Finite Group Databasebeta

← #35196500

Subgroups — #35196500

Order 20224.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777490C214yesmaximal, complemented
2#23777479C214yesmaximal, complemented
3#23777395C214yesmaximal, complemented
4#23777385C214yesmaximal, complemented
5#23777258C216yesmaximal, complemented
6#23777206C211yesmaximal, characteristic, complemented
7#23777167C211yesmaximal, characteristic, complemented
8#23777103C216yesmaximal, complemented
9#23777052C211yesmaximal, characteristic, complemented
10#23777048C211yesmaximal, characteristic, complemented
11#23777022C214yesmaximal, complemented
12#23777017C214yesmaximal, complemented
13#23776998C214yesmaximal, complemented
14Q8×#11929624C214yesmaximal, complemented
15#23776827C216yesmaximal, complemented
16#23776693C216yesmaximal, complemented
17C4×#14579209C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
19C4×2−1+4×C79C211yesmaximal, characteristic, complemented
20C2×#14579209C2211yescharacteristic
21C22×Q8×D79C2211yescharacteristic
22#19099296C22112yescomplemented
23Q8×Dic158C2214yescomplemented
24#19099292C2214yescomplemented
25#19099291C22112yescomplemented
26#19099289C2214yescomplemented
27#19099289C2214yescomplemented
28#19099285C22112yescomplemented
29#19099283C22112yescomplemented
30#19099281C22112yescomplemented
31#19099273C22112yes—
32#19099268C22112yes—
33#19099268C22112yescomplemented
34#19099263C22112yes—
35#19099257C22112yes—
36#19099254C22112yes—
37#19099252C22112yes—
38#19099252C22112yescomplemented
39#19099248C22112yescomplemented
40#19099232C2214yescomplemented
41Q8×D316C2214yes—
42Q8×D316C2214yes—
43Q8×C22⋊D79C2214yes—
44Q8×C22⋊D79C2214yes—
45Q8×C22⋊D79C2214yescomplemented
46#19099225C2214yes—
47#19099225C2214yes—
48#19099224C2214yescomplemented
49#19099220C2214yes—
50#19099220C2214yes—
51#19099220C2214yescomplemented
52#19099218C22112yes—
53#19099214C22112yes—
54#19099191C2216yes—
55#19099184C22112yescomplemented
56#19099178C22112yescomplemented
57#19099175C22112yescomplemented
58#19099171C22112yescomplemented
59#19099155C22124yes—
60#19099141C2216yes—
61#19099139C2216yes—
62#19099134C2216yes—
63#19099120C22112yescomplemented
64#19099117C2216yes—
65#19099117C2216yes—
66#19099117C22112yescomplemented
67#19099116C2216yes—
68#19099110C2216yes—
69#19099110C2216yes—
70#19099109C2216yes—
71#19099100C2216yes—
72#19099100C2216yes—
73#19099097C22112yescomplemented
74#19099095C2216yes—
75#19099095C2216yes—
76#19099095C22112yescomplemented
77#19099093C22112yes—
78#19099093C22112yes—
79#19099091C22112yes—
80#19099091C22112yes—
81#19099075C2216yes—
82#19099072C22112yes—
83#19099072C2214yes—
84#19099070C2216yes—
85#19099045C2214yescomplemented
86#19099044C2216yes—
87#19099041C2211yescharacteristic
88#19099039C2214yescomplemented
89C4×#11929625C2214yescomplemented
90C4×#11929624C2216yes—
91C4×#11929624C22112yes—
92C4×#11929624C22112yes—
93C2×Q8×Dic79C2211yescharacteristic
94C2×C4×Dic158C2213yes—
95C2×#14579126C2213yes—
96C4×Q8×D79C2214yes—
97C4×Q8×D79C2214yes—
98C4×Q8×D79C2214yes—
99C4×Q8×D79C2214yes—
100C4×Q8×D79C2214yescomplemented
101C2×C4⋊C4×D79C2213yes—
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×#11929625C2314yes—
114C2×#11929624C2316yes—
115C2×#11929624C2314yes—
116C2×#11929624C23112yes—
117C22×Dic158C2313yes—
118C2×Q8×D79—28no—
119C2×Q8×D79C2314yes—
120C2×Q8×D79C2314yes—
121C2×Q8×D79C2314yes—
122C22×C4×D79C2311yescharacteristic
123C22×C4×D79C2313yes—
124C22×C4×D79C2313yes—
125#14579161C23112yes—
126#14579161C23112yes—
127#14579160C23112yes—
128#14579160C2316yes—
129#14579160C2316yes—
130#14579159C23112yes—
131#14579159C2316yes—
132#14579157C2316yes—
133#14579156C23112yes—
134#14579156C23112yes—
135#14579155C23124yes—
136#14579154C23124yes—
137#14579154C23112yes—
138#14579154C23112yes—
139#14579153C23124yes—
140#14579153C23112yes—
141#14579152C23112yes—
142#14579152C2316yes—
143#14579152C2316yes—
144#14579151C23124yes—
145#14579151C23112yes—
146#14579151C23112yes—
147#14579150C2316yes—
148#14579149C23112yes—
149#14579148C23112yes—
150#14579148C2316yes—
151#14579147C23112yes—
152#14579147C23112yes—
153#14579146C23112yes—
154#14579146C2314yes—
155#14579145C23112yes—
156#14579144C23124yes—
157#14579143C23124yes—
158#14579143C23112yes—
159#14579143C2314yes—
160#14579142C23112yes—
161#14579141C23112yes—
162#14579141C23112yes—
163#14579141C2316yes—
164#14579141C2316yes—
165#14579140C23112yes—
166#14579140C23124yes—
167#14579140C23112yes—
168#14579140C23112yes—
169#14579139C23124yes—
170#14579139C23112yes—
171#14579139C2314yes—
172#14579138C23112yes—
173#14579138C2314yes—
174#14579137C23112yes—
175#14579137C2316yes—
176#14579137C2316yes—
177#14579136C2316yes—
178#14579136C2316yes—
179#14579135C23112yes—
180#14579134C23112yes—
181#14579134C2314yes—
182#14579133C23112yes—
183#14579133C2314yes—
184#14579132C23112yes—
185#14579132C2316yes—
186#14579132C2316yes—
187#14579131C2314yes—
188#14579129C2314yes—
189Q8×Dic79C2314yes—
190Q8×Dic79C2314yes—
191Q8×Dic79C2314yes—
192Q8×Dic79C2314yes—
193C4×Dic158C23112yes—
194C4×Dic158C2316yes—
195C4×Dic158C23112yes—
196C4×Dic158C23112yes—
197C4×Dic158C2316yes—
198C4×Dic158C23112yes—
199C4×Dic158C23112yes—
200C4×Dic158C23112yes—
201#14579126C23112yes—
202#14579126C23112yes—
203#14579126C23112yes—
204C4×D316C2316yes—
205C4×D316C23112yes—
206C4×D316C23112yes—
207C4×D316C23112yes—
208C4×D316C2314yes—
209C4×D316C2316yes—
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#14579120C23112yes—
224#14579119C23112yes—
225#14579118C23112yes—
226#14579118C23112yes—
227#14579118C23112yes—
228#14579118C2314yes—
229#14579118C23112yes—
230C2×C4⋊Dic79C2313yes—
231C2×Dic79⋊C4C2316yes—
232C4⋊C4×D79C23112yes—
233C4⋊C4×D79C23112yes—
234C4⋊C4×D79C23112yes—
235C2×C4×Dic79C2313yes—
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×C79C2316yes—
261#117×C79C23112yes—
262#117×C79C23112yes—
263C2×C4⋊C4×C79C23112yes—
264C2×C4⋊C4×C79C2313yes—
265C2×C42×C79C2313yes—
266C2×C42×C79C23112yes—
267C23×D79C2411yescharacteristic
268#11929625—216no—
269#11929624—216no—
270#11929624—224no—
271#11929624—424no—
272C2×Dic158—212no—
273C2×Dic158C24112yes—
274C2×Dic158C2416yes—
275C2×Dic158C2414yes—
276C2×Dic158C24112yes—
277Q8×D79—216no—
278Q8×D79—216no—
279Q8×D79—216no—
280C2×D316C2414yes—
281C2×D316C2416yes—
282C2×D316C2414yes—
283C2×C22⋊D79C2414yes—
284C2×C22⋊D79C2414yes—
285C2×C22⋊D79C2414yes—
286C2×C22⋊D79C2414yes—
287C2×C22⋊D79C24112yes—
288C22×Dic79C2413yes—
289C22×Dic79C2411yescharacteristic
290C22×Dic79C2413yes—
291C2×C4×D79—24no—
292C2×C4×D79—212no—
293C2×C4×D79—46no—
294C2×C4×D79C2416yes—
295C2×C4×D79C2416yes—
296C2×C4×D79C24112yes—
297C2×C4×D79C2416yes—
298C2×C4×D79C2414yes—
299C2×C4×D79C2411yescharacteristic
300C2×C4×D79C2411yescharacteristic
301C2×C4×D79C2411yescharacteristic
302C2×C4×D79C24112yes—
303C2×C4×D79C2416yes—
304C2×C4×D79C2411yescharacteristic
305C4⋊Dic79C24112yes—
306C4⋊Dic79C2416yes—
307C4⋊Dic79C2416yes—
308C4⋊Dic79C2414yes—
309C4⋊Dic79C24112yes—
310C4⋊Dic79C24112yes—
311C4⋊Dic79C24112yes—
312Dic79⋊C4C24124yes—
313Dic79⋊C4C24112yes—
314Dic79⋊C4C2414yes—
315Dic79⋊C4C2414yes—
316Dic79⋊C4C2414yes—
317Dic79⋊C4C2414yes—
318Dic79⋊C4C24112yes—
319Dic79⋊C4C24112yes—
320Dic79⋊C4C24112yes—
321Dic79⋊C4C24112yes—
322Dic79⋊C4C24112yes—
323C22⋊Dic79C2414yes—
324C22⋊Dic79C2414yes—
325C22⋊Dic79C24112yes—
326C22⋊Dic79C24112yes—
327C22⋊Dic79C24112yes—
328(C2×D79)⋊C4C2414yes—
329(C2×D79)⋊C4C2414yes—
330(C2×D79)⋊C4C2414yes—
331(C2×D79)⋊C4C2414yes—
332(C2×D79)⋊C4C24112yes—
333(C2×D79)⋊C4C2414yes—
334(C2×D79)⋊C4C2414yes—
335(C2×D79)⋊C4C24112yes—
336(C2×D79)⋊C4C24112yes—
337(C2×D79)⋊C4C24112yes—
338C4×Dic79C2414yes—
339C4×Dic79C2416yes—
340C4×Dic79C2416yes—
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×C79C24112yes—
368C22⋊C4×C79C2414yes—
369C42×C79C2416yes—
370C42×C79C2414yes—
371C42×C79C2416yes—
372C42×C79C24112yes—
373C42×C79C24112yes—
374C23×C79C2514yes—
375C23×C79C2511yescharacteristic
376C22×D79—22no—
377C22×D79—22no—
378C22×D79—22no—
379C22×D79C2514yes—
380C22×D79C2511yescharacteristic
381C22×D79C2511yescharacteristic
382Q8×C79—212no—
383Q8×C79C2×#41116yes—
384D4×C79—28no—
385D4×C79—212no—
386C2×C4×C79—224no—
387C2×C4×C79—22no—
388C2×C4×C79—28no—
389C2×C4×C79—43no—
390C2×C4×C79—412no—
391C2×C4×C79C2×#41112yes—
392C2×C4×C79C2511yescharacteristic
393C2×C4×C79C2516yes—
394C2×C4×C79C2514yes—
395C2×C4×C79C2514yes—
396C2×C4×C79C2514yes—
397C2×C4×C79C2516yes—
398C2×C4×C79C2511yescharacteristic
399C22⋊D79—28no—
400C22⋊D79—28no—
401C22⋊D79—28no—
402C22⋊D79—28no—
403C22⋊D79—412no—
404C2×Dic79—26no—
405C2×Dic79—22no—
406C2×Dic79—43no—
407C2×Dic79C2511yescharacteristic
408C2×Dic79C2514yes—
409C2×Dic79C2516yes—
410C2×Dic79C2514yes—
411C2×Dic79C2514yes—
412C2×Dic79C2516yes—
413C2×Dic79C2511yescharacteristic
414D316—28no—
415D316—28no—
416D316—212no—
417C4×D79—22no—
418C4×D79—212no—
419C4×D79—212no—
420C4×D79—212no—
421C4×D79—224no—
422C4×D79—22no—
423C4×D79—28no—
424C4×D79—22no—
425C4×D79—46no—
426C4×D79—412no—
427C4×D792−1+414yescomplemented
428Dic158—224no—
429Dic158—212no—
430Dic158—28no—
431Dic158—412no—
432C22×C79—21no—
433C22×C79—21no—
434C22×C79—24no—
435C22×C79—24no—
436C22×C79—24no—
437C22×C79C22×#4112yes—
438C22×C79C2611yescharacteristic
439C2×D79—28no—
440C2×D79—21no—
441C2×D79—21no—
442C2×D79—21no—
443C2×D79—21no—
444C2×D79—24no—
445C2×D79—24no—
446C2×D79—24no—
447C2×D79C2×2−1+412yes—
448C2×D79#58512yes—
449C4×C79—24no—
450C4×C79—24no—
451C4×C79—21no—
452C4×C79—24no—
453C4×C79—26no—
454C4×C79C22×#41112yes—
455C4×C79C2×2−1+412yes—
456Dic79—24no—
457Dic79—26no—
458Dic79—24no—
459Dic79—21no—
460Dic79—24no—
461Dic79—26no—
462Dic79C2×2−1+412yes—
463#62788—791nomaximal, Sylow
464C2×C79—22no—
465C2×C79—44no—
466C2×C79C23×#4111yescharacteristic
467C2×C79C22×2−1+411yescharacteristic
468C2×C79C2×#58511yescharacteristic
469D79—22no—
470D79—22no—
471D79—44no—
472#3523—794no—
473#3522—794no—
474#3516—794no—
475#3516—794no—
476#3507—796no—
477#3502—791no—
478#3497—791no—
479#3492—796no—
480#3486—791no—
481#3486—791no—
482#3482—794no—
483#3482—794no—
484#3480—794no—
485Q8×#41—794no—
486#3461—796no—
487#3444—796no—
488C4×2−1+4—791no—
489C4×2−1+4D7911yescharacteristic, complemented
490C22×C4×Q8—791no—
491C79#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—791no—
493C2×2−1+4C2×D7911yescharacteristic
494C23×Q8—791no—
495#559—7912no—
496Q82—794no—
497#557—7912no—
498#557—794no—
499#557—794no—
500#557—794no—
501#556—7912no—
502#556—7912no—
503#556—7912no—
504#554—7912no—
505#554—7912no—
506#554—7912no—
507#553—7912no—
508#553—7912no—
509#552—7912no—
510#552—7912no—
511#552—7912no—
512#552—7912no—
513#550—794no—
514D4×Q8—794no—
515D4×Q8—794no—
516D4×Q8—794no—
517D4×Q8—794no—
518D4×Q8—794no—
519#548—794no—
520#548—794no—
521#548—794no—
522#548—794no—
523#548—794no—
524#548—794no—
525#547—7912no—
526#547—7912no—
527#544—796no—
528#542—7912no—
529#542—7912no—
530#541—7912no—
531#541—7912no—
532#539—7924no—
533#537—796no—
534#536—796no—
535#536—796no—
536#533—796no—
537#533—796no—
538#533—7912no—
539#533—796no—
540#533—7912no—
541#532—796no—
542#532—796no—
543#532—796no—
544#529—796no—
545#529—796no—
546#529—7912no—
547#529—796no—
548#529—7912no—
549#529—796no—
550#529—7912no—
551#529—7912no—
552#529—7912no—
553#529—7912no—
554#525—796no—
555#525—794no—
556#525—7912no—
557#525—796no—
558#520—794no—
559#520—796no—
560#520C2×D7916yes—
561#520C2×D7914yescomplemented
562#519—791no—
563#519—794no—
564#519C2×D7911yescharacteristic
565#519C2×D7914yescomplemented
566C4×#41—794no—
567C4×#41—796no—
568C4×#41—7912no—
569C4×#41—7912no—
570C4×#41C2×D7916yes—
571C4×#41C2×D7914yescomplemented
572C2×C4×Q8—791no—
573C2×C4×Q8—794no—
574C2×C4×Q8—794no—
575C2×C4×Q8—794no—
576C2×C4×Q8—794no—
577C2×C4×Q8—794no—
578C2×C4×Q8—793no—
579C2×C4×Q8—793no—
580C2×C4×Q8C2×D7911yescharacteristic
581C2×C4×Q8C2×D7914yescomplemented
582C22×C4⋊C4—793no—
583C22×C42—793no—
5842−1+4—28no—
5852−1+4—1588no—
586C2×#41—794no—
587C2×#41—7912no—
588C2×#41—794no—
589C2×#41—796no—
590C2×#41C22×D7916yes—
591C2×#41C22×D7914yes—
592C22×Q8—794no—
593C22×Q8—794no—
594C22×Q8—794no—
595C22×Q8—793no—
596C22×Q8—1588no—
597C22×Q8C22×D7914yes—
598C22×Q8C22×D7911yescharacteristic
599C23×C4—793no—
600C23×C4—793no—
601C23×C4—791no—
602C4⋊Q8—796no—
603C4⋊Q8—7912no—
604C4⋊Q8—796no—
605C4⋊Q8—796no—
606C4⋊Q8—7912no—
607C4⋊Q8—7912no—
608C4⋊Q8—7912no—
609#127—796no—
610#126—7912no—
611#126—7912no—
612#126—7912no—
613#126—7912no—
614#126—7924no—
615#126—7924no—
616#125—7912no—
617#125—796no—
618#125—796no—
619#125—7912no—
620#125—7912no—
621#125—7924no—
622#125—7912no—
623#125—7924no—
624#124—796no—
625#124—796no—
626#124—7912no—
627#124—7912no—
628#124—7912no—
629#124—7912no—
630#123—7912no—
631#123—7924no—
632#123—794no—
633#123—7912no—
634#123—794no—
635#123—7912no—
636#123—7912no—
637#123—7924no—
638C22⋊Q8—796no—
639C22⋊Q8—796no—
640C22⋊Q8—7912no—
641C22⋊Q8—7912no—
642C22⋊Q8—7912no—
643C22⋊Q8—7912no—
644C22⋊Q8—7924no—
645C22⋊Q8—794no—
646C22⋊Q8—796no—
647C22⋊Q8—796no—
648C22⋊Q8—7912no—
649C22⋊Q8—7912no—
650C22⋊Q8—7912no—
651C22⋊Q8—7924no—
652C22⋊Q8—794no—
653C22⋊Q8—7912no—
654#121—794no—
655#121—7912no—
656#121—796no—
657#121—796no—
658#121—7912no—
659#121—7912no—
660#121—796no—
661#121—796no—
662#121—794no—
663#121—7912no—
664#120—794no—
665#120—794no—
666C4×Q8—794no—
667C4×Q8—794no—
668C4×Q8—794no—
669C4×Q8—794no—
670C4×Q8—7912no—
671C4×Q8—7912no—
672C4×Q8—7912no—
673C4×Q8—7912no—
674C4×Q8—7912no—
675C4×Q8—796no—
676C4×Q8—796no—
677C4×Q8—7912no—
678C4×Q8—7912no—
679C4×Q8—7912no—
680C4×Q8—7912no—
681C4×Q8C22×D7914yes—
682C4×Q8C22×D7914yes—
683C4×Q8C22×D7916yes—
684C4×Q8C22×D7914yes—
685C4×Q8C22×D79112yes—
686C4×Q8C22×D7916yes—
687C4×Q8C22×D7914yes—
688C4×D4—794no—
689C4×D4—794no—
690C4×D4—7912no—
691C4×D4—7912no—
692C4×D4—7912no—
693C4×D4—7912no—
694C4×D4—7912no—
695C4×D4—7912no—
696C4×D4—7912no—
697C4×D4—7912no—
698C4×D4—7912no—
699C4×D4—794no—
700C4×D4—796no—
701C4×D4—796no—
702C4×D4—7912no—
703C4×D4—7912no—
704C4×D4—7912no—
705C4×D4C22×D7914yes—
706C4×D4C22×D7916yes—
707C4×D4C22×D79112yes—
708C4×D4C22×D7916yes—
709C4×D4C22×D79112yes—
710#117—796no—
711#117—7912no—
712#117—7912no—
713#117—7912no—
714#117—794no—
715#117—7912no—
716#117—7912no—
717#117—7912no—
718#117—7912no—
719#117C22×D7916yes—
720#117C22×D79112yes—
721#117C22×D79112yes—
722C2×C4⋊C4—793no—
723C2×C4⋊C4—796no—
724C2×C4⋊C4—7912no—
725C2×C4⋊C4—7912no—
726C2×C4⋊C4—7912no—
727C2×C4⋊C4C22×D7913yes—
728C2×C4⋊C4C22×D79112yes—
729C2×C42—793no—
730C2×C42—793no—
731C2×C42—793no—
732C2×C42—796no—
733C2×C42—796no—
734C2×C42—796no—
735C2×C42—796no—
736C2×C42—7912no—
737C2×C42C22×D7913yes—
738C2×C42C22×D79112yes—
739C24—791no—
740#41—216no—
741#41—224no—
742#41—31624no—
743#41—15816no—
744#41—15816no—
745#41—15824no—
746C2×Q8—216no—
747C2×Q8—7912no—
748C2×Q8—794no—
749C2×Q8—7912no—
750C2×Q8—796no—
751C2×Q8—15816no—
752C2×Q8—15816no—
753C2×Q8—15816no—
754C2×Q8—15812no—
755C2×Q8#1192962418yescomplemented
756C2×Q8C23×D7916yes—
757C2×Q8C23×D7914yes—
758C2×D4—7912no—
759C2×D4—794no—
760C2×D4—794no—
761C2×D4—794no—
762C2×D4—794no—
763C2×D4—794no—
764C2×D4—794no—
765C2×D4—796no—
766C2×D4C23×D7914yes—
767C2×D4C23×D7916yes—
768C22×C4—3166no—
769C22×C4—793no—
770C22×C4—796no—
771C22×C4—7912no—
772C22×C4—791no—
773C22×C4—791no—
774C22×C4—793no—
775C22×C4—791no—
776C22×C4—791no—
777C22×C4—796no—
778C22×C4—796no—
779C22×C4—796no—
780C22×C4—7912no—
781C22×C4—791no—
782C22×C4—794no—
783C22×C4—1584no—
784C22×C4—15812no—
785C22×C4C23×D79112yes—
786C22×C4C23×D7911yescharacteristic
787C22×C4C23×D7914yes—
788C22×C4C23×D7913yes—
789C22×C4C23×D79112yes—
790C22×C4C23×D7913yes—
791C4⋊C4—7924no—
792C4⋊C4—7912no—
793C4⋊C4—794no—
794C4⋊C4—794no—
795C4⋊C4—794no—
796C4⋊C4—794no—
797C4⋊C4—7912no—
798C4⋊C4—7912no—
799C4⋊C4—7912no—
800C4⋊C4—7912no—
801C4⋊C4—7912no—
802C4⋊C4—7912no—
803C4⋊C4—796no—
804C4⋊C4—796no—
805C4⋊C4—794no—
806C4⋊C4—7912no—
807C4⋊C4—7912no—
808C4⋊C4—7912no—
809C4⋊C4C23×D79112yes—
810C4⋊C4C23×D7916yes—
811C4⋊C4C23×D79112yes—
812C4⋊C4C23×D7916yes—
813C4⋊C4C23×D7914yes—
814C22⋊C4—794no—
815C22⋊C4—794no—
816C22⋊C4—7912no—
817C22⋊C4—7912no—
818C22⋊C4—7912no—
819C22⋊C4—794no—
820C22⋊C4—794no—
821C22⋊C4—7912no—
822C22⋊C4—794no—
823C22⋊C4—794no—
824C22⋊C4—794no—
825C22⋊C4—794no—
826C22⋊C4—7912no—
827C22⋊C4—7912no—
828C22⋊C4—7912no—
829C22⋊C4C23×D7914yes—
830C22⋊C4C23×D79112yes—
831C22⋊C4C23×D7914yes—
832C42—796no—
833C42—796no—
834C42—796no—
835C42—796no—
836C42—796no—
837C42—7912no—
838C42—7912no—
839C42—796no—
840C42—794no—
841C42C23×D7916yes—
842C42C23×D79112yes—
843C42C23×D79112yes—
844C42C23×D7916yes—
845C42C23×D7914yes—
846C23—791no—
847C23—791no—
848C23—794no—
849C23—1582no—
850C23—1582no—
851C23—1582no—
852C23C24×D7914yes—
853C23C24×D7911yescharacteristic
854Q8—212no—
855Q8—31612no—
856Q8—1588no—
857Q8—15824no—
858Q8—15812no—
859Q8C2×#11929624116yes—
860D4—28no—
861D4—212no—
862D4—31612no—
863D4—1588no—
864D4—1588no—
865D4—1588no—
866D4—1588no—
867D4—1588no—
868D4—1588no—
869D4—15812no—
870C2×C4—22no—
871C2×C4—28no—
872C2×C4—224no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—3166no—
876C2×C4—31612no—
877C2×C4—3163no—
878C2×C4—791no—
879C2×C4—794no—
880C2×C4—791no—
881C2×C4—794no—
882C2×C4—796no—
883C2×C4—794no—
884C2×C4—794no—
885C2×C4—796no—
886C2×C4—1582no—
887C2×C4—15812no—
888C2×C4—1582no—
889C2×C4—1582no—
890C2×C4—1586no—
891C2×C4—1582no—
892C2×C4—1588no—
893C2×C4—15812no—
894C2×C4—15812no—
895C2×C4—15824no—
896C2×C4C2×#11929624112yes—
897C2×C4C24×D7911yescharacteristic
898C2×C4C24×D7916yes—
899C2×C4C24×D7914yes—
900C2×C4C24×D7914yes—
901C2×C4C24×D7914yes—
902C2×C4C24×D7916yes—
903C2×C4C24×D7911yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—792no—
910C22—792no—
911C22—1588no—
912C22—1584no—
913C22—1584no—
914C22—1584no—
915C22—1581no—
916C22—1581no—
917C22—1581no—
918C22—1581no—
919C22C22×#1192962412yes—
920C22C25×D7911yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—792no—
927C4—1584no—
928C4—1586no—
929C4—1581no—
930C4—1584no—
931C4—1584no—
932C4—1586no—
933C4C22×#11929624112yes—
934C42−1+4×D7912yes—
935C2—22no—
936C2—44no—
937C2—3164no—
938C2—1582no—
939C2—1582no—
940C2C23×#1192962411yescharacteristic
941C2C2×2−1+4×D7911yescharacteristic
942C2#585×D7911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62788
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. #23777490C2semidirect
2. #23777479C2semidirect
3. #23777395C2semidirect
4. #23777385C2semidirect
5. #23777258C2semidirect
6. #23777206C2semidirect
7. #23777167C2semidirect
8. #23777103C2semidirect
9. #23777052C2semidirect
10. #23777048C2semidirect
11. #23777022C2semidirect
12. #23777017C2semidirect
13. #23776998C2semidirect
14. Q8×#11929624C2semidirect
15. #23776827C2semidirect
16. #23776693C2semidirect
17. C4×#14579209C2semidirect
18. C2×C4×Q8×D79C2semidirect
19. C4×2−1+4×C79C2semidirect
22. #19099296C22semidirect
23. Q8×Dic158C22semidirect
24. #19099292C22semidirect
25. #19099291C22semidirect
26. #19099289C22semidirect
27. #19099289C22semidirect
28. #19099285C22semidirect
29. #19099283C22semidirect
30. #19099281C22semidirect
33. #19099268C22semidirect
38. #19099252C22semidirect
39. #19099248C22semidirect
40. #19099232C22semidirect
45. Q8×C22⋊D79C22semidirect
48. #19099224C22semidirect
51. #19099220C22semidirect
55. #19099184C22semidirect
56. #19099178C22semidirect
57. #19099175C22semidirect
58. #19099171C22semidirect
63. #19099120C22semidirect
66. #19099117C22semidirect
73. #19099097C22semidirect
76. #19099095C22semidirect
85. #19099045C22semidirect
88. #19099039C22semidirect
89. C4×#11929625C22semidirect
100. C4×Q8×D79C22semidirect
105. #520×C79C22semidirect
107. #519×C79C22semidirect
109. C4×#41×C79C22semidirect
111. C2×C4×Q8×C79C22semidirect
350. C2×Q8×C79#41semidirect
427. C4×D792−1+4semidirect
489. C4×2−1+4D79semidirect
491. C79#62788semidirect
561. #520C2×D79semidirect
565. #519C2×D79semidirect
571. C4×#41C2×D79semidirect
581. C2×C4×Q8C2×D79semidirect
755. C2×Q8#11929624semidirect

Maximal subgroups

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

subgroupindex
#237774902
#237774792
#237773952
#237773852
#237772582
#237772062
#237771672
#237771032
#237770522
#237770482
#237770222
#237770172
#237769982
Q8×#119296242
#237768272
#237766932
C4×#145792092
C2×C4×Q8×D792
C4×2−1+4×C792
#6278879