Finite Group Databasebeta

← #35197276

Subgroups — #35197276

Order 20224.

6624 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778097C218yesmaximal, complemented
2#23777811C212yesmaximal, complemented
3#23777805C211yesmaximal, characteristic, complemented
4#23777677C214yesmaximal, complemented
5#23777672C218yesmaximal, complemented
6#23777418C214yesmaximal, complemented
7#23777414C214yesmaximal, complemented
8#23777412C214yesmaximal, complemented
9#23777364C214yesmaximal, complemented
10#23777362C214yesmaximal, complemented
11#23777360C214yesmaximal, complemented
12#23777299C214yesmaximal, complemented
13#23777292C218yesmaximal, complemented
14#23776697C212yesmaximal, complemented
15#23776695C211yesmaximal, characteristic, complemented
16C79×#3550C211yesmaximal, characteristic, complemented
17#19099317C2218yescomplemented
18#19099305C2214yescomplemented
19#19099305C2218yescomplemented
20#19099303C2218yescomplemented
21#19099298C2214yescomplemented
22#19099297C2218yescomplemented
23#19099295C22116yescomplemented
24Q8×Dic158C2214yescomplemented
25#19099287C22116yescomplemented
26#19099287C2214yescomplemented
27#19099287C2218yescomplemented
28#19099286C2214yescomplemented
29#19099286C2218yescomplemented
30#19099284C22116yescomplemented
31#19099284C2218yescomplemented
32#19099280C22116yescomplemented
33#19099279C2212yescomplemented
34#19099279C2218yescomplemented
35#19099278C2214yescomplemented
36#19099278C2218yescomplemented
37#19099276C2218yescomplemented
38#19099243C2218yescomplemented
39#19099240C22116yescomplemented
40#19099238C22116yescomplemented
41#19099236C22116yescomplemented
42#19099236C22116yescomplemented
43Q8×D316C2214yescomplemented
44#19099228C2214yescomplemented
45#19099225C2218yescomplemented
46#19099224C2218yescomplemented
47#19099221C2218yescomplemented
48#19099208C2218yescomplemented
49#19099206C2218yescomplemented
50#19099204C2218yescomplemented
51D4×D316C2214yescomplemented
52#19099198C2212yescomplemented
53#19099187C2218yescomplemented
54#19099187C22116yescomplemented
55#19099186C2218yescomplemented
56#19099186C2218yescomplemented
57#19099186C22116yescomplemented
58#19099184C2218yescomplemented
59#19099182C2218yescomplemented
60#19099179C22116yescomplemented
61#19099153C22116yescomplemented
62#19099152C22116yescomplemented
63#19099149C22116yescomplemented
64#19099136C2218yescomplemented
65#19099129C2218yes—
66#19099127C2214yes—
67#19099120C2211yescharacteristic, complemented
68#19099118C2218yescomplemented
69#19099118C2212yescomplemented
70#19099118C2212yescomplemented
71#19099118C2212yescomplemented
72#19099116C2214yescomplemented
73#19099114C2212yes—
74#19099114C2212yes—
75#19099113C2212yes—
76#19099111C2212yes—
77#19099100C2218yescomplemented
78#19099100C2214yescomplemented
79#19099100C2214yescomplemented
80#19099099C2214yescomplemented
81#19099099C2214yescomplemented
82#19099099C2218yescomplemented
83#19099098C2214yescomplemented
84#19099098C2214yescomplemented
85#19099095C2218yescomplemented
86#19099095C2214yescomplemented
87#19099094C2214yescomplemented
88#19099092C2214yescomplemented
89C2×#14579150C2214yescomplemented
90#124×D79C2218yescomplemented
91#19099076C2214yescomplemented
92#19099076C2214yescomplemented
93#19099075C2214yescomplemented
94#19099073C2214yescomplemented
95#19099070C2212yescomplemented
96#19099041C2214yescomplemented
97#19099039C2218yescomplemented
98#19099037C2214yescomplemented
99#19099035C2218yescomplemented
100#41×Dic79C2212yescomplemented
101C4×#11929625C2214yescomplemented
102C4×#11929625C2214yescomplemented
103#19099031C2214yescomplemented
104C4×#11929623C2214yescomplemented
105C2×C42×D79C2211yescharacteristic, complemented
106#563×C79C2214yescomplemented
107#559×C79C2212yescomplemented
108Q82×C79C2212yescomplemented
109#556×C79C2214yescomplemented
110D4×Q8×C79C2214yescomplemented
111#542×C79C2218yescomplemented
112#536×C79C2214yescomplemented
113#533×C79C2212yescomplemented
114#532×C79C2211yescharacteristic
115C2×#11929625C2314yes—
116C2×#11929625C2314yes—
117C2×#11929624C2314yes—
118C2×#11929623C2314yes—
119C2×Q8×D79C2318yes—
120C22×D316C2314yes—
121C2×D4×D79C2318yes—
122C22×C4×D79C2311yescharacteristic
123C22×C4×D79C2312yes—
124#14579161C2318yes—
125#14579161C2312yes—
126#14579161C2312yes—
127#14579160C23116yes—
128#14579160C2318yes—
129#14579158C2312yes—
130#14579157C2318yes—
131#14579156C23116yes—
132#14579156C23116yes—
133#14579156C23116yes—
134#14579156C23116yes—
135#14579156C23116yes—
136#14579156C2318yes—
137#14579156C2318yes—
138#14579154C23116yes—
139#14579154C2318yes—
140#14579153C2312yes—
141#14579152C2314yes—
142#14579152C2314yes—
143#14579152C2314yes—
144#14579150C23116yes—
145#14579150C23116yes—
146#14579150C2318yes—
147#14579150C2318yes—
148#14579150C2314yes—
149#14579150C2314yes—
150#14579149C23116yes—
151#14579149C2318yes—
152#14579149C2314yes—
153#14579148C2314yes—
154#14579147C23116yes—
155#14579147C23116yes—
156#14579147C23116yes—
157#14579147C23116yes—
158#14579147C23116yes—
159#14579146C23116yes—
160#14579146C2318yes—
161#14579146C2318yes—
162#14579146C23116yes—
163#14579145C23116yes—
164#14579145C2318yes—
165#14579143C23116yes—
166#14579143C2318yes—
167#14579143C23116yes—
168#14579142C2314yes—
169#14579141C2318yes—
170#14579141C23116yes—
171#14579141C2314yes—
172#14579141C2314yes—
173#14579141C23116yes—
174#14579141C2314yes—
175#14579140C2314yes—
176#14579139C23116yes—
177#14579138C23116yes—
178#14579137C2318yes—
179#14579137C2314yes—
180#14579137C23116yes—
181#14579137C2314yes—
182#14579137C2314yes—
183#14579136C2314yes—
184#14579136C23116yes—
185#14579136C2314yes—
186#14579136C2318yes—
187#14579136C2314yes—
188#14579136C2314yes—
189#14579135C23116yes—
190#14579135C2314yes—
191#14579135C2314yes—
192#14579135C2318yes—
193#14579134C23116yes—
194#14579132C2314yes—
195#14579132C2318yes—
196#14579132C2314yes—
197#14579131C23116yes—
198#14579131C23116yes—
199#14579131C2318yes—
200#14579129C2318yes—
201#14579129C2318yes—
202#14579129C2314yes—
203Q8×Dic79C2314yes—
204Q8×Dic79C2314yes—
205Q8×Dic79C2318yes—
206Q8×Dic79C23116yes—
207Q8×Dic79C2314yes—
208C4×Dic158C23116yes—
209C4×Dic158C2318yes—
210C4×Dic158C2314yes—
211#14579126C2314yes—
212#14579126C23116yes—
213#14579126C2314yes—
214#14579126C2314yes—
215C4×D316C23116yes—
216C4×D316C2318yes—
217C4×D316C2314yes—
218C4×D316C2314yes—
219C4×D316C2318yes—
220C4×D316C2318yes—
221D4×Dic79C2314yes—
222D4×Dic79C2314yes—
223D4×Dic79C2318yes—
224#14579123C2318yes—
225#14579123C2318yes—
226#14579123C2314yes—
227#14579123C2318yes—
228#14579123C2314yes—
229#14579123C2314yes—
230#14579123C2314yes—
231C4×C22⋊D79C23116yes—
232C4×C22⋊D79C2318yes—
233(C22⋊D79)⋊C4C2318yes—
234(C22⋊D79)⋊C4C23116yes—
235(C22⋊D79)⋊C4C2318yes—
236(C22⋊D79)⋊C4C2318yes—
237#14579120C2312yes—
238#14579120C2314yes—
239#14579120C23116yes—
240#14579120C2314yes—
241#14579119C2318yes—
242#14579119C23116yes—
243#14579119C2318yes—
244#14579119C2318yes—
245#14579119C2314yes—
246#14579119C2314yes—
247#14579119C2318yes—
248#14579119C2314yes—
249#14579118C2318yes—
250#14579118C23116yes—
251#14579117C2318yes—
252C2×(C2×D79)⋊C4C23116yes—
253C22⋊C4×D79C23116yes—
254C22⋊C4×D79C23116yes—
255C2×C4×Dic79C2312yes—
256C2×C4×Dic79C2311yescharacteristic
257C2×C4×Dic79C2314yes—
258C42×D79C2312yes—
259C42×D79C2312yes—
260C42×D79C2312yes—
261C42×D79C2312yes—
262C42×D79C2318yes—
263C2×#41×C79C2312yes—
264C22×Q8×C79C2314yes—
265C4⋊Q8×C79C2318yes—
266C4⋊Q8×C79C2318yes—
267C4⋊Q8×C79C2312yes—
268C4⋊Q8×C79C2311yescharacteristic
269C4⋊Q8×C79C2312yes—
270#127×C79C2311yescharacteristic
271#126×C79C23116yes—
272#125×C79C2314yes—
273#124×C79C2318yes—
274#124×C79C2318yes—
275#124×C79C2312yes—
276#123×C79C2318yes—
277#123×C79C2318yes—
278C22⋊Q8×C79C2314yes—
279C22⋊Q8×C79C23116yes—
280C22⋊Q8×C79C2314yes—
281C22⋊Q8×C79C2318yes—
282#121×C79C2314yes—
283C4×Q8×C79C2318yes—
284C4×Q8×C79C2314yes—
285C4×Q8×C79C2314yes—
286C4×D4×C79C2314yes—
287C4×D4×C79C2318yes—
288#117×C79C2314yes—
289#117×C79C2314yes—
290C2×C42×C79C2311yescharacteristic
291C23×D79C2418yes—
292C23×D79C2411yescharacteristic
293#11929625—48no—
294#11929625—48no—
295#11929624—48no—
296#11929623—48no—
297C2×Dic158C2414yes—
298C2×Dic158C24116yes—
299C2×Dic158C2414yes—
300Q8×D79—416no—
301C2×D316—48no—
302C2×D316C2414yes—
303C2×D316C2414yes—
304C2×D316C2414yes—
305C2×D316C2418yes—
306C2×D316C2418yes—
307C2×D316C2418yes—
308C2×C22⋊D79C2418yes—
309C2×C22⋊D79C2418yes—
310C2×C22⋊D79C24116yes—
311D4×D79—416no—
312C22×Dic79C2418yes—
313C22×Dic79C2411yescharacteristic
314C22×Dic79C2412yes—
315C2×C4×D79—44no—
316C2×C4×D79—42no—
317C2×C4×D79C2418yes—
318C2×C4×D79C2412yes—
319C2×C4×D79C2412yes—
320C2×C4×D79C2412yes—
321C2×C4×D79C24116yes—
322C2×C4×D79C2418yes—
323C2×C4×D79C2418yes—
324C2×C4×D79C2412yes—
325C2×C4×D79C2412yes—
326C2×C4×D79C2412yes—
327C4⋊Dic79C2414yes—
328C4⋊Dic79C2414yes—
329C4⋊Dic79C2418yes—
330C4⋊Dic79C2414yes—
331C4⋊Dic79C2418yes—
332C4⋊Dic79C2418yes—
333C4⋊Dic79C2414yes—
334C4⋊Dic79C24116yes—
335Dic79⋊C4C2418yes—
336Dic79⋊C4C2418yes—
337Dic79⋊C4C2418yes—
338Dic79⋊C4C2418yes—
339Dic79⋊C4C24116yes—
340C22⋊Dic79C2418yes—
341C22⋊Dic79C2418yes—
342C22⋊Dic79C2418yes—
343C22⋊Dic79C2414yes—
344(C2×D79)⋊C4C2418yes—
345(C2×D79)⋊C4C2418yes—
346(C2×D79)⋊C4C24116yes—
347(C2×D79)⋊C4C24116yes—
348(C2×D79)⋊C4C2418yes—
349(C2×D79)⋊C4C2418yes—
350(C2×D79)⋊C4C24116yes—
351(C2×D79)⋊C4C24116yes—
352(C2×D79)⋊C4C2418yes—
353(C2×D79)⋊C4C2418yes—
354(C2×D79)⋊C4C2418yes—
355(C2×D79)⋊C4C2418yes—
356(C2×D79)⋊C4C2418yes—
357C4×Dic79C2412yes—
358C4×Dic79C2411yescharacteristic
359C4×Dic79C2412yes—
360C4×Dic79C2412yes—
361C4×Dic79C2412yes—
362C4×Dic79C2412yes—
363C4×Dic79C2411yescharacteristic
364C4×Dic79C2418yes—
365C4×Dic79C2418yes—
366C4×Dic79C2418yes—
367C4×Dic79C2414yes—
368C4×Dic79C24116yes—
369C4×Dic79C2418yes—
370#41×C79—44no—
371C2×Q8×C79—48no—
372C2×Q8×C79C2414yes—
373C2×Q8×C79C2414yes—
374C2×Q8×C79C2418yes—
375C2×Q8×C79C2412yes—
376C2×D4×C79C2414yes—
377C2×D4×C79C2414yes—
378C2×D4×C79C2412yes—
379C22×C4×C79C2412yes—
380C22×C4×C79C2411yescharacteristic
381C22×C4×C79C2414yes—
382C22×C4×C79C2418yes—
383C4⋊C4×C79C2414yes—
384C4⋊C4×C79C2414yes—
385C4⋊C4×C79C2414yes—
386C4⋊C4×C79C2414yes—
387C4⋊C4×C79C2414yes—
388C4⋊C4×C79C2418yes—
389C4⋊C4×C79C24116yes—
390C4⋊C4×C79C2418yes—
391C22⋊C4×C79C2418yes—
392C22⋊C4×C79C2418yes—
393C22⋊C4×C79C2418yes—
394C22⋊C4×C79C24116yes—
395C42×C79C2412yes—
396C42×C79C2411yescharacteristic
397C42×C79C2411yescharacteristic
398C42×C79C2418yes—
399C42×C79C2418yes—
400C23×C79C2514yes—
401C23×C79C2511yescharacteristic
402C22×D79—42no—
403C22×D79—41no—
404C22×D79—416no—
405C22×D79—48no—
406C22×D79C2518yes—
407C22×D79C2512yes—
408Q8×C79—28no—
409Q8×C79—28no—
410Q8×C79—48no—
411Q8×C79—42no—
412D4×C79—28no—
413D4×C79—42no—
414D4×C79—44no—
415C2×C4×C79—24no—
416C2×C4×C79—22no—
417C2×C4×C79—28no—
418C2×C4×C79—48no—
419C2×C4×C79C2514yes—
420C2×C4×C79C2518yes—
421C2×C4×C79C2511yescharacteristic
422C2×C4×C79C2512yes—
423C2×C4×C79C2518yes—
424C2×C4×C79C2511yescharacteristic
425C2×C4×C79C2512yes—
426C22⋊D79—416no—
427C22⋊D79—48no—
428C22⋊D79—48no—
429C2×Dic79—41no—
430C2×Dic79—42no—
431C2×Dic79—48no—
432C2×Dic79C2512yes—
433C2×Dic79C2512yes—
434C2×Dic79C2512yes—
435C2×Dic79C2518yes—
436C2×Dic79C2518yes—
437D316—28no—
438D316—28no—
439D316—48no—
440D316—44no—
441D316—48no—
442D316—48no—
443C4×D79—24no—
444C4×D79—24no—
445C4×D79—24no—
446C4×D79—216no—
447C4×D79—42no—
448C4×D79—42no—
449C4×D79—42no—
450C4×D79—416no—
451C4×D79—48no—
452C4×D79—48no—
453Dic158—28no—
454Dic158—416no—
455Dic158—44no—
456C22×C79—22no—
457C22×C79—28no—
458C22×C79—24no—
459C22×C79—21no—
460C22×C79C2611yescharacteristic
461C2×D79—22no—
462C2×D79—28no—
463C2×D79—28no—
464C2×D79—28no—
465C2×D79—22no—
466C2×D79—22no—
467C2×D79—44no—
468C2×D79—168no—
469C4×C79—21no—
470C4×C79—24no—
471C4×C79—22no—
472C4×C79—28no—
473C4×C79—28no—
474C4×C79#58512yes—
475C4×C79#58514yes—
476Dic79—28no—
477Dic79—28no—
478Dic79—22no—
479Dic79—22no—
480Dic79—22no—
481#62841—791nomaximal, Sylow
482C2×C79—41no—
483C2×C79—44no—
484C2×C79C2×#58511yescharacteristic
485C2×C79C2×#58512yes—
486D79—42no—
487D79—48no—
488#3568—798no—
489#3550—792no—
490#3550D7911yescharacteristic, complemented
491#3549—791no—
492#3540—798no—
493#3540—794no—
494#3518—794no—
495#3518—794no—
496#3518—794no—
497#3514—794no—
498#3514—794no—
499#3514—794no—
500#3510—798no—
501#3510—794no—
502#3444—792no—
503#3444—791no—
504C79#6284111yescharacteristic, complemented, Sylow
505#563—798no—
506#563C2×D7914yescomplemented
507H(3,𝔽4)—798no—
508H(3,𝔽4)—794no—
509#560—798no—
510#559—7916no—
511#559—798no—
512#559—794no—
513#559C2×D7912yescomplemented
514Q82—794no—
515Q82C2×D7912yescomplemented
516#556—7916no—
517#556—794no—
518#556—798no—
519#556—7916no—
520#556—7916no—
521#556—798no—
522#556—794no—
523#556—798no—
524#556C2×D7914yescomplemented
525#555—798no—
526#555—792no—
527#555—798no—
528#555—794no—
529#555—798no—
530#551—7916no—
531#551—798no—
532#551—7916no—
533#551—7916no—
534#551—7916no—
535D4×Q8—794no—
536D4×Q8—794no—
537D4×Q8C2×D7914yescomplemented
538#548—798no—
539#548—798no—
540#548—798no—
541#546—798no—
542#546—798no—
543#546—798no—
544D42—792no—
545D42—794no—
546#542—798no—
547#542—7916no—
548#542—7916no—
549#542—798no—
550#542—798no—
551#542—798no—
552#542—7916no—
553#542—798no—
554#542C2×D7918yescomplemented
555#538—7916no—
556#538—7916no—
557#538—7916no—
558#536—798no—
559#536C2×D7914yescomplemented
560#535—794no—
561#535—798no—
562#533—792no—
563#533—792no—
564#533—792no—
565#533—798no—
566#533—794no—
567#533—791no—
568#533C2×D7912yescomplemented
569#532—792no—
570#532—792no—
571#532—792no—
572#532—792no—
573#532C2×D7911yescharacteristic
574#529—794no—
575#529—794no—
576#529—794no—
577#529—794no—
578#529—794no—
579#529—798no—
580#529—794no—
581#529—794no—
582#529—794no—
583#529—798no—
584#529—794no—
585#529—798no—
586C2×#124—794no—
587C2×#124—798no—
588#525—792no—
589#525—794no—
590#525—794no—
591#525—794no—
592#525—794no—
593#519—794no—
594#519—798no—
595#518—798no—
596#518—794no—
597C4×#41—792no—
598C4×#41—794no—
599C4×#41—794no—
600C4×#41—794no—
601C4×#41—794no—
602C22×C42—791no—
603C2×#41—794no—
604C2×#41—794no—
605C2×#41—794no—
606C2×#41—794no—
607C2×#41C22×D7912yes—
608C22×Q8—798no—
609C22×Q8C22×D7914yes—
610C22×D4—798no—
611C22×D4—794no—
612C23×C4—791no—
613C23×C4—792no—
614C4⋊Q8—798no—
615C4⋊Q8—7916no—
616C4⋊Q8—792no—
617C4⋊Q8—792no—
618C4⋊Q8—798no—
619C4⋊Q8C22×D7912yes—
620C4⋊Q8C22×D7912yes—
621C4⋊Q8C22×D7911yescharacteristic
622C4⋊Q8C22×D7918yes—
623C4⋊Q8C22×D7918yes—
624#127—798no—
625#127—792no—
626#127C22×D7911yescharacteristic
627#126—798no—
628#126—798no—
629#126—7916no—
630#126—7916no—
631#126—7916no—
632#126—7916no—
633#126—7916no—
634#126—798no—
635#126—7916no—
636#126C22×D79116yes—
637#125—794no—
638#125—794no—
639#125—794no—
640#125—792no—
641#125C22×D7914yes—
642#124—794no—
643#124—794no—
644#124—7916no—
645#124—798no—
646#124—798no—
647#124—7916no—
648#124—794no—
649#124—7916no—
650#124—7916no—
651#124—7916no—
652#124—7916no—
653#124—7916no—
654#124—798no—
655#124—794no—
656#124—7916no—
657#124C22×D7918yes—
658#124C22×D7912yes—
659#124C22×D7918yes—
660#123—794no—
661#123—798no—
662#123—798no—
663#123—7916no—
664#123—7916no—
665#123—798no—
666#123—798no—
667#123—7916no—
668#123—7916no—
669#123—7916no—
670#123C22×D7918yes—
671#123C22×D7918yes—
672C22⋊Q8—794no—
673C22⋊Q8—794no—
674C22⋊Q8—794no—
675C22⋊Q8—798no—
676C22⋊Q8—7916no—
677C22⋊Q8—794no—
678C22⋊Q8—794no—
679C22⋊Q8—794no—
680C22⋊Q8—794no—
681C22⋊Q8—798no—
682C22⋊Q8—7916no—
683C22⋊Q8—7916no—
684C22⋊Q8—7916no—
685C22⋊Q8—7916no—
686C22⋊Q8C22×D7914yes—
687C22⋊Q8C22×D7914yes—
688C22⋊Q8C22×D7918yes—
689C22⋊Q8C22×D79116yes—
690#121—794no—
691#121—794no—
692#121—798no—
693#121—794no—
694#121—794no—
695#121—798no—
696#121—7916no—
697#121—794no—
698#121—794no—
699#121—794no—
700#121—794no—
701#121—798no—
702#121—7916no—
703#121—7916no—
704#121C22×D7914yes—
705#120—794no—
706#120—798no—
707#120—798no—
708#120—798no—
709#120—7916no—
710#120—7916no—
711C4×Q8—794no—
712C4×Q8—794no—
713C4×Q8—794no—
714C4×Q8—798no—
715C4×Q8—7916no—
716C4×Q8—794no—
717C4×Q8—794no—
718C4×Q8—794no—
719C4×Q8—7916no—
720C4×Q8—794no—
721C4×Q8—798no—
722C4×Q8—7916no—
723C4×Q8C22×D7914yes—
724C4×Q8C22×D7914yes—
725C4×Q8C22×D7918yes—
726C4×D4—794no—
727C4×D4—798no—
728C4×D4—794no—
729C4×D4—798no—
730C4×D4—7916no—
731C4×D4—794no—
732C4×D4—794no—
733C4×D4—798no—
734C4×D4—798no—
735C4×D4—794no—
736C4×D4—794no—
737C4×D4—798no—
738C4×D4—798no—
739C4×D4—798no—
740C4×D4—798no—
741C4×D4—7916no—
742C4×D4—798no—
743C4×D4—798no—
744C4×D4—794no—
745C4×D4—794no—
746C4×D4—7916no—
747C4×D4—798no—
748C4×D4C22×D7914yes—
749C4×D4C22×D7918yes—
750#117—794no—
751#117—792no—
752#117—7916no—
753#117—794no—
754#117—794no—
755#117—794no—
756#117—794no—
757#117—798no—
758#117—798no—
759#117—798no—
760#117—7916no—
761#117—798no—
762#117—798no—
763#117—798no—
764#117—7916no—
765#117C22×D7914yes—
766#117C22×D7914yes—
767C2×C22⋊C4—7916no—
768C2×C22⋊C4—7916no—
769C2×C22⋊C4—7916no—
770C2×C42—794no—
771C2×C42—791no—
772C2×C42—792no—
773C2×C42—798no—
774C2×C42—792no—
775C2×C42—792no—
776C2×C42—792no—
777C2×C42—792no—
778C2×C42C22×D7911yescharacteristic
779C24—798no—
780C24—791no—
781#41—44no—
782#41—3168no—
783#41—3168no—
784#41—3168no—
785#41—3168no—
786C2×Q8—48no—
787C2×Q8—31616no—
788C2×Q8—7916no—
789C2×Q8—794no—
790C2×Q8—794no—
791C2×Q8C23×D7914yes—
792C2×Q8C23×D7914yes—
793C2×Q8C23×D7918yes—
794C2×Q8C23×D7912yes—
795C2×D4—3168no—
796C2×D4—31616no—
797C2×D4—798no—
798C2×D4—798no—
799C2×D4—7916no—
800C2×D4—794no—
801C2×D4—798no—
802C2×D4—798no—
803C2×D4—798no—
804C2×D4—794no—
805C2×D4—794no—
806C2×D4C23×D7914yes—
807C2×D4C23×D7912yes—
808C2×D4C23×D7914yes—
809C22×C4—3162no—
810C22×C4—3164no—
811C22×C4—791no—
812C22×C4—792no—
813C22×C4—798no—
814C22×C4—792no—
815C22×C4—792no—
816C22×C4—792no—
817C22×C4—798no—
818C22×C4—798no—
819C22×C4—7916no—
820C22×C4—792no—
821C22×C4—792no—
822C22×C4—792no—
823C22×C4—798no—
824C22×C4C23×D7911yescharacteristic
825C22×C4C23×D7912yes—
826C22×C4C23×D7914yes—
827C22×C4C23×D7918yes—
828C4⋊C4—798no—
829C4⋊C4—798no—
830C4⋊C4—798no—
831C4⋊C4—798no—
832C4⋊C4—7916no—
833C4⋊C4—794no—
834C4⋊C4—794no—
835C4⋊C4—794no—
836C4⋊C4—798no—
837C4⋊C4—798no—
838C4⋊C4—798no—
839C4⋊C4—794no—
840C4⋊C4—7916no—
841C4⋊C4C23×D7914yes—
842C4⋊C4C23×D7914yes—
843C4⋊C4C23×D7914yes—
844C4⋊C4C23×D7918yes—
845C4⋊C4C23×D7918yes—
846C4⋊C4C23×D79116yes—
847C4⋊C4C23×D7914yes—
848C4⋊C4C23×D7914yes—
849C22⋊C4—798no—
850C22⋊C4—798no—
851C22⋊C4—798no—
852C22⋊C4—794no—
853C22⋊C4—798no—
854C22⋊C4—798no—
855C22⋊C4—798no—
856C22⋊C4—798no—
857C22⋊C4—7916no—
858C22⋊C4—7916no—
859C22⋊C4—7916no—
860C22⋊C4—7916no—
861C22⋊C4—798no—
862C22⋊C4—798no—
863C22⋊C4—798no—
864C22⋊C4—798no—
865C22⋊C4—798no—
866C22⋊C4C23×D7918yes—
867C22⋊C4C23×D79116yes—
868C22⋊C4C23×D7918yes—
869C22⋊C4C23×D7918yes—
870C42—791no—
871C42—792no—
872C42—791no—
873C42—792no—
874C42—792no—
875C42—792no—
876C42—792no—
877C42—798no—
878C42—798no—
879C42—798no—
880C42—794no—
881C42—7916no—
882C42—798no—
883C42C23×D7911yescharacteristic
884C42C23×D7912yes—
885C42C23×D7911yescharacteristic
886C42C23×D7918yes—
887C42C23×D7918yes—
888C23—3161no—
889C23—3162no—
890C23—3168no—
891C23—31616no—
892C23—798no—
893C23—792no—
894C23C24×D7914yes—
895C23C24×D7911yescharacteristic
896Q8—28no—
897Q8—28no—
898Q8—48no—
899Q8—42no—
900Q8—31616no—
901Q8—3164no—
902Q8—1588no—
903D4—28no—
904D4—42no—
905D4—44no—
906D4—3168no—
907D4—3168no—
908D4—3164no—
909D4—3168no—
910D4—31616no—
911D4—3168no—
912D4—3168no—
913D4—1588no—
914D4—1588no—
915C2×C4—22no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—48no—
919C2×C4—3162no—
920C2×C4—3162no—
921C2×C4—3162no—
922C2×C4—31616no—
923C2×C4—3168no—
924C2×C4—3168no—
925C2×C4—3161no—
926C2×C4—3162no—
927C2×C4—3168no—
928C2×C4—792no—
929C2×C4—792no—
930C2×C4—792no—
931C2×C4—798no—
932C2×C4—798no—
933C2×C4—1584no—
934C2×C4—1584no—
935C2×C4—1584no—
936C2×C4—15816no—
937C2×C4C24×D7914yes—
938C2×C4C24×D7918yes—
939C2×C4C24×D7911yescharacteristic
940C2×C4C24×D7912yes—
941C2×C4C24×D7918yes—
942C2×C4C24×D7911yescharacteristic
943C2×C4C24×D7912yes—
944C22—24no—
945C22—21no—
946C22—22no—
947C22—28no—
948C22—3164no—
949C22—1582no—
950C22—1588no—
951C22—1588no—
952C22—1582no—
953C22—1582no—
954C22—1588no—
955C22—12648no—
956C22C25×D7911yescharacteristic
957C4—21no—
958C4—24no—
959C4—28no—
960C4—22no—
961C4—28no—
962C4—1582no—
963C4—1582no—
964C4—1582no—
965C4—1588no—
966C4—1588no—
967C4#1909939812yes—
968C4#1909940014yes—
969C2—41no—
970C2—44no—
971C2—3162no—
972C2—3168no—
973C2C2×#1909939811yescharacteristic
974C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3550C2
hypercenter#3550D79
hypocenterC79#62841
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #23778097C2semidirect
2. #23777811C2semidirect
3. #23777805C2semidirect
4. #23777677C2semidirect
5. #23777672C2semidirect
6. #23777418C2semidirect
7. #23777414C2semidirect
8. #23777412C2semidirect
9. #23777364C2semidirect
10. #23777362C2semidirect
11. #23777360C2semidirect
12. #23777299C2semidirect
13. #23777292C2semidirect
14. #23776697C2semidirect
15. #23776695C2semidirect
16. C79×#3550C2semidirect
17. #19099317C22semidirect
18. #19099305C22semidirect
19. #19099305C22semidirect
20. #19099303C22semidirect
21. #19099298C22semidirect
22. #19099297C22semidirect
23. #19099295C22semidirect
24. Q8×Dic158C22semidirect
25. #19099287C22semidirect
26. #19099287C22semidirect
27. #19099287C22semidirect
28. #19099286C22semidirect
29. #19099286C22semidirect
30. #19099284C22semidirect
31. #19099284C22semidirect
32. #19099280C22semidirect
33. #19099279C22semidirect
34. #19099279C22semidirect
35. #19099278C22semidirect
36. #19099278C22semidirect
37. #19099276C22semidirect
38. #19099243C22semidirect
39. #19099240C22semidirect
40. #19099238C22semidirect
41. #19099236C22semidirect
42. #19099236C22semidirect
43. Q8×D316C22semidirect
44. #19099228C22semidirect
45. #19099225C22semidirect
46. #19099224C22semidirect
47. #19099221C22semidirect
48. #19099208C22semidirect
49. #19099206C22semidirect
50. #19099204C22semidirect
51. D4×D316C22semidirect
52. #19099198C22semidirect
53. #19099187C22semidirect
54. #19099187C22semidirect
55. #19099186C22semidirect
56. #19099186C22semidirect
57. #19099186C22semidirect
58. #19099184C22semidirect
59. #19099182C22semidirect
60. #19099179C22semidirect
61. #19099153C22semidirect
62. #19099152C22semidirect
63. #19099149C22semidirect
64. #19099136C22semidirect
67. #19099120C22semidirect
68. #19099118C22semidirect
69. #19099118C22semidirect
70. #19099118C22semidirect
71. #19099118C22semidirect
72. #19099116C22semidirect
77. #19099100C22semidirect
78. #19099100C22semidirect
79. #19099100C22semidirect
80. #19099099C22semidirect
81. #19099099C22semidirect
82. #19099099C22semidirect
83. #19099098C22semidirect
84. #19099098C22semidirect
85. #19099095C22semidirect
86. #19099095C22semidirect
87. #19099094C22semidirect
88. #19099092C22semidirect
89. C2×#14579150C22semidirect
90. #124×D79C22semidirect
91. #19099076C22semidirect
92. #19099076C22semidirect
93. #19099075C22semidirect
94. #19099073C22semidirect
95. #19099070C22semidirect
96. #19099041C22semidirect
97. #19099039C22semidirect
98. #19099037C22semidirect
99. #19099035C22semidirect
100. #41×Dic79C22semidirect
101. C4×#11929625C22semidirect
102. C4×#11929625C22semidirect
103. #19099031C22semidirect
104. C4×#11929623C22semidirect
105. C2×C42×D79C22semidirect
106. #563×C79C22semidirect
107. #559×C79C22semidirect
108. Q82×C79C22semidirect
109. #556×C79C22semidirect
110. D4×Q8×C79C22semidirect
111. #542×C79C22semidirect
112. #536×C79C22semidirect
113. #533×C79C22semidirect
490. #3550D79semidirect
504. C79#62841semidirect
506. #563C2×D79semidirect
513. #559C2×D79semidirect
515. Q82C2×D79semidirect
524. #556C2×D79semidirect
537. D4×Q8C2×D79semidirect
554. #542C2×D79semidirect
559. #536C2×D79semidirect
568. #533C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780972
#237778112
#237778052
#237776772
#237776722
#237774182
#237774142
#237774122
#237773642
#237773622
#237773602
#237772992
#237772922
#237766972
#237766952
C79×#35502
#6284179