Finite Group Databasebeta

← #27124509

Subgroups — #27124509

Order 12032.

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#20257478C214yesmaximal, complemented
2#20257467C214yesmaximal, complemented
3#20257383C214yesmaximal, complemented
4#20257373C214yesmaximal, complemented
5#20257246C216yesmaximal, complemented
6#20257194C211yesmaximal, characteristic, complemented
7#20257155C211yesmaximal, characteristic, complemented
8#20257091C216yesmaximal, complemented
9#20257040C211yesmaximal, characteristic, complemented
10#20257036C211yesmaximal, characteristic, complemented
11#20257010C214yesmaximal, complemented
12#20257005C214yesmaximal, complemented
13#20256986C214yesmaximal, complemented
14Q8×#10625350C214yesmaximal, complemented
15#20256815C216yesmaximal, complemented
16#20256681C216yesmaximal, complemented
17C4×#13094072C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
19C4×2−1+4×C47C211yesmaximal, characteristic, complemented
20C2×#13094072C2211yescharacteristic
21C22×Q8×D47C2211yescharacteristic
22#15689856C22112yescomplemented
23Q8×Dic94C2214yescomplemented
24#15689852C2214yescomplemented
25#15689851C22112yescomplemented
26#15689849C2214yescomplemented
27#15689849C2214yescomplemented
28#15689845C22112yescomplemented
29#15689843C22112yescomplemented
30#15689841C22112yescomplemented
31#15689833C22112yes—
32#15689828C22112yes—
33#15689828C22112yescomplemented
34#15689823C22112yes—
35#15689817C22112yes—
36#15689814C22112yes—
37#15689812C22112yes—
38#15689812C22112yescomplemented
39#15689808C22112yescomplemented
40#15689792C2214yescomplemented
41Q8×D188C2214yes—
42Q8×D188C2214yes—
43Q8×C22⋊D47C2214yes—
44Q8×C22⋊D47C2214yes—
45Q8×C22⋊D47C2214yescomplemented
46#15689785C2214yes—
47#15689785C2214yes—
48#15689784C2214yescomplemented
49#15689780C2214yes—
50#15689780C2214yes—
51#15689780C2214yescomplemented
52#15689778C22112yes—
53#15689774C22112yes—
54#15689751C2216yes—
55#15689744C22112yescomplemented
56#15689738C22112yescomplemented
57#15689735C22112yescomplemented
58#15689731C22112yescomplemented
59#15689715C22124yes—
60#15689701C2216yes—
61#15689699C2216yes—
62#15689694C2216yes—
63#15689680C22112yescomplemented
64#15689677C2216yes—
65#15689677C2216yes—
66#15689677C22112yescomplemented
67#15689676C2216yes—
68#15689670C2216yes—
69#15689670C2216yes—
70#15689669C2216yes—
71#15689660C2216yes—
72#15689660C2216yes—
73#15689657C22112yescomplemented
74#15689655C2216yes—
75#15689655C2216yes—
76#15689655C22112yescomplemented
77#15689653C22112yes—
78#15689653C22112yes—
79#15689651C22112yes—
80#15689651C22112yes—
81#15689635C2216yes—
82#15689632C22112yes—
83#15689632C2214yes—
84#15689630C2216yes—
85#15689605C2214yescomplemented
86#15689604C2216yes—
87#15689601C2211yescharacteristic
88#15689599C2214yescomplemented
89C4×#10625354C2214yescomplemented
90C4×#10625350C2216yes—
91C4×#10625350C22112yes—
92C4×#10625350C22112yes—
93C2×Q8×Dic47C2211yescharacteristic
94C2×C4×Dic94C2213yes—
95C2×#13093989C2213yes—
96C4×Q8×D47C2214yes—
97C4×Q8×D47C2214yes—
98C4×Q8×D47C2214yes—
99C4×Q8×D47C2214yes—
100C4×Q8×D47C2214yescomplemented
101C2×C4⋊C4×D47C2213yes—
102C2×C42×D47C2213yes—
103C2×2−1+4×C47C2211yescharacteristic
104C47×#520C2216yes—
105C47×#520C2214yescomplemented
106C47×#519C2211yescharacteristic
107C47×#519C2214yescomplemented
108C4×#41×C47C2216yes—
109C4×#41×C47C2214yescomplemented
110C2×C4×Q8×C47C2211yescharacteristic
111C2×C4×Q8×C47C2214yescomplemented
112#13094072—28no—
113C2×#10625354C2314yes—
114C2×#10625350C2314yes—
115C2×#10625350C2316yes—
116C2×#10625350C23112yes—
117C22×Dic94C2313yes—
118C2×Q8×D47—28no—
119C2×Q8×D47C2314yes—
120C2×Q8×D47C2314yes—
121C2×Q8×D47C2314yes—
122C22×C4×D47C2311yescharacteristic
123C22×C4×D47C2313yes—
124C22×C4×D47C2313yes—
125#13094024C23112yes—
126#13094024C23112yes—
127#13094023C23112yes—
128#13094023C2316yes—
129#13094023C2316yes—
130#13094022C23112yes—
131#13094022C2316yes—
132#13094020C2316yes—
133#13094019C23112yes—
134#13094019C23112yes—
135#13094018C23124yes—
136#13094017C23112yes—
137#13094017C23124yes—
138#13094017C23112yes—
139#13094016C23124yes—
140#13094016C23112yes—
141#13094015C23112yes—
142#13094015C2316yes—
143#13094015C2316yes—
144#13094014C23112yes—
145#13094014C23124yes—
146#13094014C23112yes—
147#13094013C2316yes—
148#13094012C23112yes—
149#13094011C23112yes—
150#13094011C2316yes—
151#13094010C23112yes—
152#13094010C23112yes—
153#13094009C23112yes—
154#13094009C2314yes—
155#13094008C23112yes—
156#13094007C23124yes—
157#13094006C23124yes—
158#13094006C23112yes—
159#13094006C2314yes—
160#13094005C23112yes—
161#13094004C23112yes—
162#13094004C23112yes—
163#13094004C2316yes—
164#13094004C2316yes—
165#13094003C23112yes—
166#13094003C23112yes—
167#13094003C23124yes—
168#13094003C23112yes—
169#13094002C23124yes—
170#13094002C23112yes—
171#13094002C2314yes—
172#13094001C23112yes—
173#13094001C2314yes—
174#13094000C23112yes—
175#13094000C2316yes—
176#13094000C2316yes—
177#13093999C2316yes—
178#13093999C2316yes—
179#13093998C23112yes—
180#13093997C23112yes—
181#13093997C2314yes—
182#13093996C2314yes—
183#13093996C23112yes—
184#13093995C23112yes—
185#13093995C2316yes—
186#13093995C2316yes—
187#13093994C2314yes—
188#13093992C2314yes—
189Q8×Dic47C2314yes—
190Q8×Dic47C2314yes—
191Q8×Dic47C2314yes—
192Q8×Dic47C2314yes—
193C4×Dic94C23112yes—
194C4×Dic94C2316yes—
195C4×Dic94C23112yes—
196C4×Dic94C23112yes—
197C4×Dic94C2316yes—
198C4×Dic94C23112yes—
199C4×Dic94C23112yes—
200C4×Dic94C23112yes—
201#13093989C23112yes—
202#13093989C23112yes—
203#13093989C23112yes—
204C4×D188C2316yes—
205C4×D188C23112yes—
206C4×D188C23112yes—
207C4×D188C23112yes—
208C4×D188C2314yes—
209C4×D188C2316yes—
210#13093986C23112yes—
211C4×C22⋊D47C23112yes—
212C4×C22⋊D47C23112yes—
213C4×C22⋊D47C23112yes—
214C4×C22⋊D47C23112yes—
215C4×C22⋊D47C23112yes—
216C4×C22⋊D47C23112yes—
217C4×C22⋊D47C2314yes—
218C4×C22⋊D47C2314yes—
219C4×C22⋊D47C23112yes—
220C4×C22⋊D47C23112yes—
221#13093983C2316yes—
222#13093983C23112yes—
223#13093983C23112yes—
224#13093982C23112yes—
225#13093981C23112yes—
226#13093981C23112yes—
227#13093981C23112yes—
228#13093981C2314yes—
229#13093981C23112yes—
230C2×C4⋊Dic47C2313yes—
231C2×Dic47⋊C4C2316yes—
232C4⋊C4×D47C23112yes—
233C4⋊C4×D47C23112yes—
234C4⋊C4×D47C23112yes—
235C2×C4×Dic47C2313yes—
236C2×C4×Dic47C2313yes—
237C2×C4×Dic47C2313yes—
238C42×D47C2316yes—
239C42×D47C2316yes—
240C42×D47C2316yes—
241C42×D47C2316yes—
242C42×D47C23112yes—
2432−1+4×C47—28no—
244C2×#41×C47C2314yes—
245C2×#41×C47C2316yes—
246C22×Q8×C47C2314yes—
247C22×Q8×C47C2311yescharacteristic
248C4×Q8×C47C2316yes—
249C4×Q8×C47C2314yes—
250C4×Q8×C47C2314yes—
251C4×Q8×C47C2314yes—
252C4×Q8×C47C2314yes—
253C4×Q8×C47C2316yes—
254C4×Q8×C47C23112yes—
255C4×D4×C47C2316yes—
256C4×D4×C47C23112yes—
257C4×D4×C47C2314yes—
258C4×D4×C47C2316yes—
259C4×D4×C47C23112yes—
260#117×C47C23112yes—
261#117×C47C2316yes—
262#117×C47C23112yes—
263C2×C4⋊C4×C47C23112yes—
264C2×C4⋊C4×C47C2313yes—
265C2×C42×C47C2313yes—
266C2×C42×C47C23112yes—
267C23×D47C2411yescharacteristic
268#41×C47—216no—
269#41×C47—224no—
270C2×Q8×C47—216no—
271C2×Q8×C47#4118yescomplemented
272C2×Q8×C47C2416yes—
273C2×Q8×C47C2414yes—
274C2×D4×C47C2414yes—
275C2×D4×C47C2416yes—
276C22×C4×C47C2411yescharacteristic
277C22×C4×C47C2414yes—
278C22×C4×C47C24112yes—
279C22×C4×C47C2413yes—
280C22×C4×C47C24112yes—
281C22×C4×C47C2413yes—
282C2×C22⋊D47C2414yes—
283C2×C22⋊D47C2414yes—
284C2×C22⋊D47C2414yes—
285C2×C22⋊D47C2414yes—
286C2×C22⋊D47C24112yes—
287C22×Dic47C2411yescharacteristic
288C22×Dic47C2413yes—
289C22×Dic47C2413yes—
290#10625354—216no—
291Q8×D47—216no—
292Q8×D47—216no—
293Q8×D47—216no—
294#10625350—224no—
295#10625350—216no—
296#10625350—424no—
297C2×D188C2416yes—
298C2×D188C2414yes—
299C2×D188C2414yes—
300C2×C4×D47—212no—
301C2×C4×D47—24no—
302C2×C4×D47—46no—
303C2×C4×D47C2411yescharacteristic
304C2×C4×D47C2411yescharacteristic
305C2×C4×D47C2411yescharacteristic
306C2×C4×D47C2414yes—
307C2×C4×D47C2416yes—
308C2×C4×D47C2416yes—
309C2×C4×D47C2416yes—
310C2×C4×D47C24112yes—
311C2×C4×D47C2416yes—
312C2×C4×D47C24112yes—
313C2×C4×D47C2411yescharacteristic
314C2×Dic94—212no—
315C2×Dic94C24112yes—
316C2×Dic94C2416yes—
317C2×Dic94C2414yes—
318C2×Dic94C24112yes—
319C4⋊C4×C47C24112yes—
320C4⋊C4×C47C2416yes—
321C4⋊C4×C47C24112yes—
322C4⋊C4×C47C2416yes—
323C4⋊C4×C47C2414yes—
324C22⋊C4×C47C2414yes—
325C22⋊C4×C47C24112yes—
326C22⋊C4×C47C2414yes—
327C42×C47C2416yes—
328C42×C47C2414yes—
329C42×C47C2416yes—
330C42×C47C24112yes—
331C42×C47C24112yes—
332C22⋊Dic47C2414yes—
333C22⋊Dic47C2414yes—
334C22⋊Dic47C24112yes—
335C22⋊Dic47C24112yes—
336C22⋊Dic47C24112yes—
337(C2×D47)⋊C4C2414yes—
338(C2×D47)⋊C4C2414yes—
339(C2×D47)⋊C4C2414yes—
340(C2×D47)⋊C4C2414yes—
341(C2×D47)⋊C4C24112yes—
342(C2×D47)⋊C4C2414yes—
343(C2×D47)⋊C4C2414yes—
344(C2×D47)⋊C4C24112yes—
345(C2×D47)⋊C4C24112yes—
346(C2×D47)⋊C4C24112yes—
347C4⋊Dic47C24112yes—
348C4⋊Dic47C2416yes—
349C4⋊Dic47C2416yes—
350C4⋊Dic47C2414yes—
351C4⋊Dic47C24112yes—
352C4⋊Dic47C24112yes—
353C4⋊Dic47C24112yes—
354Dic47⋊C4C24124yes—
355Dic47⋊C4C24112yes—
356Dic47⋊C4C2414yes—
357Dic47⋊C4C2414yes—
358Dic47⋊C4C2414yes—
359Dic47⋊C4C2414yes—
360Dic47⋊C4C24112yes—
361Dic47⋊C4C24112yes—
362Dic47⋊C4C24112yes—
363Dic47⋊C4C24112yes—
364Dic47⋊C4C24112yes—
365C4×Dic47C2414yes—
366C4×Dic47C2416yes—
367C4×Dic47C2416yes—
368C4×Dic47C2416yes—
369C4×Dic47C2416yes—
370C4×Dic47C2416yes—
371C4×Dic47C2416yes—
372C4×Dic47C24112yes—
373C4×Dic47C24112yes—
374C23×C47C2514yes—
375C23×C47C2511yescharacteristic
376C22×D47—22no—
377C22×D47—22no—
378C22×D47—22no—
379C22×D47C2514yes—
380C22×D47C2511yescharacteristic
381C22×D47C2511yescharacteristic
382Q8×C47—212no—
383Q8×C47C2×#41116yes—
384D4×C47—28no—
385D4×C47—212no—
386C2×C4×C47—224no—
387C2×C4×C47—22no—
388C2×C4×C47—28no—
389C2×C4×C47—43no—
390C2×C4×C47—412no—
391C2×C4×C47C2×#41112yes—
392C2×C4×C47C2511yescharacteristic
393C2×C4×C47C2516yes—
394C2×C4×C47C2514yes—
395C2×C4×C47C2514yes—
396C2×C4×C47C2514yes—
397C2×C4×C47C2516yes—
398C2×C4×C47C2511yescharacteristic
399C22⋊D47—28no—
400C22⋊D47—28no—
401C22⋊D47—28no—
402C22⋊D47—28no—
403C22⋊D47—412no—
404C2×Dic47—26no—
405C2×Dic47—22no—
406C2×Dic47—43no—
407C2×Dic47C2511yescharacteristic
408C2×Dic47C2514yes—
409C2×Dic47C2516yes—
410C2×Dic47C2514yes—
411C2×Dic47C2514yes—
412C2×Dic47C2516yes—
413C2×Dic47C2511yescharacteristic
414D188—28no—
415D188—28no—
416D188—212no—
417C4×D47—22no—
418C4×D47—212no—
419C4×D47—212no—
420C4×D47—212no—
421C4×D47—224no—
422C4×D47—22no—
423C4×D47—28no—
424C4×D47—22no—
425C4×D47—46no—
426C4×D47—412no—
427C4×D472−1+414yescomplemented
428Dic94—224no—
429Dic94—212no—
430Dic94—28no—
431Dic94—412no—
432#62788—471nomaximal, Sylow
433C22×C47—21no—
434C22×C47—21no—
435C22×C47—24no—
436C22×C47—24no—
437C22×C47—24no—
438C22×C47C22×#4112yes—
439C22×C47C2611yescharacteristic
440C2×D47—28no—
441C2×D47—21no—
442C2×D47—21no—
443C2×D47—21no—
444C2×D47—21no—
445C2×D47—24no—
446C2×D47—24no—
447C2×D47—24no—
448C2×D47C2×2−1+412yes—
449C2×D47#58512yes—
450C4×C47—24no—
451C4×C47—24no—
452C4×C47—21no—
453C4×C47—24no—
454C4×C47—26no—
455C4×C47C22×#41112yes—
456C4×C47C2×2−1+412yes—
457Dic47—26no—
458Dic47—24no—
459Dic47—24no—
460Dic47—21no—
461Dic47—24no—
462Dic47—26no—
463Dic47C2×2−1+412yes—
464#3523—474no—
465#3522—474no—
466#3516—474no—
467#3516—474no—
468#3507—476no—
469#3502—471no—
470#3497—471no—
471#3492—476no—
472#3486—471no—
473#3486—471no—
474#3482—474no—
475#3482—474no—
476#3480—474no—
477Q8×#41—474no—
478#3461—476no—
479#3444—476no—
480C4×2−1+4—471no—
481C4×2−1+4D4711yescharacteristic, complemented
482C22×C4×Q8—471no—
483C2×C47—22no—
484C2×C47—44no—
485C2×C47C23×#4111yescharacteristic
486C2×C47C22×2−1+411yescharacteristic
487C2×C47C2×#58511yescharacteristic
488D47—22no—
489D47—22no—
490D47—44no—
491C2×2−1+4—471no—
492C2×2−1+4C2×D4711yescharacteristic
493C23×Q8—471no—
494#559—4712no—
495Q82—474no—
496#557—474no—
497#557—474no—
498#557—4712no—
499#557—474no—
500#556—4712no—
501#556—4712no—
502#556—4712no—
503#554—4712no—
504#554—4712no—
505#554—4712no—
506#553—4712no—
507#553—4712no—
508#552—4712no—
509#552—4712no—
510#552—4712no—
511#552—4712no—
512#550—474no—
513D4×Q8—474no—
514D4×Q8—474no—
515D4×Q8—474no—
516D4×Q8—474no—
517D4×Q8—474no—
518#548—474no—
519#548—474no—
520#548—474no—
521#548—474no—
522#548—474no—
523#548—474no—
524#547—4712no—
525#547—4712no—
526#544—476no—
527#542—4712no—
528#542—4712no—
529#541—4712no—
530#541—4712no—
531#539—4724no—
532#537—476no—
533#536—476no—
534#536—476no—
535#533—476no—
536#533—476no—
537#533—4712no—
538#533—476no—
539#533—4712no—
540#532—476no—
541#532—476no—
542#532—476no—
543#529—476no—
544#529—476no—
545#529—4712no—
546#529—476no—
547#529—4712no—
548#529—476no—
549#529—4712no—
550#529—4712no—
551#529—4712no—
552#529—4712no—
553#525—476no—
554#525—474no—
555#525—4712no—
556#525—476no—
557#520—474no—
558#520—476no—
559#520C2×D4716yes—
560#520C2×D4714yescomplemented
561#519—471no—
562#519—474no—
563#519C2×D4711yescharacteristic
564#519C2×D4714yescomplemented
565C4×#41—474no—
566C4×#41—476no—
567C4×#41—4712no—
568C4×#41—4712no—
569C4×#41C2×D4716yes—
570C4×#41C2×D4714yescomplemented
571C2×C4×Q8—471no—
572C2×C4×Q8—474no—
573C2×C4×Q8—474no—
574C2×C4×Q8—474no—
575C2×C4×Q8—474no—
576C2×C4×Q8—474no—
577C2×C4×Q8—473no—
578C2×C4×Q8—473no—
579C2×C4×Q8C2×D4711yescharacteristic
580C2×C4×Q8C2×D4714yescomplemented
581C22×C4⋊C4—473no—
582C22×C42—473no—
583C47#6278811yescharacteristic, complemented, Sylow
5842−1+4—28no—
5852−1+4—948no—
586C2×#41—474no—
587C2×#41—474no—
588C2×#41—476no—
589C2×#41—4712no—
590C2×#41C22×D4716yes—
591C2×#41C22×D4714yes—
592C22×Q8—474no—
593C22×Q8—474no—
594C22×Q8—474no—
595C22×Q8—473no—
596C22×Q8—948no—
597C22×Q8C22×D4714yes—
598C22×Q8C22×D4711yescharacteristic
599C23×C4—473no—
600C23×C4—471no—
601C23×C4—473no—
602C4⋊Q8—476no—
603C4⋊Q8—4712no—
604C4⋊Q8—476no—
605C4⋊Q8—476no—
606C4⋊Q8—4712no—
607C4⋊Q8—4712no—
608C4⋊Q8—4712no—
609#127—476no—
610#126—4712no—
611#126—4712no—
612#126—4712no—
613#126—4712no—
614#126—4724no—
615#126—4724no—
616#125—4712no—
617#125—476no—
618#125—476no—
619#125—4712no—
620#125—4712no—
621#125—4724no—
622#125—4712no—
623#125—4724no—
624#124—476no—
625#124—476no—
626#124—4712no—
627#124—4712no—
628#124—4712no—
629#124—4712no—
630#123—4712no—
631#123—4724no—
632#123—474no—
633#123—4712no—
634#123—474no—
635#123—4712no—
636#123—4712no—
637#123—4724no—
638C22⋊Q8—476no—
639C22⋊Q8—476no—
640C22⋊Q8—4712no—
641C22⋊Q8—4712no—
642C22⋊Q8—4712no—
643C22⋊Q8—4712no—
644C22⋊Q8—4724no—
645C22⋊Q8—474no—
646C22⋊Q8—476no—
647C22⋊Q8—476no—
648C22⋊Q8—4712no—
649C22⋊Q8—4712no—
650C22⋊Q8—4712no—
651C22⋊Q8—4724no—
652C22⋊Q8—474no—
653C22⋊Q8—4712no—
654#121—474no—
655#121—4712no—
656#121—476no—
657#121—476no—
658#121—4712no—
659#121—4712no—
660#121—476no—
661#121—476no—
662#121—474no—
663#121—4712no—
664#120—474no—
665#120—474no—
666C4×Q8—474no—
667C4×Q8—474no—
668C4×Q8—474no—
669C4×Q8—474no—
670C4×Q8—4712no—
671C4×Q8—4712no—
672C4×Q8—4712no—
673C4×Q8—4712no—
674C4×Q8—4712no—
675C4×Q8—476no—
676C4×Q8—476no—
677C4×Q8—4712no—
678C4×Q8—4712no—
679C4×Q8—4712no—
680C4×Q8—4712no—
681C4×Q8C22×D4714yes—
682C4×Q8C22×D4714yes—
683C4×Q8C22×D4716yes—
684C4×Q8C22×D4714yes—
685C4×Q8C22×D47112yes—
686C4×Q8C22×D4716yes—
687C4×Q8C22×D4714yes—
688C4×D4—474no—
689C4×D4—474no—
690C4×D4—4712no—
691C4×D4—4712no—
692C4×D4—4712no—
693C4×D4—4712no—
694C4×D4—4712no—
695C4×D4—4712no—
696C4×D4—4712no—
697C4×D4—4712no—
698C4×D4—4712no—
699C4×D4—474no—
700C4×D4—476no—
701C4×D4—476no—
702C4×D4—4712no—
703C4×D4—4712no—
704C4×D4—4712no—
705C4×D4C22×D4714yes—
706C4×D4C22×D4716yes—
707C4×D4C22×D47112yes—
708C4×D4C22×D4716yes—
709C4×D4C22×D47112yes—
710#117—476no—
711#117—4712no—
712#117—4712no—
713#117—4712no—
714#117—474no—
715#117—4712no—
716#117—4712no—
717#117—4712no—
718#117—4712no—
719#117C22×D4716yes—
720#117C22×D47112yes—
721#117C22×D47112yes—
722C2×C4⋊C4—473no—
723C2×C4⋊C4—476no—
724C2×C4⋊C4—4712no—
725C2×C4⋊C4—4712no—
726C2×C4⋊C4—4712no—
727C2×C4⋊C4C22×D4713yes—
728C2×C4⋊C4C22×D47112yes—
729C2×C42—473no—
730C2×C42—473no—
731C2×C42—473no—
732C2×C42—476no—
733C2×C42—476no—
734C2×C42—476no—
735C2×C42—476no—
736C2×C42—4712no—
737C2×C42C22×D4713yes—
738C2×C42C22×D47112yes—
739C24—471no—
740#41—216no—
741#41—224no—
742#41—9416no—
743#41—9416no—
744#41—9424no—
745#41—18824no—
746C2×Q8—216no—
747C2×Q8—474no—
748C2×Q8—4712no—
749C2×Q8—476no—
750C2×Q8—4712no—
751C2×Q8—9416no—
752C2×Q8—9416no—
753C2×Q8—9416no—
754C2×Q8—9412no—
755C2×Q8#1062535018yescomplemented
756C2×Q8C23×D4716yes—
757C2×Q8C23×D4714yes—
758C2×D4—474no—
759C2×D4—474no—
760C2×D4—474no—
761C2×D4—474no—
762C2×D4—4712no—
763C2×D4—474no—
764C2×D4—474no—
765C2×D4—476no—
766C2×D4C23×D4714yes—
767C2×D4C23×D4716yes—
768C22×C4—471no—
769C22×C4—471no—
770C22×C4—473no—
771C22×C4—473no—
772C22×C4—471no—
773C22×C4—471no—
774C22×C4—476no—
775C22×C4—476no—
776C22×C4—476no—
777C22×C4—4712no—
778C22×C4—471no—
779C22×C4—474no—
780C22×C4—476no—
781C22×C4—4712no—
782C22×C4—944no—
783C22×C4—9412no—
784C22×C4—1886no—
785C22×C4C23×D47112yes—
786C22×C4C23×D4711yescharacteristic
787C22×C4C23×D4714yes—
788C22×C4C23×D4713yes—
789C22×C4C23×D47112yes—
790C22×C4C23×D4713yes—
791C4⋊C4—4724no—
792C4⋊C4—4712no—
793C4⋊C4—474no—
794C4⋊C4—474no—
795C4⋊C4—474no—
796C4⋊C4—474no—
797C4⋊C4—4712no—
798C4⋊C4—4712no—
799C4⋊C4—4712no—
800C4⋊C4—4712no—
801C4⋊C4—4712no—
802C4⋊C4—4712no—
803C4⋊C4—476no—
804C4⋊C4—476no—
805C4⋊C4—474no—
806C4⋊C4—4712no—
807C4⋊C4—4712no—
808C4⋊C4—4712no—
809C4⋊C4C23×D47112yes—
810C4⋊C4C23×D4716yes—
811C4⋊C4C23×D47112yes—
812C4⋊C4C23×D4716yes—
813C4⋊C4C23×D4714yes—
814C22⋊C4—474no—
815C22⋊C4—474no—
816C22⋊C4—4712no—
817C22⋊C4—4712no—
818C22⋊C4—4712no—
819C22⋊C4—474no—
820C22⋊C4—474no—
821C22⋊C4—4712no—
822C22⋊C4—474no—
823C22⋊C4—474no—
824C22⋊C4—474no—
825C22⋊C4—474no—
826C22⋊C4—4712no—
827C22⋊C4—4712no—
828C22⋊C4—4712no—
829C22⋊C4C23×D4714yes—
830C22⋊C4C23×D47112yes—
831C22⋊C4C23×D4714yes—
832C42—476no—
833C42—476no—
834C42—476no—
835C42—476no—
836C42—476no—
837C42—4712no—
838C42—4712no—
839C42—476no—
840C42—474no—
841C42C23×D4716yes—
842C42C23×D47112yes—
843C42C23×D47112yes—
844C42C23×D4716yes—
845C42C23×D4714yes—
846C23—471no—
847C23—471no—
848C23—474no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23C24×D4714yes—
853C23C24×D4711yescharacteristic
854Q8—212no—
855Q8—948no—
856Q8—9424no—
857Q8—9412no—
858Q8—18812no—
859Q8C2×#10625350116yes—
860D4—28no—
861D4—212no—
862D4—948no—
863D4—948no—
864D4—948no—
865D4—948no—
866D4—948no—
867D4—948no—
868D4—9412no—
869D4—18812no—
870C2×C4—224no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—471no—
876C2×C4—474no—
877C2×C4—471no—
878C2×C4—474no—
879C2×C4—476no—
880C2×C4—474no—
881C2×C4—474no—
882C2×C4—476no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—9412no—
886C2×C4—942no—
887C2×C4—946no—
888C2×C4—9412no—
889C2×C4—9412no—
890C2×C4—9424no—
891C2×C4—942no—
892C2×C4—948no—
893C2×C4—1886no—
894C2×C4—18812no—
895C2×C4—1883no—
896C2×C4C2×#10625350112yes—
897C2×C4C24×D4711yescharacteristic
898C2×C4C24×D4716yes—
899C2×C4C24×D4714yes—
900C2×C4C24×D4714yes—
901C2×C4C24×D4714yes—
902C2×C4C24×D4716yes—
903C2×C4C24×D4711yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—472no—
910C22—472no—
911C22—948no—
912C22—941no—
913C22—941no—
914C22—941no—
915C22—941no—
916C22—944no—
917C22—944no—
918C22—944no—
919C22C22×#1062535012yes—
920C22C25×D4711yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—472no—
927C4—944no—
928C4—946no—
929C4—941no—
930C4—944no—
931C4—946no—
932C4—944no—
933C4C22×#10625350112yes—
934C42−1+4×D4712yes—
935C2—22no—
936C2—44no—
937C2—942no—
938C2—942no—
939C2—1884no—
940C2C23×#1062535011yescharacteristic
941C2C2×2−1+4×D4711yescharacteristic
942C2#585×D4711yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC4×2−1+4×C47C2
hypercenterC4×2−1+4D47
hypocenterC47#62788
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20257478C2semidirect
2. #20257467C2semidirect
3. #20257383C2semidirect
4. #20257373C2semidirect
5. #20257246C2semidirect
6. #20257194C2semidirect
7. #20257155C2semidirect
8. #20257091C2semidirect
9. #20257040C2semidirect
10. #20257036C2semidirect
11. #20257010C2semidirect
12. #20257005C2semidirect
13. #20256986C2semidirect
14. Q8×#10625350C2semidirect
15. #20256815C2semidirect
16. #20256681C2semidirect
17. C4×#13094072C2semidirect
18. C2×C4×Q8×D47C2semidirect
19. C4×2−1+4×C47C2semidirect
22. #15689856C22semidirect
23. Q8×Dic94C22semidirect
24. #15689852C22semidirect
25. #15689851C22semidirect
26. #15689849C22semidirect
27. #15689849C22semidirect
28. #15689845C22semidirect
29. #15689843C22semidirect
30. #15689841C22semidirect
33. #15689828C22semidirect
38. #15689812C22semidirect
39. #15689808C22semidirect
40. #15689792C22semidirect
45. Q8×C22⋊D47C22semidirect
48. #15689784C22semidirect
51. #15689780C22semidirect
55. #15689744C22semidirect
56. #15689738C22semidirect
57. #15689735C22semidirect
58. #15689731C22semidirect
63. #15689680C22semidirect
66. #15689677C22semidirect
73. #15689657C22semidirect
76. #15689655C22semidirect
85. #15689605C22semidirect
88. #15689599C22semidirect
89. C4×#10625354C22semidirect
100. C4×Q8×D47C22semidirect
105. C47×#520C22semidirect
107. C47×#519C22semidirect
109. C4×#41×C47C22semidirect
111. C2×C4×Q8×C47C22semidirect
271. C2×Q8×C47#41semidirect
427. C4×D472−1+4semidirect
481. C4×2−1+4D47semidirect
560. #520C2×D47semidirect
564. #519C2×D47semidirect
570. C4×#41C2×D47semidirect
580. C2×C4×Q8C2×D47semidirect
583. C47#62788semidirect
755. C2×Q8#10625350semidirect

Maximal subgroups

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

subgroupindex
#202574782
#202574672
#202573832
#202573732
#202572462
#202571942
#202571552
#202570912
#202570402
#202570362
#202570102
#202570052
#202569862
Q8×#106253502
#202568152
#202566812
C4×#130940722
C2×C4×Q8×D472
C4×2−1+4×C472
#6278847