Finite Group Databasebeta

← #35196663

Subgroups — #35196663

Order 20224.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777485C212yesmaximal, complemented
2#23777432C216yesmaximal, complemented
3#23777406C212yesmaximal, complemented
4#23777361C216yesmaximal, complemented
5#23777311C213yesmaximal, complemented
6#23777276C213yesmaximal, complemented
7#23777219C211yesmaximal, characteristic, complemented
8#23777178C211yesmaximal, characteristic, complemented
9#23777135C216yesmaximal, complemented
10#23777069C212yesmaximal, complemented
11#23777026C212yesmaximal, complemented
12#23777010C216yesmaximal, complemented
13#23776995C212yesmaximal, complemented
14D4×#11929624C216yesmaximal, complemented
15#23776816C216yesmaximal, complemented
16#23776696C213yesmaximal, complemented
17C2×#19099113C213yesmaximal, complemented
18C4×#14579207C212yesmaximal, complemented
19C2×C4×#41×C79C211yesmaximal, characteristic, complemented
20C2×#14579207C2212yes—
21C22×#11929624C2216yescomplemented
22#19099298C2216yescomplemented
23#19099298C2216yescomplemented
24Q8×Dic158C2212yescomplemented
25#19099292C2212yescomplemented
26#19099286C2216yescomplemented
27#19099278C2216yescomplemented
28#19099276C22112yescomplemented
29#19099273C2216yescomplemented
30#19099270C2216yescomplemented
31#19099261C22112yescomplemented
32#19099259C22112yescomplemented
33#19099257C22112yescomplemented
34#19099237C22124yescomplemented
35#19099235C2212yescomplemented
36#19099235C2212yescomplemented
37#19099234C2216yescomplemented
38#19099234C2216yescomplemented
39#19099232C2214yescomplemented
40D4×Dic158C2216yescomplemented
41#19099224C2214yescomplemented
42#19099222C22112yescomplemented
43#19099218C2216yescomplemented
44#19099214C22112yescomplemented
45#19099209C22112yescomplemented
46#19099209C22112yescomplemented
47#19099203C22124yescomplemented
48#19099201C22112yescomplemented
49D4×D316C2216yescomplemented
50D4×D316C2216yescomplemented
51D4×C22⋊D79C22112yescomplemented
52#19099191C2216yescomplemented
53#19099185C22112yescomplemented
54#19099184C22112yescomplemented
55#19099168C22112yescomplemented
56#19099164C22112yescomplemented
57#19099146C22124yescomplemented
58#19099141C2216yescomplemented
59#19099132C2216yescomplemented
60#19099127C2216yescomplemented
61#19099120C2213yescomplemented
62#19099120C2211yescharacteristic, complemented
63#19099120C2213yescomplemented
64#19099113C2216yescomplemented
65#19099113C2213yescomplemented
66#19099113C2216yescomplemented
67#19099113C2216yescomplemented
68#19099113C2216yescomplemented
69#19099113C2216yescomplemented
70#19099113C2216yescomplemented
71#19099113C2216yescomplemented
72#19099113C2213yescomplemented
73#19099113C2213yescomplemented
74#19099110C22112yescomplemented
75C2×#14579161C2213yescomplemented
76C2×#14579158C2213yescomplemented
77#19099100C22112yescomplemented
78#19099097C2216yescomplemented
79#19099097C2216yescomplemented
80#19099097C2216yescomplemented
81#19099097C2216yescomplemented
82#19099097C2216yescomplemented
83#19099097C2216yescomplemented
84C2×#14579149C2216yescomplemented
85#19099074C2216yescomplemented
86#19099074C2216yescomplemented
87#19099074C2216yescomplemented
88#19099072C22124yescomplemented
89C2×#14579135C2216yescomplemented
90C2×#14579135C2216yescomplemented
91#19099046C2212yes—
92#19099045C2214yescomplemented
93#19099043C2216yescomplemented
94#19099037C2216yescomplemented
95#19099035C22112yescomplemented
96C4×#11929625C2214yescomplemented
97C4×#11929624C2216yescomplemented
98C4×#11929624C2216yescomplemented
99C4×#11929624C2216yescomplemented
100C2×C4×D316C2216yescomplemented
101C2×C4×D316C2216yescomplemented
102C4×D4×D79C22112yescomplemented
103C22×#41×C79C2211yescharacteristic
104C4×#41×C79C2211yescharacteristic
105C4×#41×C79C2211yescharacteristic
106C4×#41×C79C2211yescharacteristic, complemented
107C4×#41×C79C2213yescomplemented
108C4×#41×C79C2213yescomplemented
109C4×#41×C79C2213yescomplemented
110C4×#41×C79C2211yescharacteristic, complemented
111C4×#41×C79C2213yescomplemented
112C2×C4×Q8×C79C2211yescharacteristic, complemented
113C2×C4×Q8×C79C2211yescharacteristic, complemented
114C2×C4×D4×C79C2213yescomplemented
115C2×C4×D4×C79C2213yescomplemented
116C2×#117×C79C2213yescomplemented
117C22×C42×C79C2213yescomplemented
118#14579207—216no—
119C2×#11929625C2314yes—
120C2×#11929624—424no—
121C2×#11929624C2316yes—
122C2×#11929624C2316yes—
123C2×#11929624C23112yes—
124C2×#11929624C2316yes—
125C2×#11929624C23112yes—
126C2×#11929624C23112yes—
127C22×Dic158C2316yes—
128C22×D316C2316yes—
129C22×D316C2316yes—
130C22×D316C2316yes—
131C22×C22⋊D79C23112yes—
132C2×D4×D79C23112yes—
133C22×C4×D79C23112yes—
134#14579161C2316yes—
135#14579161C2316yes—
136#14579161C2316yes—
137#14579161C2313yes—
138#14579161C2311yescharacteristic
139#14579161C2311yescharacteristic
140#14579160C23112yes—
141#14579158C2316yes—
142#14579158C2316yes—
143#14579158C2316yes—
144#14579158C2313yes—
145#14579157C23112yes—
146#14579156C23124yes—
147#14579155C23112yes—
148#14579155C23112yes—
149#14579153C2316yes—
150#14579153C2316yes—
151#14579153C2312yes—
152#14579152C23112yes—
153#14579150C23112yes—
154#14579149C23112yes—
155#14579149C2316yes—
156#14579149C2316yes—
157#14579149C23112yes—
158#14579149C23112yes—
159#14579149C2316yes—
160#14579147C23124yes—
161#14579146C23124yes—
162#14579146C23124yes—
163#14579144C23112yes—
164#14579144C23112yes—
165#14579144C23112yes—
166#14579143C23124yes—
167#14579140C2316yes—
168#14579140C2316yes—
169#14579140C2316yes—
170#14579140C2316yes—
171#14579140C2312yes—
172#14579140C2312yes—
173#14579139C23124yes—
174#14579138C23124yes—
175#14579137C23112yes—
176#14579136C23112yes—
177#14579136C23112yes—
178#14579135C23112yes—
179#14579135C23112yes—
180#14579135C2316yes—
181#14579135C23112yes—
182#14579135C2316yes—
183#14579135C2316yes—
184#14579135C23112yes—
185#14579135C23112yes—
186#14579135C2316yes—
187#14579135C23112yes—
188#14579135C2316yes—
189#14579135C2316yes—
190#14579134C23124yes—
191#14579134C23124yes—
192#14579133C23124yes—
193#14579132C23112yes—
194#14579131C23124yes—
195#14579130C23112yes—
196#14579129C23124yes—
197Q8×Dic79C2314yes—
198C4×Dic158C2316yes—
199C4×Dic158C2316yes—
200C4×Dic158C2316yes—
201C4×Dic158C2316yes—
202C4×Dic158C2312yes—
203C4×Dic158C2312yes—
204C4×D316C23112yes—
205C4×D316C2316yes—
206C4×D316C23112yes—
207C4×D316C2316yes—
208C4×D316C2316yes—
209C4×D316C2316yes—
210C4×D316C23112yes—
211C4×D316C23112yes—
212C4×D316C23112yes—
213C4×D316C2316yes—
214C4×D316C2316yes—
215C4×D316C23112yes—
216D4×Dic79C23112yes—
217#14579123C23112yes—
218#14579123C23112yes—
219C4×C22⋊D79C23112yes—
220C4×C22⋊D79C23112yes—
221C4×C22⋊D79C23112yes—
222C4×C22⋊D79C23112yes—
223C4×C22⋊D79C23112yes—
224C4×C22⋊D79C23112yes—
225(C22⋊D79)⋊C4C23124yes—
226#14579120C2316yes—
227#14579120C2316yes—
228#14579120C2312yes—
229#14579119C23112yes—
230#14579118C23112yes—
231#14579118C23112yes—
232#14579118C23112yes—
233C2×C4⋊Dic79C2316yes—
234C2×C4⋊Dic79C2316yes—
235C4⋊C4×D79C23112yes—
236C2×(C2×D79)⋊C4C23112yes—
237C2×(C2×D79)⋊C4C23112yes—
238C22⋊C4×D79C23124yes—
239C42×D79C23112yes—
240C2×#41×C79—28no—
241C2×#41×C79C2313yes—
242C2×#41×C79C2313yes—
243C2×#41×C79C2311yescharacteristic
244C2×#41×C79C2311yescharacteristic
245C22×Q8×C79C2311yescharacteristic
246C22×D4×C79C2313yes—
247C23×C4×C79C2313yes—
248C23×C4×C79C2313yes—
249C23×C4×C79C2313yes—
250C4×Q8×C79C2313yes—
251C4×Q8×C79C2311yescharacteristic
252C4×Q8×C79C2311yescharacteristic
253C4×Q8×C79C2311yescharacteristic
254C4×Q8×C79C2311yescharacteristic
255C4×Q8×C79C2313yes—
256C4×Q8×C79C2313yes—
257C4×Q8×C79C2313yes—
258C4×D4×C79C2316yes—
259C4×D4×C79C2313yes—
260C4×D4×C79C2313yes—
261C4×D4×C79C2313yes—
262C4×D4×C79C2316yes—
263C4×D4×C79C2316yes—
264C4×D4×C79C2313yes—
265C4×D4×C79C2313yes—
266C4×D4×C79C2313yes—
267C4×D4×C79C2313yes—
268C4×D4×C79C2316yes—
269C4×D4×C79C2313yes—
270#117×C79C2316yes—
271#117×C79C2313yes—
272#117×C79C2313yes—
273#117×C79C2316yes—
274#117×C79C2313yes—
275#117×C79C2313yes—
276C2×C4⋊C4×C79C2313yes—
277C2×C4⋊C4×C79C2313yes—
278C2×C22⋊C4×C79C2316yes—
279C2×C42×C79C2311yescharacteristic
280C2×C42×C79C2313yes—
281C2×C42×C79C2313yes—
282C2×C42×C79C2313yes—
283C2×C42×C79C2313yes—
284C2×C42×C79C2313yes—
285C2×C42×C79C2313yes—
286C2×C42×C79C2313yes—
287C2×C42×C79C2313yes—
288C2×C42×C79C2313yes—
289C2×C42×C79C2313yes—
290C2×C42×C79C2313yes—
291C23×D79C24112yes—
292#11929625—216no—
293#11929624—224no—
294#11929624—224no—
295#11929624—424no—
296#11929624—424no—
297#11929624—412no—
298#11929624—424no—
299C2×Dic158—412no—
300C2×Dic158C2416yes—
301C2×Dic158C2412yes—
302C2×Dic158C2412yes—
303C2×Dic158C24112yes—
304C2×D316—224no—
305C2×D316—412no—
306C2×D316—412no—
307C2×D316C2416yes—
308C2×D316C2416yes—
309C2×D316C2416yes—
310C2×D316C24112yes—
311C2×D316C24112yes—
312C2×D316C24112yes—
313C2×C22⋊D79—424no—
314C2×C22⋊D79C24112yes—
315C2×C22⋊D79C24112yes—
316C2×C22⋊D79C24124yes—
317C2×C22⋊D79C24112yes—
318D4×D79—248no—
319C22×Dic79C24112yes—
320C2×C4×D79—424no—
321C2×C4×D79C24112yes—
322C2×C4×D79C24112yes—
323C2×C4×D79C24124yes—
324C2×C4×D79C24112yes—
325C4⋊Dic79C24112yes—
326C4⋊Dic79C2416yes—
327C4⋊Dic79C2416yes—
328C4⋊Dic79C24112yes—
329C4⋊Dic79C2412yes—
330C4⋊Dic79C2412yes—
331C4⋊Dic79C2412yes—
332C4⋊Dic79C2412yes—
333Dic79⋊C4C24112yes—
334Dic79⋊C4C2414yes—
335Dic79⋊C4C2414yes—
336Dic79⋊C4C24112yes—
337Dic79⋊C4C24112yes—
338Dic79⋊C4C24112yes—
339C22⋊Dic79C24112yes—
340C22⋊Dic79C2414yes—
341C22⋊Dic79C24112yes—
342(C2×D79)⋊C4C24112yes—
343(C2×D79)⋊C4C24124yes—
344(C2×D79)⋊C4C24112yes—
345(C2×D79)⋊C4C24112yes—
346(C2×D79)⋊C4C24124yes—
347(C2×D79)⋊C4C24112yes—
348(C2×D79)⋊C4C24112yes—
349(C2×D79)⋊C4C24112yes—
350C4×Dic79C2414yes—
351C4×Dic79C24112yes—
352C4×Dic79C24112yes—
353C24×C79C2413yes—
354#41×C79—24no—
355#41×C79—212no—
356#41×C79—212no—
357#41×C79#4118yescomplemented
358C2×Q8×C79—24no—
359C2×Q8×C79C2413yes—
360C2×Q8×C79C2411yescharacteristic
361C2×D4×C79—212no—
362C2×D4×C79C2416yes—
363C2×D4×C79C2413yes—
364C2×D4×C79C2413yes—
365C22×C4×C79—212no—
366C22×C4×C79—212no—
367C22×C4×C79—46no—
368C22×C4×C79C2413yes—
369C22×C4×C79C2413yes—
370C22×C4×C79C2413yes—
371C22×C4×C79C2413yes—
372C22×C4×C79C2413yes—
373C22×C4×C79C2411yescharacteristic
374C22×C4×C79C2411yescharacteristic
375C22×C4×C79C2413yes—
376C22×C4×C79C2413yes—
377C22×C4×C79C2413yes—
378C22×C4×C79C2413yes—
379C22×C4×C79C2413yes—
380C22×C4×C79C2413yes—
381C22×C4×C79C2413yes—
382C22×C4×C79C2413yes—
383C22×C4×C79C2413yes—
384C22×C4×C79C2413yes—
385C22×C4×C79C2411yescharacteristic
386C4⋊C4×C79C2413yes—
387C4⋊C4×C79C2413yes—
388C4⋊C4×C79C2413yes—
389C4⋊C4×C79C2413yes—
390C4⋊C4×C79C2416yes—
391C4⋊C4×C79C2416yes—
392C22⋊C4×C79C2416yes—
393C22⋊C4×C79C2416yes—
394C22⋊C4×C79C2416yes—
395C22⋊C4×C79C2416yes—
396C42×C79C2411yescharacteristic
397C42×C79C2411yescharacteristic
398C42×C79C2411yescharacteristic
399C42×C79C2411yescharacteristic
400C42×C79C2413yes—
401C42×C79C2413yes—
402C42×C79C2413yes—
403C42×C79C2413yes—
404C42×C79C2413yes—
405C42×C79C2413yes—
406C42×C79C2413yes—
407C42×C79C2413yes—
408C42×C79C2413yes—
409C42×C79C2413yes—
410C42×C79C2413yes—
411C42×C79C2413yes—
412C23×C79—26no—
413C23×C79—26no—
414C23×C79—43no—
415C23×C79C2513yes—
416C23×C79C2513yes—
417C23×C79C2511yescharacteristic
418C22×D79—224no—
419C22×D79—412no—
420C22×D79—412no—
421C22×D79C25112yes—
422Q8×C79—26no—
423Q8×C79C2×#4114yescomplemented
424D4×C79—212no—
425D4×C79—26no—
426D4×C79C2×#41112yescomplemented
427C2×C4×C79—26no—
428C2×C4×C79—26no—
429C2×C4×C79—22no—
430C2×C4×C79—26no—
431C2×C4×C79—26no—
432C2×C4×C79—26no—
433C2×C4×C79—26no—
434C2×C4×C79—26no—
435C2×C4×C79—26no—
436C2×C4×C79—26no—
437C2×C4×C79—26no—
438C2×C4×C79—26no—
439C2×C4×C79—22no—
440C2×C4×C79—43no—
441C2×C4×C79—43no—
442C2×C4×C79—43no—
443C2×C4×C79C2×#41112yescomplemented
444C2×C4×C79H(5,𝔽2)14yescomplemented
445C2×C4×C79C2513yes—
446C2×C4×C79C2511yescharacteristic
447C2×C4×C79C2511yescharacteristic
448C2×C4×C79C2513yes—
449C2×C4×C79C2513yes—
450C2×C4×C79C2513yes—
451C2×C4×C79C2513yes—
452C2×C4×C79C2513yes—
453C2×C4×C79C2511yescharacteristic
454C2×C4×C79C2511yescharacteristic
455C2×C4×C79C2511yescharacteristic
456C2×C4×C79C2511yescharacteristic
457C22⋊D79—224no—
458C22⋊D79—224no—
459C22⋊D79—424no—
460C22⋊D79—412no—
461C2×Dic79—412no—
462C2×Dic79C2514yes—
463C2×Dic79C2514yes—
464C2×Dic79C25112yes—
465D316—224no—
466D316—212no—
467D316—212no—
468D316—212no—
469D316—412no—
470D316—412no—
471C4×D79—224no—
472C4×D79—224no—
473C4×D79—424no—
474C4×D79—412no—
475Dic158—24no—
476Dic158—212no—
477Dic158—24no—
478Dic158—412no—
479C22×C79—21no—
480C22×C79—23no—
481C22×C79—21no—
482C22×C79—23no—
483C22×C79—23no—
484C22×C79—23no—
485C22×C79—23no—
486C22×C79—412no—
487C22×C79C22×#4116yes—
488C22×C79C2×H(5,𝔽2)12yes—
489C22×C79C2611yescharacteristic
490C2×D79—212no—
491C2×D79—212no—
492C2×D79—212no—
493C2×D79—824no—
494C4×C79—21no—
495C4×C79—23no—
496C4×C79—23no—
497C4×C79—23no—
498C4×C79—21no—
499C4×C79—23no—
500C4×C79—23no—
501C4×C79C22×#4112yes—
502C4×C79C22×#4116yes—
503C4×C79C2×H(5,𝔽2)12yes—
504C4×C79C2×H(5,𝔽2)12yes—
505C4×C79#58512yes—
506Dic79—24no—
507Dic79—212no—
508Dic79—24no—
509#62800—791nomaximal, Sylow
510C2×C79—26no—
511C2×C79—22no—
512C2×C79—43no—
513C2×C79C23×#4111yescharacteristic
514C2×C79C22×H(5,𝔽2)11yescharacteristic
515C2×C79C2×#58511yescharacteristic
516D79—412no—
517#3522—792no—
518#3519—796no—
519#3517—792no—
520#3514—796no—
521#3511—793no—
522#3508—793no—
523#3503—791no—
524#3498—791no—
525#3494—796no—
526#3488—792no—
527#3483—792no—
528#3481—796no—
529#3480—792no—
530D4×#41—796no—
531#3460—796no—
532#3444—793no—
533C2×#532—793no—
534C4×H(5,𝔽2)—792no—
535C2×C4×#41D7911yescharacteristic, complemented
536C79#6280011yescharacteristic, complemented, Sylow
537C2×H(5,𝔽2)—792no—
538C22×#41—796no—
539C22×#41C2×D7911yescharacteristic
540#559—796no—
541#559—796no—
542Q82—792no—
543#557—792no—
544#556—796no—
545#555—796no—
546#555—7912no—
547#554—796no—
548#554—796no—
549#553—7912no—
550#553—7912no—
551#553—7912no—
552#551—7924no—
553#550—794no—
554#550—792no—
555#550—792no—
556#550—796no—
557#550—796no—
558D4×Q8—796no—
559#548—794no—
560#548—7912no—
561#547—796no—
562#547—7912no—
563#546—7912no—
564#546—7912no—
565#546—7912no—
566#546—7924no—
567D42—7912no—
568D42—796no—
569D42—796no—
570#544—796no—
571#542—7912no—
572#542—7912no—
573#540—7912no—
574#540—7912no—
575#538—7924no—
576#537—796no—
577#535—796no—
578#535—796no—
579#533—791no—
580#533—793no—
581#533—793no—
582#532—7912no—
583#532—793no—
584#532—796no—
585#532—796no—
586#532—796no—
587#532—796no—
588#532—796no—
589#532—796no—
590#532—796no—
591#532—793no—
592#532—793no—
593C2×C4⋊Q8—793no—
594C2×#127—793no—
595#529—7912no—
596#529—796no—
597#529—796no—
598#529—796no—
599#529—796no—
600#529—796no—
601#529—796no—
602C2×#124—796no—
603#525—796no—
604#525—796no—
605#525—796no—
606#525—7924no—
607C2×#121—796no—
608C2×#121—796no—
609#520—792no—
610#520—794no—
611#520—796no—
612#518—7912no—
613#518—796no—
614C4×#41—794no—
615C4×#41—796no—
616C4×#41—796no—
617C4×#41—796no—
618C4×#41C2×D7911yescharacteristic
619C4×#41C2×D7911yescharacteristic
620C4×#41C2×D7913yescomplemented
621C4×#41C2×D7913yescomplemented
622C4×#41C2×D7911yescharacteristic, complemented
623C4×#41C2×D7913yescomplemented
624C4×#41C2×D7913yescomplemented
625C4×#41C2×D7911yescharacteristic, complemented
626C2×C4×Q8C2×D7911yescharacteristic, complemented
627C2×C4×Q8C2×D7911yescharacteristic, complemented
628C2×C4×D4—7912no—
629C2×C4×D4—796no—
630C2×C4×D4—796no—
631C2×C4×D4C2×D7913yescomplemented
632C2×C4×D4C2×D7913yescomplemented
633C2×#117C2×D7913yescomplemented
634C22×C42C2×D7913yescomplemented
635H(5,𝔽2)—15816no—
636C2×#41—28no—
637C2×#41—31624no—
638C2×#41—794no—
639C2×#41—796no—
640C2×#41—7912no—
641C2×#41—7912no—
642C2×#41—7912no—
643C2×#41—796no—
644C2×#41—796no—
645C2×#41C22×D7913yes—
646C2×#41C22×D7913yes—
647C2×#41C22×D7911yescharacteristic
648C2×#41C22×D7911yescharacteristic
649C22×Q8—796no—
650C22×Q8C22×D7911yescharacteristic
651C22×D4—7912no—
652C22×D4—7912no—
653C22×D4—796no—
654C22×D4—796no—
655C22×D4—796no—
656C22×D4C22×D7913yes—
657C23×C4—7912no—
658C23×C4C22×D7913yes—
659C23×C4C22×D7913yes—
660C23×C4C22×D7913yes—
661C4⋊Q8—7912no—
662C4⋊Q8—793no—
663C4⋊Q8—796no—
664C4⋊Q8—796no—
665C4⋊Q8—796no—
666C4⋊Q8—791no—
667C4⋊Q8—791no—
668#127—7912no—
669#127—793no—
670#127—796no—
671#127—796no—
672#127—796no—
673#126—7924no—
674#126—7912no—
675#126—7912no—
676#125—7912no—
677#125—792no—
678#125—796no—
679#125—796no—
680#124—7912no—
681#124—7924no—
682#124—796no—
683#124—7912no—
684#124—7912no—
685#124—7912no—
686#124—796no—
687#124—796no—
688#123—7912no—
689#123—7912no—
690#123—7912no—
691#123—7924no—
692#123—7924no—
693#123—7924no—
694C22⋊Q8—7912no—
695C22⋊Q8—792no—
696C22⋊Q8—792no—
697C22⋊Q8—796no—
698C22⋊Q8—796no—
699C22⋊Q8—796no—
700C22⋊Q8—796no—
701C22⋊Q8—7924no—
702C22⋊Q8—7924no—
703#121—7924no—
704#121—7912no—
705#121—796no—
706#121—796no—
707#121—7912no—
708#121—7912no—
709#121—7912no—
710#121—7912no—
711#121—7912no—
712#121—7912no—
713#121—796no—
714#121—796no—
715#121—796no—
716#121—796no—
717#121—7912no—
718#121—7912no—
719#121—7924no—
720#121—7924no—
721#120—7912no—
722#120—7924no—
723#120—7924no—
724C4×Q8—794no—
725C4×Q8—792no—
726C4×Q8—792no—
727C4×Q8—796no—
728C4×Q8—796no—
729C4×Q8—796no—
730C4×Q8—796no—
731C4×Q8C22×D7911yescharacteristic
732C4×Q8C22×D7911yescharacteristic
733C4×Q8C22×D7911yescharacteristic
734C4×Q8C22×D7911yescharacteristic
735C4×Q8C22×D7913yes—
736C4×Q8C22×D7913yes—
737C4×Q8C22×D7913yes—
738C4×Q8C22×D7913yes—
739C4×D4—7912no—
740C4×D4—7912no—
741C4×D4—7912no—
742C4×D4—7912no—
743C4×D4—7912no—
744C4×D4—7912no—
745C4×D4—7912no—
746C4×D4—7912no—
747C4×D4—7912no—
748C4×D4—7924no—
749C4×D4—7912no—
750C4×D4—796no—
751C4×D4—796no—
752C4×D4—7912no—
753C4×D4—7912no—
754C4×D4—7912no—
755C4×D4—7912no—
756C4×D4—7912no—
757C4×D4—796no—
758C4×D4—796no—
759C4×D4—796no—
760C4×D4—796no—
761C4×D4C22×D7913yes—
762C4×D4C22×D7913yes—
763C4×D4C22×D7913yes—
764C4×D4C22×D7913yes—
765C4×D4C22×D7916yes—
766C4×D4C22×D7913yes—
767C4×D4C22×D7916yes—
768C4×D4C22×D7913yes—
769C4×D4C22×D7916yes—
770C4×D4C22×D7916yes—
771C4×D4C22×D7913yes—
772C4×D4C22×D7913yes—
773#117—792no—
774#117—796no—
775#117—796no—
776#117—7912no—
777#117—7912no—
778#117—7912no—
779#117—7912no—
780#117C22×D7913yes—
781#117C22×D7913yes—
782#117C22×D7916yes—
783#117C22×D7916yes—
784#117C22×D7913yes—
785#117C22×D7913yes—
786C2×C4⋊C4—796no—
787C2×C4⋊C4—796no—
788C2×C4⋊C4—7912no—
789C2×C4⋊C4C22×D7913yes—
790C2×C4⋊C4C22×D7913yes—
791C2×C22⋊C4—7912no—
792C2×C22⋊C4—7912no—
793C2×C22⋊C4—7924no—
794C2×C22⋊C4C22×D7916yes—
795C2×C42—7912no—
796C2×C42C22×D7913yes—
797C2×C42C22×D7913yes—
798C2×C42C22×D7913yes—
799C2×C42C22×D7913yes—
800C2×C42C22×D7913yes—
801C2×C42C22×D7913yes—
802C2×C42C22×D7913yes—
803C2×C42C22×D7913yes—
804C2×C42C22×D7913yes—
805C2×C42C22×D7913yes—
806C2×C42C22×D7913yes—
807C2×C42C22×D7911yescharacteristic
808C24—7912no—
809C24C23×D7913yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—31624no—
814#41—31612no—
815#41—31624no—
816#41—31624no—
817#41—15816no—
818#41—15824no—
819#41—15824no—
820#41#1192962418yescomplemented
821C2×Q8—24no—
822C2×Q8—31612no—
823C2×Q8—7912no—
824C2×Q8—792no—
825C2×Q8—792no—
826C2×Q8—796no—
827C2×Q8C23×D7913yes—
828C2×Q8C23×D7911yescharacteristic
829C2×D4—212no—
830C2×D4—31612no—
831C2×D4—31612no—
832C2×D4—31624no—
833C2×D4—7912no—
834C2×D4—7924no—
835C2×D4—7912no—
836C2×D4—7912no—
837C2×D4—7912no—
838C2×D4—7912no—
839C2×D4—796no—
840C2×D4—7912no—
841C2×D4—796no—
842C2×D4—796no—
843C2×D4—15848no—
844C2×D4—15824no—
845C2×D4C23×D7916yes—
846C2×D4C23×D7913yes—
847C2×D4C23×D7913yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—31624no—
852C22×C4—7912no—
853C22×C4—7912no—
854C22×C4—7924no—
855C22×C4—7912no—
856C22×C4—7912no—
857C22×C4C23×D7911yescharacteristic
858C22×C4C23×D7911yescharacteristic
859C22×C4C23×D7913yes—
860C22×C4C23×D7913yes—
861C22×C4C23×D7913yes—
862C22×C4C23×D7913yes—
863C22×C4C23×D7913yes—
864C22×C4C23×D7913yes—
865C22×C4C23×D7913yes—
866C22×C4C23×D7913yes—
867C22×C4C23×D7913yes—
868C22×C4C23×D7913yes—
869C22×C4C23×D7913yes—
870C22×C4C23×D7913yes—
871C22×C4C23×D7913yes—
872C22×C4C23×D7913yes—
873C22×C4C23×D7913yes—
874C22×C4C23×D7911yescharacteristic
875C4⋊C4—7912no—
876C4⋊C4—794no—
877C4⋊C4—794no—
878C4⋊C4—7912no—
879C4⋊C4—7912no—
880C4⋊C4—7912no—
881C4⋊C4—796no—
882C4⋊C4—7912no—
883C4⋊C4—796no—
884C4⋊C4—7912no—
885C4⋊C4—792no—
886C4⋊C4—792no—
887C4⋊C4—792no—
888C4⋊C4—792no—
889C4⋊C4C23×D7913yes—
890C4⋊C4C23×D7913yes—
891C4⋊C4C23×D7913yes—
892C4⋊C4C23×D7913yes—
893C4⋊C4C23×D7916yes—
894C4⋊C4C23×D7916yes—
895C22⋊C4—7912no—
896C22⋊C4—794no—
897C22⋊C4—7912no—
898C22⋊C4—7912no—
899C22⋊C4—7924no—
900C22⋊C4—7912no—
901C22⋊C4—7912no—
902C22⋊C4—7924no—
903C22⋊C4—7912no—
904C22⋊C4—7912no—
905C22⋊C4—7912no—
906C22⋊C4C23×D7916yes—
907C22⋊C4C23×D7916yes—
908C22⋊C4C23×D7916yes—
909C22⋊C4C23×D7916yes—
910C42—7912no—
911C42—7912no—
912C42—794no—
913C42C23×D7911yescharacteristic
914C42C23×D7911yescharacteristic
915C42C23×D7913yes—
916C42C23×D7913yes—
917C42C23×D7913yes—
918C42C23×D7913yes—
919C42C23×D7913yes—
920C42C23×D7913yes—
921C42C23×D7913yes—
922C42C23×D7913yes—
923C42C23×D7913yes—
924C42C23×D7913yes—
925C42C23×D7913yes—
926C42C23×D7911yescharacteristic
927C42C23×D7911yescharacteristic
928C42C23×D7913yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—31612no—
933C23—31612no—
934C23—7912no—
935C23—15824no—
936C23C24×D7913yes—
937C23C24×D7911yescharacteristic
938C23C24×D7913yes—
939Q8—26no—
940Q8—31612no—
941Q8—15812no—
942Q8—1584no—
943Q8—1584no—
944Q8C2×#1192962414yescomplemented
945D4—212no—
946D4—26no—
947D4—31612no—
948D4—31612no—
949D4—31624no—
950D4—31612no—
951D4—15824no—
952D4—15824no—
953D4—15812no—
954D4—15812no—
955D4—15812no—
956D4—15824no—
957D4C2×#11929624112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—22no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—22no—
968C2×C4—26no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—31624no—
975C2×C4—31612no—
976C2×C4—31612no—
977C2×C4—794no—
978C2×C4—794no—
979C2×C4—7912no—
980C2×C4—15824no—
981C2×C4—15824no—
982C2×C4C2×#11929624112yescomplemented
983C2×C4#1457920714yescomplemented
984C2×C4C24×D7913yes—
985C2×C4C24×D7911yescharacteristic
986C2×C4C24×D7911yescharacteristic
987C2×C4C24×D7913yes—
988C2×C4C24×D7913yes—
989C2×C4C24×D7913yes—
990C2×C4C24×D7913yes—
991C2×C4C24×D7911yescharacteristic
992C2×C4C24×D7911yescharacteristic
993C2×C4C24×D7913yes—
994C2×C4C24×D7911yescharacteristic
995C2×C4C24×D7911yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—63224no—
1005C22—15812no—
1006C22—15812no—
1007C22—15812no—
1008C22C22×#1192962416yes—
1009C22C2×#1457920712yes—
1010C22C25×D7911yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—1584no—
1019C4—15812no—
1020C4—1584no—
1021C4C22×#1192962412yes—
1022C4C22×#1192962416yes—
1023C4C2×#1457920712yes—
1024C4C2×#1457920712yes—
1025C4#1909939912yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—31612no—
1030C2C23×#1192962411yescharacteristic
1031C2C22×#1457920711yescharacteristic
1032C2C2×#1909939911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×C4×#41×C79C2
hypercenterC2×C4×#41D79
hypocenterC79#62800
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #23777485C2semidirect
2. #23777432C2semidirect
3. #23777406C2semidirect
4. #23777361C2semidirect
5. #23777311C2semidirect
6. #23777276C2semidirect
7. #23777219C2semidirect
8. #23777178C2semidirect
9. #23777135C2semidirect
10. #23777069C2semidirect
11. #23777026C2semidirect
12. #23777010C2semidirect
13. #23776995C2semidirect
14. D4×#11929624C2semidirect
15. #23776816C2semidirect
16. #23776696C2semidirect
17. C2×#19099113C2semidirect
18. C4×#14579207C2semidirect
19. C2×C4×#41×C79C2semidirect
21. C22×#11929624C22semidirect
22. #19099298C22semidirect
23. #19099298C22semidirect
24. Q8×Dic158C22semidirect
25. #19099292C22semidirect
26. #19099286C22semidirect
27. #19099278C22semidirect
28. #19099276C22semidirect
29. #19099273C22semidirect
30. #19099270C22semidirect
31. #19099261C22semidirect
32. #19099259C22semidirect
33. #19099257C22semidirect
34. #19099237C22semidirect
35. #19099235C22semidirect
36. #19099235C22semidirect
37. #19099234C22semidirect
38. #19099234C22semidirect
39. #19099232C22semidirect
40. D4×Dic158C22semidirect
41. #19099224C22semidirect
42. #19099222C22semidirect
43. #19099218C22semidirect
44. #19099214C22semidirect
45. #19099209C22semidirect
46. #19099209C22semidirect
47. #19099203C22semidirect
48. #19099201C22semidirect
49. D4×D316C22semidirect
50. D4×D316C22semidirect
51. D4×C22⋊D79C22semidirect
52. #19099191C22semidirect
53. #19099185C22semidirect
54. #19099184C22semidirect
55. #19099168C22semidirect
56. #19099164C22semidirect
57. #19099146C22semidirect
58. #19099141C22semidirect
59. #19099132C22semidirect
60. #19099127C22semidirect
61. #19099120C22semidirect
62. #19099120C22semidirect
63. #19099120C22semidirect
64. #19099113C22semidirect
65. #19099113C22semidirect
66. #19099113C22semidirect
67. #19099113C22semidirect
68. #19099113C22semidirect
69. #19099113C22semidirect
70. #19099113C22semidirect
71. #19099113C22semidirect
72. #19099113C22semidirect
73. #19099113C22semidirect
74. #19099110C22semidirect
75. C2×#14579161C22semidirect
76. C2×#14579158C22semidirect
77. #19099100C22semidirect
78. #19099097C22semidirect
79. #19099097C22semidirect
80. #19099097C22semidirect
81. #19099097C22semidirect
82. #19099097C22semidirect
83. #19099097C22semidirect
84. C2×#14579149C22semidirect
85. #19099074C22semidirect
86. #19099074C22semidirect
87. #19099074C22semidirect
88. #19099072C22semidirect
89. C2×#14579135C22semidirect
90. C2×#14579135C22semidirect
92. #19099045C22semidirect
93. #19099043C22semidirect
94. #19099037C22semidirect
95. #19099035C22semidirect
96. C4×#11929625C22semidirect
97. C4×#11929624C22semidirect
98. C4×#11929624C22semidirect
99. C4×#11929624C22semidirect
100. C2×C4×D316C22semidirect
101. C2×C4×D316C22semidirect
102. C4×D4×D79C22semidirect
106. C4×#41×C79C22semidirect
107. C4×#41×C79C22semidirect
108. C4×#41×C79C22semidirect
109. C4×#41×C79C22semidirect
110. C4×#41×C79C22semidirect
111. C4×#41×C79C22semidirect
112. C2×C4×Q8×C79C22semidirect
113. C2×C4×Q8×C79C22semidirect
114. C2×C4×D4×C79C22semidirect
115. C2×C4×D4×C79C22semidirect
116. C2×#117×C79C22semidirect
117. C22×C42×C79C22semidirect
357. #41×C79#41semidirect
423. Q8×C79C2×#41semidirect
426. D4×C79C2×#41semidirect
443. C2×C4×C79C2×#41semidirect
444. C2×C4×C79H(5,𝔽2)semidirect
535. C2×C4×#41D79semidirect
536. C79#62800semidirect
620. C4×#41C2×D79semidirect
621. C4×#41C2×D79semidirect
622. C4×#41C2×D79semidirect
623. C4×#41C2×D79semidirect
624. C4×#41C2×D79semidirect
625. C4×#41C2×D79semidirect
626. C2×C4×Q8C2×D79semidirect
627. C2×C4×Q8C2×D79semidirect
631. C2×C4×D4C2×D79semidirect
632. C2×C4×D4C2×D79semidirect
633. C2×#117C2×D79semidirect
634. C22×C42C2×D79semidirect
820. #41#11929624semidirect
944. Q8C2×#11929624semidirect
957. D4C2×#11929624semidirect
982. C2×C4C2×#11929624semidirect
983. C2×C4#14579207semidirect

Maximal subgroups

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

subgroupindex
#237774852
#237774322
#237774062
#237773612
#237773112
#237772762
#237772192
#237771782
#237771352
#237770692
#237770262
#237770102
#237769952
D4×#119296242
#237768162
#237766962
C2×#190991132
C4×#145792072
C2×C4×#41×C792
#6280079