Finite Group Databasebeta

← #35196563

Subgroups — #35196563

Order 20224.

7190 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777511C214yesmaximal, complemented
2#23777501C214yesmaximal, complemented
3#23777411C214yesmaximal, complemented
4#23777400C214yesmaximal, complemented
5#23777245C216yesmaximal, complemented
6#23777206C211yesmaximal, characteristic, complemented
7#23777167C211yesmaximal, characteristic, complemented
8#23777113C216yesmaximal, complemented
9#23777059C211yesmaximal, characteristic, complemented
10#23777055C211yesmaximal, characteristic, complemented
11#23777026C214yesmaximal, complemented
12#23777017C214yesmaximal, complemented
13#23776998C214yesmaximal, complemented
14#23776995C214yesmaximal, complemented
15#23776816C216yesmaximal, complemented
16#23776693C216yesmaximal, complemented
17C4×#14579209C211yesmaximal, characteristic, complemented
18C2×C4×#11929625C211yesmaximal, characteristic, complemented
19C4×2−1+4×C79C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21C22×#11929625C2211yescharacteristic
22#19099298C22112yescomplemented
23#19099296C22112yescomplemented
24Q8×Dic158C2214yescomplemented
25#19099292C2214yescomplemented
26#19099289C2214yescomplemented
27#19099289C2214yescomplemented
28#19099286C22112yescomplemented
29#19099285C22112yescomplemented
30#19099281C22112yescomplemented
31#19099278C22112yescomplemented
32#19099276C22112yescomplemented
33#19099276C22112yescomplemented
34#19099263C22112yescomplemented
35#19099261C22112yescomplemented
36#19099261C22112yescomplemented
37#19099257C22112yescomplemented
38#19099254C22112yescomplemented
39#19099248C22112yescomplemented
40#19099235C2214yes—
41#19099235C2214yes—
42#19099234C22112yescomplemented
43#19099232C2214yes—
44#19099232C2214yes—
45#19099232C2214yescomplemented
46Q8×C22⋊D79C2214yescomplemented
47#19099225C2214yes—
48#19099225C2214yes—
49#19099224C2214yes—
50#19099224C2214yes—
51#19099224C2214yescomplemented
52#19099220C2214yescomplemented
53#19099214C22112yescomplemented
54#19099191C2216yes—
55#19099185C22112yescomplemented
56#19099184C22112yescomplemented
57#19099168C22112yescomplemented
58#19099164C22112yescomplemented
59#19099146C22124yes—
60#19099141C2216yes—
61#19099132C2216yes—
62#19099127C2216yes—
63#19099117C2216yescomplemented
64#19099117C2216yescomplemented
65#19099116C2216yes—
66#19099113C22112yescomplemented
67#19099110C2216yescomplemented
68#19099110C22112yescomplemented
69#19099110C2216yescomplemented
70#19099109C2216yes—
71#19099100C22112yescomplemented
72#19099100C2216yescomplemented
73#19099100C2216yescomplemented
74#19099097C22112yescomplemented
75#19099095C2216yescomplemented
76#19099095C2216yescomplemented
77#19099093C22112yes—
78#19099093C2214yes—
79#19099091C22112yescomplemented
80#19099091C22112yescomplemented
81#19099075C2216yes—
82#19099072C22112yes—
83#19099072C22112yes—
84#19099070C2216yes—
85#19099045C2214yescomplemented
86#19099044C2216yes—
87#19099041C2211yescharacteristic
88#19099039C2214yescomplemented
89C4×#11929625C2214yes—
90C4×#11929625C2214yes—
91C4×#11929625C2214yes—
92C4×#11929625C2214yes—
93C4×#11929625C2214yescomplemented
94C4×#11929624C2216yes—
95C4×#11929624C22112yescomplemented
96C4×#11929624C22112yescomplemented
97C2×Q8×Dic79C2211yescharacteristic
98C4×Q8×D79C2214yescomplemented
99C2×C4×D316C2213yes—
100C2×#14579123C2213yes—
101C2×#14579119C2213yes—
102C2×C42×D79C2213yes—
103C2×2−1+4×C79C2211yescharacteristic
104#520×C79C2216yes—
105#520×C79C2214yescomplemented
106#519×C79C2211yescharacteristic
107#519×C79C2214yescomplemented
108C4×#41×C79C2216yes—
109C4×#41×C79C2214yescomplemented
110C2×C4×Q8×C79C2211yescharacteristic
111C2×C4×Q8×C79C2214yescomplemented
112#14579209—28no—
113C2×#11929625—28no—
114C2×#11929625C2314yes—
115C2×#11929625C2314yes—
116C2×#11929625C2314yes—
117C2×#11929624C2316yes—
118C2×#11929624C23112yes—
119C2×#11929624C23112yes—
120C2×Q8×D79C2314yes—
121C22×D316C2313yes—
122C22×C4×D79C2313yes—
123C22×C4×D79C2313yes—
124C22×C4×D79C2313yes—
125#14579161C23112yes—
126#14579160C23112yes—
127#14579160C2316yes—
128#14579160C2316yes—
129#14579159C2316yes—
130#14579158C23112yes—
131#14579157C23112yes—
132#14579157C2316yes—
133#14579156C23124yes—
134#14579156C23112yes—
135#14579156C2314yes—
136#14579155C23124yes—
137#14579154C23112yes—
138#14579154C2314yes—
139#14579153C23112yes—
140#14579152C23112yes—
141#14579152C2316yes—
142#14579152C2316yes—
143#14579151C23112yes—
144#14579151C2314yes—
145#14579150C23112yes—
146#14579150C2316yes—
147#14579149C23124yes—
148#14579149C23112yes—
149#14579148C2316yes—
150#14579147C23124yes—
151#14579147C23112yes—
152#14579147C2314yes—
153#14579146C23124yes—
154#14579146C23112yes—
155#14579146C23112yes—
156#14579145C2314yes—
157#14579144C23124yes—
158#14579143C23112yes—
159#14579143C23112yes—
160#14579142C2314yes—
161#14579141C2316yes—
162#14579141C2316yes—
163#14579140C23112yes—
164#14579139C23112yes—
165#14579139C23112yes—
166#14579138C23112yes—
167#14579138C2314yes—
168#14579137C23112yes—
169#14579137C2316yes—
170#14579137C2316yes—
171#14579136C23112yes—
172#14579136C23112yes—
173#14579136C2316yes—
174#14579136C2316yes—
175#14579135C23112yes—
176#14579135C23124yes—
177#14579135C23112yes—
178#14579135C23112yes—
179#14579134C23124yes—
180#14579134C23112yes—
181#14579134C23112yes—
182#14579133C23112yes—
183#14579133C2314yes—
184#14579132C23112yes—
185#14579132C2316yes—
186#14579132C2316yes—
187#14579131C23112yes—
188#14579129C23112yes—
189Q8×Dic79C2314yes—
190Q8×Dic79C2314yes—
191Q8×Dic79C2314yes—
192Q8×Dic79C2314yes—
193C4×Dic158C2316yes—
194C4×Dic158C23112yes—
195C4×Dic158C23112yes—
196C4×Dic158C2316yes—
197C4×Dic158C2314yes—
198C4×Dic158C23112yes—
199#14579126C23112yes—
200C4×D316C23112yes—
201C4×D316C2316yes—
202C4×D316C23112yes—
203C4×D316C23112yes—
204C4×D316C23112yes—
205C4×D316C23112yes—
206C4×D316C2316yes—
207C4×D316C23112yes—
208#14579123C23112yes—
209#14579123C23112yes—
210#14579123C23112yes—
211C4×C22⋊D79C23112yes—
212C4×C22⋊D79C23112yes—
213C4×C22⋊D79C23112yes—
214C4×C22⋊D79C23112yes—
215C4×C22⋊D79C23112yes—
216C4×C22⋊D79C23112yes—
217C4×C22⋊D79C23112yes—
218C4×C22⋊D79C2314yes—
219C4×C22⋊D79C2314yes—
220C4×C22⋊D79C23112yes—
221#14579120C2316yes—
222#14579120C23112yes—
223#14579120C2314yes—
224#14579119C23112yes—
225#14579119C23112yes—
226#14579119C23112yes—
227#14579118C23112yes—
228#14579118C23112yes—
229#14579118C23112yes—
230#14579118C2314yes—
231#14579118C23112yes—
232C2×C4⋊Dic79C2313yes—
233C4⋊C4×D79C23112yes—
234C2×(C2×D79)⋊C4C2316yes—
235C2×C4×Dic79C2311yescharacteristic
236C2×C4×Dic79C2313yes—
237C2×C4×Dic79C2313yes—
238C42×D79C2316yes—
239C42×D79C2316yes—
240C42×D79C2316yes—
241C42×D79C2316yes—
242C42×D79C23112yes—
2432−1+4×C79—28no—
244C2×#41×C79C2316yes—
245C2×#41×C79C2314yes—
246C22×Q8×C79C2314yes—
247C22×Q8×C79C2311yescharacteristic
248C4×Q8×C79C2316yes—
249C4×Q8×C79C2314yes—
250C4×Q8×C79C2314yes—
251C4×Q8×C79C2314yes—
252C4×Q8×C79C2314yes—
253C4×Q8×C79C2316yes—
254C4×Q8×C79C23112yes—
255C4×D4×C79C23112yes—
256C4×D4×C79C2316yes—
257C4×D4×C79C23112yes—
258C4×D4×C79C2314yes—
259C4×D4×C79C2316yes—
260#117×C79C23112yes—
261#117×C79C2316yes—
262#117×C79C23112yes—
263C2×C4⋊C4×C79C23112yes—
264C2×C4⋊C4×C79C2313yes—
265C2×C42×C79C2313yes—
266C2×C42×C79C23112yes—
267C23×D79C2413yes—
268#11929625—216no—
269#11929625—216no—
270#11929625—216no—
271#11929624—224no—
272#11929624—424no—
273#11929624—424no—
274C2×Dic158C2416yes—
275C2×Dic158C2414yes—
276C2×Dic158C24112yes—
277Q8×D79—216no—
278C2×D316—212no—
279C2×D316C2416yes—
280C2×D316C24112yes—
281C2×D316C24112yes—
282C2×D316C24112yes—
283C2×C22⋊D79C2414yes—
284C2×C22⋊D79C2414yes—
285C2×C22⋊D79C24112yes—
286C2×C22⋊D79C24112yes—
287C2×C22⋊D79C24112yes—
288C22×Dic79C2411yescharacteristic
289C22×Dic79C2411yescharacteristic
290C22×Dic79C2413yes—
291C2×C4×D79—212no—
292C2×C4×D79—46no—
293C2×C4×D79—46no—
294C2×C4×D79C24112yes—
295C2×C4×D79C2414yes—
296C2×C4×D79C2416yes—
297C2×C4×D79C2416yes—
298C2×C4×D79C2416yes—
299C2×C4×D79C2416yes—
300C2×C4×D79C24112yes—
301C2×C4×D79C2416yes—
302C2×C4×D79C2416yes—
303C4⋊Dic79C2416yes—
304C4⋊Dic79C24112yes—
305C4⋊Dic79C2416yes—
306C4⋊Dic79C2414yes—
307C4⋊Dic79C2414yes—
308C4⋊Dic79C2414yes—
309C4⋊Dic79C24112yes—
310Dic79⋊C4C24112yes—
311Dic79⋊C4C2414yes—
312Dic79⋊C4C2414yes—
313Dic79⋊C4C2414yes—
314Dic79⋊C4C2414yes—
315Dic79⋊C4C2414yes—
316Dic79⋊C4C2414yes—
317Dic79⋊C4C24112yes—
318Dic79⋊C4C24112yes—
319Dic79⋊C4C24112yes—
320C22⋊Dic79C2414yes—
321C22⋊Dic79C2414yes—
322C22⋊Dic79C2414yes—
323C22⋊Dic79C2414yes—
324C22⋊Dic79C24112yes—
325(C2×D79)⋊C4C24124yes—
326(C2×D79)⋊C4C2414yes—
327(C2×D79)⋊C4C2414yes—
328(C2×D79)⋊C4C24112yes—
329(C2×D79)⋊C4C2414yes—
330(C2×D79)⋊C4C2414yes—
331(C2×D79)⋊C4C24112yes—
332(C2×D79)⋊C4C24112yes—
333(C2×D79)⋊C4C24112yes—
334(C2×D79)⋊C4C24112yes—
335(C2×D79)⋊C4C24112yes—
336C4×Dic79C2411yescharacteristic
337C4×Dic79C2411yescharacteristic
338C4×Dic79C2411yescharacteristic
339C4×Dic79C2411yescharacteristic
340C4×Dic79C2414yes—
341C4×Dic79C2416yes—
342C4×Dic79C2416yes—
343C4×Dic79C2416yes—
344C4×Dic79C2416yes—
345C4×Dic79C24112yes—
346C4×Dic79C24112yes—
347#41×C79—216no—
348#41×C79—224no—
349C2×Q8×C79—216no—
350C2×Q8×C79#4118yescomplemented
351C2×Q8×C79C2416yes—
352C2×Q8×C79C2414yes—
353C2×D4×C79C2414yes—
354C2×D4×C79C2416yes—
355C22×C4×C79C2414yes—
356C22×C4×C79C2411yescharacteristic
357C22×C4×C79C24112yes—
358C22×C4×C79C24112yes—
359C22×C4×C79C2413yes—
360C22×C4×C79C2413yes—
361C4⋊C4×C79C24112yes—
362C4⋊C4×C79C2416yes—
363C4⋊C4×C79C24112yes—
364C4⋊C4×C79C2416yes—
365C4⋊C4×C79C2414yes—
366C22⋊C4×C79C2414yes—
367C22⋊C4×C79C2414yes—
368C22⋊C4×C79C24112yes—
369C42×C79C2416yes—
370C42×C79C2414yes—
371C42×C79C2416yes—
372C42×C79C24112yes—
373C42×C79C24112yes—
374C23×C79C2514yes—
375C23×C79C2511yescharacteristic
376C22×D79—26no—
377C22×D79—43no—
378C22×D79—43no—
379C22×D79C2516yes—
380C22×D79C2514yes—
381Q8×C79—212no—
382Q8×C79C2×#41116yes—
383D4×C79—28no—
384D4×C79—212no—
385C2×C4×C79—224no—
386C2×C4×C79—22no—
387C2×C4×C79—28no—
388C2×C4×C79—43no—
389C2×C4×C79—412no—
390C2×C4×C79C2×#41112yes—
391C2×C4×C79C2516yes—
392C2×C4×C79C2511yescharacteristic
393C2×C4×C79C2514yes—
394C2×C4×C79C2514yes—
395C2×C4×C79C2514yes—
396C2×C4×C79C2516yes—
397C2×C4×C79C2511yescharacteristic
398C22⋊D79—28no—
399C22⋊D79—28no—
400C22⋊D79—412no—
401C22⋊D79—412no—
402C22⋊D79—412no—
403C2×Dic79—22no—
404C2×Dic79—22no—
405C2×Dic79—43no—
406C2×Dic79C2511yescharacteristic
407C2×Dic79C2511yescharacteristic
408C2×Dic79C2511yescharacteristic
409C2×Dic79C2514yes—
410C2×Dic79C2514yes—
411C2×Dic79C2516yes—
412C2×Dic79C2514yes—
413C2×Dic79C2511yescharacteristic
414D316—224no—
415D316—212no—
416D316—412no—
417D316—412no—
418C4×D79—212no—
419C4×D79—212no—
420C4×D79—224no—
421C4×D79—212no—
422C4×D79—28no—
423C4×D79—212no—
424C4×D79—46no—
425C4×D79—46no—
426C4×D79—412no—
427Dic158—212no—
428Dic158—28no—
429Dic158—412no—
430C22×C79—21no—
431C22×C79—21no—
432C22×C79—24no—
433C22×C79—24no—
434C22×C79—24no—
435C22×C79C22×#4112yes—
436C22×C79C2611yescharacteristic
437C2×D79—24no—
438C2×D79—26no—
439C2×D79—24no—
440C2×D79—24no—
441C2×D79—26no—
442C2×D79—26no—
443C2×D79—412no—
444C4×C79—24no—
445C4×C79—24no—
446C4×C79—21no—
447C4×C79—24no—
448C4×C79—26no—
449C4×C79C22×#41112yes—
450C4×C79#58512yes—
451Dic79—24no—
452Dic79—21no—
453Dic79—21no—
454Dic79—24no—
455Dic79—24no—
456Dic79—26no—
457Dic79—21no—
458Dic79#58512yes—
459#62793—791nomaximal, Sylow
460C2×C79—22no—
461C2×C79—44no—
462C2×C79C23×#4111yescharacteristic
463C2×C79C2×#58511yescharacteristic
464C2×C79C2×#58511yescharacteristic
465D79—44no—
466D79—46no—
467#3524—794no—
468#3524—794no—
469#3518—794no—
470#3517—794no—
471#3506—796no—
472#3502—791no—
473#3497—791no—
474#3493—796no—
475#3487—791no—
476#3487—791no—
477#3483—794no—
478#3482—794no—
479#3480—794no—
480#3480—794no—
481#3460—796no—
482#3444—796no—
483C4×2−1+4—791no—
484C4×2−1+4D7911yescharacteristic, complemented
485C2×C4×#41—791no—
486C79#6279311yescharacteristic, complemented, Sylow
487C2×2−1+4—791no—
488C2×2−1+4C2×D7911yescharacteristic
489C22×#41—791no—
490#559—7912no—
491#559—7912no—
492Q82—794no—
493#557—794no—
494#557—794no—
495#557—794no—
496#556—7912no—
497#556—7912no—
498#556—7912no—
499#555—7912no—
500#555—7912no—
501#555—7912no—
502#553—7912no—
503#553—7912no—
504#553—7912no—
505#553—7912no—
506#552—7912no—
507#552—7912no—
508#550—794no—
509#550—794no—
510#550—794no—
511#550—794no—
512#550—794no—
513#550—7912no—
514D4×Q8—794no—
515#548—794no—
516#548—794no—
517#548—794no—
518#548—794no—
519#548—794no—
520#548—794no—
521#547—7912no—
522#544—796no—
523#542—7912no—
524#542—7912no—
525#540—7912no—
526#540—7912no—
527#538—7924no—
528#537—796no—
529#535—796no—
530#535—796no—
531#533—796no—
532#533—796no—
533#533—796no—
534#532—796no—
535#532—796no—
536#532—796no—
537#532—7912no—
538#532—7912no—
539#529—796no—
540#529—796no—
541#529—7912no—
542#529—794no—
543#529—796no—
544#529—7912no—
545#529—796no—
546#529—7912no—
547#529—7912no—
548#529—7912no—
549#525—796no—
550#525—7912no—
551#525—7912no—
552#525—796no—
553#520—794no—
554#520—796no—
555#520C2×D7916yes—
556#520C2×D7914yescomplemented
557#519—791no—
558#519—794no—
559#519C2×D7911yescharacteristic
560#519C2×D7914yescomplemented
561C4×#41—794no—
562C4×#41—794no—
563C4×#41—794no—
564C4×#41—794no—
565C4×#41—794no—
566C4×#41—796no—
567C4×#41—7912no—
568C4×#41—7912no—
569C4×#41C2×D7916yes—
570C4×#41C2×D7914yescomplemented
571C2×C4×Q8—791no—
572C2×C4×Q8—794no—
573C2×C4×Q8C2×D7911yescharacteristic
574C2×C4×Q8C2×D7914yescomplemented
575C2×C4×D4—793no—
576C2×C4×D4—793no—
577C2×#117—793no—
578C22×C42—793no—
5792−1+4—28no—
5802−1+4—1588no—
581C2×#41—794no—
582C2×#41—794no—
583C2×#41—794no—
584C2×#41—7912no—
585C2×#41—7912no—
586C2×#41—796no—
587C2×#41—1588no—
588C2×#41C22×D7916yes—
589C2×#41C22×D7914yes—
590C22×Q8—794no—
591C22×Q8C22×D7914yes—
592C22×Q8C22×D7911yescharacteristic
593C22×D4—793no—
594C23×C4—793no—
595C23×C4—793no—
596C23×C4—793no—
597C4⋊Q8—796no—
598C4⋊Q8—796no—
599C4⋊Q8—796no—
600C4⋊Q8—7912no—
601C4⋊Q8—7912no—
602#127—796no—
603#127—7912no—
604#127—7912no—
605#126—794no—
606#126—7912no—
607#126—7924no—
608#126—794no—
609#126—7912no—
610#126—7924no—
611#125—794no—
612#125—7912no—
613#125—796no—
614#125—796no—
615#125—7912no—
616#125—7912no—
617#124—796no—
618#124—7912no—
619#124—796no—
620#124—794no—
621#124—7912no—
622#124—7924no—
623#124—7912no—
624#124—7924no—
625#123—794no—
626#123—7924no—
627#123—7912no—
628#123—7912no—
629#123—7924no—
630#123—794no—
631#123—7912no—
632#123—7912no—
633C22⋊Q8—796no—
634C22⋊Q8—796no—
635C22⋊Q8—7912no—
636C22⋊Q8—7912no—
637C22⋊Q8—7912no—
638C22⋊Q8—7912no—
639C22⋊Q8—796no—
640C22⋊Q8—796no—
641C22⋊Q8—794no—
642C22⋊Q8—7912no—
643#121—794no—
644#121—7912no—
645#121—796no—
646#121—796no—
647#121—7912no—
648#121—7912no—
649#121—7912no—
650#121—7912no—
651#121—7924no—
652#121—796no—
653#121—796no—
654#121—7912no—
655#121—7912no—
656#121—7912no—
657#121—7912no—
658#121—7924no—
659#120—7912no—
660#120—7912no—
661C4×Q8—794no—
662C4×Q8—794no—
663C4×Q8—794no—
664C4×Q8—794no—
665C4×Q8—7912no—
666C4×Q8—796no—
667C4×Q8—794no—
668C4×Q8—796no—
669C4×Q8—7912no—
670C4×Q8—7912no—
671C4×Q8—7912no—
672C4×Q8C22×D7914yes—
673C4×Q8C22×D7914yes—
674C4×Q8C22×D7916yes—
675C4×Q8C22×D7914yes—
676C4×Q8C22×D79112yes—
677C4×Q8C22×D7916yes—
678C4×Q8C22×D7914yes—
679C4×D4—794no—
680C4×D4—794no—
681C4×D4—7912no—
682C4×D4—7912no—
683C4×D4—7912no—
684C4×D4—7912no—
685C4×D4—7912no—
686C4×D4—7912no—
687C4×D4—7912no—
688C4×D4—7912no—
689C4×D4—7912no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—796no—
695C4×D4—796no—
696C4×D4—7912no—
697C4×D4—7912no—
698C4×D4—7912no—
699C4×D4—7912no—
700C4×D4C22×D7914yes—
701C4×D4C22×D7916yes—
702C4×D4C22×D79112yes—
703C4×D4C22×D7916yes—
704C4×D4C22×D79112yes—
705#117—794no—
706#117—796no—
707#117—7912no—
708#117—7912no—
709#117—7912no—
710#117—7912no—
711#117—794no—
712#117—7912no—
713#117—7912no—
714#117—7912no—
715#117—7912no—
716#117C22×D7916yes—
717#117C22×D79112yes—
718#117C22×D79112yes—
719C2×C4⋊C4—793no—
720C2×C4⋊C4—7912no—
721C2×C4⋊C4C22×D7913yes—
722C2×C4⋊C4C22×D79112yes—
723C2×C22⋊C4—796no—
724C2×C42—793no—
725C2×C42—793no—
726C2×C42—791no—
727C2×C42—7912no—
728C2×C42—796no—
729C2×C42—796no—
730C2×C42—796no—
731C2×C42—796no—
732C2×C42C22×D7913yes—
733C2×C42C22×D79112yes—
734C24—793no—
735#41—216no—
736#41—224no—
737#41—31624no—
738#41—31624no—
739#41—15816no—
740#41—15816no—
741#41—15816no—
742#41—15824no—
743C2×Q8—216no—
744C2×Q8—7912no—
745C2×Q8—796no—
746C2×Q8—794no—
747C2×Q8—15816no—
748C2×Q8#1192962418yescomplemented
749C2×Q8C23×D7916yes—
750C2×Q8C23×D7914yes—
751C2×D4—7912no—
752C2×D4—7912no—
753C2×D4—7912no—
754C2×D4—794no—
755C2×D4—794no—
756C2×D4—7912no—
757C2×D4—7912no—
758C2×D4—7912no—
759C2×D4—796no—
760C2×D4—15812no—
761C2×D4C23×D7914yes—
762C2×D4C23×D7916yes—
763C22×C4—3166no—
764C22×C4—3166no—
765C22×C4—793no—
766C22×C4—796no—
767C22×C4—796no—
768C22×C4—7912no—
769C22×C4—791no—
770C22×C4—791no—
771C22×C4—796no—
772C22×C4—796no—
773C22×C4—796no—
774C22×C4—7912no—
775C22×C4—794no—
776C22×C4—796no—
777C22×C4—15812no—
778C22×C4C23×D79112yes—
779C22×C4C23×D7911yescharacteristic
780C22×C4C23×D7914yes—
781C22×C4C23×D7913yes—
782C22×C4C23×D79112yes—
783C22×C4C23×D7913yes—
784C4⋊C4—7912no—
785C4⋊C4—794no—
786C4⋊C4—794no—
787C4⋊C4—794no—
788C4⋊C4—794no—
789C4⋊C4—794no—
790C4⋊C4—794no—
791C4⋊C4—7912no—
792C4⋊C4—7912no—
793C4⋊C4—7912no—
794C4⋊C4—796no—
795C4⋊C4—7912no—
796C4⋊C4—794no—
797C4⋊C4—796no—
798C4⋊C4—794no—
799C4⋊C4—794no—
800C4⋊C4—7912no—
801C4⋊C4C23×D79112yes—
802C4⋊C4C23×D7916yes—
803C4⋊C4C23×D79112yes—
804C4⋊C4C23×D7916yes—
805C4⋊C4C23×D7914yes—
806C22⋊C4—794no—
807C22⋊C4—794no—
808C22⋊C4—794no—
809C22⋊C4—794no—
810C22⋊C4—7912no—
811C22⋊C4—7924no—
812C22⋊C4—794no—
813C22⋊C4—794no—
814C22⋊C4—7912no—
815C22⋊C4—794no—
816C22⋊C4—794no—
817C22⋊C4—7912no—
818C22⋊C4—7912no—
819C22⋊C4—7912no—
820C22⋊C4—7912no—
821C22⋊C4—7912no—
822C22⋊C4C23×D7914yes—
823C22⋊C4C23×D7914yes—
824C22⋊C4C23×D79112yes—
825C42—791no—
826C42—791no—
827C42—796no—
828C42—796no—
829C42—796no—
830C42—796no—
831C42—7912no—
832C42—7912no—
833C42—791no—
834C42—791no—
835C42—794no—
836C42C23×D7916yes—
837C42C23×D79112yes—
838C42C23×D79112yes—
839C42C23×D7916yes—
840C42C23×D7914yes—
841C23—3163no—
842C23—3163no—
843C23—796no—
844C23—794no—
845C23—1586no—
846C23C24×D7914yes—
847C23C24×D7911yescharacteristic
848Q8—212no—
849Q8—31612no—
850Q8—1588no—
851Q8—15812no—
852Q8C2×#11929624116yes—
853D4—28no—
854D4—212no—
855D4—31612no—
856D4—31612no—
857D4—31612no—
858D4—31612no—
859D4—31612no—
860D4—1588no—
861D4—1588no—
862D4—15824no—
863D4—15812no—
864C2×C4—22no—
865C2×C4—28no—
866C2×C4—224no—
867C2×C4—43no—
868C2×C4—412no—
869C2×C4—3166no—
870C2×C4—3166no—
871C2×C4—31612no—
872C2×C4—3163no—
873C2×C4—791no—
874C2×C4—791no—
875C2×C4—791no—
876C2×C4—791no—
877C2×C4—794no—
878C2×C4—794no—
879C2×C4—796no—
880C2×C4—794no—
881C2×C4—15812no—
882C2×C4—1582no—
883C2×C4—1582no—
884C2×C4—15812no—
885C2×C4—1588no—
886C2×C4—15812no—
887C2×C4—15812no—
888C2×C4—15824no—
889C2×C4C2×#11929624112yes—
890C2×C4C24×D7916yes—
891C2×C4C24×D7911yescharacteristic
892C2×C4C24×D7914yes—
893C2×C4C24×D7914yes—
894C2×C4C24×D7914yes—
895C2×C4C24×D7916yes—
896C2×C4C24×D7911yescharacteristic
897C22—21no—
898C22—21no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—31612no—
903C22—1584no—
904C22—1586no—
905C22—1584no—
906C22—1586no—
907C22—1586no—
908C22—1584no—
909C22C22×#1192962412yes—
910C22C25×D7911yescharacteristic
911C4—24no—
912C4—26no—
913C4—24no—
914C4—21no—
915C4—24no—
916C4—792no—
917C4—1581no—
918C4—1581no—
919C4—1584no—
920C4—1581no—
921C4—1584no—
922C4—1586no—
923C4—1584no—
924C4C22×#11929624112yes—
925C4#1909940012yes—
926C2—22no—
927C2—44no—
928C2—3166no—
929C2—3164no—
930C2C23×#1192962411yescharacteristic
931C2#585×D7911yescharacteristic
932C2C2×#1909940011yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62793
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #23777511C2semidirect
2. #23777501C2semidirect
3. #23777411C2semidirect
4. #23777400C2semidirect
5. #23777245C2semidirect
6. #23777206C2semidirect
7. #23777167C2semidirect
8. #23777113C2semidirect
9. #23777059C2semidirect
10. #23777055C2semidirect
11. #23777026C2semidirect
12. #23777017C2semidirect
13. #23776998C2semidirect
14. #23776995C2semidirect
15. #23776816C2semidirect
16. #23776693C2semidirect
17. C4×#14579209C2semidirect
18. C2×C4×#11929625C2semidirect
19. C4×2−1+4×C79C2semidirect
22. #19099298C22semidirect
23. #19099296C22semidirect
24. Q8×Dic158C22semidirect
25. #19099292C22semidirect
26. #19099289C22semidirect
27. #19099289C22semidirect
28. #19099286C22semidirect
29. #19099285C22semidirect
30. #19099281C22semidirect
31. #19099278C22semidirect
32. #19099276C22semidirect
33. #19099276C22semidirect
34. #19099263C22semidirect
35. #19099261C22semidirect
36. #19099261C22semidirect
37. #19099257C22semidirect
38. #19099254C22semidirect
39. #19099248C22semidirect
42. #19099234C22semidirect
45. #19099232C22semidirect
46. Q8×C22⋊D79C22semidirect
51. #19099224C22semidirect
52. #19099220C22semidirect
53. #19099214C22semidirect
55. #19099185C22semidirect
56. #19099184C22semidirect
57. #19099168C22semidirect
58. #19099164C22semidirect
63. #19099117C22semidirect
64. #19099117C22semidirect
66. #19099113C22semidirect
67. #19099110C22semidirect
68. #19099110C22semidirect
69. #19099110C22semidirect
71. #19099100C22semidirect
72. #19099100C22semidirect
73. #19099100C22semidirect
74. #19099097C22semidirect
75. #19099095C22semidirect
76. #19099095C22semidirect
79. #19099091C22semidirect
80. #19099091C22semidirect
85. #19099045C22semidirect
88. #19099039C22semidirect
93. C4×#11929625C22semidirect
95. C4×#11929624C22semidirect
96. C4×#11929624C22semidirect
98. C4×Q8×D79C22semidirect
105. #520×C79C22semidirect
107. #519×C79C22semidirect
109. C4×#41×C79C22semidirect
111. C2×C4×Q8×C79C22semidirect
350. C2×Q8×C79#41semidirect
484. C4×2−1+4D79semidirect
486. C79#62793semidirect
556. #520C2×D79semidirect
560. #519C2×D79semidirect
570. C4×#41C2×D79semidirect
574. C2×C4×Q8C2×D79semidirect
748. C2×Q8#11929624semidirect

Maximal subgroups

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

subgroupindex
#237775112
#237775012
#237774112
#237774002
#237772452
#237772062
#237771672
#237771132
#237770592
#237770552
#237770262
#237770172
#237769982
#237769952
#237768162
#237766932
C4×#145792092
C2×C4×#119296252
C4×2−1+4×C792
#6279379