Finite Group Databasebeta

← #35201979

Subgroups — #35201979

Order 20224.

7352 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777919C216yesmaximal, complemented
2#23777829C216yesmaximal, complemented
3#23777805C213yesmaximal, complemented
4#23777732C2112yesmaximal, complemented
5#23777714C2112yesmaximal, complemented
6#23777633C216yesmaximal, complemented
7#23777536C213yesmaximal, complemented
8#23777510C214yesmaximal, complemented
9#23777406C212yesmaximal, complemented
10#23777174C212yesmaximal, complemented
11#23777066C214yesmaximal, complemented
12#23777055C212yesmaximal, complemented
13C79×#3500C211yesmaximal, characteristic, complemented
14C2×#14579207C2212yescomplemented
15C22×#11929625C2212yescomplemented
16#19099313C2211yescharacteristic, complemented
17#19099312C2216yescomplemented
18#19099308C22112yescomplemented
19#19099307C2216yescomplemented
20#19099305C2213yescomplemented
21#19099305C2216yescomplemented
22#19099303C22112yescomplemented
23#19099302C22112yescomplemented
24#19099301C22112yescomplemented
25#19099300C2216yescomplemented
26#19099295C22112yescomplemented
27#19099292C2212yescomplemented
28#19099279C2216yescomplemented
29#19099278C22112yescomplemented
30#19099260C22112yescomplemented
31#19099257C22112yescomplemented
32#19099247C22112yescomplemented
33#19099241C22112yescomplemented
34#19099235C2212yescomplemented
35#19099234C2216yescomplemented
36#19099232C2214yescomplemented
37#19099232C22112yescomplemented
38#19099232C2214yescomplemented
39#19099224C22112yescomplemented
40#19099224C2214yescomplemented
41#19099218C2216yescomplemented
42#19099206C22112yescomplemented
43#19099204C22112yescomplemented
44#19099203C22124yescomplemented
45D4×D316C22112yescomplemented
46#19099198C2216yescomplemented
47#19099197C22112yescomplemented
48D4×C22⋊D79C22112yescomplemented
49D4×C22⋊D79C22112yescomplemented
50#19099195C22112yescomplemented
51#19099182C22112yescomplemented
52#19099166C22112yescomplemented
53#19099165C22124yescomplemented
54#19099164C22112yescomplemented
55#19099151C22112yescomplemented
56#19099147C22124yescomplemented
57#19099143C22112yescomplemented
58#19099131C22112yescomplemented
59#19099130C2216yescomplemented
60#19099129C22124yescomplemented
61#19099127C2216yescomplemented
62#19099127C2216yescomplemented
63#19099127C2216yescomplemented
64#19099125C22112yescomplemented
65#19099123C22124yescomplemented
66#19099113C2216yescomplemented
67#19099109C2216yescomplemented
68C2×#14579157C2216yescomplemented
69#19099099C22112yescomplemented
70#19099097C2216yescomplemented
71#19099093C22112yescomplemented
72#19099072C22112yescomplemented
73#19099070C2216yescomplemented
74#19099070C2216yescomplemented
75#121×D79C22112yescomplemented
76#19099045C2214yescomplemented
77#19099041C2212yescomplemented
78#41×Dic79C2212yescomplemented
79C2×2−1+4×C79C2211yescharacteristic, complemented
80C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
81#548×C79C2214yescomplemented
82#546×C79C22112yescomplemented
83#536×C79C2213yescomplemented
84#535×C79C2213yescomplemented
85#532×C79C2213yescomplemented
86C2×#124×C79C2213yescomplemented
87C4×#41×C79C2211yescharacteristic, complemented
88#14579207—48no—
89C2×#11929625—48no—
90C2×#11929625C2314yes—
91C2×#11929625C23112yes—
92C2×#11929624C2316yes—
93C2×#11929624C23112yes—
94C22×D316C2316yes—
95C22×D316C2316yes—
96C22×C22⋊D79C23124yes—
97C2×D4×D79C23112yes—
98C2×D4×D79C23124yes—
99C22×C4×D79C2316yes—
100#14579161C2316yes—
101#14579159C2312yes—
102#14579158C2316yes—
103#14579157C23112yes—
104#14579157C23112yes—
105#14579157C23112yes—
106#14579157C23112yes—
107#14579157C2316yes—
108#14579156C23112yes—
109#14579155C23112yes—
110#14579154C23124yes—
111#14579154C2314yes—
112#14579153C2312yes—
113#14579152C23112yes—
114#14579151C23112yes—
115#14579150C23112yes—
116#14579150C23112yes—
117#14579150C2316yes—
118#14579149C2316yes—
119#14579148C2316yes—
120#14579147C23124yes—
121#14579147C23112yes—
122#14579146C23112yes—
123#14579145C23124yes—
124#14579145C23112yes—
125#14579144C23112yes—
126#14579143C23124yes—
127#14579143C23112yes—
128#14579143C23124yes—
129#14579142C23112yes—
130#14579142C2312yes—
131#14579142C2316yes—
132#14579140C2316yes—
133#14579139C23112yes—
134#14579138C23112yes—
135#14579138C2314yes—
136#14579137C23112yes—
137#14579137C23112yes—
138#14579136C23112yes—
139#14579136C23124yes—
140#14579135C23112yes—
141#14579135C23112yes—
142#14579135C23124yes—
143#14579135C23112yes—
144#14579135C23112yes—
145#14579135C2316yes—
146#14579134C23124yes—
147#14579134C23124yes—
148#14579134C23124yes—
149#14579134C23112yes—
150#14579133C23112yes—
151#14579133C23112yes—
152#14579133C23112yes—
153#14579133C23112yes—
154#14579132C23112yes—
155#14579132C23124yes—
156#14579132C23112yes—
157#14579132C23112yes—
158#14579131C23124yes—
159#14579131C23112yes—
160#14579131C23124yes—
161#14579130C23124yes—
162#14579129C23112yes—
163#14579129C2316yes—
164#14579129C23112yes—
165#14579129C23112yes—
166#14579129C2316yes—
167#14579129C23112yes—
168Q8×Dic79C23112yes—
169Q8×Dic79C2314yes—
170C4×Dic158C2316yes—
171C4×D316C23112yes—
172C4×D316C23112yes—
173C4×D316C2316yes—
174D4×Dic79C23112yes—
175#14579123C23112yes—
176C4×C22⋊D79C23124yes—
177C4×C22⋊D79C23112yes—
178C4×C22⋊D79C23112yes—
179C4×C22⋊D79C23112yes—
180(C22⋊D79)⋊C4C23124yes—
181#14579120C2316yes—
182#14579120C2316yes—
183#14579120C2316yes—
184#14579119C23124yes—
185#14579118C23112yes—
186C4⋊C4×D79C23112yes—
187C22⋊C4×D79C23124yes—
188C2×C4×Dic79C2316yes—
1892−1+4×C79—44no—
190H(5,𝔽2)×C79—44no—
191C2×#41×C79C2312yes—
192C2×#41×C79C2311yescharacteristic
193C2×#41×C79C2316yes—
194C2×#41×C79C2313yes—
195C2×#41×C79C2313yes—
196C22×Q8×C79C2312yes—
197C22×Q8×C79C2313yes—
198C22×D4×C79C2313yes—
199C22×D4×C79C2316yes—
200C4⋊Q8×C79C2313yes—
201#127×C79C2313yes—
202#124×C79C2316yes—
203#124×C79C23112yes—
204#124×C79C2313yes—
205#124×C79C2311yescharacteristic
206#123×C79C23112yes—
207C22⋊Q8×C79C23112yes—
208#121×C79C23112yes—
209#121×C79C23112yes—
210#120×C79C23112yes—
211C4×Q8×C79C2312yes—
212C4×D4×C79C2316yes—
213C4×D4×C79C23112yes—
214#117×C79C2313yes—
215C2×C22⋊C4×C79C23112yes—
216C2×C42×C79C2313yes—
217C23×D79C24112yes—
218C23×D79C2416yes—
219#11929625—216no—
220#11929625—424no—
221#11929624—412no—
222#11929624—812no—
223C2×Dic158C2412yes—
224C2×Dic158C2416yes—
225C2×D316—412no—
226C2×D316—412no—
227C2×D316C24112yes—
228C2×D316C2416yes—
229C2×D316C2416yes—
230C2×D316C24112yes—
231C2×D316C24112yes—
232C2×C22⋊D79—824no—
233C2×C22⋊D79C24124yes—
234C2×C22⋊D79C24112yes—
235C2×C22⋊D79C24124yes—
236C2×C22⋊D79C24112yes—
237C2×C22⋊D79C24112yes—
238C2×C22⋊D79C24112yes—
239D4×D79—424no—
240D4×D79—824no—
241C22×Dic79C24112yes—
242C22×Dic79C2412yes—
243C2×C4×D79—412no—
244C2×C4×D79C24112yes—
245C2×C4×D79C24124yes—
246C2×C4×D79C24112yes—
247C4⋊Dic79C24112yes—
248C4⋊Dic79C24112yes—
249C4⋊Dic79C24112yes—
250C4⋊Dic79C2412yes—
251C4⋊Dic79C2412yes—
252Dic79⋊C4C24112yes—
253Dic79⋊C4C2414yes—
254Dic79⋊C4C24112yes—
255Dic79⋊C4C2414yes—
256Dic79⋊C4C2414yes—
257Dic79⋊C4C24112yes—
258C22⋊Dic79C24112yes—
259C22⋊Dic79C2416yes—
260C22⋊Dic79C2412yes—
261C22⋊Dic79C24112yes—
262C22⋊Dic79C2414yes—
263C22⋊Dic79C24112yes—
264(C2×D79)⋊C4C24112yes—
265(C2×D79)⋊C4C24124yes—
266(C2×D79)⋊C4C24112yes—
267(C2×D79)⋊C4C24112yes—
268(C2×D79)⋊C4C24112yes—
269(C2×D79)⋊C4C24112yes—
270(C2×D79)⋊C4C24112yes—
271C4×Dic79C2412yes—
272C4×Dic79C24112yes—
273C4×Dic79C2416yes—
274C4×Dic79C24112yes—
275C24×C79C2416yes—
276#41×C79—28no—
277#41×C79—24no—
278#41×C79—46no—
279#41×C79—46no—
280#41×C79—412no—
281C2×Q8×C79—28no—
282C2×Q8×C79—46no—
283C2×Q8×C79C2416yes—
284C2×Q8×C79C2413yes—
285C2×Q8×C79C2411yescharacteristic
286C2×Q8×C79C2411yescharacteristic
287C2×D4×C79—412no—
288C2×D4×C79—46no—
289C2×D4×C79C2413yes—
290C2×D4×C79C2416yes—
291C2×D4×C79C24112yes—
292C2×D4×C79C2416yes—
293C2×D4×C79C2416yes—
294C2×D4×C79C2413yes—
295C2×D4×C79C2411yescharacteristic
296C22×C4×C79C2416yes—
297C22×C4×C79C2413yes—
298C22×C4×C79C2416yes—
299C22×C4×C79C2416yes—
300C22×C4×C79C2416yes—
301C4⋊C4×C79C2416yes—
302C4⋊C4×C79C24112yes—
303C22⋊C4×C79C24112yes—
304C22⋊C4×C79C24124yes—
305C22⋊C4×C79C2416yes—
306C22⋊C4×C79C2414yes—
307C42×C79C2411yescharacteristic
308C42×C79C2413yes—
309C42×C79C2416yes—
310C23×C79—412no—
311C23×C79—46no—
312C23×C79C2512yes—
313C23×C79C2516yes—
314C23×C79C2513yes—
315C22×D79—46no—
316C22×D79—412no—
317C22×D79—412no—
318C22×D79—424no—
319C22×D79C25112yes—
320Q8×C79—212no—
321Q8×C79—43no—
322Q8×C79—41no—
323Q8×C79H(5,𝔽2)14yes—
324D4×C79—212no—
325D4×C79—26no—
326D4×C79—412no—
327D4×C79—43no—
328D4×C79—46no—
329D4×C79—41no—
330D4×C79—46no—
331C2×C4×C79—212no—
332C2×C4×C79—212no—
333C2×C4×C79—26no—
334C2×C4×C79—46no—
335C2×C4×C79—46no—
336C2×C4×C79C2512yes—
337C2×C4×C79C2516yes—
338C2×C4×C79C2511yescharacteristic
339C2×C4×C79C2512yes—
340C2×C4×C79C2516yes—
341C2×C4×C79C2513yes—
342C22⋊D79—412no—
343C22⋊D79—412no—
344C22⋊D79—424no—
345C22⋊D79—412no—
346C22⋊D79—412no—
347C22⋊D79—424no—
348C2×Dic79—42no—
349C2×Dic79—412no—
350C2×Dic79C2514yes—
351C2×Dic79C25112yes—
352C2×Dic79C2514yes—
353D316—224no—
354D316—412no—
355D316—46no—
356D316—412no—
357D316—46no—
358C4×D79—224no—
359C4×D79—412no—
360C4×D79—424no—
361Dic158—42no—
362Dic158—46no—
363C22×C79—26no—
364C22×C79—22no—
365C22×C79—23no—
366C22×C79—26no—
367C22×C79—24no—
368C22×C79—212no—
369C22×C79—166no—
370C22×C79C2611yescharacteristic
371C2×D79—212no—
372C2×D79—212no—
373C2×D79—212no—
374C2×D79—812no—
375C2×D79—1612no—
376C4×C79—21no—
377C4×C79—22no—
378C4×C79—26no—
379C4×C79—22no—
380C4×C79—26no—
381C4×C79C2×H(5,𝔽2)16yes—
382Dic79—24no—
383Dic79—24no—
384Dic79—212no—
385#63066—791nomaximal, Sylow
386C2×C79—42no—
387C2×C79—46no—
388C2×C79—43no—
389C2×C79C22×H(5,𝔽2)11yescharacteristic
390C2×C79H(7,𝔽2)12yes—
391D79—412no—
392#3558—796no—
393#3551—796no—
394#3549—793no—
395#3543—7912no—
396#3542—7912no—
397#3537—796no—
398#3529—793no—
399#3524—794no—
400#3517—792no—
401#3500D7911yescharacteristic, complemented
402#3498—792no—
403#3488—794no—
404#3487—792no—
405C79#6306611yescharacteristic, complemented, Sylow
406C2×2−1+4C2×D7911yescharacteristic, complemented
407C2×H(5,𝔽2)—792no—
408C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
409C22×#41—792no—
410#563—796no—
411#563—791no—
412#562—796no—
413#562—7912no—
414H(3,𝔽4)—793no—
415H(3,𝔽4)—796no—
416#560—796no—
417#560—7912no—
418#560—7912no—
419#560—7912no—
420#559—7912no—
421#557—792no—
422#555—796no—
423#555—7912no—
424#553—7912no—
425#553—7912no—
426#552—7912no—
427#551—7912no—
428#550—794no—
429#550—7912no—
430#550—794no—
431#550—792no—
432#550—796no—
433#548—794no—
434#548—7912no—
435#548C2×D7914yescomplemented
436#547—796no—
437#546—7912no—
438#546—7912no—
439#546—7924no—
440#546C2×D79112yescomplemented
441D42—7912no—
442D42—7912no—
443D42—796no—
444D42—7912no—
445D42—7912no—
446D42—7912no—
447#542—7912no—
448#540—7924no—
449#540—7912no—
450#540—7912no—
451#538—7924no—
452#538—7912no—
453#537—7912no—
454#536C2×D7913yescomplemented
455#535—796no—
456#535—796no—
457#535—796no—
458#535—796no—
459#535—7912no—
460#535—7924no—
461#535C2×D7913yescomplemented
462#534—7924no—
463#534—7912no—
464#532—796no—
465#532—796no—
466#532C2×D7913yescomplemented
467C2×#127—796no—
468#529—7912no—
469#529—7912no—
470#529—796no—
471C2×#124C2×D7913yescomplemented
472#525—796no—
473#525—796no—
474#525—7912no—
475C2×#121—7912no—
476#520—794no—
477#519—792no—
478C4×#41—792no—
479C4×#41C2×D7911yescharacteristic, complemented
4802−1+4—44no—
481H(5,𝔽2)—44no—
482H(5,𝔽2)—3168no—
483C2×#41—3168no—
484C2×#41—7912no—
485C2×#41—794no—
486C2×#41—796no—
487C2×#41—7912no—
488C2×#41C22×D7912yes—
489C2×#41C22×D7911yescharacteristic
490C2×#41C22×D7913yes—
491C2×#41C22×D7916yes—
492C2×#41C22×D7913yes—
493C22×Q8C22×D7912yes—
494C22×Q8C22×D7913yes—
495C22×D4—7912no—
496C22×D4—7924no—
497C22×D4—7924no—
498C22×D4—796no—
499C22×D4—796no—
500C22×D4C22×D7913yes—
501C22×D4C22×D7916yes—
502C23×C4—796no—
503C4⋊Q8—792no—
504C4⋊Q8—796no—
505C4⋊Q8C22×D7913yes—
506#127—796no—
507#127—7912no—
508#127—7912no—
509#127—7912no—
510#127—7912no—
511#127—796no—
512#127C22×D7913yes—
513#126—7912no—
514#126—794no—
515#126—7924no—
516#126—7912no—
517#125—7912no—
518#125—7912no—
519#125—792no—
520#124—7912no—
521#124—796no—
522#124—7912no—
523#124—796no—
524#124—7912no—
525#124—7924no—
526#124—796no—
527#124C22×D7913yes—
528#124C22×D79112yes—
529#124C22×D7916yes—
530#124C22×D7911yescharacteristic
531#123—792no—
532#123—796no—
533#123—7912no—
534#123—7912no—
535#123—7912no—
536#123—7912no—
537#123—7924no—
538#123—7912no—
539#123—7924no—
540#123—7924no—
541#123C22×D79112yes—
542C22⋊Q8—7912no—
543C22⋊Q8—7912no—
544C22⋊Q8—796no—
545C22⋊Q8—7912no—
546C22⋊Q8—794no—
547C22⋊Q8—7912no—
548C22⋊Q8C22×D79112yes—
549#121—7912no—
550#121—7912no—
551#121—7912no—
552#121—7912no—
553#121—7912no—
554#121—7912no—
555#121—7912no—
556#121—7924no—
557#121—7912no—
558#121—796no—
559#121—7912no—
560#121—7912no—
561#121—7912no—
562#121—7924no—
563#121—7912no—
564#121—7924no—
565#121—7924no—
566#121—7912no—
567#121—7924no—
568#121—7924no—
569#121C22×D79112yes—
570#121C22×D79112yes—
571#120—7924no—
572#120—7912no—
573#120—7912no—
574#120—796no—
575#120—796no—
576#120—7912no—
577#120—7912no—
578#120—7912no—
579#120—7924no—
580#120—7924no—
581#120C22×D79112yes—
582C4×Q8—794no—
583C4×Q8—7912no—
584C4×Q8—796no—
585C4×Q8C22×D7912yes—
586C4×D4—7912no—
587C4×D4—7912no—
588C4×D4—7912no—
589C4×D4—7912no—
590C4×D4—7924no—
591C4×D4—7912no—
592C4×D4—7924no—
593C4×D4—7912no—
594C4×D4—796no—
595C4×D4—7912no—
596C4×D4C22×D7916yes—
597C4×D4C22×D79112yes—
598#117—796no—
599#117—796no—
600#117—796no—
601#117—7924no—
602#117—7912no—
603#117C22×D7913yes—
604C2×C4⋊C4—7912no—
605C2×C22⋊C4—7924no—
606C2×C22⋊C4C22×D79112yes—
607C2×C42—796no—
608C2×C42C22×D7913yes—
609C24—7912no—
610C24—796no—
611C24C23×D7916yes—
612#41—28no—
613#41—24no—
614#41—46no—
615#41—46no—
616#41—412no—
617#41—31612no—
618#41—31624no—
619#41—63212no—
620#41—15816no—
621C2×Q8—28no—
622C2×Q8—46no—
623C2×Q8—796no—
624C2×Q8—792no—
625C2×Q8C23×D7916yes—
626C2×Q8C23×D7913yes—
627C2×Q8C23×D7911yescharacteristic
628C2×Q8C23×D7911yescharacteristic
629C2×D4—412no—
630C2×D4—46no—
631C2×D4—31612no—
632C2×D4—31612no—
633C2×D4—31624no—
634C2×D4—7924no—
635C2×D4—7924no—
636C2×D4—7912no—
637C2×D4—7912no—
638C2×D4—7912no—
639C2×D4—7912no—
640C2×D4—796no—
641C2×D4—7912no—
642C2×D4—7912no—
643C2×D4—796no—
644C2×D4—7912no—
645C2×D4—63224no—
646C2×D4—63224no—
647C2×D4C23×D7916yes—
648C2×D4C23×D7913yes—
649C2×D4C23×D79112yes—
650C2×D4C23×D7911yescharacteristic
651C2×D4C23×D7913yes—
652C2×D4C23×D7916yes—
653C2×D4C23×D7916yes—
654C22×C4—31612no—
655C22×C4—7912no—
656C22×C4—792no—
657C22×C4—7912no—
658C22×C4—7924no—
659C22×C4—7912no—
660C22×C4C23×D7916yes—
661C22×C4C23×D7913yes—
662C22×C4C23×D7916yes—
663C22×C4C23×D7916yes—
664C22×C4C23×D7916yes—
665C4⋊C4—7912no—
666C4⋊C4—794no—
667C4⋊C4—794no—
668C4⋊C4—794no—
669C4⋊C4—7912no—
670C4⋊C4—7912no—
671C4⋊C4—7912no—
672C4⋊C4—7912no—
673C4⋊C4—7912no—
674C4⋊C4—792no—
675C4⋊C4—792no—
676C4⋊C4C23×D7916yes—
677C4⋊C4C23×D79112yes—
678C22⋊C4—7912no—
679C22⋊C4—792no—
680C22⋊C4—796no—
681C22⋊C4—7912no—
682C22⋊C4—794no—
683C22⋊C4—7912no—
684C22⋊C4—7912no—
685C22⋊C4—7924no—
686C22⋊C4—7912no—
687C22⋊C4—7912no—
688C22⋊C4—7912no—
689C22⋊C4—7912no—
690C22⋊C4—7912no—
691C22⋊C4C23×D79124yes—
692C22⋊C4C23×D79112yes—
693C22⋊C4C23×D7916yes—
694C22⋊C4C23×D7914yes—
695C42—792no—
696C42—796no—
697C42—7912no—
698C42—7912no—
699C42C23×D7911yescharacteristic
700C42C23×D7916yes—
701C42C23×D7913yes—
702C23—46no—
703C23—412no—
704C23—3166no—
705C23—31612no—
706C23—31612no—
707C23—31624no—
708C23—7912no—
709C23C24×D7912yes—
710C23C24×D7916yes—
711C23C24×D7913yes—
712Q8—212no—
713Q8—43no—
714Q8—41no—
715Q8—3162no—
716Q8—3166no—
717Q8#1457920614yes—
718D4—212no—
719D4—26no—
720D4—43no—
721D4—46no—
722D4—412no—
723D4—41no—
724D4—46no—
725D4—3166no—
726D4—31612no—
727D4—31612no—
728D4—3166no—
729D4—31612no—
730D4—31612no—
731D4—31612no—
732D4—31624no—
733D4—31612no—
734D4—31624no—
735D4—15824no—
736C2×C4—212no—
737C2×C4—212no—
738C2×C4—26no—
739C2×C4—46no—
740C2×C4—46no—
741C2×C4—31612no—
742C2×C4—31624no—
743C2×C4—3162no—
744C2×C4—31612no—
745C2×C4—7912no—
746C2×C4—794no—
747C2×C4—794no—
748C2×C4—15824no—
749C2×C4C24×D7912yes—
750C2×C4C24×D7916yes—
751C2×C4C24×D7911yescharacteristic
752C2×C4C24×D7912yes—
753C2×C4C24×D7916yes—
754C2×C4C24×D7913yes—
755C22—22no—
756C22—23no—
757C22—26no—
758C22—26no—
759C22—212no—
760C22—24no—
761C22—166no—
762C22—63212no—
763C22—15812no—
764C22—15812no—
765C22—15812no—
766C22—126412no—
767C22C25×D7911yescharacteristic
768C4—21no—
769C4—22no—
770C4—26no—
771C4—22no—
772C4—26no—
773C4—1584no—
774C4—1584no—
775C4—15812no—
776C4C2×#1457920616yes—
777C2—46no—
778C2—43no—
779C2—42no—
780C2—31612no—
781C2C22×#1457920611yescharacteristic
782C2#2377821112yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3500C2
hypercenter#3500D79
hypocenterC79#63066
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. #23777919C2semidirect
2. #23777829C2semidirect
3. #23777805C2semidirect
4. #23777732C2semidirect
5. #23777714C2semidirect
6. #23777633C2semidirect
7. #23777536C2semidirect
8. #23777510C2semidirect
9. #23777406C2semidirect
10. #23777174C2semidirect
11. #23777066C2semidirect
12. #23777055C2semidirect
13. C79×#3500C2semidirect
14. C2×#14579207C22semidirect
15. C22×#11929625C22semidirect
16. #19099313C22semidirect
17. #19099312C22semidirect
18. #19099308C22semidirect
19. #19099307C22semidirect
20. #19099305C22semidirect
21. #19099305C22semidirect
22. #19099303C22semidirect
23. #19099302C22semidirect
24. #19099301C22semidirect
25. #19099300C22semidirect
26. #19099295C22semidirect
27. #19099292C22semidirect
28. #19099279C22semidirect
29. #19099278C22semidirect
30. #19099260C22semidirect
31. #19099257C22semidirect
32. #19099247C22semidirect
33. #19099241C22semidirect
34. #19099235C22semidirect
35. #19099234C22semidirect
36. #19099232C22semidirect
37. #19099232C22semidirect
38. #19099232C22semidirect
39. #19099224C22semidirect
40. #19099224C22semidirect
41. #19099218C22semidirect
42. #19099206C22semidirect
43. #19099204C22semidirect
44. #19099203C22semidirect
45. D4×D316C22semidirect
46. #19099198C22semidirect
47. #19099197C22semidirect
48. D4×C22⋊D79C22semidirect
49. D4×C22⋊D79C22semidirect
50. #19099195C22semidirect
51. #19099182C22semidirect
52. #19099166C22semidirect
53. #19099165C22semidirect
54. #19099164C22semidirect
55. #19099151C22semidirect
56. #19099147C22semidirect
57. #19099143C22semidirect
58. #19099131C22semidirect
59. #19099130C22semidirect
60. #19099129C22semidirect
61. #19099127C22semidirect
62. #19099127C22semidirect
63. #19099127C22semidirect
64. #19099125C22semidirect
65. #19099123C22semidirect
66. #19099113C22semidirect
67. #19099109C22semidirect
68. C2×#14579157C22semidirect
69. #19099099C22semidirect
70. #19099097C22semidirect
71. #19099093C22semidirect
72. #19099072C22semidirect
73. #19099070C22semidirect
74. #19099070C22semidirect
75. #121×D79C22semidirect
76. #19099045C22semidirect
77. #19099041C22semidirect
78. #41×Dic79C22semidirect
79. C2×2−1+4×C79C22semidirect
80. C2×H(5,𝔽2)×C79C22semidirect
81. #548×C79C22semidirect
82. #546×C79C22semidirect
83. #536×C79C22semidirect
84. #535×C79C22semidirect
85. #532×C79C22semidirect
86. C2×#124×C79C22semidirect
87. C4×#41×C79C22semidirect
401. #3500D79semidirect
405. C79#63066semidirect
406. C2×2−1+4C2×D79semidirect
408. C2×H(5,𝔽2)C2×D79semidirect
435. #548C2×D79semidirect
440. #546C2×D79semidirect
454. #536C2×D79semidirect
461. #535C2×D79semidirect
466. #532C2×D79semidirect
471. C2×#124C2×D79semidirect
479. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779192
#237778292
#237778052
#237777322
#237777142
#237776332
#237775362
#237775102
#237774062
#237771742
#237770662
#237770552
C79×#35002
#6306679