Finite Group Databasebeta

← #27124572

Subgroups — #27124572

Order 12032.

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#20257499C214yesmaximal, complemented
2#20257489C214yesmaximal, complemented
3#20257399C214yesmaximal, complemented
4#20257388C214yesmaximal, complemented
5#20257233C216yesmaximal, complemented
6#20257194C211yesmaximal, characteristic, complemented
7#20257155C211yesmaximal, characteristic, complemented
8#20257101C216yesmaximal, complemented
9#20257047C211yesmaximal, characteristic, complemented
10#20257043C211yesmaximal, characteristic, complemented
11#20257014C214yesmaximal, complemented
12#20257005C214yesmaximal, complemented
13#20256986C214yesmaximal, complemented
14#20256983C214yesmaximal, complemented
15#20256804C216yesmaximal, complemented
16#20256681C216yesmaximal, complemented
17C4×#13094072C211yesmaximal, characteristic, complemented
18C2×C4×#10625354C211yesmaximal, characteristic, complemented
19C4×2−1+4×C47C211yesmaximal, characteristic, complemented
20C2×#13094072C2211yescharacteristic
21C22×#10625354C2211yescharacteristic
22#15689858C22112yescomplemented
23#15689856C22112yescomplemented
24Q8×Dic94C2214yescomplemented
25#15689852C2214yescomplemented
26#15689849C2214yescomplemented
27#15689849C2214yescomplemented
28#15689846C22112yescomplemented
29#15689845C22112yescomplemented
30#15689841C22112yescomplemented
31#15689838C22112yescomplemented
32#15689836C22112yescomplemented
33#15689836C22112yescomplemented
34#15689823C22112yescomplemented
35#15689821C22112yescomplemented
36#15689821C22112yescomplemented
37#15689817C22112yescomplemented
38#15689814C22112yescomplemented
39#15689808C22112yescomplemented
40#15689795C2214yes—
41#15689795C2214yes—
42#15689794C22112yescomplemented
43#15689792C2214yes—
44#15689792C2214yes—
45#15689792C2214yescomplemented
46Q8×C22⋊D47C2214yescomplemented
47#15689785C2214yes—
48#15689785C2214yes—
49#15689784C2214yes—
50#15689784C2214yes—
51#15689784C2214yescomplemented
52#15689780C2214yescomplemented
53#15689774C22112yescomplemented
54#15689751C2216yes—
55#15689745C22112yescomplemented
56#15689744C22112yescomplemented
57#15689728C22112yescomplemented
58#15689724C22112yescomplemented
59#15689706C22124yes—
60#15689701C2216yes—
61#15689692C2216yes—
62#15689687C2216yes—
63#15689677C2216yescomplemented
64#15689677C2216yescomplemented
65#15689676C2216yes—
66#15689673C22112yescomplemented
67#15689670C22112yescomplemented
68#15689670C2216yescomplemented
69#15689670C2216yescomplemented
70#15689669C2216yes—
71#15689660C22112yescomplemented
72#15689660C2216yescomplemented
73#15689660C2216yescomplemented
74#15689657C22112yescomplemented
75#15689655C2216yescomplemented
76#15689655C2216yescomplemented
77#15689653C22112yes—
78#15689653C2214yes—
79#15689651C22112yescomplemented
80#15689651C22112yescomplemented
81#15689635C2216yes—
82#15689632C22112yes—
83#15689632C22112yes—
84#15689630C2216yes—
85#15689605C2214yescomplemented
86#15689604C2216yes—
87#15689601C2211yescharacteristic
88#15689599C2214yescomplemented
89C4×#10625354C2214yes—
90C4×#10625354C2214yes—
91C4×#10625354C2214yes—
92C4×#10625354C2214yes—
93C4×#10625354C2214yescomplemented
94C4×#10625350C2216yes—
95C4×#10625350C22112yescomplemented
96C4×#10625350C22112yescomplemented
97C2×Q8×Dic47C2211yescharacteristic
98C4×Q8×D47C2214yescomplemented
99C2×C4×D188C2213yes—
100C2×#13093986C2213yes—
101C2×#13093982C2213yes—
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×#10625354—28no—
114C2×#10625354C2314yes—
115C2×#10625354C2314yes—
116C2×#10625354C2314yes—
117C2×#10625350C2316yes—
118C2×#10625350C23112yes—
119C2×#10625350C23112yes—
120C2×Q8×D47C2314yes—
121C22×D188C2313yes—
122C22×C4×D47C2313yes—
123C22×C4×D47C2313yes—
124C22×C4×D47C2313yes—
125#13094024C23112yes—
126#13094023C23112yes—
127#13094023C2316yes—
128#13094023C2316yes—
129#13094022C2316yes—
130#13094021C23112yes—
131#13094020C23112yes—
132#13094020C2316yes—
133#13094019C23124yes—
134#13094019C23112yes—
135#13094019C2314yes—
136#13094018C23124yes—
137#13094017C23112yes—
138#13094017C2314yes—
139#13094016C23112yes—
140#13094015C23112yes—
141#13094015C2316yes—
142#13094015C2316yes—
143#13094014C23112yes—
144#13094014C2314yes—
145#13094013C23112yes—
146#13094013C2316yes—
147#13094012C23112yes—
148#13094012C23124yes—
149#13094011C2316yes—
150#13094010C23124yes—
151#13094010C23112yes—
152#13094010C2314yes—
153#13094009C23112yes—
154#13094009C23124yes—
155#13094009C23112yes—
156#13094008C2314yes—
157#13094007C23124yes—
158#13094006C23112yes—
159#13094006C23112yes—
160#13094005C2314yes—
161#13094004C2316yes—
162#13094004C2316yes—
163#13094003C23112yes—
164#13094002C23112yes—
165#13094002C23112yes—
166#13094001C23112yes—
167#13094001C2314yes—
168#13094000C23112yes—
169#13094000C2316yes—
170#13094000C2316yes—
171#13093999C23112yes—
172#13093999C23112yes—
173#13093999C2316yes—
174#13093999C2316yes—
175#13093998C23112yes—
176#13093998C23112yes—
177#13093998C23112yes—
178#13093998C23124yes—
179#13093997C23112yes—
180#13093997C23124yes—
181#13093997C23112yes—
182#13093996C2314yes—
183#13093996C23112yes—
184#13093995C23112yes—
185#13093995C2316yes—
186#13093995C2316yes—
187#13093994C23112yes—
188#13093992C23112yes—
189Q8×Dic47C2314yes—
190Q8×Dic47C2314yes—
191Q8×Dic47C2314yes—
192Q8×Dic47C2314yes—
193C4×Dic94C2316yes—
194C4×Dic94C23112yes—
195C4×Dic94C23112yes—
196C4×Dic94C2316yes—
197C4×Dic94C2314yes—
198C4×Dic94C23112yes—
199#13093989C23112yes—
200C4×D188C2316yes—
201C4×D188C23112yes—
202C4×D188C23112yes—
203C4×D188C23112yes—
204C4×D188C23112yes—
205C4×D188C23112yes—
206C4×D188C2316yes—
207C4×D188C23112yes—
208#13093986C23112yes—
209#13093986C23112yes—
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⋊D47C23112yes—
219C4×C22⋊D47C2314yes—
220C4×C22⋊D47C23112yes—
221#13093983C2316yes—
222#13093983C23112yes—
223#13093983C2314yes—
224#13093982C23112yes—
225#13093982C23112yes—
226#13093982C23112yes—
227#13093981C23112yes—
228#13093981C23112yes—
229#13093981C23112yes—
230#13093981C2314yes—
231#13093981C23112yes—
232C2×C4⋊Dic47C2313yes—
233C4⋊C4×D47C23112yes—
234C2×(C2×D47)⋊C4C2316yes—
235C2×C4×Dic47C2311yescharacteristic
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×C47C23112yes—
256C4×D4×C47C2314yes—
257C4×D4×C47C2316yes—
258C4×D4×C47C23112yes—
259C4×D4×C47C2316yes—
260#117×C47C23112yes—
261#117×C47C2316yes—
262#117×C47C23112yes—
263C2×C4⋊C4×C47C23112yes—
264C2×C4⋊C4×C47C2313yes—
265C2×C42×C47C2313yes—
266C2×C42×C47C23112yes—
267C23×D47C2413yes—
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⋊D47C24112yes—
285C2×C22⋊D47C24112yes—
286C2×C22⋊D47C24112yes—
287C22×Dic47C2411yescharacteristic
288C22×Dic47C2411yescharacteristic
289C22×Dic47C2413yes—
290#10625354—216no—
291#10625354—216no—
292#10625354—216no—
293Q8×D47—216no—
294#10625350—224no—
295#10625350—424no—
296#10625350—424no—
297C2×D188—212no—
298C2×D188C24112yes—
299C2×D188C2416yes—
300C2×D188C24112yes—
301C2×D188C24112yes—
302C2×C4×D47—212no—
303C2×C4×D47—46no—
304C2×C4×D47—46no—
305C2×C4×D47C2414yes—
306C2×C4×D47C2416yes—
307C2×C4×D47C2416yes—
308C2×C4×D47C2416yes—
309C2×C4×D47C2416yes—
310C2×C4×D47C24112yes—
311C2×C4×D47C2416yes—
312C2×C4×D47C2416yes—
313C2×C4×D47C24112yes—
314C2×Dic94C2416yes—
315C2×Dic94C2414yes—
316C2×Dic94C24112yes—
317C4⋊C4×C47C24112yes—
318C4⋊C4×C47C2416yes—
319C4⋊C4×C47C24112yes—
320C4⋊C4×C47C2416yes—
321C4⋊C4×C47C2414yes—
322C22⋊C4×C47C2414yes—
323C22⋊C4×C47C2414yes—
324C22⋊C4×C47C24112yes—
325C42×C47C2416yes—
326C42×C47C2414yes—
327C42×C47C2416yes—
328C42×C47C24112yes—
329C42×C47C24112yes—
330C22⋊Dic47C2414yes—
331C22⋊Dic47C2414yes—
332C22⋊Dic47C2414yes—
333C22⋊Dic47C2414yes—
334C22⋊Dic47C24112yes—
335(C2×D47)⋊C4C24124yes—
336(C2×D47)⋊C4C2414yes—
337(C2×D47)⋊C4C2414yes—
338(C2×D47)⋊C4C24112yes—
339(C2×D47)⋊C4C2414yes—
340(C2×D47)⋊C4C2414yes—
341(C2×D47)⋊C4C24112yes—
342(C2×D47)⋊C4C24112yes—
343(C2×D47)⋊C4C24112yes—
344(C2×D47)⋊C4C24112yes—
345(C2×D47)⋊C4C24112yes—
346C4⋊Dic47C2416yes—
347C4⋊Dic47C24112yes—
348C4⋊Dic47C2416yes—
349C4⋊Dic47C2414yes—
350C4⋊Dic47C2414yes—
351C4⋊Dic47C2414yes—
352C4⋊Dic47C24112yes—
353Dic47⋊C4C24112yes—
354Dic47⋊C4C2414yes—
355Dic47⋊C4C2414yes—
356Dic47⋊C4C2414yes—
357Dic47⋊C4C2414yes—
358Dic47⋊C4C2414yes—
359Dic47⋊C4C2414yes—
360Dic47⋊C4C24112yes—
361Dic47⋊C4C24112yes—
362Dic47⋊C4C24112yes—
363C4×Dic47C2411yescharacteristic
364C4×Dic47C2411yescharacteristic
365C4×Dic47C2411yescharacteristic
366C4×Dic47C2411yescharacteristic
367C4×Dic47C2414yes—
368C4×Dic47C2416yes—
369C4×Dic47C2416yes—
370C4×Dic47C2416yes—
371C4×Dic47C2416yes—
372C4×Dic47C24112yes—
373C4×Dic47C24112yes—
374C23×C47C2514yes—
375C23×C47C2511yescharacteristic
376C22×D47—26no—
377C22×D47—43no—
378C22×D47—43no—
379C22×D47C2516yes—
380C22×D47C2514yes—
381Q8×C47—212no—
382Q8×C47C2×#41116yes—
383D4×C47—28no—
384D4×C47—212no—
385C2×C4×C47—224no—
386C2×C4×C47—22no—
387C2×C4×C47—28no—
388C2×C4×C47—43no—
389C2×C4×C47—412no—
390C2×C4×C47C2×#41112yes—
391C2×C4×C47C2516yes—
392C2×C4×C47C2511yescharacteristic
393C2×C4×C47C2514yes—
394C2×C4×C47C2514yes—
395C2×C4×C47C2514yes—
396C2×C4×C47C2516yes—
397C2×C4×C47C2511yescharacteristic
398C22⋊D47—28no—
399C22⋊D47—28no—
400C22⋊D47—412no—
401C22⋊D47—412no—
402C22⋊D47—412no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—43no—
406C2×Dic47C2511yescharacteristic
407C2×Dic47C2511yescharacteristic
408C2×Dic47C2511yescharacteristic
409C2×Dic47C2514yes—
410C2×Dic47C2514yes—
411C2×Dic47C2514yes—
412C2×Dic47C2516yes—
413C2×Dic47C2511yescharacteristic
414D188—224no—
415D188—212no—
416D188—412no—
417D188—412no—
418C4×D47—212no—
419C4×D47—212no—
420C4×D47—224no—
421C4×D47—212no—
422C4×D47—28no—
423C4×D47—212no—
424C4×D47—46no—
425C4×D47—46no—
426C4×D47—412no—
427Dic94—212no—
428Dic94—28no—
429Dic94—412no—
430#62793—471nomaximal, Sylow
431C22×C47—21no—
432C22×C47—21no—
433C22×C47—24no—
434C22×C47—24no—
435C22×C47—24no—
436C22×C47C22×#4112yes—
437C22×C47C2611yescharacteristic
438C2×D47—24no—
439C2×D47—26no—
440C2×D47—26no—
441C2×D47—26no—
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—412no—
445C4×C47—24no—
446C4×C47—24no—
447C4×C47—24no—
448C4×C47—26no—
449C4×C47—21no—
450C4×C47C22×#41112yes—
451C4×C47#58512yes—
452Dic47—24no—
453Dic47—21no—
454Dic47—21no—
455Dic47—24no—
456Dic47—24no—
457Dic47—26no—
458Dic47—21no—
459Dic47#58512yes—
460#3524—474no—
461#3524—474no—
462#3518—474no—
463#3517—474no—
464#3506—476no—
465#3502—471no—
466#3497—471no—
467#3493—476no—
468#3487—471no—
469#3487—471no—
470#3483—474no—
471#3482—474no—
472#3480—474no—
473#3480—474no—
474#3460—476no—
475#3444—476no—
476C4×2−1+4—471no—
477C4×2−1+4D4711yescharacteristic, complemented
478C2×C4×#41—471no—
479C2×C47—22no—
480C2×C47—44no—
481C2×C47C23×#4111yescharacteristic
482C2×C47C2×#58511yescharacteristic
483C2×C47C2×#58511yescharacteristic
484D47—44no—
485D47—46no—
486C2×2−1+4—471no—
487C2×2−1+4C2×D4711yescharacteristic
488C22×#41—471no—
489#559—4712no—
490#559—4712no—
491Q82—474no—
492#557—474no—
493#557—474no—
494#557—474no—
495#556—4712no—
496#556—4712no—
497#556—4712no—
498#555—4712no—
499#555—4712no—
500#555—4712no—
501#553—4712no—
502#553—4712no—
503#553—4712no—
504#553—4712no—
505#552—4712no—
506#552—4712no—
507#550—474no—
508#550—474no—
509#550—474no—
510#550—474no—
511#550—474no—
512#550—4712no—
513D4×Q8—474no—
514#548—474no—
515#548—474no—
516#548—474no—
517#548—474no—
518#548—474no—
519#548—474no—
520#547—4712no—
521#544—476no—
522#542—4712no—
523#542—4712no—
524#540—4712no—
525#540—4712no—
526#538—4724no—
527#537—476no—
528#535—476no—
529#535—476no—
530#533—476no—
531#533—476no—
532#533—476no—
533#532—476no—
534#532—476no—
535#532—476no—
536#532—4712no—
537#532—4712no—
538#529—476no—
539#529—476no—
540#529—4712no—
541#529—474no—
542#529—476no—
543#529—4712no—
544#529—476no—
545#529—4712no—
546#529—4712no—
547#529—4712no—
548#525—476no—
549#525—4712no—
550#525—4712no—
551#525—476no—
552#520—474no—
553#520—476no—
554#520C2×D4716yes—
555#520C2×D4714yescomplemented
556#519—471no—
557#519—474no—
558#519C2×D4711yescharacteristic
559#519C2×D4714yescomplemented
560C4×#41—474no—
561C4×#41—474no—
562C4×#41—474no—
563C4×#41—474no—
564C4×#41—474no—
565C4×#41—476no—
566C4×#41—4712no—
567C4×#41—4712no—
568C4×#41C2×D4716yes—
569C4×#41C2×D4714yescomplemented
570C2×C4×Q8—471no—
571C2×C4×Q8—474no—
572C2×C4×Q8C2×D4711yescharacteristic
573C2×C4×Q8C2×D4714yescomplemented
574C2×C4×D4—473no—
575C2×C4×D4—473no—
576C2×#117—473no—
577C22×C42—473no—
578C47#6279311yescharacteristic, complemented, Sylow
5792−1+4—28no—
5802−1+4—948no—
581C2×#41—474no—
582C2×#41—474no—
583C2×#41—474no—
584C2×#41—476no—
585C2×#41—4712no—
586C2×#41—4712no—
587C2×#41—948no—
588C2×#41C22×D4716yes—
589C2×#41C22×D4714yes—
590C22×Q8—474no—
591C22×Q8C22×D4714yes—
592C22×Q8C22×D4711yescharacteristic
593C22×D4—473no—
594C23×C4—473no—
595C23×C4—473no—
596C23×C4—473no—
597C4⋊Q8—476no—
598C4⋊Q8—476no—
599C4⋊Q8—476no—
600C4⋊Q8—4712no—
601C4⋊Q8—4712no—
602#127—476no—
603#127—4712no—
604#127—4712no—
605#126—474no—
606#126—4712no—
607#126—4724no—
608#126—474no—
609#126—4712no—
610#126—4724no—
611#125—474no—
612#125—4712no—
613#125—476no—
614#125—476no—
615#125—4712no—
616#125—4712no—
617#124—476no—
618#124—4712no—
619#124—476no—
620#124—474no—
621#124—4712no—
622#124—4724no—
623#124—4712no—
624#124—4724no—
625#123—474no—
626#123—4724no—
627#123—4712no—
628#123—4712no—
629#123—4724no—
630#123—474no—
631#123—4712no—
632#123—4712no—
633C22⋊Q8—476no—
634C22⋊Q8—476no—
635C22⋊Q8—4712no—
636C22⋊Q8—4712no—
637C22⋊Q8—4712no—
638C22⋊Q8—4712no—
639C22⋊Q8—476no—
640C22⋊Q8—476no—
641C22⋊Q8—474no—
642C22⋊Q8—4712no—
643#121—474no—
644#121—4712no—
645#121—476no—
646#121—476no—
647#121—4712no—
648#121—4712no—
649#121—4712no—
650#121—4712no—
651#121—4724no—
652#121—476no—
653#121—476no—
654#121—4712no—
655#121—4712no—
656#121—4712no—
657#121—4712no—
658#121—4724no—
659#120—4712no—
660#120—4712no—
661C4×Q8—474no—
662C4×Q8—474no—
663C4×Q8—474no—
664C4×Q8—474no—
665C4×Q8—4712no—
666C4×Q8—476no—
667C4×Q8—474no—
668C4×Q8—476no—
669C4×Q8—4712no—
670C4×Q8—4712no—
671C4×Q8—4712no—
672C4×Q8C22×D4714yes—
673C4×Q8C22×D4714yes—
674C4×Q8C22×D4716yes—
675C4×Q8C22×D4714yes—
676C4×Q8C22×D47112yes—
677C4×Q8C22×D4716yes—
678C4×Q8C22×D4714yes—
679C4×D4—474no—
680C4×D4—474no—
681C4×D4—4712no—
682C4×D4—4712no—
683C4×D4—4712no—
684C4×D4—4712no—
685C4×D4—4712no—
686C4×D4—4712no—
687C4×D4—4712no—
688C4×D4—4712no—
689C4×D4—4712no—
690C4×D4—4712no—
691C4×D4—4712no—
692C4×D4—4712no—
693C4×D4—4712no—
694C4×D4—476no—
695C4×D4—476no—
696C4×D4—4712no—
697C4×D4—4712no—
698C4×D4—4712no—
699C4×D4—4712no—
700C4×D4C22×D4714yes—
701C4×D4C22×D4716yes—
702C4×D4C22×D47112yes—
703C4×D4C22×D4716yes—
704C4×D4C22×D47112yes—
705#117—474no—
706#117—476no—
707#117—4712no—
708#117—4712no—
709#117—4712no—
710#117—4712no—
711#117—474no—
712#117—4712no—
713#117—4712no—
714#117—4712no—
715#117—4712no—
716#117C22×D4716yes—
717#117C22×D47112yes—
718#117C22×D47112yes—
719C2×C4⋊C4—473no—
720C2×C4⋊C4—4712no—
721C2×C4⋊C4C22×D4713yes—
722C2×C4⋊C4C22×D47112yes—
723C2×C22⋊C4—476no—
724C2×C42—473no—
725C2×C42—473no—
726C2×C42—471no—
727C2×C42—4712no—
728C2×C42—476no—
729C2×C42—476no—
730C2×C42—476no—
731C2×C42—476no—
732C2×C42C22×D4713yes—
733C2×C42C22×D47112yes—
734C24—473no—
735#41—216no—
736#41—224no—
737#41—9416no—
738#41—9416no—
739#41—9416no—
740#41—9424no—
741#41—18824no—
742#41—18824no—
743C2×Q8—216no—
744C2×Q8—476no—
745C2×Q8—474no—
746C2×Q8—4712no—
747C2×Q8—9416no—
748C2×Q8#1062535018yescomplemented
749C2×Q8C23×D4716yes—
750C2×Q8C23×D4714yes—
751C2×D4—474no—
752C2×D4—474no—
753C2×D4—4712no—
754C2×D4—4712no—
755C2×D4—4712no—
756C2×D4—4712no—
757C2×D4—476no—
758C2×D4—4712no—
759C2×D4—4712no—
760C2×D4—9412no—
761C2×D4C23×D4714yes—
762C2×D4C23×D4716yes—
763C22×C4—471no—
764C22×C4—471no—
765C22×C4—473no—
766C22×C4—476no—
767C22×C4—476no—
768C22×C4—476no—
769C22×C4—4712no—
770C22×C4—474no—
771C22×C4—476no—
772C22×C4—476no—
773C22×C4—476no—
774C22×C4—4712no—
775C22×C4—9412no—
776C22×C4—1886no—
777C22×C4—1886no—
778C22×C4C23×D47112yes—
779C22×C4C23×D4711yescharacteristic
780C22×C4C23×D4714yes—
781C22×C4C23×D4713yes—
782C22×C4C23×D47112yes—
783C22×C4C23×D4713yes—
784C4⋊C4—4712no—
785C4⋊C4—474no—
786C4⋊C4—474no—
787C4⋊C4—474no—
788C4⋊C4—474no—
789C4⋊C4—474no—
790C4⋊C4—474no—
791C4⋊C4—4712no—
792C4⋊C4—4712no—
793C4⋊C4—4712no—
794C4⋊C4—476no—
795C4⋊C4—4712no—
796C4⋊C4—474no—
797C4⋊C4—476no—
798C4⋊C4—474no—
799C4⋊C4—474no—
800C4⋊C4—4712no—
801C4⋊C4C23×D47112yes—
802C4⋊C4C23×D4716yes—
803C4⋊C4C23×D47112yes—
804C4⋊C4C23×D4716yes—
805C4⋊C4C23×D4714yes—
806C22⋊C4—474no—
807C22⋊C4—474no—
808C22⋊C4—474no—
809C22⋊C4—474no—
810C22⋊C4—4712no—
811C22⋊C4—4724no—
812C22⋊C4—474no—
813C22⋊C4—474no—
814C22⋊C4—4712no—
815C22⋊C4—474no—
816C22⋊C4—474no—
817C22⋊C4—4712no—
818C22⋊C4—4712no—
819C22⋊C4—4712no—
820C22⋊C4—4712no—
821C22⋊C4—4712no—
822C22⋊C4C23×D4714yes—
823C22⋊C4C23×D4714yes—
824C22⋊C4C23×D47112yes—
825C42—471no—
826C42—471no—
827C42—476no—
828C42—476no—
829C42—476no—
830C42—476no—
831C42—4712no—
832C42—4712no—
833C42—471no—
834C42—471no—
835C42—474no—
836C42C23×D4716yes—
837C42C23×D47112yes—
838C42C23×D47112yes—
839C42C23×D4716yes—
840C42C23×D4714yes—
841C23—476no—
842C23—474no—
843C23—946no—
844C23—1883no—
845C23—1883no—
846C23C24×D4714yes—
847C23C24×D4711yescharacteristic
848Q8—212no—
849Q8—948no—
850Q8—9412no—
851Q8—18812no—
852Q8C2×#10625350116yes—
853D4—28no—
854D4—212no—
855D4—948no—
856D4—948no—
857D4—9424no—
858D4—9412no—
859D4—18812no—
860D4—18812no—
861D4—18812no—
862D4—18812no—
863D4—18812no—
864C2×C4—224no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—43no—
868C2×C4—412no—
869C2×C4—471no—
870C2×C4—471no—
871C2×C4—471no—
872C2×C4—471no—
873C2×C4—474no—
874C2×C4—474no—
875C2×C4—476no—
876C2×C4—474no—
877C2×C4—9412no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—9412no—
881C2×C4—9412no—
882C2×C4—9424no—
883C2×C4—9412no—
884C2×C4—948no—
885C2×C4—1886no—
886C2×C4—1886no—
887C2×C4—18812no—
888C2×C4—1883no—
889C2×C4C2×#10625350112yes—
890C2×C4C24×D4716yes—
891C2×C4C24×D4711yescharacteristic
892C2×C4C24×D4714yes—
893C2×C4C24×D4714yes—
894C2×C4C24×D4714yes—
895C2×C4C24×D4716yes—
896C2×C4C24×D4711yescharacteristic
897C22—21no—
898C22—21no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—944no—
903C22—946no—
904C22—946no—
905C22—944no—
906C22—946no—
907C22—944no—
908C22—18812no—
909C22C22×#1062535012yes—
910C22C25×D4711yescharacteristic
911C4—24no—
912C4—26no—
913C4—24no—
914C4—21no—
915C4—24no—
916C4—472no—
917C4—941no—
918C4—941no—
919C4—944no—
920C4—941no—
921C4—944no—
922C4—946no—
923C4—944no—
924C4C22×#10625350112yes—
925C4#1568996012yes—
926C2—22no—
927C2—44no—
928C2—1886no—
929C2—1884no—
930C2C23×#1062535011yescharacteristic
931C2#585×D4711yescharacteristic
932C2C2×#1568996011yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC4×2−1+4×C47C2
hypercenterC4×2−1+4D47
hypocenterC47#62793
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. #20257499C2semidirect
2. #20257489C2semidirect
3. #20257399C2semidirect
4. #20257388C2semidirect
5. #20257233C2semidirect
6. #20257194C2semidirect
7. #20257155C2semidirect
8. #20257101C2semidirect
9. #20257047C2semidirect
10. #20257043C2semidirect
11. #20257014C2semidirect
12. #20257005C2semidirect
13. #20256986C2semidirect
14. #20256983C2semidirect
15. #20256804C2semidirect
16. #20256681C2semidirect
17. C4×#13094072C2semidirect
18. C2×C4×#10625354C2semidirect
19. C4×2−1+4×C47C2semidirect
22. #15689858C22semidirect
23. #15689856C22semidirect
24. Q8×Dic94C22semidirect
25. #15689852C22semidirect
26. #15689849C22semidirect
27. #15689849C22semidirect
28. #15689846C22semidirect
29. #15689845C22semidirect
30. #15689841C22semidirect
31. #15689838C22semidirect
32. #15689836C22semidirect
33. #15689836C22semidirect
34. #15689823C22semidirect
35. #15689821C22semidirect
36. #15689821C22semidirect
37. #15689817C22semidirect
38. #15689814C22semidirect
39. #15689808C22semidirect
42. #15689794C22semidirect
45. #15689792C22semidirect
46. Q8×C22⋊D47C22semidirect
51. #15689784C22semidirect
52. #15689780C22semidirect
53. #15689774C22semidirect
55. #15689745C22semidirect
56. #15689744C22semidirect
57. #15689728C22semidirect
58. #15689724C22semidirect
63. #15689677C22semidirect
64. #15689677C22semidirect
66. #15689673C22semidirect
67. #15689670C22semidirect
68. #15689670C22semidirect
69. #15689670C22semidirect
71. #15689660C22semidirect
72. #15689660C22semidirect
73. #15689660C22semidirect
74. #15689657C22semidirect
75. #15689655C22semidirect
76. #15689655C22semidirect
79. #15689651C22semidirect
80. #15689651C22semidirect
85. #15689605C22semidirect
88. #15689599C22semidirect
93. C4×#10625354C22semidirect
95. C4×#10625350C22semidirect
96. C4×#10625350C22semidirect
98. C4×Q8×D47C22semidirect
105. C47×#520C22semidirect
107. C47×#519C22semidirect
109. C4×#41×C47C22semidirect
111. C2×C4×Q8×C47C22semidirect
271. C2×Q8×C47#41semidirect
477. C4×2−1+4D47semidirect
555. #520C2×D47semidirect
559. #519C2×D47semidirect
569. C4×#41C2×D47semidirect
573. C2×C4×Q8C2×D47semidirect
578. C47#62793semidirect
748. C2×Q8#10625350semidirect

Maximal subgroups

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

subgroupindex
#202574992
#202574892
#202573992
#202573882
#202572332
#202571942
#202571552
#202571012
#202570472
#202570432
#202570142
#202570052
#202569862
#202569832
#202568042
#202566812
C4×#130940722
C2×C4×#106253542
C4×2−1+4×C472
#6279347