Finite Group Databasebeta

← #35201991

Subgroups — #35201991

Order 20224.

6184 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778010C214yesmaximal, complemented
2#23778006C212yesmaximal, complemented
3#23778004C218yesmaximal, complemented
4#23778002C214yesmaximal, complemented
5#23777999C218yesmaximal, complemented
6#23777996C214yesmaximal, complemented
7#23777895C211yesmaximal, characteristic, complemented
8#23777892C214yesmaximal, complemented
9#23777856C212yesmaximal, complemented
10#23777852C218yesmaximal, complemented
11#23777547C211yesmaximal, characteristic, complemented
12C2×C79⋊#564C212yesmaximal, complemented
13#23777379C214yesmaximal, complemented
14#23777378C212yesmaximal, complemented
15#23777368C214yesmaximal, complemented
16#23777220C214yesmaximal, complemented
17C79×#3504C211yesmaximal, characteristic, complemented
18C79⋊#564C2211yescharacteristic
19C79⋊#564C2218yes—
20C79⋊#564C2212yes—
21C79⋊#564C2218yes—
22C79⋊#564C2218yes—
23C79⋊#564C2214yes—
24C79⋊#564C2218yes—
25C79⋊#564C2212yes—
26#19099317C2212yes—
27#19099317C2214yes—
28#19099314C2214yes—
29#19099314C2218yes—
30#19099312C2214yes—
31#19099312C2218yes—
32#19099311C2211yescharacteristic
33#19099309C2214yes—
34#19099292C2214yes—
35#19099291C2214yes—
36#19099291C2212yes—
37#19099291C2214yes—
38#19099290C2214yes—
39#19099290C2214yes—
40#19099289C2218yes—
41#19099288C2214yes—
42#19099288C2218yes—
43#19099288C2214yes—
44#19099274C2214yes—
45#19099273C2212yes—
46#19099272C2214yes—
47#19099271C2218yes—
48#19099270C2212yes—
49#19099268C2218yes—
50#19099268C2214yes—
51#19099267C2218yes—
52#19099267C2218yes—
53#19099262C2218yes—
54#19099261C2218yes—
55#19099259C2214yes—
56#19099255C2218yes—
57#19099255C2218yes—
58#19099255C2218yes—
59#19099254C2218yes—
60#19099254C2214yes—
61#19099253C2218yes—
62#19099253C2214yes—
63#19099252C2214yes—
64#19099251C2214yes—
65#19099251C2214yes—
66#19099248C2218yes—
67#19099248C2214yes—
68#19099247C2218yes—
69#19099246C2218yes—
70#19099246C2218yes—
71#19099246C2218yes—
72#19099245C2218yes—
73#19099245C2218yes—
74#19099217C2214yes—
75#19099217C2212yes—
76#19099212C2214yes—
77#19099194C2214yes—
78#19099193C2214yes—
79#19099192C2218yes—
80#19099192C2218yes—
81#19099190C2214yes—
82#19099190C2218yes—
83#19099190C2218yes—
84#19099176C2214yes—
85#19099176C2214yes—
86#19099175C2214yes—
87#19099174C2218yes—
88#19099174C2218yes—
89#19099173C2218yes—
90#19099173C2218yes—
91#19099172C2218yes—
92#19099172C2218yes—
93#19099172C2218yes—
94#19099172C2218yes—
95#19099171C2218yes—
96#19099171C2214yes—
97#19099171C2214yes—
98#19099171C2218yes—
99#19099162C2218yes—
100#19099162C2218yes—
101#19099161C2218yes—
102#19099160C2214yes—
103#19099160C2218yes—
104#19099159C2218yes—
105#19099155C2218yes—
106#19099155C2218yes—
107#19099120C2212yes—
108#19099118C2214yes—
109#19099117C2214yes—
110#19099117C2214yes—
111#19099115C2218yes—
112#19099100C2214yes—
113#19099099C2218yes—
114#19099097C2212yes—
115#19099097C2214yes—
116#19099093C2218yes—
117#19099091C2214yes—
118C2×#14579153C2214yes—
119C2×#14579152C2218yes—
120C2×#14579151C2218yes—
121C2×#14579151C2218yes—
122#125×D79C2214yes—
123#19099042C2214yes—
124#19099042C2214yes—
125C4×#11929623C2214yes—
126#557×C79C2214yes—
127#554×C79C2218yes—
128#554×C79C2214yes—
129#544×C79C2214yes—
130#544×C79C2212yes—
131#533×C79C2211yescharacteristic
132#533×C79C2212yes—
133C2×#125×C79C2212yes—
134C2×#125×C79C2211yescharacteristic
135#520×C79C2212yes—
136C4×#41×C79C2211yescharacteristic
137C2×#11929623C2314yes—
138#14579161C2314yes—
139#14579161C2312yes—
140#14579161C2312yes—
141#14579160C2318yes—
142#14579160C2318yes—
143#14579160C2318yes—
144#14579160C2314yes—
145#14579160C2314yes—
146#14579159C2314yes—
147#14579159C2318yes—
148#14579159C2318yes—
149#14579159C2318yes—
150#14579159C2314yes—
151#14579156C2318yes—
152#14579156C2318yes—
153#14579156C2318yes—
154#14579156C2318yes—
155#14579156C2318yes—
156#14579156C2318yes—
157#14579156C2314yes—
158#14579156C2318yes—
159#14579156C2318yes—
160#14579156C2314yes—
161#14579156C2318yes—
162#14579156C2314yes—
163#14579155C2318yes—
164#14579155C2318yes—
165#14579155C2318yes—
166#14579155C2314yes—
167#14579154C2318yes—
168#14579154C2318yes—
169#14579154C2318yes—
170#14579154C2314yes—
171#14579153C2318yes—
172#14579153C2318yes—
173#14579153C2318yes—
174#14579153C2314yes—
175#14579153C2314yes—
176#14579153C2318yes—
177#14579153C2314yes—
178#14579153C2312yes—
179#14579153C2314yes—
180#14579152C2318yes—
181#14579152C2318yes—
182#14579152C2318yes—
183#14579152C2318yes—
184#14579152C2314yes—
185#14579152C2314yes—
186#14579152C2318yes—
187#14579152C2318yes—
188#14579152C2318yes—
189#14579152C2318yes—
190#14579152C2318yes—
191#14579152C2318yes—
192#14579152C2314yes—
193#14579152C2318yes—
194#14579151C2318yes—
195#14579151C2318yes—
196#14579151C2318yes—
197#14579151C2318yes—
198#14579151C2318yes—
199#14579151C2318yes—
200#14579151C2318yes—
201#14579151C2318yes—
202#14579151C2318yes—
203#14579151C2318yes—
204#14579151C2318yes—
205#14579151C2318yes—
206#14579151C2318yes—
207#14579151C2318yes—
208#14579151C2318yes—
209#14579151C2318yes—
210#14579151C2318yes—
211#14579151C2318yes—
212#14579151C2318yes—
213#14579151C2318yes—
214#14579151C2318yes—
215#14579151C2314yes—
216#14579151C2318yes—
217#14579151C2314yes—
218#14579151C2314yes—
219#14579151C2318yes—
220#14579150C2314yes—
221#14579149C2312yes—
222#14579147C2314yes—
223#14579146C2318yes—
224#14579146C2314yes—
225#14579146C2318yes—
226#14579146C2318yes—
227#14579146C2314yes—
228#14579146C2314yes—
229#14579145C2318yes—
230#14579145C2318yes—
231#14579145C2318yes—
232#14579144C2314yes—
233#14579144C2318yes—
234#14579144C2318yes—
235#14579143C2314yes—
236#14579143C2318yes—
237#14579142C2318yes—
238#14579141C2318yes—
239#14579141C2314yes—
240#14579141C2314yes—
241#14579141C2314yes—
242#14579141C2314yes—
243#14579140C2314yes—
244#14579140C2318yes—
245#14579140C2318yes—
246#14579140C2314yes—
247#14579140C2314yes—
248#14579140C2312yes—
249#14579139C2318yes—
250#14579139C2318yes—
251#14579139C2318yes—
252#14579139C2318yes—
253#14579139C2318yes—
254#14579139C2314yes—
255#14579139C2314yes—
256#14579139C2314yes—
257#14579138C2318yes—
258#14579138C2318yes—
259#14579138C2318yes—
260#14579137C2318yes—
261#14579137C2318yes—
262#14579137C2318yes—
263#14579137C2318yes—
264#14579137C2314yes—
265#14579137C2314yes—
266#14579137C2314yes—
267#14579136C2314yes—
268#14579135C2312yes—
269#14579135C2318yes—
270#14579135C2314yes—
271#14579134C2314yes—
272#14579133C2318yes—
273Q8×Dic79C2318yes—
274Q8×Dic79C2318yes—
275Q8×Dic79C2318yes—
276C4×Dic158C2318yes—
277C4×Dic158C2318yes—
278C4×Dic158C2314yes—
279C4×Dic158C2314yes—
280C4×Dic158C2314yes—
281C4×Dic158C2314yes—
282C4×Dic158C2314yes—
283C4×Dic158C2312yes—
284C4×Dic158C2314yes—
285#14579126C2318yes—
286#14579126C2318yes—
287#14579126C2318yes—
288#14579126C2314yes—
289#14579126C2314yes—
290#14579126C2314yes—
291C4×D316C2314yes—
292C4×D316C2312yes—
293C4×D316C2314yes—
294D4×Dic79C2314yes—
295#14579123C2318yes—
296C4×C22⋊D79C2318yes—
297C4×C22⋊D79C2318yes—
298C4×C22⋊D79C2318yes—
299C4×C22⋊D79C2318yes—
300C4×C22⋊D79C2314yes—
301(C22⋊D79)⋊C4C2318yes—
302(C22⋊D79)⋊C4C2318yes—
303(C22⋊D79)⋊C4C2318yes—
304#14579120C2314yes—
305#14579120C2318yes—
306#14579119C2318yes—
307#14579119C2318yes—
308#14579119C2318yes—
309#14579119C2314yes—
310#14579118C2318yes—
311#14579118C2314yes—
312#14579118C2314yes—
313#14579118C2318yes—
314#14579118C2318yes—
315#14579117C2318yes—
316#14579117C2318yes—
317#14579117C2318yes—
318C2×C4⋊Dic79C2318yes—
319C2×C4⋊Dic79C2314yes—
320C2×C4⋊Dic79C2314yes—
321C2×Dic79⋊C4C2318yes—
322C2×Dic79⋊C4C2318yes—
323C2×Dic79⋊C4C2318yes—
324C2×Dic79⋊C4C2318yes—
325C4⋊C4×D79C2318yes—
326C4⋊C4×D79C2318yes—
327C4⋊C4×D79C2314yes—
328C4⋊C4×D79C2314yes—
329C2×C4×Dic79C2318yes—
330C42×D79C2314yes—
331C2×#41×C79C2311yescharacteristic
332C4⋊Q8×C79C2314yes—
333C4⋊Q8×C79C2318yes—
334C4⋊Q8×C79C2314yes—
335C4⋊Q8×C79C2312yes—
336#125×C79C2318yes—
337#125×C79C2312yes—
338#125×C79C2318yes—
339#125×C79C2314yes—
340#125×C79C2314yes—
341#125×C79C2314yes—
342#125×C79C2311yescharacteristic
343#125×C79C2312yes—
344#125×C79C2311yescharacteristic
345C22⋊Q8×C79C2318yes—
346C22⋊Q8×C79C2318yes—
347C22⋊Q8×C79C2318yes—
348C22⋊Q8×C79C2314yes—
349C22⋊Q8×C79C2318yes—
350C4×Q8×C79C2312yes—
351C4×Q8×C79C2318yes—
352C4×Q8×C79C2314yes—
353C4×Q8×C79C2314yes—
354C4×D4×C79C2314yes—
355C4×D4×C79C2318yes—
356C4×D4×C79C2312yes—
357C4×D4×C79C2314yes—
358#117×C79C2312yes—
359#117×C79C2312yes—
360#117×C79C2311yescharacteristic
361#117×C79C2314yes—
362C2×C4⋊C4×C79C2314yes—
363C2×C4⋊C4×C79C2314yes—
364C2×C4⋊C4×C79C2312yes—
365C2×C4⋊C4×C79C2318yes—
366C2×C42×C79C2312yes—
367C2×C42×C79C2311yescharacteristic
368#11929623—216no—
369C2×Dic158C2414yes—
370C2×Dic158C2414yes—
371C2×Dic158C2418yes—
372C2×Dic158C2414yes—
373C2×Dic158C2412yes—
374C2×D316C2414yes—
375C2×D316C2412yes—
376C2×C22⋊D79C2418yes—
377C2×C22⋊D79C2414yes—
378C22×Dic79C2418yes—
379C22×Dic79C2418yes—
380C2×C4×D79C2414yes—
381C2×C4×D79C2414yes—
382C2×C4×D79C2414yes—
383C2×C4×D79C2418yes—
384C2×C4×D79C2418yes—
385C4⋊Dic79C2414yes—
386C4⋊Dic79C2418yes—
387C4⋊Dic79C2418yes—
388C4⋊Dic79C2414yes—
389C4⋊Dic79C2412yes—
390C4⋊Dic79C2412yes—
391C4⋊Dic79C2418yes—
392C4⋊Dic79C2418yes—
393C4⋊Dic79C2418yes—
394C4⋊Dic79C2414yes—
395C4⋊Dic79C2414yes—
396C4⋊Dic79C2418yes—
397C4⋊Dic79C2414yes—
398C4⋊Dic79C2418yes—
399C4⋊Dic79C2414yes—
400Dic79⋊C4C2418yes—
401Dic79⋊C4C2418yes—
402Dic79⋊C4C2418yes—
403Dic79⋊C4C2418yes—
404Dic79⋊C4C2418yes—
405Dic79⋊C4C2418yes—
406Dic79⋊C4C2414yes—
407Dic79⋊C4C2414yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C2414yes—
410Dic79⋊C4C2418yes—
411Dic79⋊C4C2418yes—
412Dic79⋊C4C2418yes—
413Dic79⋊C4C2418yes—
414Dic79⋊C4C2418yes—
415Dic79⋊C4C2418yes—
416Dic79⋊C4C2418yes—
417Dic79⋊C4C2418yes—
418Dic79⋊C4C2414yes—
419Dic79⋊C4C2414yes—
420Dic79⋊C4C2418yes—
421Dic79⋊C4C2418yes—
422Dic79⋊C4C2414yes—
423Dic79⋊C4C2414yes—
424Dic79⋊C4C2418yes—
425C22⋊Dic79C2418yes—
426C22⋊Dic79C2418yes—
427C22⋊Dic79C2414yes—
428(C2×D79)⋊C4C2414yes—
429(C2×D79)⋊C4C2418yes—
430(C2×D79)⋊C4C2414yes—
431(C2×D79)⋊C4C2418yes—
432(C2×D79)⋊C4C2418yes—
433(C2×D79)⋊C4C2414yes—
434(C2×D79)⋊C4C2414yes—
435(C2×D79)⋊C4C2414yes—
436(C2×D79)⋊C4C2414yes—
437(C2×D79)⋊C4C2418yes—
438(C2×D79)⋊C4C2414yes—
439(C2×D79)⋊C4C2414yes—
440(C2×D79)⋊C4C2418yes—
441C4×Dic79C2414yes—
442C4×Dic79C2414yes—
443C4×Dic79C2414yes—
444C4×Dic79C2418yes—
445C4×Dic79C2418yes—
446C4×Dic79C2418yes—
447C4×Dic79C2418yes—
448C4×Dic79C2418yes—
449C4×Dic79C2418yes—
450C4×Dic79C2418yes—
451#41×C79—24no—
452C2×Q8×C79C2411yescharacteristic
453C2×Q8×C79C2418yes—
454C2×Q8×C79C2414yes—
455C2×D4×C79C2412yes—
456C2×D4×C79C2411yescharacteristic
457C22×C4×C79C2412yes—
458C22×C4×C79C2411yescharacteristic
459C22×C4×C79C2414yes—
460C22×C4×C79C2412yes—
461C22×C4×C79C2418yes—
462C22×C4×C79C2414yes—
463C4⋊C4×C79C2414yes—
464C4⋊C4×C79C2412yes—
465C4⋊C4×C79C2414yes—
466C4⋊C4×C79C2418yes—
467C4⋊C4×C79C2414yes—
468C4⋊C4×C79C2418yes—
469C4⋊C4×C79C2418yes—
470C4⋊C4×C79C2418yes—
471C4⋊C4×C79C2418yes—
472C4⋊C4×C79C2412yes—
473C4⋊C4×C79C2412yes—
474C4⋊C4×C79C2414yes—
475C4⋊C4×C79C2414yes—
476C4⋊C4×C79C2418yes—
477C4⋊C4×C79C2414yes—
478C22⋊C4×C79C2414yes—
479C22⋊C4×C79C2418yes—
480C22⋊C4×C79C2414yes—
481C22⋊C4×C79C2412yes—
482C42×C79C2411yescharacteristic
483C42×C79C2412yes—
484C42×C79C2411yescharacteristic
485C42×C79C2412yes—
486C42×C79C2414yes—
487C42×C79C2414yes—
488C42×C79C2418yes—
489C23×C79C2511yescharacteristic
490C23×C79C2512yes—
491C22×D79C2514yes—
492Q8×C79—22no—
493Q8×C79—48no—
494Q8×C79—44no—
495D4×C79—24no—
496D4×C792−1+414yes—
497C2×C4×C79—24no—
498C2×C4×C79—22no—
499C2×C4×C79—42no—
500C2×C4×C79—44no—
501C2×C4×C79—44no—
502C2×C4×C79—48no—
503C2×C4×C79C2512yes—
504C2×C4×C79C2514yes—
505C2×C4×C79C2518yes—
506C2×C4×C79C2514yes—
507C2×C4×C79C2514yes—
508C2×C4×C79C2512yes—
509C2×C4×C79C2511yescharacteristic
510C2×C4×C79C2512yes—
511C2×C4×C79C2511yescharacteristic
512C22⋊D79—216no—
513C22⋊D79—44no—
514C2×Dic79—216no—
515C2×Dic79—48no—
516C2×Dic79C2514yes—
517C2×Dic79C2518yes—
518C2×Dic79C2514yes—
519C2×Dic79C2518yes—
520C2×Dic79C2514yes—
521D316—42no—
522D316—44no—
523C4×D79—28no—
524C4×D79—44no—
525C4×D79—44no—
526C4×D79—48no—
527C4×D79—48no—
528Dic158—28no—
529Dic158—44no—
530Dic158—42no—
531Dic158—48no—
532Dic158—44no—
533C22×C79—24no—
534C22×C79—21no—
535C22×C79—22no—
536C22×C79C2×2−1+414yes—
537C22×C79C2611yescharacteristic
538C2×D79—24no—
539C2×D79—24no—
540C2×D79—24no—
541C4×C79—21no—
542C4×C79—22no—
543C4×C79—22no—
544C4×C79—28no—
545C4×C79—24no—
546C4×C79—22no—
547C4×C79—24no—
548C4×C79—24no—
549C4×C79C2×2−1+412yes—
550Dic79—28no—
551Dic79—24no—
552Dic79—24no—
553Dic79—24no—
554Dic79—28no—
555#63067—791nomaximal, Sylow
556C2×C79—24no—
557C2×C79—41no—
558C2×C79C22×2−1+411yescharacteristic
559C2×C792−1+612yes—
560D79—44no—
561#3563—794no—
562#3563—798no—
563#3563—798no—
564#3563—794no—
565#3563—794no—
566#3563—792no—
567#3556—794no—
568#3556—791no—
569#3553—798no—
570#3553—792no—
571#3531—791no—
572C2×#564—792no—
573#3515—794no—
574#3515—794no—
575#3515—792no—
576#3504—794no—
577#3504D7911yescharacteristic, complemented
578C79#6306711yescharacteristic, complemented, Sylow
579#564—791no—
580#564—798no—
581#564—792no—
582#564—798no—
583#564—798no—
584#564—794no—
585#564—798no—
586#564—792no—
587#563—794no—
588#563—798no—
589#563—792no—
590#563—794no—
591#563—794no—
592#563—798no—
593#562—791no—
594#562—794no—
595#557—794no—
596#557—794no—
597#557—798no—
598#557—794no—
599#557—794no—
600#557—798no—
601#557—794no—
602#557—794no—
603#557—792no—
604#557—794no—
605#557C2×D7914yes—
606#554—794no—
607#554—798no—
608#554—798no—
609#554—798no—
610#554—792no—
611#554—792no—
612#554—794no—
613#554—798no—
614#554—794no—
615#554C2×D7914yes—
616#554C2×D7918yes—
617#553—794no—
618#553—798no—
619#553—798no—
620#552—798no—
621#552—798no—
622#552—794no—
623#552—794no—
624#552—798no—
625#552—798no—
626#552—798no—
627#552—798no—
628#552—794no—
629#552—798no—
630#552—798no—
631#552—794no—
632#552—798no—
633#552—798no—
634#552—798no—
635#552—794no—
636#552—794no—
637#552—798no—
638#547—794no—
639#547—794no—
640#547—792no—
641#544—794no—
642#544—798no—
643#544—798no—
644#544—794no—
645#544—798no—
646#544—798no—
647#544—794no—
648#544C2×D7914yes—
649#544C2×D7912yes—
650#541—798no—
651#541—798no—
652#541—798no—
653#541—798no—
654#541—798no—
655#541—798no—
656#541—794no—
657#541—794no—
658#541—798no—
659#541—798no—
660#541—794no—
661#541—794no—
662#541—798no—
663#541—798no—
664#541—794no—
665#539—798no—
666#539—798no—
667#539—798no—
668#539—798no—
669#539—798no—
670#539—798no—
671#539—798no—
672#539—794no—
673#533—794no—
674#533—798no—
675#533—794no—
676#533—794no—
677#533—792no—
678#533C2×D7911yescharacteristic
679#533C2×D7912yes—
680#529—798no—
681#529—794no—
682#529—798no—
683#529—794no—
684#529—792no—
685#529—794no—
686C2×#125—794no—
687C2×#125—798no—
688C2×#125—798no—
689C2×#125—798no—
690C2×#125—794no—
691C2×#125C2×D7912yes—
692C2×#125C2×D7911yescharacteristic
693#520—794no—
694#520—794no—
695#520C2×D7912yes—
696C4×#41—794no—
697C4×#41C2×D7911yescharacteristic
698C2×#41—794no—
699C2×#41C22×D7911yescharacteristic
700C4⋊Q8—798no—
701C4⋊Q8—794no—
702C4⋊Q8—794no—
703C4⋊Q8—798no—
704C4⋊Q8—798no—
705C4⋊Q8—798no—
706C4⋊Q8—794no—
707C4⋊Q8—794no—
708C4⋊Q8—798no—
709C4⋊Q8—798no—
710C4⋊Q8—794no—
711C4⋊Q8—792no—
712C4⋊Q8—792no—
713C4⋊Q8C22×D7914yes—
714C4⋊Q8C22×D7914yes—
715C4⋊Q8C22×D7912yes—
716C4⋊Q8C22×D7918yes—
717#126—798no—
718#126—798no—
719#126—798no—
720#126—794no—
721#126—794no—
722#126—794no—
723#126—798no—
724#126—798no—
725#126—798no—
726#126—798no—
727#126—798no—
728#126—798no—
729#126—798no—
730#126—794no—
731#126—798no—
732#126—798no—
733#126—798no—
734#126—794no—
735#126—798no—
736#126—798no—
737#125—794no—
738#125—794no—
739#125—794no—
740#125—798no—
741#125—798no—
742#125—798no—
743#125—798no—
744#125—798no—
745#125—798no—
746#125—798no—
747#125—798no—
748#125—798no—
749#125—798no—
750#125—798no—
751#125—798no—
752#125—798no—
753#125—798no—
754#125—798no—
755#125—798no—
756#125—798no—
757#125—798no—
758#125—798no—
759#125—798no—
760#125—794no—
761#125—794no—
762#125—798no—
763#125—798no—
764#125—794no—
765#125—798no—
766#125—798no—
767#125—798no—
768#125—798no—
769#125—798no—
770#125—798no—
771#125—798no—
772#125—798no—
773#125—798no—
774#125—798no—
775#125—798no—
776#125—798no—
777#125—792no—
778#125—794no—
779#125—798no—
780#125—794no—
781#125—794no—
782#125—798no—
783#125—794no—
784#125—798no—
785#125—798no—
786#125C22×D7914yes—
787#125C22×D7911yescharacteristic
788#125C22×D7912yes—
789#125C22×D7918yes—
790#125C22×D7912yes—
791#125C22×D7914yes—
792#125C22×D7914yes—
793#125C22×D7911yescharacteristic
794#125C22×D7918yes—
795#124—794no—
796#124—794no—
797#124—792no—
798#123—798no—
799#123—798no—
800#123—794no—
801#123—798no—
802#123—794no—
803#123—794no—
804#123—794no—
805#123—798no—
806#123—798no—
807#123—798no—
808#123—798no—
809#123—798no—
810#123—798no—
811#123—794no—
812#123—798no—
813C22⋊Q8—794no—
814C22⋊Q8—798no—
815C22⋊Q8—794no—
816C22⋊Q8—794no—
817C22⋊Q8—798no—
818C22⋊Q8—798no—
819C22⋊Q8—798no—
820C22⋊Q8—792no—
821C22⋊Q8—794no—
822C22⋊Q8—794no—
823C22⋊Q8—798no—
824C22⋊Q8—794no—
825C22⋊Q8—798no—
826C22⋊Q8—794no—
827C22⋊Q8—798no—
828C22⋊Q8—794no—
829C22⋊Q8—794no—
830C22⋊Q8—794no—
831C22⋊Q8—794no—
832C22⋊Q8—794no—
833C22⋊Q8—794no—
834C22⋊Q8—798no—
835C22⋊Q8—798no—
836C22⋊Q8—798no—
837C22⋊Q8—798no—
838C22⋊Q8—798no—
839C22⋊Q8—798no—
840C22⋊Q8—798no—
841C22⋊Q8—798no—
842C22⋊Q8C22×D7918yes—
843C22⋊Q8C22×D7918yes—
844C22⋊Q8C22×D7918yes—
845C22⋊Q8C22×D7914yes—
846C22⋊Q8C22×D7918yes—
847#121—798no—
848#121—798no—
849#121—794no—
850#121—792no—
851#121—794no—
852#121—794no—
853C4×Q8—798no—
854C4×Q8—798no—
855C4×Q8—798no—
856C4×Q8—794no—
857C4×Q8—794no—
858C4×Q8—794no—
859C4×Q8—798no—
860C4×Q8—798no—
861C4×Q8—798no—
862C4×Q8—794no—
863C4×Q8—794no—
864C4×Q8—794no—
865C4×Q8—794no—
866C4×Q8—792no—
867C4×Q8—798no—
868C4×Q8—794no—
869C4×Q8—798no—
870C4×Q8—794no—
871C4×Q8C22×D7912yes—
872C4×Q8C22×D7914yes—
873C4×Q8C22×D7914yes—
874C4×Q8C22×D7918yes—
875C4×D4—794no—
876C4×D4—798no—
877C4×D4—798no—
878C4×D4—798no—
879C4×D4—794no—
880C4×D4—798no—
881C4×D4—798no—
882C4×D4—798no—
883C4×D4—798no—
884C4×D4—798no—
885C4×D4—794no—
886C4×D4—792no—
887C4×D4—794no—
888C4×D4C22×D7914yes—
889C4×D4C22×D7912yes—
890C4×D4C22×D7914yes—
891C4×D4C22×D7918yes—
892#117—798no—
893#117—794no—
894#117—794no—
895#117—798no—
896#117—798no—
897#117—798no—
898#117—798no—
899#117—798no—
900#117—798no—
901#117—794no—
902#117—794no—
903#117—798no—
904#117—798no—
905#117—798no—
906#117C22×D7911yescharacteristic
907#117C22×D7912yes—
908#117C22×D7912yes—
909#117C22×D7914yes—
910C2×C4⋊C4—798no—
911C2×C4⋊C4—798no—
912C2×C4⋊C4—798no—
913C2×C4⋊C4—798no—
914C2×C4⋊C4—794no—
915C2×C4⋊C4—798no—
916C2×C4⋊C4—794no—
917C2×C4⋊C4—794no—
918C2×C4⋊C4—794no—
919C2×C4⋊C4—798no—
920C2×C4⋊C4—798no—
921C2×C4⋊C4C22×D7914yes—
922C2×C4⋊C4C22×D7912yes—
923C2×C4⋊C4C22×D7918yes—
924C2×C4⋊C4C22×D7914yes—
925C2×C42—798no—
926C2×C42—794no—
927C2×C42C22×D7912yes—
928C2×C42C22×D7911yescharacteristic
929#41—24no—
930#41—15816no—
931C2×Q8—798no—
932C2×Q8—794no—
933C2×Q8—792no—
934C2×Q8—794no—
935C2×Q8—794no—
936C2×Q8C23×D7911yescharacteristic
937C2×Q8C23×D7918yes—
938C2×Q8C23×D7914yes—
939C2×D4—794no—
940C2×D4—798no—
941C2×D4—794no—
942C2×D4—792no—
943C2×D4C23×D7912yes—
944C2×D4C23×D7911yescharacteristic
945C22×C4—798no—
946C22×C4—794no—
947C22×C4—794no—
948C22×C4—798no—
949C22×C4—798no—
950C22×C4—798no—
951C22×C4—794no—
952C22×C4C23×D7912yes—
953C22×C4C23×D7911yescharacteristic
954C22×C4C23×D7918yes—
955C22×C4C23×D7914yes—
956C22×C4C23×D7912yes—
957C22×C4C23×D7914yes—
958C4⋊C4—798no—
959C4⋊C4—798no—
960C4⋊C4—794no—
961C4⋊C4—794no—
962C4⋊C4—794no—
963C4⋊C4—794no—
964C4⋊C4—798no—
965C4⋊C4—798no—
966C4⋊C4—798no—
967C4⋊C4—798no—
968C4⋊C4—798no—
969C4⋊C4—798no—
970C4⋊C4—798no—
971C4⋊C4—798no—
972C4⋊C4—798no—
973C4⋊C4—798no—
974C4⋊C4—798no—
975C4⋊C4—798no—
976C4⋊C4—794no—
977C4⋊C4—794no—
978C4⋊C4—798no—
979C4⋊C4—798no—
980C4⋊C4—794no—
981C4⋊C4—794no—
982C4⋊C4—798no—
983C4⋊C4—794no—
984C4⋊C4—794no—
985C4⋊C4—792no—
986C4⋊C4—792no—
987C4⋊C4—798no—
988C4⋊C4—794no—
989C4⋊C4—798no—
990C4⋊C4—794no—
991C4⋊C4—798no—
992C4⋊C4—798no—
993C4⋊C4—798no—
994C4⋊C4—798no—
995C4⋊C4—794no—
996C4⋊C4—794no—
997C4⋊C4—798no—
998C4⋊C4C23×D7912yes—
999C4⋊C4C23×D7914yes—
1000C4⋊C4C23×D7918yes—
1001C4⋊C4C23×D7918yes—
1002C4⋊C4C23×D7914yes—
1003C4⋊C4C23×D7912yes—
1004C4⋊C4C23×D7914yes—
1005C4⋊C4C23×D7918yes—
1006C4⋊C4C23×D7918yes—
1007C4⋊C4C23×D7918yes—
1008C4⋊C4C23×D7918yes—
1009C4⋊C4C23×D7912yes—
1010C4⋊C4C23×D7914yes—
1011C4⋊C4C23×D7914yes—
1012C4⋊C4C23×D7914yes—
1013C22⋊C4—798no—
1014C22⋊C4—798no—
1015C22⋊C4—794no—
1016C22⋊C4—798no—
1017C22⋊C4—798no—
1018C22⋊C4—798no—
1019C22⋊C4—798no—
1020C22⋊C4—794no—
1021C22⋊C4—794no—
1022C22⋊C4—794no—
1023C22⋊C4—794no—
1024C22⋊C4—794no—
1025C22⋊C4—794no—
1026C22⋊C4—794no—
1027C22⋊C4—794no—
1028C22⋊C4—798no—
1029C22⋊C4C23×D7914yes—
1030C22⋊C4C23×D7918yes—
1031C22⋊C4C23×D7914yes—
1032C22⋊C4C23×D7912yes—
1033C42—794no—
1034C42—798no—
1035C42—794no—
1036C42—794no—
1037C42—798no—
1038C42—798no—
1039C42—798no—
1040C42—798no—
1041C42—798no—
1042C42—798no—
1043C42C23×D7914yes—
1044C42C23×D7911yescharacteristic
1045C42C23×D7912yes—
1046C42C23×D7912yes—
1047C42C23×D7911yescharacteristic
1048C42C23×D7914yes—
1049C42C23×D7918yes—
1050C23—794no—
1051C23C24×D7911yescharacteristic
1052C23C24×D7912yes—
1053Q8—22no—
1054Q8—44no—
1055Q8—48no—
1056Q8—3162no—
1057Q8—3168no—
1058Q8—3164no—
1059Q8—3164no—
1060Q8—1588no—
1061D4—24no—
1062D4—3162no—
1063D4—3164no—
1064D4—3164no—
1065D4—15816no—
1066D4#1457920914yes—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—44no—
1070C2×C4—42no—
1071C2×C4—48no—
1072C2×C4—44no—
1073C2×C4—3164no—
1074C2×C4—3168no—
1075C2×C4—3168no—
1076C2×C4—3164no—
1077C2×C4—3168no—
1078C2×C4—794no—
1079C2×C4—798no—
1080C2×C4—794no—
1081C2×C4—798no—
1082C2×C4—794no—
1083C2×C4—15816no—
1084C2×C4—1588no—
1085C2×C4C24×D7912yes—
1086C2×C4C24×D7914yes—
1087C2×C4C24×D7918yes—
1088C2×C4C24×D7914yes—
1089C2×C4C24×D7914yes—
1090C2×C4C24×D7912yes—
1091C2×C4C24×D7911yescharacteristic
1092C2×C4C24×D7912yes—
1093C2×C4C24×D7911yescharacteristic
1094C22—24no—
1095C22—21no—
1096C22—22no—
1097C22—1584no—
1098C22—1584no—
1099C22—1584no—
1100C22C2×#1457920914yes—
1101C22C25×D7911yescharacteristic
1102C4—21no—
1103C4—22no—
1104C4—22no—
1105C4—24no—
1106C4—28no—
1107C4—24no—
1108C4—22no—
1109C4—24no—
1110C4—1584no—
1111C4—1588no—
1112C4—1584no—
1113C4—1588no—
1114C4—1584no—
1115C4C2×#1457920912yes—
1116C2—24no—
1117C2—41no—
1118C2—3164no—
1119C2C22×#1457920911yescharacteristic
1120C2#2377821312yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3504C2
hypercenter#3504D79
hypocenterC79#63067
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #23778010C2semidirect
2. #23778006C2semidirect
3. #23778004C2semidirect
4. #23778002C2semidirect
5. #23777999C2semidirect
6. #23777996C2semidirect
7. #23777895C2semidirect
8. #23777892C2semidirect
9. #23777856C2semidirect
10. #23777852C2semidirect
11. #23777547C2semidirect
12. C2×C79⋊#564C2semidirect
13. #23777379C2semidirect
14. #23777378C2semidirect
15. #23777368C2semidirect
16. #23777220C2semidirect
17. C79×#3504C2semidirect
577. #3504D79semidirect
578. C79#63067semidirect

Maximal subgroups

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

subgroupindex
#237780102
#237780062
#237780042
#237780022
#237779992
#237779962
#237778952
#237778922
#237778562
#237778522
#237775472
C2×C79⋊#5642
#237773792
#237773782
#237773682
#237772202
C79×#35042
#6306779