Finite Group Databasebeta

← #35197259

Subgroups — #35197259

Order 20224.

6616 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777902C216yesmaximal, complemented
2#23777822C216yesmaximal, complemented
3#23777668C216yesmaximal, complemented
4#23777656C216yesmaximal, complemented
5#23777509C216yesmaximal, complemented
6#23777499C216yesmaximal, complemented
7#23777468C216yesmaximal, complemented
8#23777462C216yesmaximal, complemented
9#23777312C213yesmaximal, complemented
10#23777301C213yesmaximal, complemented
11#23777279C213yesmaximal, complemented
12#23777269C213yesmaximal, complemented
13#23776696C211yesmaximal, characteristic, complemented
14#23776696C211yesmaximal, characteristic, complemented
15C79×#3444C211yesmaximal, characteristic, complemented
16#19099315C22112yescomplemented
17#19099306C2214yes—
18#19099304C2214yescomplemented
19#19099302C22112yescomplemented
20#19099296C2216yescomplemented
21#19099296C22112yescomplemented
22#19099295C2216yescomplemented
23#19099290C2216yescomplemented
24#19099289C2216yescomplemented
25#19099285C2216yescomplemented
26#19099284C2216yes—
27#19099282C2216yescomplemented
28#19099281C2216yes—
29#19099277C2216yescomplemented
30#19099276C22112yescomplemented
31#19099276C2216yescomplemented
32#19099272C2216yescomplemented
33#19099269C2216yescomplemented
34#19099266C2216yescomplemented
35#19099263C2216yescomplemented
36#19099263C22112yescomplemented
37#19099262C22112yescomplemented
38#19099260C2216yescomplemented
39#19099257C2216yescomplemented
40#19099254C2216yescomplemented
41#19099252C22112yescomplemented
42#19099252C2216yescomplemented
43#19099251C2216yescomplemented
44#19099247C2216yescomplemented
45#19099246C22112yescomplemented
46#19099242C22112yes—
47#19099237C22112yescomplemented
48#19099232C2216yes—
49#19099231C2216yes—
50#19099225C2216yescomplemented
51#19099223C2216yescomplemented
52#19099221C2216yescomplemented
53#19099220C2216yescomplemented
54#19099215C2216yescomplemented
55#19099212C2216yescomplemented
56#19099210C2216yes—
57#19099208C2216yescomplemented
58#19099206C2216yescomplemented
59#19099201C2216yes—
60#19099186C2216yescomplemented
61#19099185C2216yescomplemented
62#19099181C22112yescomplemented
63#19099180C2216yescomplemented
64#19099178C2216yescomplemented
65#19099178C22112yescomplemented
66#19099173C2216yescomplemented
67#19099171C2216yescomplemented
68#19099166C2216yes—
69#19099165C22112yescomplemented
70#19099164C22112yescomplemented
71#19099164C2216yescomplemented
72#19099156C22112yescomplemented
73#19099155C22112yescomplemented
74#19099149C22112yes—
75#19099146C22112yes—
76#19099143C2216yescomplemented
77#19099142C2216yescomplemented
78#19099136C2216yes—
79#19099129C2216yes—
80#19099120C2213yescomplemented
81#19099120C2213yescomplemented
82#19099118C2213yescomplemented
83#19099118C2213yescomplemented
84#19099114C2213yescomplemented
85#19099113C2213yes—
86#19099113C2213yes—
87#19099111C2213yescomplemented
88C4⋊Q8×D79C2213yescomplemented
89#127×D79C2211yescharacteristic, complemented
90#19099097C2213yes—
91#19099097C2213yes—
92#19099097C2216yescomplemented
93#19099097C2216yescomplemented
94#19099097C2213yescomplemented
95#19099097C2213yescomplemented
96#19099097C22112yescomplemented
97#19099096C22112yescomplemented
98C2×#14579155C2214yescomplemented
99#126×D79C2214yescomplemented
100#19099074C2213yes—
101#19099074C2213yescomplemented
102#19099074C2216yescomplemented
103#19099045C2216yescomplemented
104#19099042C2216yescomplemented
105#19099039C2216yescomplemented
106#19099035C2216yescomplemented
107C4×#11929624C2213yes—
108C4×#11929624C2213yescomplemented
109C4×#11929624C2216yescomplemented
110#533×C79C2213yescomplemented
111#532×C79C2213yes—
112#529×C79C2216yescomplemented
113#529×C79C2216yescomplemented
114#525×C79C2216yescomplemented
115C4×#41×C79C2216yescomplemented
116C22×C42×C79C2211yescharacteristic, complemented
117C2×#11929625C2316yes—
118C2×#11929624C2313yes—
119C2×#11929624C2313yes—
120C2×#11929624C2316yes—
121C2×#11929623C2316yes—
122C2×Q8×D79C2316yes—
123C2×D4×D79C2316yes—
124#14579161C2313yes—
125#14579161C2313yes—
126#14579160C23112yes—
127#14579160C2316yes—
128#14579160C2316yes—
129#14579159C2316yes—
130#14579158C2311yescharacteristic
131#14579158C2311yescharacteristic
132#14579157C23112yes—
133#14579157C2316yes—
134#14579156C23112yes—
135#14579156C23112yes—
136#14579155C23112yes—
137#14579155C23112yes—
138#14579155C2314yes—
139#14579155C2311yescharacteristic
140#14579155C2311yescharacteristic
141#14579155C2314yes—
142#14579155C2313yes—
143#14579155C2313yes—
144#14579154C23112yes—
145#14579154C23112yes—
146#14579154C23112yes—
147#14579154C23112yes—
148#14579153C23112yes—
149#14579153C2313yes—
150#14579153C2313yes—
151#14579153C2316yes—
152#14579152C23112yes—
153#14579152C2316yes—
154#14579152C2316yes—
155#14579151C23112yes—
156#14579151C23112yes—
157#14579150C2316yes—
158#14579149C23112yes—
159#14579149C2316yes—
160#14579149C2313yes—
161#14579149C2313yes—
162#14579148C23112yes—
163#14579148C2316yes—
164#14579147C23112yes—
165#14579147C23112yes—
166#14579147C23112yes—
167#14579147C23112yes—
168#14579146C23112yes—
169#14579146C23112yes—
170#14579145C23112yes—
171#14579144C23112yes—
172#14579144C23112yes—
173#14579144C23112yes—
174#14579144C2313yes—
175#14579144C2313yes—
176#14579144C2313yes—
177#14579144C2313yes—
178#14579143C23112yes—
179#14579143C23112yes—
180#14579143C23112yes—
181#14579143C23112yes—
182#14579142C23112yes—
183#14579141C2316yes—
184#14579141C2316yes—
185#14579141C23112yes—
186#14579140C2316yes—
187#14579140C2313yes—
188#14579140C2313yes—
189#14579140C2313yes—
190#14579140C23112yes—
191#14579140C2313yes—
192#14579140C2316yes—
193#14579139C23112yes—
194#14579139C23112yes—
195#14579138C23112yes—
196#14579138C23112yes—
197#14579137C2316yes—
198#14579137C2316yes—
199#14579136C23112yes—
200#14579136C2316yes—
201#14579136C2316yes—
202#14579135C2316yes—
203#14579135C2313yes—
204#14579135C2313yes—
205#14579135C2313yes—
206#14579135C23112yes—
207#14579135C2313yes—
208#14579135C2316yes—
209#14579134C23112yes—
210#14579134C23112yes—
211#14579134C23112yes—
212#14579134C23112yes—
213#14579133C23112yes—
214#14579133C23112yes—
215#14579132C23112yes—
216#14579132C2316yes—
217#14579132C23112yes—
218#14579132C2316yes—
219#14579131C23112yes—
220#14579130C2313yes—
221#14579130C2314yes—
222#14579130C2311yescharacteristic
223#14579129C23112yes—
224Q8×Dic79C2316yes—
225Q8×Dic79C2316yes—
226C4×Dic158C2316yes—
227C4×Dic158C23112yes—
228C4×Dic158C2316yes—
229C4×Dic158C2313yes—
230C4×Dic158C2313yes—
231C4×Dic158C2313yes—
232C4×Dic158C2313yes—
233#14579126C2316yes—
234#14579126C2316yes—
235#14579126C23112yes—
236C4×D316C2316yes—
237C4×D316C23112yes—
238C4×D316C2313yes—
239C4×D316C2316yes—
240C4×D316C2313yes—
241C4×D316C2313yes—
242C4×D316C2313yes—
243D4×Dic79C2316yes—
244D4×Dic79C2316yes—
245#14579123C23112yes—
246#14579123C2316yes—
247#14579123C2316yes—
248C4×C22⋊D79C23112yes—
249C4×C22⋊D79C23112yes—
250C4×C22⋊D79C23112yes—
251C4×C22⋊D79C2313yes—
252C4×C22⋊D79C2313yes—
253C4×C22⋊D79C2313yes—
254C4×C22⋊D79C2313yes—
255C4×C22⋊D79C2313yes—
256C4×C22⋊D79C2313yes—
257C4×C22⋊D79C2313yes—
258C4×C22⋊D79C2313yes—
259C4×C22⋊D79C23112yes—
260(C22⋊D79)⋊C4C23112yes—
261(C22⋊D79)⋊C4C23112yes—
262#14579120C2313yes—
263#14579120C2313yes—
264#14579120C2316yes—
265#14579119C2316yes—
266#14579119C23112yes—
267#14579119C2316yes—
268#14579118C2313yes—
269#14579118C23112yes—
270#14579118C2313yes—
271#14579118C2313yes—
272#14579118C23112yes—
273#14579118C2313yes—
274#14579118C23112yes—
275#14579117C23112yes—
276C2×Dic79⋊C4C23112yes—
277C4⋊C4×D79C2316yes—
278C4⋊C4×D79C2316yes—
279C4⋊C4×D79C23112yes—
280C2×(C2×D79)⋊C4C23112yes—
281C22⋊C4×D79C23112yes—
282C42×D79C2311yescharacteristic
283C42×D79C2313yes—
284C42×D79C2314yes—
285C2×#41×C79C2316yes—
286C23×C4×C79C2313yes—
287C4⋊Q8×C79C2313yes—
288#127×C79C2311yescharacteristic
289#126×C79C2314yes—
290#126×C79C2314yes—
291#125×C79C2316yes—
292#124×C79C2316yes—
293#123×C79C23112yes—
294C22⋊Q8×C79C2316yes—
295C22⋊Q8×C79C2316yes—
296#121×C79C2316yes—
297#121×C79C2316yes—
298#120×C79C2314yes—
299C4×Q8×C79C2316yes—
300C4×Q8×C79C2316yes—
301C4×D4×C79C23112yes—
302C4×D4×C79C2316yes—
303C4×D4×C79C2316yes—
304C4×D4×C79C23112yes—
305#117×C79C23112yes—
306#117×C79C2316yes—
307C2×C42×C79C2313yes—
308C2×C42×C79C2313yes—
309C2×C42×C79C2313yes—
310C2×C42×C79C2313yes—
311C2×C42×C79C2314yes—
312C23×D79C2414yes—
313#11929625—412no—
314#11929624—412no—
315#11929624—46no—
316#11929624—46no—
317#11929623—412no—
318C2×Dic158C2416yes—
319C2×Dic158C24112yes—
320C2×Dic158C2413yes—
321C2×Dic158C2413yes—
322Q8×D79—412no—
323C2×D316C2416yes—
324C2×D316C2413yes—
325C2×D316C2413yes—
326C2×D316C24112yes—
327C2×C22⋊D79C24112yes—
328C2×C22⋊D79C2413yes—
329C2×C22⋊D79C24112yes—
330C2×C22⋊D79C2413yes—
331C2×C22⋊D79C2413yes—
332C2×C22⋊D79C2413yes—
333C2×C22⋊D79C24112yes—
334D4×D79—412no—
335C22×Dic79C24112yes—
336C2×C4×D79C2413yes—
337C2×C4×D79C2413yes—
338C2×C4×D79C2413yes—
339C2×C4×D79C2413yes—
340C2×C4×D79C24112yes—
341C2×C4×D79C24112yes—
342C2×C4×D79C24112yes—
343C4⋊Dic79C2416yes—
344C4⋊Dic79C2416yes—
345C4⋊Dic79C24112yes—
346C4⋊Dic79C24112yes—
347C4⋊Dic79C2413yes—
348C4⋊Dic79C2413yes—
349C4⋊Dic79C2413yes—
350C4⋊Dic79C2413yes—
351Dic79⋊C4C2413yes—
352Dic79⋊C4C24112yes—
353Dic79⋊C4C24112yes—
354Dic79⋊C4C2413yes—
355Dic79⋊C4C24112yes—
356Dic79⋊C4C24112yes—
357Dic79⋊C4C2413yes—
358Dic79⋊C4C2413yes—
359Dic79⋊C4C2413yes—
360Dic79⋊C4C2413yes—
361Dic79⋊C4C2413yes—
362Dic79⋊C4C2413yes—
363Dic79⋊C4C24112yes—
364Dic79⋊C4C24112yes—
365C22⋊Dic79C24112yes—
366C22⋊Dic79C24112yes—
367C22⋊Dic79C2413yes—
368C22⋊Dic79C24112yes—
369C22⋊Dic79C2413yes—
370C22⋊Dic79C2413yes—
371C22⋊Dic79C2413yes—
372(C2×D79)⋊C4C2413yes—
373(C2×D79)⋊C4C24112yes—
374(C2×D79)⋊C4C2413yes—
375(C2×D79)⋊C4C24112yes—
376(C2×D79)⋊C4C24112yes—
377(C2×D79)⋊C4C2413yes—
378(C2×D79)⋊C4C2413yes—
379(C2×D79)⋊C4C24112yes—
380(C2×D79)⋊C4C2413yes—
381(C2×D79)⋊C4C2413yes—
382(C2×D79)⋊C4C2413yes—
383(C2×D79)⋊C4C2413yes—
384(C2×D79)⋊C4C24112yes—
385(C2×D79)⋊C4C24112yes—
386C4×Dic79C24112yes—
387C4×Dic79C2413yes—
388C4×Dic79C2413yes—
389C4×Dic79C2413yes—
390C4×Dic79C2413yes—
391C4×Dic79C24112yes—
392C4×Dic79C24112yes—
393C24×C79C2411yescharacteristic
394#41×C79—412no—
395C2×Q8×C79C2416yes—
396C2×D4×C79C2416yes—
397C2×D4×C79C24112yes—
398C22×C4×C79—46no—
399C22×C4×C79C2413yes—
400C22×C4×C79C2413yes—
401C22×C4×C79C2413yes—
402C22×C4×C79C2413yes—
403C22×C4×C79C2413yes—
404C22×C4×C79C2413yes—
405C22×C4×C79C24112yes—
406C4⋊C4×C79C2416yes—
407C4⋊C4×C79C2416yes—
408C4⋊C4×C79C24112yes—
409C4⋊C4×C79C24112yes—
410C22⋊C4×C79C24112yes—
411C22⋊C4×C79C24112yes—
412C22⋊C4×C79C24112yes—
413C42×C79C2411yescharacteristic
414C42×C79C2413yes—
415C42×C79C2413yes—
416C42×C79C2413yes—
417C42×C79C2413yes—
418C42×C79C2411yescharacteristic
419C42×C79C2411yescharacteristic
420C42×C79C2411yescharacteristic
421C42×C79C24112yes—
422C23×C79—43no—
423C23×C79C2513yes—
424C23×C79C2514yes—
425C22×D79—412no—
426C22×D79C2511yescharacteristic
427C22×D79C2514yes—
428C22×D79C2513yes—
429Q8×C79—212no—
430D4×C79—212no—
431D4×C79—412no—
432C2×C4×C79—26no—
433C2×C4×C79—26no—
434C2×C4×C79—26no—
435C2×C4×C79—43no—
436C2×C4×C79—43no—
437C2×C4×C79—43no—
438C2×C4×C79—412no—
439C2×C4×C79C2513yes—
440C2×C4×C79C25112yes—
441C2×C4×C79C2513yes—
442C2×C4×C79C2513yes—
443C2×C4×C79C2513yes—
444C22⋊D79—412no—
445C22⋊D79—412no—
446C22⋊D79—43no—
447C22⋊D79—412no—
448C22⋊D79—43no—
449C22⋊D79—43no—
450C22⋊D79—43no—
451C2×Dic79—412no—
452C2×Dic79C2513yes—
453C2×Dic79C2513yes—
454C2×Dic79C25112yes—
455C2×Dic79C2513yes—
456C2×Dic79C2513yes—
457D316—212no—
458D316—43no—
459D316—43no—
460D316—412no—
461C4×D79—26no—
462C4×D79—26no—
463C4×D79—26no—
464C4×D79—26no—
465C4×D79—412no—
466C4×D79—412no—
467C4×D79—412no—
468Dic158—212no—
469Dic158—412no—
470Dic158—43no—
471Dic158—43no—
472C22×C79—23no—
473C22×C79—23no—
474C22×C79—212no—
475C22×C79—23no—
476C22×C79—44no—
477C22×C79C2611yescharacteristic
478C2×D79—23no—
479C2×D79—212no—
480C2×D79—23no—
481C2×D79—23no—
482C2×D79—23no—
483C2×D79—164no—
484C4×C79—23no—
485C4×C79—23no—
486C4×C79—23no—
487C4×C79—212no—
488C4×C79#58516yes—
489Dic79—23no—
490Dic79—212no—
491Dic79—23no—
492Dic79—23no—
493Dic79—23no—
494#62839—791nomaximal, Sylow
495C2×C79—44no—
496C2×C79—43no—
497C2×C79C2×#58513yes—
498D79—43no—
499D79—44no—
500D79—41no—
501#3557—796no—
502#3551—796no—
503#3540—796no—
504#3539—796no—
505#3524—796no—
506#3524—796no—
507#3521—796no—
508#3521—796no—
509#3511—793no—
510#3511—793no—
511#3509—793no—
512#3508—793no—
513#3444—791no—
514#3444—791no—
515#3444D7911yescharacteristic, complemented
516C79#6283911yescharacteristic, complemented, Sylow
517#563—7912no—
518H(3,𝔽4)—794no—
519#560—794no—
520#560—7912no—
521#559—796no—
522#559—796no—
523#559—7912no—
524#557—796no—
525#557—796no—
526#556—796no—
527#556—796no—
528#556—796no—
529#556—796no—
530#555—796no—
531#555—796no—
532#555—7912no—
533#554—796no—
534#554—796no—
535#553—796no—
536#553—796no—
537#553—7912no—
538#553—796no—
539#553—7912no—
540#553—796no—
541#552—796no—
542#552—796no—
543#552—796no—
544#552—7912no—
545#552—796no—
546#552—7912no—
547#551—7912no—
548#551—7912no—
549#550—796no—
550#550—796no—
551#548—796no—
552#548—796no—
553#548—796no—
554#548—796no—
555#547—796no—
556#547—796no—
557#546—796no—
558#546—796no—
559#546—796no—
560#546—796no—
561#542—7912no—
562#542—796no—
563#542—796no—
564#542—796no—
565#542—796no—
566#542—7912no—
567#541—796no—
568#541—796no—
569#540—7912no—
570#540—796no—
571#540—796no—
572#540—7912no—
573#539—7912no—
574#539—7912no—
575#538—7912no—
576#538—7912no—
577#537—796no—
578#537—796no—
579#536—796no—
580#535—796no—
581#533—793no—
582#533—793no—
583#533—793no—
584#533—793no—
585#533C2×D7913yescomplemented
586#532—793no—
587#532—793no—
588#532—793no—
589#532—793no—
590#532C2×D7913yes—
591C2×C4⋊Q8—793no—
592C2×#127—791no—
593#529—7912no—
594#529—793no—
595#529—793no—
596#529—796no—
597#529—793no—
598#529—793no—
599#529—796no—
600#529—7912no—
601#529C2×D7916yescomplemented
602#529C2×D7916yescomplemented
603C2×#126—794no—
604C2×#126—794no—
605#525—793no—
606#525—793no—
607#525—796no—
608#525C2×D7916yescomplemented
609#520—796no—
610#520—796no—
611#519—796no—
612#518—796no—
613C4×#41—793no—
614C4×#41—793no—
615C4×#41—796no—
616C4×#41C2×D7916yescomplemented
617C22×C42C2×D7911yescharacteristic, complemented
618C2×#41—796no—
619C2×#41—796no—
620C2×#41—793no—
621C2×#41—793no—
622C2×#41—796no—
623C2×#41C22×D7916yes—
624C22×Q8—796no—
625C22×D4—796no—
626C23×C4C22×D7913yes—
627C4⋊Q8—796no—
628C4⋊Q8—796no—
629C4⋊Q8—796no—
630C4⋊Q8—7912no—
631C4⋊Q8—793no—
632C4⋊Q8—793no—
633C4⋊Q8C22×D7913yes—
634#127—796no—
635#127—7912no—
636#127—791no—
637#127—791no—
638#127C22×D7911yescharacteristic
639#126—7912no—
640#126—7912no—
641#126—7912no—
642#126—7912no—
643#126—7912no—
644#126—7912no—
645#126—791no—
646#126—791no—
647#126—794no—
648#126—7912no—
649#126—7912no—
650#126—793no—
651#126—793no—
652#126—794no—
653#126C22×D7914yes—
654#126C22×D7914yes—
655#125—7912no—
656#125—796no—
657#125—796no—
658#125—7912no—
659#125—7912no—
660#125—793no—
661#125—793no—
662#125—796no—
663#125—7912no—
664#125C22×D7916yes—
665#124—796no—
666#124—796no—
667#124—7912no—
668#124—7912no—
669#124—7912no—
670#124—7912no—
671#124—7912no—
672#124—796no—
673#124—793no—
674#124—793no—
675#124—7912no—
676#124C22×D7916yes—
677#123—7912no—
678#123—7912no—
679#123—793no—
680#123—793no—
681#123—793no—
682#123—793no—
683#123—7912no—
684#123—7912no—
685#123—7912no—
686#123—7912no—
687#123—7912no—
688#123—7912no—
689#123—7912no—
690#123—7912no—
691#123—7912no—
692#123C22×D79112yes—
693C22⋊Q8—796no—
694C22⋊Q8—796no—
695C22⋊Q8—796no—
696C22⋊Q8—793no—
697C22⋊Q8—793no—
698C22⋊Q8—793no—
699C22⋊Q8—793no—
700C22⋊Q8—796no—
701C22⋊Q8—7912no—
702C22⋊Q8—7912no—
703C22⋊Q8—796no—
704C22⋊Q8—796no—
705C22⋊Q8—7912no—
706C22⋊Q8—7912no—
707C22⋊Q8—7912no—
708C22⋊Q8—7912no—
709C22⋊Q8C22×D7916yes—
710C22⋊Q8C22×D7916yes—
711#121—796no—
712#121—796no—
713#121—7912no—
714#121—7912no—
715#121—7912no—
716#121—7912no—
717#121—796no—
718#121—793no—
719#121—793no—
720#121—793no—
721#121—793no—
722#121—796no—
723#121—7912no—
724#121—796no—
725#121—796no—
726#121—7912no—
727#121—7912no—
728#121—7912no—
729#121—7912no—
730#121—7912no—
731#121C22×D7916yes—
732#121C22×D7916yes—
733#120—793no—
734#120—794no—
735#120—791no—
736#120—7912no—
737#120—7912no—
738#120C22×D7914yes—
739C4×Q8—796no—
740C4×Q8—796no—
741C4×Q8—7912no—
742C4×Q8—796no—
743C4×Q8—796no—
744C4×Q8—796no—
745C4×Q8—796no—
746C4×Q8—793no—
747C4×Q8—793no—
748C4×Q8—793no—
749C4×Q8—793no—
750C4×Q8—7912no—
751C4×Q8C22×D7916yes—
752C4×Q8C22×D7916yes—
753C4×D4—796no—
754C4×D4—796no—
755C4×D4—7912no—
756C4×D4—793no—
757C4×D4—793no—
758C4×D4—793no—
759C4×D4—793no—
760C4×D4—793no—
761C4×D4—793no—
762C4×D4—793no—
763C4×D4—793no—
764C4×D4—7912no—
765C4×D4—7912no—
766C4×D4—7912no—
767C4×D4—796no—
768C4×D4—7912no—
769C4×D4—796no—
770C4×D4—7912no—
771C4×D4—7912no—
772C4×D4—796no—
773C4×D4—793no—
774C4×D4—793no—
775C4×D4—796no—
776C4×D4—793no—
777C4×D4—793no—
778C4×D4—7912no—
779C4×D4C22×D7916yes—
780C4×D4C22×D79112yes—
781C4×D4C22×D79112yes—
782C4×D4C22×D7916yes—
783#117—793no—
784#117—793no—
785#117—796no—
786#117—796no—
787#117—7912no—
788#117—796no—
789#117—7912no—
790#117—793no—
791#117—793no—
792#117—793no—
793#117—793no—
794#117—7912no—
795#117—7912no—
796#117—7912no—
797#117C22×D7916yes—
798#117C22×D79112yes—
799C2×C4⋊C4—7912no—
800C2×C4⋊C4—7912no—
801C2×C4⋊C4—796no—
802C2×C4⋊C4—796no—
803C2×C22⋊C4—7912no—
804C2×C22⋊C4—7912no—
805C2×C42—794no—
806C2×C42—791no—
807C2×C42—793no—
808C2×C42C22×D7913yes—
809C2×C42C22×D7913yes—
810C2×C42C22×D7914yes—
811C2×C42C22×D7913yes—
812C2×C42C22×D7913yes—
813C24—794no—
814C24C23×D7911yescharacteristic
815#41—412no—
816#41—31612no—
817#41—3166no—
818#41—3166no—
819#41—31612no—
820#41—31612no—
821C2×Q8—31612no—
822C2×Q8—793no—
823C2×Q8—7912no—
824C2×Q8—793no—
825C2×Q8—796no—
826C2×Q8C23×D7916yes—
827C2×D4—31612no—
828C2×D4—793no—
829C2×D4—7912no—
830C2×D4—793no—
831C2×D4—793no—
832C2×D4—7912no—
833C2×D4—793no—
834C2×D4—7912no—
835C2×D4—793no—
836C2×D4—7912no—
837C2×D4—793no—
838C2×D4—796no—
839C2×D4C23×D7916yes—
840C2×D4C23×D79112yes—
841C22×C4—46no—
842C22×C4—7912no—
843C22×C4—7912no—
844C22×C4—7912no—
845C22×C4—7912no—
846C22×C4—793no—
847C22×C4—793no—
848C22×C4—793no—
849C22×C4—793no—
850C22×C4C23×D7913yes—
851C22×C4C23×D7913yes—
852C22×C4C23×D7913yes—
853C22×C4C23×D7913yes—
854C22×C4C23×D7913yes—
855C22×C4C23×D7913yes—
856C22×C4C23×D79112yes—
857C4⋊C4—793no—
858C4⋊C4—793no—
859C4⋊C4—7912no—
860C4⋊C4—7912no—
861C4⋊C4—7912no—
862C4⋊C4—7912no—
863C4⋊C4—793no—
864C4⋊C4—793no—
865C4⋊C4—793no—
866C4⋊C4—793no—
867C4⋊C4—793no—
868C4⋊C4—793no—
869C4⋊C4—7912no—
870C4⋊C4—7912no—
871C4⋊C4—796no—
872C4⋊C4—796no—
873C4⋊C4—7912no—
874C4⋊C4—793no—
875C4⋊C4—793no—
876C4⋊C4—793no—
877C4⋊C4—793no—
878C4⋊C4—7912no—
879C4⋊C4C23×D7916yes—
880C4⋊C4C23×D7916yes—
881C4⋊C4C23×D79112yes—
882C4⋊C4C23×D79112yes—
883C22⋊C4—7912no—
884C22⋊C4—793no—
885C22⋊C4—793no—
886C22⋊C4—7912no—
887C22⋊C4—7912no—
888C22⋊C4—793no—
889C22⋊C4—793no—
890C22⋊C4—793no—
891C22⋊C4—793no—
892C22⋊C4—7912no—
893C22⋊C4—7912no—
894C22⋊C4—7912no—
895C22⋊C4—793no—
896C22⋊C4—793no—
897C22⋊C4—7912no—
898C22⋊C4—793no—
899C22⋊C4—793no—
900C22⋊C4—793no—
901C22⋊C4—793no—
902C22⋊C4—7912no—
903C22⋊C4—7912no—
904C22⋊C4C23×D79112yes—
905C22⋊C4C23×D79112yes—
906C22⋊C4C23×D79112yes—
907C42—7912no—
908C42—793no—
909C42—793no—
910C42—793no—
911C42—793no—
912C42—7912no—
913C42—7912no—
914C42C23×D7911yescharacteristic
915C42C23×D7911yescharacteristic
916C42C23×D7911yescharacteristic
917C42C23×D7913yes—
918C42C23×D7913yes—
919C42C23×D7913yes—
920C42C23×D7913yes—
921C42C23×D7911yescharacteristic
922C42C23×D79112yes—
923C23—43no—
924C23—31612no—
925C23—791no—
926C23—794no—
927C23—793no—
928C23C24×D7913yes—
929C23C24×D7914yes—
930Q8—212no—
931Q8—31612no—
932Q8—3163no—
933Q8—3163no—
934Q8—15812no—
935D4—212no—
936D4—412no—
937D4—3163no—
938D4—3163no—
939D4—31612no—
940D4—31612no—
941D4—3163no—
942D4—3163no—
943D4—31612no—
944D4—31612no—
945D4—3163no—
946D4—3163no—
947D4—15812no—
948C2×C4—26no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—43no—
952C2×C4—43no—
953C2×C4—43no—
954C2×C4—412no—
955C2×C4—31612no—
956C2×C4—31612no—
957C2×C4—31612no—
958C2×C4—31612no—
959C2×C4—793no—
960C2×C4—793no—
961C2×C4—7912no—
962C2×C4—793no—
963C2×C4—793no—
964C2×C4—1586no—
965C2×C4—1586no—
966C2×C4—1586no—
967C2×C4—1586no—
968C2×C4C24×D7913yes—
969C2×C4C24×D79112yes—
970C2×C4C24×D7913yes—
971C2×C4C24×D7913yes—
972C2×C4C24×D7913yes—
973C22—23no—
974C22—23no—
975C22—23no—
976C22—212no—
977C22—44no—
978C22—1583no—
979C22—15812no—
980C22—1583no—
981C22—1583no—
982C22—1583no—
983C22—12644no—
984C22C25×D7911yescharacteristic
985C4—23no—
986C4—23no—
987C4—23no—
988C4—212no—
989C4—1583no—
990C4—1583no—
991C4—15812no—
992C4—1583no—
993C4—1583no—
994C4#1909939916yes—
995C2—43no—
996C2—44no—
997C2—3161no—
998C2—3164no—
999C2—3163no—
1000C2C2×#1909939913yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62839
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23777902C2semidirect
2. #23777822C2semidirect
3. #23777668C2semidirect
4. #23777656C2semidirect
5. #23777509C2semidirect
6. #23777499C2semidirect
7. #23777468C2semidirect
8. #23777462C2semidirect
9. #23777312C2semidirect
10. #23777301C2semidirect
11. #23777279C2semidirect
12. #23777269C2semidirect
13. #23776696C2semidirect
14. #23776696C2semidirect
15. C79×#3444C2semidirect
16. #19099315C22semidirect
18. #19099304C22semidirect
19. #19099302C22semidirect
20. #19099296C22semidirect
21. #19099296C22semidirect
22. #19099295C22semidirect
23. #19099290C22semidirect
24. #19099289C22semidirect
25. #19099285C22semidirect
27. #19099282C22semidirect
29. #19099277C22semidirect
30. #19099276C22semidirect
31. #19099276C22semidirect
32. #19099272C22semidirect
33. #19099269C22semidirect
34. #19099266C22semidirect
35. #19099263C22semidirect
36. #19099263C22semidirect
37. #19099262C22semidirect
38. #19099260C22semidirect
39. #19099257C22semidirect
40. #19099254C22semidirect
41. #19099252C22semidirect
42. #19099252C22semidirect
43. #19099251C22semidirect
44. #19099247C22semidirect
45. #19099246C22semidirect
47. #19099237C22semidirect
50. #19099225C22semidirect
51. #19099223C22semidirect
52. #19099221C22semidirect
53. #19099220C22semidirect
54. #19099215C22semidirect
55. #19099212C22semidirect
57. #19099208C22semidirect
58. #19099206C22semidirect
60. #19099186C22semidirect
61. #19099185C22semidirect
62. #19099181C22semidirect
63. #19099180C22semidirect
64. #19099178C22semidirect
65. #19099178C22semidirect
66. #19099173C22semidirect
67. #19099171C22semidirect
69. #19099165C22semidirect
70. #19099164C22semidirect
71. #19099164C22semidirect
72. #19099156C22semidirect
73. #19099155C22semidirect
76. #19099143C22semidirect
77. #19099142C22semidirect
80. #19099120C22semidirect
81. #19099120C22semidirect
82. #19099118C22semidirect
83. #19099118C22semidirect
84. #19099114C22semidirect
87. #19099111C22semidirect
88. C4⋊Q8×D79C22semidirect
89. #127×D79C22semidirect
92. #19099097C22semidirect
93. #19099097C22semidirect
94. #19099097C22semidirect
95. #19099097C22semidirect
96. #19099097C22semidirect
97. #19099096C22semidirect
98. C2×#14579155C22semidirect
99. #126×D79C22semidirect
101. #19099074C22semidirect
102. #19099074C22semidirect
103. #19099045C22semidirect
104. #19099042C22semidirect
105. #19099039C22semidirect
106. #19099035C22semidirect
108. C4×#11929624C22semidirect
109. C4×#11929624C22semidirect
110. #533×C79C22semidirect
112. #529×C79C22semidirect
113. #529×C79C22semidirect
114. #525×C79C22semidirect
115. C4×#41×C79C22semidirect
116. C22×C42×C79C22semidirect
515. #3444D79semidirect
516. C79#62839semidirect
585. #533C2×D79semidirect
601. #529C2×D79semidirect
602. #529C2×D79semidirect
608. #525C2×D79semidirect
616. C4×#41C2×D79semidirect
617. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779022
#237778222
#237776682
#237776562
#237775092
#237774992
#237774682
#237774622
#237773122
#237773012
#237772792
#237772692
#237766962
C79×#34442
#6283979