×D316—412no—
367C2×D316—46no—
368C2×D316C2416yes—
369C2×D316C2416yes—
370C2×D316C2413yes—
371C2×D316C2416yes—
372C2×D316C2416yes—
373C2×D316C24112yes—
374C2×D316C2416yes—
375C2×C22⋊D79—812no—
376C2×C22⋊D79C2416yes—
377C2×C22⋊D79C24112yes—
378C2×C22⋊D79C2416yes—
379C2×C22⋊D79C2416yes—
380C2×C22⋊D79C2416yes—
381C2×C22⋊D79C24112yes—
382C2×C22⋊D79C24112yes—
383C2×C22⋊D79C2416yes—
384C2×C22⋊D79C2416yes—
385C2×C22⋊D79C2416yes—
386C2×C22⋊D79C2416yes—
387C2×C22⋊D79C2416yes—
388D4×D79—412no—
389D4×D79—412no—
390D4×D79—412no—
391D4×D79—812no—
392D4×D79—812no—
393D4×D79—812no—
394C22×Dic79C2416yes—
395C22×Dic79C24112yes—
396C22×Dic79C2411yescharacteristic
397C2×C4×D79—46no—
398C2×C4×D79C2416yes—
399C2×C4×D79C2416yes—
400C2×C4×D79C24112yes—
401C2×C4×D79C2416yes—
402C2×C4×D79C2416yes—
403C2×C4×D79C2416yes—
404C4⋊Dic79C2416yes—
405C4⋊Dic79C2416yes—
406C4⋊Dic79C2416yes—
407C4⋊Dic79C2412yes—
408C4⋊Dic79C2416yes—
409C4⋊Dic79C2412yes—
410C4⋊Dic79C2416yes—
411Dic79⋊C4C2416yes—
412Dic79⋊C4C2416yes—
413Dic79⋊C4C24112yes—
414Dic79⋊C4C2412yes—
415Dic79⋊C4C2416yes—
416Dic79⋊C4C2416yes—
417Dic79⋊C4C2416yes—
418Dic79⋊C4C2412yes—
419Dic79⋊C4C2412yes—
420Dic79⋊C4C2412yes—
421Dic79⋊C4C2412yes—
422C22⋊Dic79C2416yes—
423C22⋊Dic79C2416yes—
424C22⋊Dic79C2411yescharacteristic
425C22⋊Dic79C2413yes—
426C22⋊Dic79C2416yes—
427C22⋊Dic79C2416yes—
428C22⋊Dic79C2416yes—
429C22⋊Dic79C2412yes—
430C22⋊Dic79C2416yes—
431C22⋊Dic79C2412yes—
432C22⋊Dic79C2412yes—
433(C2×D79)⋊C4C2416yes—
434(C2×D79)⋊C4C24112yes—
435(C2×D79)⋊C4C2416yes—
436(C2×D79)⋊C4C2416yes—
437(C2×D79)⋊C4C2416yes—
438(C2×D79)⋊C4C2416yes—
439(C2×D79)⋊C4C24112yes—
440(C2×D79)⋊C4C24112yes—
441(C2×D79)⋊C4C2416yes—
442(C2×D79)⋊C4C2416yes—
443(C2×D79)⋊C4C2416yes—
444(C2×D79)⋊C4C24112yes—
445(C2×D79)⋊C4C2416yes—
446(C2×D79)⋊C4C2416yes—
447C4×Dic79C2412yes—
448C4×Dic79C2416yes—
449C4×Dic79C2416yes—
450C4×Dic79C2411yescharacteristic
451C4×Dic79C2416yes—
452C4×Dic79C2413yes—
453C4×Dic79C2416yes—
454C24×C79C2413yes—
455#41×C79—28no—
456#41×C79—24no—
457#41×C79—46no—
458#41×C79—412no—
459#41×C79—46no—
460#41×C79—46no—
461C2×Q8×C79—24no—
462C2×Q8×C79—24no—
463C2×Q8×C79—46no—
464C2×Q8×C79C2413yes—
465C2×Q8×C79C2413yes—
466C2×Q8×C79C2413yes—
467C2×Q8×C79C2411yescharacteristic
468C2×D4×C79—46no—
469C2×D4×C79C2416yes—
470C2×D4×C79C2413yes—
471C2×D4×C79C24112yes—
472C2×D4×C79C2416yes—
473C2×D4×C79C2416yes—
474C2×D4×C79C2411yescharacteristic
475C2×D4×C79C2413yes—
476C2×D4×C79C2416yes—
477C2×D4×C79C2413yes—
478C22×C4×C79—46no—
479C22×C4×C79C2413yes—
480C22×C4×C79C2416yes—
481C22×C4×C79C2413yes—
482C22×C4×C79C2413yes—
483C22×C4×C79C2416yes—
484C22×C4×C79C2416yes—
485C22×C4×C79C2411yescharacteristic
486C4⋊C4×C79C2416yes—
487C4⋊C4×C79C2416yes—
488C4⋊C4×C79C2412yes—
489C4⋊C4×C79C2416yes—
490C22⋊C4×C79C2411yescharacteristic
491C22⋊C4×C79C2413yes—
492C22⋊C4×C79C2412yes—
493C22⋊C4×C79C2416yes—
494C22⋊C4×C79C24112yes—
495C22⋊C4×C79C2416yes—
496C22⋊C4×C79C2416yes—
497C42×C79C2416yes—
498C42×C79C2416yes—
499C23×C79—46no—
500C23×C79—43no—
501C23×C79C2511yescharacteristic
502C23×C79C2516yes—
503C23×C79C2513yes—
504C23×C79C2511yescharacteristic
505C22×D79—43no—
506C22×D79—46no—
507C22×D79—46no—
508C22×D79—412no—
509C22×D79—412no—
510C22×D79—412no—
511C22×D79—412no—
512C22×D79C2516yes—
513C22×D79C2516yes—
514Q8×C79—26no—
515Q8×C79—26no—
516Q8×C79—43no—
517Q8×C79H(5,𝔽2)14yes—
518D4×C79—212no—
519D4×C79—26no—
520D4×C79—46no—
521D4×C79—46no—
522D4×C79—412no—
523D4×C79—46no—
524D4×C79—41no—
525D4×C79—43no—
526D4×C79—43no—
527C2×C4×C79—26no—
528C2×C4×C79—212no—
529C2×C4×C79—26no—
530C2×C4×C79—26no—
531C2×C4×C79—41no—
532C2×C4×C79—46no—
533C2×C4×C79—46no—
534C2×C4×C79C2511yescharacteristic
535C2×C4×C79C2513yes—
536C2×C4×C79C2516yes—
537C2×C4×C79C2512yes—
538C2×C4×C79C2513yes—
539C2×C4×C79C2512yes—
540C2×C4×C79C2513yes—
541C22⋊D79—46no—
542C22⋊D79—46no—
543C22⋊D79—46no—
544C22⋊D79—46no—
545C22⋊D79—46no—
546C22⋊D79—46no—
547C22⋊D79—412no—
548C22⋊D79—412no—
549C22⋊D79—412no—
550C22⋊D79—46no—
551C22⋊D79—46no—
552C22⋊D79—46no—
553C2×Dic79—41no—
554C2×Dic79—412no—
555C2×Dic79—46no—
556C2×Dic79C2512yes—
557C2×Dic79C2516yes—
558C2×Dic79C2512yes—
559C2×Dic79C2512yes—
560C2×Dic79C2516yes—
561C2×Dic79C2512yes—
562D316—212no—
563D316—212no—
564D316—412no—
565D316—46no—
566D316—46no—
567D316—43no—
568D316—46no—
569C4×D79—212no—
570C4×D79—212no—
571C4×D79—46no—
572C4×D79—46no—
573C4×D79—46no—
574C4×D79—412no—
575Dic158—46no—
576Dic158—41no—
577Dic158—42no—
578C22×C79—23no—
579C22×C79—26no—
580C22×C79—21no—
581C22×C79—21no—
582C22×C79—22no—
583C22×C79—26no—
584C22×C79—22no—
585C22×C79—26no—
586C22×C79—26no—
587C22×C79—86no—
588C22×C79C2611yescharacteristic
589C2×D79—26no—
590C2×D79—26no—
591C2×D79—26no—
592C2×D79—26no—
593C2×D79—26no—
594C2×D79—26no—
595C2×D79—86no—
596C2×D79—1612no—
597C2×D79—166no—
598C4×C79—22no—
599C4×C79—21no—
600C4×C79—23no—
601C4×C79—23no—
602C4×C79—26no—
603C4×C79—22no—
604C4×C79C2×H(5,𝔽2)16yes—
605Dic79—22no—
606Dic79—22no—
607Dic79—22no—
608Dic79—26no—
609Dic79—26no—
610Dic79—22no—
611#63066—791nomaximal, Sylow
612C2×C79—41no—
613C2×C79—43no—
614C2×C79—46no—
615C2×C79—41no—
616C2×C79C22×H(5,𝔽2)11yescharacteristic
617C2×C79H(7,𝔽2)12yes—
618D79—46no—
619D79—46no—
620#3558—796no—
621#3551—796no—
622#3549—793no—
623#3543—796no—
624#3543—796no—
625#3542—796no—
626#3542—796no—
627#3537—793no—
628#3537—793no—
629#3529—793no—
630#3524—792no—
631#3524—792no—
632#3517—792no—
633#3500—791no—
634#3498—792no—
635#3488—792no—
636#3488—792no—
637#3487—791no—
638#3487D7911yescharacteristic, complemented
639C79#6306611yescharacteristic, complemented, Sylow
640C2×2−1+4C2×D7911yescharacteristic, complemented
641C2×H(5,𝔽2)—792no—
642C2×H(5,𝔽2)—791no—
643C22×#41—791no—
644C22×#41C2×D7911yescharacteristic, complemented
645#563—791no—
646#563—796no—
647#562—796no—
648#562—796no—
649#562—796no—
650H(3,𝔽4)—796no—
651H(3,𝔽4)—793no—
652#560—796no—
653#560—793no—
654#560—796no—
655#560—796no—
656#560—7912no—
657#560—793no—
658#560—796no—
659#559—796no—
660#559—796no—
661#557—792no—
662#555—796no—
663#555—796no—
664#555—796no—
665#553—796no—
666#553—796no—
667#553—796no—
668#553—796no—
669#552—796no—
670#552—796no—
671#551—7912no—
672#550—792no—
673#550—796no—
674#550—792no—
675#550—792no—
676#550—796no—
677#550—792no—
678#550C2×D7912yescomplemented
679#550C2×D7916yescomplemented
680#548—792no—
681#548—796no—
682#548—792no—
683#548—792no—
684#548C2×D7912yescomplemented
685#548C2×D7916yescomplemented
686#547—796no—
687#546—796no—
688#546—796no—
689#546—796no—
690#546—796no—
691#546—796no—
692#546—796no—
693#546—7912no—
694#546—7912no—
695D42—796no—
696D42—796no—
697D42—796no—
698D42—796no—
699D42—796no—
700D42—796no—
701D42—796no—
702D42—796no—
703D42—796no—
704D42—796no—
705D42—796no—
706#542—796no—
707#542—796no—
708#540—796no—
709#540—7912no—
710#540—796no—
711#540—796no—
712#540—7912no—
713#540—796no—
714#538—7912no—
715#538—7912no—
716#538—7912no—
717#537—796no—
718#537—796no—
719#536—793no—
720#535—793no—
721#535—793no—
722#535—796no—
723#535—793no—
724#535—7912no—
725#535—796no—
726#535—796no—
727#535—796no—
728#535—7912no—
729#535C2×D7913yescomplemented
730#535C2×D7913yescomplemented
731#534—7912no—
732#534—7912no—
733#534—7912no—
734#532—793no—
735#532—796no—
736#532—796no—
737C2×#127—796no—
738#529—796no—
739#529—796no—
740#529—796no—
741#529—796no—
742#529—796no—
743C2×#124—793no—
744#525—793no—
745#525—793no—
746#525—796no—
747#525—796no—
748#525C2×D7913yescomplemented
749#525C2×D7913yescomplemented
750C2×#121—796no—
751C2×#121—796no—
752#520—792no—
753#520—792no—
754#519—791no—
755#519C2×D7911yescharacteristic, complemented
756C4×#41—791no—
757C4×#41—792no—
7582−1+4—44no—
759H(5,𝔽2)—3168no—
760H(5,𝔽2)—3164no—
761C2×#41—44no—
762C2×#41—3164no—
763C2×#41—796no—
764C2×#41—792no—
765C2×#41—792no—
766C2×#41—7912no—
767C2×#41—796no—
768C2×#41—793no—
769C2×#41C22×D7911yescharacteristic
770C2×#41C22×D7912yes—
771C2×#41C22×D7913yes—
772C2×#41C22×D7913yes—
773C2×#41C22×D7913yes—
774C2×#41C22×D7916yes—
775C22×Q8C22×D7911yescharacteristic
776C22×Q8C22×D7911yescharacteristic
777C22×Q8C22×D7913yes—
778C22×D4—796no—
779C22×D4—796no—
780C22×D4—796no—
781C22×D4—7912no—
782C22×D4—7912no—
783C22×D4—7912no—
784C22×D4—7912no—
785C22×D4—796no—
786C22×D4—793no—
787C22×D4—793no—
788C22×D4C22×D7913yes—
789C23×C4—793no—
790C23×C4C22×D7913yes—
791C4⋊Q8—793no—
792C4⋊Q8—792no—
793C4⋊Q8—796no—
794#127—796no—
795#127—7912no—
796#127—796no—
797#127—796no—
798#127—796no—
799#127—793no—
800#127—796no—
801#127—796no—
802#127C22×D7916yes—
803#127C22×D7916yes—
804#126—796no—
805#126—796no—
806#126—7912no—
807#126—792no—
808#126—796no—
809#126—792no—
810#126—796no—
811#126—7912no—
812#125—792no—
813#125—796no—
814#125—796no—
815#125—796no—
816#125—796no—
817#124—793no—
818#124—796no—
819#124—796no—
820#124—796no—
821#124—796no—
822#124—796no—
823#124—796no—
824#124—791no—
825#124—796no—
826#124—796no—
827#124—796no—
828#124—796no—
829#124—7912no—
830#124—7912no—
831#124C22×D7916yes—
832#124C22×D7916yes—
833#123—791no—
834#123—793no—
835#123—796no—
836#123—7912no—
837#123—796no—
838#123—796no—
839#123—7912no—
840#123—796no—
841#123—7912no—
842#123—796no—
843#123—7912no—
844#123—796no—
845#123—7912no—
846#123—796no—
847#123—796no—
848#123—796no—
849#123—796no—
850#123—7912no—
851#123—7912no—
852#123C22×D7911yescharacteristic
853#123C22×D7913yes—
854C22⋊Q8—796no—
855C22⋊Q8—796no—
856C22⋊Q8—796no—
857C22⋊Q8—796no—
858C22⋊Q8—792no—
859C22⋊Q8—796no—
860C22⋊Q8—796no—
861C22⋊Q8—796no—
862C22⋊Q8—796no—
863C22⋊Q8—792no—
864C22⋊Q8—796no—
865C22⋊Q8C22×D7916yes—
866C22⋊Q8C22×D7916yes—
867#121—796no—
868#121—796no—
869#121—796no—
870#121—796no—
871#121—796no—
872#121—796no—
873#121—796no—
874#121—7912no—
875#121—796no—
876#121—796no—
877#121—796no—
878#121—7912no—
879#121—7912no—
880#121—7912no—
881#121—7912no—
882#121—7912no—
883#121—796no—
884#121—7912no—
885#121—796no—
886#121—796no—
887#121—796no—
888#121—796no—
889#121—796no—
890#121—796no—
891#121—796no—
892#121—7912no—
893#121—796no—
894#121—796no—
895#121—796no—
896#121—7912no—
897#121—7912no—
898#121—796no—
899#121—796no—
900#121—796no—
901#121—796no—
902#121—7912no—
903#121—7912no—
904#121C22×D7916yes—
905#121C22×D7916yes—
906#121C22×D7916yes—
907#121C22×D7916yes—
908#121C22×D79112yes—
909#120—796no—
910#120—796no—
911#120—796no—
912#120—793no—
913#120—793no—
914#120—796no—
915#120—796no—
916#120—796no—
917#120—7912no—
918#120—7912no—
919#120—7912no—
920#120—7912no—
921#120—796no—
922#120—7912no—
923#120—7912no—
924#120—7912no—
925#120—7912no—
926#120C22×D7916yes—
927#120C22×D7913yes—
928#120C22×D7913yes—
929C4×Q8—792no—
930C4×Q8—792no—
931C4×Q8—796no—
932C4×Q8—796no—
933C4×Q8C22×D7912yes—
934C4×Q8C22×D7916yes—
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—7912no—
945C4×D4—796no—
946C4×D4—796no—
947C4×D4—7912no—
948C4×D4—7912no—
949C4×D4—796no—
950C4×D4—796no—
951C4×D4—796no—
952C4×D4—7912no—
953C4×D4C22×D7916yes—
954C4×D4C22×D7916yes—
955C4×D4C22×D79112yes—
956#117—793no—
957#117—793no—
958#117—793no—
959#117—796no—
960#117—796no—
961#117—7912no—
962#117—796no—
963#117—7912no—
964#117C22×D7913yes—
965#117C22×D7913yes—
966C2×C4⋊C4—796no—
967C2×C4⋊C4—796no—
968C2×C22⋊C4—7912no—
969C2×C22⋊C4—7912no—
970C2×C22⋊C4—7912no—
971C2×C42—793no—
972C2×C42—796no—
973C24—796no—
974C24—7912no—
975C24—793no—
976C24C23×D7913yes—
977#41—28no—
978#41—24no—
979#41—46no—
980#41—412no—
981#41—46no—
982#41—46no—
983#41—31612no—
984#41—3166no—
985#41—31612no—
986#41—63212no—
987#41—1588no—
988#41—1588no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—46no—
992C2×Q8—796no—
993C2×Q8—792no—
994C2×Q8—791no—
995C2×Q8C23×D7913yes—
996C2×Q8C23×D7913yes—
997C2×Q8C23×D7913yes—
998C2×Q8C23×D7911yescharacteristic
999C2×D4—46no—
1000C2×D4—3166no—
1001C2×D4—31612no—
1002C2×D4—3166no—
1003C2×D4—31612no—
1004C2×D4—31612no—
1005C2×D4—31612no—
1006C2×D4—796no—
1007C2×D4—796no—
1008C2×D4—796no—
1009C2×D4—7912no—
1010C2×D4—7912no—
1011C2×D4—796no—
1012C2×D4—7912no—
1013C2×D4—796no—
1014C2×D4—796no—
1015C2×D4—796no—
1016C2×D4—796no—
1017C2×D4—796no—
1018C2×D4—7912no—
1019C2×D4—796no—
1020C2×D4—796no—
1021C2×D4—793no—
1022C2×D4—796no—
1023C2×D4—796no—
1024C2×D4—796no—
1025C2×D4—63212no—
1026C2×D4—63212no—
1027C2×D4—63212no—
1028C2×D4—63212no—
1029C2×D4C23×D7916yes—
1030C2×D4C23×D7913yes—
1031C2×D4C23×D79112yes—
1032C2×D4C23×D7916yes—
1033C2×D4C23×D7916yes—
1034C2×D4C23×D7913yes—
1035C2×D4C23×D7916yes—
1036C2×D4C23×D7911yescharacteristic
1037C2×D4C23×D7913yes—
1038C22×C4—46no—
1039C22×C4—3166no—
1040C22×C4—796no—
1041C22×C4—7912no—
1042C22×C4—791no—
1043C22×C4—796no—
1044C22×C4—796no—
1045C22×C4—796no—
1046C22×C4—7912no—
1047C22×C4—796no—
1048C22×C4—796no—
1049C22×C4C23×D7913yes—
1050C22×C4C23×D7916yes—
1051C22×C4C23×D7913yes—
1052C22×C4C23×D7913yes—
1053C22×C4C23×D7916yes—
1054C22×C4C23×D7916yes—
1055C22×C4C23×D7911yescharacteristic
1056C4⋊C4—796no—
1057C4⋊C4—792no—
1058C4⋊C4—796no—
1059C4⋊C4—796no—
1060C4⋊C4—7912no—
1061C4⋊C4—792no—
1062C4⋊C4—792no—
1063C4⋊C4—796no—
1064C4⋊C4—792no—
1065C4⋊C4—796no—
1066C4⋊C4—792no—
1067C4⋊C4—796no—
1068C4⋊C4—796no—
1069C4⋊C4—796no—
1070C4⋊C4—792no—
1071C4⋊C4—796no—
1072C4⋊C4—792no—
1073C4⋊C4—796no—
1074C4⋊C4C23×D7916yes—
1075C4⋊C4C23×D7916yes—
1076C4⋊C4C23×D7912yes—
1077C4⋊C4C23×D7916yes—
1078C22⋊C4—796no—
1079C22⋊C4—791no—
1080C22⋊C4—793no—
1081C22⋊C4—796no—
1082C22⋊C4—796no—
1083C22⋊C4—796no—
1084C22⋊C4—796no—
1085C22⋊C4—792no—
1086C22⋊C4—792no—
1087C22⋊C4—792no—
1088C22⋊C4—796no—
1089C22⋊C4—796no—
1090C22⋊C4—796no—
1091C22⋊C4—7912no—
1092C22⋊C4—7912no—
1093C22⋊C4—796no—
1094C22⋊C4—796no—
1095C22⋊C4—796no—
1096C22⋊C4—7912no—
1097C22⋊C4—796no—
1098C22⋊C4—7912no—
1099C22⋊C4—796no—
1100C22⋊C4—796no—
1101C22⋊C4—796no—
1102C22⋊C4—796no—
1103C22⋊C4C23×D79112yes—
1104C22⋊C4C23×D7911yescharacteristic
1105C22⋊C4C23×D7913yes—
1106C22⋊C4C23×D7916yes—
1107C22⋊C4C23×D7916yes—
1108C22⋊C4C23×D7912yes—
1109C22⋊C4C23×D7916yes—
1110C42—791no—
1111C42—792no—
1112C42—796no—
1113C42—796no—
1114C42—796no—
1115C42—793no—
1116C42—796no—
1117C42C23×D7916yes—
1118C42C23×D7916yes—
1119C23—43no—
1120C23—46no—
1121C23—3163no—
1122C23—3166no—
1123C23—3166no—
1124C23—31612no—
1125C23—31612no—
1126C23—31612no—
1127C23—31612no—
1128C23—796no—
1129C23—796no—
1130C23C24×D7911yescharacteristic
1131C23C24×D7916yes—
1132C23C24×D7911yescharacteristic
1133C23C24×D7913yes—
1134Q8—26no—
1135Q8—26no—
1136Q8—43no—
1137Q8—3162no—
1138Q8—3161no—
1139Q8—3166no—
1140Q8#1457920614yes—
1141D4—212no—
1142D4—26no—
1143D4—46no—
1144D4—46no—
1145D4—46no—
1146D4—412no—
1147D4—41no—
1148D4—43no—
1149D4—43no—
1150D4—3166no—
1151D4—3163no—
1152D4—3166no—
1153D4—3166no—
1154D4—31612no—
1155D4—3166no—
1156D4—3166no—
1157D4—3166no—
1158D4—3166no—
1159D4—31612no—
1160D4—3166no—
1161D4—3166no—
1162D4—3166no—
1163D4—31612no—
1164D4—3166no—
1165D4—31612no—
1166D4—3166no—
1167D4—15812no—
1168D4—15812no—
1169C2×C4—26no—
1170C2×C4—212no—
1171C2×C4—26no—
1172C2×C4—26no—
1173C2×C4—41no—
1174C2×C4—46no—
1175C2×C4—46no—
1176C2×C4—3166no—
1177C2×C4—3166no—
1178C2×C4—3166no—
1179C2×C4—31612no—
1180C2×C4—3161no—
1181C2×C4—31612no—
1182C2×C4—3166no—
1183C2×C4—792no—
1184C2×C4—796no—
1185C2×C4—792no—
1186C2×C4—792no—
1187C2×C4—796no—
1188C2×C4—792no—
1189C2×C4—15812no—
1190C2×C4—15812no—
1191C2×C4C24×D7911yescharacteristic
1192C2×C4C24×D7913yes—
1193C2×C4C24×D7916yes—
1194C2×C4C24×D7912yes—
1195C2×C4C24×D7913yes—
1196C2×C4C24×D7912yes—
1197C2×C4C24×D7913yes—
1198C22—21no—
1199C22—21no—
1200C22—23no—
1201C22—26no—
1202C22—26no—
1203C22—26no—
1204C22—22no—
1205C22—26no—
1206C22—22no—
1207C22—86no—
1208C22—6326no—
1209C22—1586no—
1210C22—1586no—
1211C22—1586no—
1212C22—1586no—
1213C22—1586no—
1214C22—1586no—
1215C22—126412no—
1216C22—12646no—
1217C22C25×D7911yescharacteristic
1218C4—22no—
1219C4—21no—
1220C4—23no—
1221C4—23no—
1222C4—22no—
1223C4—26no—
1224C4—1582no—
1225C4—1582no—
1226C4—1586no—
1227C4—1582no—
1228C4—1586no—
1229C4—1582no—
1230C4C2×#1457920616yes—
1231C2—41no—
1232C2—46no—
1233C2—41no—
1234C2—43no—
1235C2—3166no—
1236C2—3166no—
1237C2C22×#1457920611yescharacteristic
1238C2#2377821112yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3487C2
hypercenter#3487D79
hypocenterC79#63066
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #23777917C2semidirect
2. #23777816C2semidirect
3. #23777803C2semidirect
4. #23777726C2semidirect
5. #23777724C2semidirect
6. #23777708C2semidirect
7. #23777706C2semidirect
8. #23777639C2semidirect
9. #23777633C2semidirect
10. #23777538C2semidirect
11. #23777511C2semidirect
12. #23777502C2semidirect
13. #23777397C2semidirect
14. #23777194C2semidirect
15. #23777177C2semidirect
16. #23777069C2semidirect
17. #23777066C2semidirect
18. #23777055C2semidirect
19. C79×#3487C2semidirect
20. C2×#14579207C22semidirect
21. C2×#14579207C22semidirect
22. C22×#11929625C22semidirect
23. #19099316C22semidirect
24. #19099314C22semidirect
25. #19099310C22semidirect
26. #19099309C22semidirect
27. #19099308C22semidirect
28. #19099306C22semidirect
29. #19099305C22semidirect
30. #19099303C22semidirect
31. #19099303C22semidirect
32. #19099302C22semidirect
33. #19099302C22semidirect
34. #19099301C22semidirect
35. #19099301C22semidirect
36. #19099300C22semidirect
37. #19099298C22semidirect
38. #19099295C22semidirect
39. #19099289C22semidirect
40. #19099277C22semidirect
41. #19099276C22semidirect
42. #19099275C22semidirect
43. #19099260C22semidirect
44. #19099259C22semidirect
45. #19099259C22semidirect
46. #19099257C22semidirect
47. #19099255C22semidirect
48. #19099254C22semidirect
49. #19099242C22semidirect
50. #19099235C22semidirect
51. #19099233C22semidirect
52. #19099232C22semidirect
53. #19099232C22semidirect
54. #19099232C22semidirect
55. #19099232C22semidirect
56. #19099224C22semidirect
57. #19099224C22semidirect
58. #19099224C22semidirect
59. #19099224C22semidirect
60. #19099213C22semidirect
61. #19099208C22semidirect
62. #19099206C22semidirect
63. #19099204C22semidirect
64. #19099202C22semidirect
65. #19099201C22semidirect
66. #19099201C22semidirect
67. #19099201C22semidirect
68. #19099201C22semidirect
69. D4×D316C22semidirect
70. D4×D316C22semidirect
71. #19099198C22semidirect
72. #19099198C22semidirect
73. #19099197C22semidirect
74. #19099197C22semidirect
75. #19099197C22semidirect
76. D4×C22⋊D79C22semidirect
77. D4×C22⋊D79C22semidirect
78. #19099195C22semidirect
79. #19099195C22semidirect
80. #19099186C22semidirect
81. #19099185C22semidirect
82. #19099168C22semidirect
83. #19099167C22semidirect
84. #19099166C22semidirect
85. #19099166C22semidirect
86. #19099164C22semidirect
87. #19099163C22semidirect
88. #19099153C22semidirect
89. #19099147C22semidirect
90. #19099146C22semidirect
91. #19099143C22semidirect
92. #19099141C22semidirect
93. #19099137C22semidirect
94. #19099131C22semidirect
95. #19099129C22semidirect
96. #19099129C22semidirect
97. #19099128C22semidirect
98. #19099127C22semidirect
99. #19099127C22semidirect
100. #19099127C22semidirect
101. #19099127C22semidirect
102. #19099126C22semidirect
103. #19099123C22semidirect
104. #19099121C22semidirect
105. #19099121C22semidirect
106. #19099110C22semidirect
107. #19099109C22semidirect
108. #19099108C22semidirect
109. #127×D79C22semidirect
110. #19099100C22semidirect
111. #19099095C22semidirect
112. #19099093C22semidirect
113. #19099092C22semidirect
114. #19099091C22semidirect
115. C2×#14579150C22semidirect
116. #19099074C22semidirect
117. #19099072C22semidirect
118. #19099070C22semidirect
119. #19099070C22semidirect
120. C2×#14579135C22semidirect
121. #121×D79C22semidirect
122. #19099046C22semidirect
123. #19099045C22semidirect
124. #19099041C22semidirect
125. #41×Dic79C22semidirect
126. C4×#11929625C22semidirect
127. C2×2−1+4×C79C22semidirect
128. C22×#41×C79C22semidirect
129. #550×C79C22semidirect
130. #550×C79C22semidirect
131. #548×C79C22semidirect
132. #548×C79C22semidirect
133. #535×C79C22semidirect
134. #535×C79C22semidirect
135. #525×C79C22semidirect
136. #525×C79C22semidirect
137. #519×C79C22semidirect
638. #3487D79semidirect
639. C79#63066semidirect
640. C2×2−1+4C2×D79semidirect
644. C22×#41C2×D79semidirect
678. #550C2×D79semidirect
679. #550C2×D79semidirect
684. #548C2×D79semidirect
685. #548C2×D79semidirect
729. #535C2×D79semidirect
730. #535C2×D79semidirect
748. #525C2×D79semidirect
749. #525C2×D79semidirect
755. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779172
#237778162
#237778032
#237777262
#237777242
#237777082
#237777062
#237776392
#237776332
#237775382
#237775112
#237775022
#237773972
#237771942
#237771772
#237770692
#237770662
#237770552
C79×#34872
#6306679