Finite Group Databasebeta

← #27124503

Subgroups — #27124503

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#20257475C214yesmaximal, complemented
2#20257464C214yesmaximal, complemented
3#20257382C214yesmaximal, complemented
4#20257370C214yesmaximal, complemented
5#20257252C216yesmaximal, complemented
6#20257194C211yesmaximal, characteristic, complemented
7#20257155C211yesmaximal, characteristic, complemented
8#20257094C216yesmaximal, complemented
9#20257039C211yesmaximal, characteristic, complemented
10#20257009C214yesmaximal, complemented
11#20257004C214yesmaximal, complemented
12#20256978C214yesmaximal, complemented
13Q8×#10625352C214yesmaximal, complemented
14#20256812C216yesmaximal, complemented
15#20256680C216yesmaximal, complemented
162−1+4×Dic47C211yesmaximal, characteristic, complemented
17#20256597C211yesmaximal, characteristic, complemented
18C22×Q8×Dic47C211yesmaximal, characteristic, complemented
19C47×#3486C211yesmaximal, characteristic, complemented
20C2×#13094072C2211yescharacteristic
21#15689855C22112yescomplemented
22Q8×Dic94C2214yescomplemented
23#15689852C2214yescomplemented
24#15689849C2214yescomplemented
25#15689849C2214yescomplemented
26#15689848C22112yescomplemented
27#15689847C22112yescomplemented
28#15689844C22112yescomplemented
29#15689842C22112yescomplemented
30#15689831C22112yes—
31#15689831C22112yescomplemented
32#15689830C22112yes—
33#15689825C22112yes—
34#15689819C22112yes—
35#15689815C22112yes—
36#15689815C22112yescomplemented
37#15689813C22112yes—
38#15689807C22112yescomplemented
39#15689792C2214yescomplemented
40Q8×C22⋊D47C2214yes—
41Q8×C22⋊D47C2214yes—
42Q8×C22⋊D47C2214yescomplemented
43#15689784C2214yes—
44#15689784C2214yes—
45#15689784C2214yescomplemented
46#15689780C2214yescomplemented
47#15689777C22112yes—
48#15689773C22112yes—
49#15689751C2216yes—
50#15689746C22112yescomplemented
51#15689742C22112yescomplemented
52#15689734C22112yescomplemented
53#15689733C22112yescomplemented
54#15689717C22124yes—
55#15689701C2216yes—
56#15689697C2216yes—
57#15689678C22112yescomplemented
58#15689676C2216yes—
59#15689675C2216yes—
60#15689675C2216yes—
61#15689675C22112yescomplemented
62#15689669C2216yes—
63#15689668C2216yes—
64#15689668C2216yes—
65#15689659C2216yes—
66#15689659C2216yes—
67#15689659C22112yescomplemented
68#15689654C2216yes—
69#15689654C2216yes—
70#15689653C22112yes—
71#15689653C22112yes—
72#15689652C22112yescomplemented
73#15689650C22112yes—
74#15689650C22112yes—
75#15689634C2216yes—
76#15689629C22112yes—
77#15689629C2214yes—
78#15689606C2216yes—
79#15689606C2214yescomplemented
80#15689605C2214yescomplemented
81#15689603C2216yes—
82#15689601C2211yescharacteristic
83#15689601C2214yescomplemented
84#15689599C2214yescomplemented
85#41×Dic47C2216yes—
86#41×Dic47C2214yescomplemented
87C4×#10625354C2214yescomplemented
88#15689591C2216yes—
89C4×#10625352C22112yes—
90C4×#10625352C22112yes—
91C2×Q8×Dic47C2213yes—
92C2×Q8×Dic47C2211yescharacteristic
93C2×Q8×Dic47C2214yes—
94C2×Q8×Dic47C2211yescharacteristic
95C2×Q8×Dic47C2214yes—
96C2×Q8×Dic47C2214yes—
97C2×Q8×Dic47C2213yes—
98C2×Q8×Dic47C2214yes—
99C2×Q8×Dic47C2214yescomplemented
100C4×Q8×D47C2214yescomplemented
101C22×C4⋊Dic47C2213yes—
102C22×C4×Dic47C2213yes—
103C2×2−1+4×C47C2211yescharacteristic
104C23×Q8×C47C2211yescharacteristic
105D4×Q8×C47C2214yes—
106D4×Q8×C47C2214yes—
107C47×#548C2214yes—
108C47×#548C2214yes—
109C47×#536C2216yes—
110C47×#525C2216yes—
111C47×#519C2211yescharacteristic
112#13094072—28no—
113C2×#10625354C2314yes—
114C2×#10625350C2316yes—
115C2×#10625352C2314yes—
116C2×#10625352C23112yes—
117C2×Q8×D47C2314yes—
118C23×Dic47C2311yescharacteristic
119C23×Dic47C2313yes—
120#13094024C23112yes—
121#13094023C23112yes—
122#13094023C2316yes—
123#13094023C2316yes—
124#13094022C23112yes—
125#13094022C2316yes—
126#13094020C2316yes—
127#13094019C23112yes—
128#13094019C23124yes—
129#13094019C23112yes—
130#13094017C23112yes—
131#13094017C23124yes—
132#13094017C23112yes—
133#13094016C23112yes—
134#13094015C23112yes—
135#13094015C23124yes—
136#13094015C2316yes—
137#13094015C2316yes—
138#13094014C23112yes—
139#13094014C23124yes—
140#13094014C23112yes—
141#13094013C23112yes—
142#13094013C2316yes—
143#13094011C2316yes—
144#13094010C23112yes—
145#13094010C23112yes—
146#13094008C23124yes—
147#13094008C23112yes—
148#13094008C2314yes—
149#13094007C23112yes—
150#13094006C23124yes—
151#13094005C23112yes—
152#13094005C2314yes—
153#13094004C23124yes—
154#13094003C23112yes—
155#13094003C2316yes—
156#13094003C2316yes—
157#13094001C23124yes—
158#13094001C23112yes—
159#13094001C23112yes—
160#13094001C2314yes—
161#13094001C2314yes—
162#13094000C23112yes—
163#13094000C23112yes—
164#13094000C23112yes—
165#13093998C23112yes—
166#13093998C2316yes—
167#13093998C2316yes—
168#13093996C23112yes—
169#13093996C2314yes—
170#13093996C23112yes—
171#13093996C2314yes—
172#13093995C23112yes—
173#13093993C2314yes—
174Q8×Dic47C23112yes—
175Q8×Dic47C2316yes—
176Q8×Dic47C2314yes—
177Q8×Dic47C2314yes—
178Q8×Dic47C2314yes—
179Q8×Dic47C2314yes—
180Q8×Dic47C23112yes—
181Q8×Dic47C23112yes—
182Q8×Dic47C23112yes—
183Q8×Dic47C2314yes—
184Q8×Dic47C2314yes—
185Q8×Dic47C23112yes—
186Q8×Dic47C2316yes—
187C4×Dic94C23112yes—
188C4×Dic94C23112yes—
189C4×Dic94C23112yes—
190#13093989C2316yes—
191#13093989C2316yes—
192#13093989C23112yes—
193#13093989C23112yes—
194C4×D188C23112yes—
195D4×Dic47C2316yes—
196D4×Dic47C23112yes—
197D4×Dic47C23112yes—
198D4×Dic47C2314yes—
199D4×Dic47C2314yes—
200D4×Dic47C2316yes—
201D4×Dic47C23112yes—
202#13093986C2316yes—
203#13093986C2316yes—
204C4×C22⋊D47C23112yes—
205C4×C22⋊D47C23112yes—
206C4×C22⋊D47C23112yes—
207C4×C22⋊D47C23112yes—
208(C22⋊D47)⋊C4C23112yes—
209(C22⋊D47)⋊C4C23112yes—
210(C22⋊D47)⋊C4C2314yes—
211(C22⋊D47)⋊C4C23112yes—
212(C22⋊D47)⋊C4C2314yes—
213(C22⋊D47)⋊C4C23112yes—
214#13093983C23112yes—
215#13093983C2316yes—
216#13093983C23112yes—
217#13093982C23112yes—
218#13093982C23112yes—
219#13093982C23112yes—
220#13093981C23112yes—
221#13093980C23112yes—
222#13093980C23112yes—
223#13093980C2314yes—
224#13093980C23112yes—
225C2×C4⋊Dic47C2313yes—
226C2×C4⋊Dic47C23112yes—
227C2×C4⋊Dic47C23112yes—
228C2×C4⋊Dic47C23112yes—
229C2×C4⋊Dic47C2313yes—
230C2×C4⋊Dic47C2316yes—
231C4⋊C4×D47C23112yes—
232C2×C4×Dic47C2316yes—
233C2×C4×Dic47C2316yes—
234C2×C4×Dic47C2313yes—
235C2×C4×Dic47C2313yes—
236C2×C4×Dic47C2313yes—
237C2×C4×Dic47C2316yes—
238C2×C4×Dic47C2316yes—
239C2×C4×Dic47C2313yes—
240C2×C4×Dic47C23112yes—
241C42×D47C23112yes—
2422−1+4×C47—28no—
243C2×#41×C47C2314yes—
244C2×#41×C47C2316yes—
245C22×Q8×C47—28no—
246C22×Q8×C47C2314yes—
247C22×Q8×C47C2314yes—
248C22×Q8×C47C2314yes—
249C22×Q8×C47C2313yes—
250C22×Q8×C47C2311yescharacteristic
251C23×C4×C47C2313yes—
252C4⋊Q8×C47C23112yes—
253#124×C47C23112yes—
254#123×C47C23112yes—
255C22⋊Q8×C47C23112yes—
256C22⋊Q8×C47C23112yes—
257C22⋊Q8×C47C2316yes—
258C22⋊Q8×C47C2316yes—
259#121×C47C2316yes—
260#121×C47C2316yes—
261#120×C47C2314yes—
262C4×Q8×C47C2314yes—
263C4×Q8×C47C2314yes—
264C4×D4×C47C23112yes—
265C4×D4×C47C23112yes—
266#117×C47C2316yes—
267C24×C47C2411yescharacteristic
268#41×C47—216no—
269#41×C47—224no—
270C2×Q8×C47—216no—
271C2×Q8×C47—216no—
272C2×Q8×C47—216no—
273C2×Q8×C47—212no—
274C2×Q8×C47#4118yescomplemented
275C2×Q8×C47C24112yes—
276C2×Q8×C47C2416yes—
277C2×Q8×C47C2414yes—
278C2×D4×C47C2414yes—
279C2×D4×C47C2414yes—
280C2×D4×C47C2414yes—
281C2×D4×C47C2416yes—
282C22×C4×C47—212no—
283C22×C4×C47C2416yes—
284C22×C4×C47C2416yes—
285C22×C4×C47C24112yes—
286C22×C4×C47C2413yes—
287C22×C4×C47C2413yes—
288C2×C22⋊D47C2414yes—
289C2×C22⋊D47C2414yes—
290C2×C22⋊D47C2414yes—
291C2×C22⋊D47C2414yes—
292C2×C22⋊D47C24112yes—
293C22×Dic47—24no—
294C22×Dic47—46no—
295C22×Dic47C2411yescharacteristic
296C22×Dic47C2411yescharacteristic
297C22×Dic47C2411yescharacteristic
298C22×Dic47C2411yescharacteristic
299C22×Dic47C2411yescharacteristic
300C22×Dic47C2414yes—
301C22×Dic47C2416yes—
302C22×Dic47C2413yes—
303C22×Dic47C2416yes—
304C22×Dic47C2413yes—
305C22×Dic47C24112yes—
306C22×Dic47C2411yescharacteristic
307#10625354—216no—
308Q8×D47—216no—
309#10625352—216no—
310#10625352—424no—
311#10625350—224no—
312C2×D188C2416yes—
313C2×C4×D47C2414yes—
314C2×C4×D47C24112yes—
315C2×C4×D47C24112yes—
316C2×Dic94C2414yes—
317C2×Dic94C2416yes—
318C2×Dic94C24112yes—
319C4⋊C4×C47C2416yes—
320C4⋊C4×C47C2416yes—
321C4⋊C4×C47C24112yes—
322C4⋊C4×C47C24112yes—
323C22⋊C4×C47C2414yes—
324C22⋊C4×C47C2414yes—
325C22⋊C4×C47C2414yes—
326C22⋊C4×C47C24112yes—
327C22⋊C4×C47C24112yes—
328C42×C47C24112yes—
329C22⋊Dic47C2414yes—
330C22⋊Dic47C2414yes—
331C22⋊Dic47C2414yes—
332C22⋊Dic47C24112yes—
333C22⋊Dic47C2414yes—
334C22⋊Dic47C24112yes—
335C22⋊Dic47C2414yes—
336(C2×D47)⋊C4C2414yes—
337(C2×D47)⋊C4C24112yes—
338(C2×D47)⋊C4C2414yes—
339(C2×D47)⋊C4C24112yes—
340(C2×D47)⋊C4C24112yes—
341(C2×D47)⋊C4C24112yes—
342C4⋊Dic47C24112yes—
343C4⋊Dic47C24112yes—
344C4⋊Dic47C24124yes—
345C4⋊Dic47C2416yes—
346C4⋊Dic47C24112yes—
347C4⋊Dic47C2414yes—
348C4⋊Dic47C24112yes—
349C4⋊Dic47C2416yes—
350C4⋊Dic47C2414yes—
351Dic47⋊C4C24112yes—
352Dic47⋊C4C2414yes—
353Dic47⋊C4C2414yes—
354Dic47⋊C4C24112yes—
355Dic47⋊C4C24112yes—
356Dic47⋊C4C2414yes—
357Dic47⋊C4C24112yes—
358Dic47⋊C4C24112yes—
359Dic47⋊C4C24112yes—
360Dic47⋊C4C2414yes—
361C4×Dic47C2414yes—
362C4×Dic47C2416yes—
363C4×Dic47C24112yes—
364C4×Dic47C2416yes—
365C4×Dic47C2416yes—
366C4×Dic47C2414yes—
367C4×Dic47C2416yes—
368C4×Dic47C2416yes—
369C4×Dic47C2416yes—
370C4×Dic47C2416yes—
371C4×Dic47C2416yes—
372C4×Dic47C24112yes—
373C4×Dic47C24112yes—
374C23×C47—22no—
375C23×C47—22no—
376C23×C47—22no—
377C23×C47C2514yes—
378C23×C47C2511yescharacteristic
379C23×C47C2511yescharacteristic
380C23×C47C2511yescharacteristic
381C22×D47C2514yes—
382Q8×C47—224no—
383Q8×C47—212no—
384Q8×C47C2×#41116yes—
385D4×C47—28no—
386D4×C47—28no—
387D4×C47—28no—
388D4×C47—212no—
389C2×C4×C47—26no—
390C2×C4×C47—212no—
391C2×C4×C47—212no—
392C2×C4×C47—224no—
393C2×C4×C47C2×#41112yes—
394C2×C4×C47C2516yes—
395C2×C4×C47C2514yes—
396C2×C4×C47C2514yes—
397C2×C4×C47C2514yes—
398C2×C4×C47C2516yes—
399C22⋊D47—28no—
400C22⋊D47—28no—
401C22⋊D47—28no—
402C22⋊D47—28no—
403C22⋊D47—412no—
404C2×Dic47—22no—
405C2×Dic47—212no—
406C2×Dic47—28no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—412no—
412C2×Dic47—43no—
413C2×Dic47—46no—
414C2×Dic47—43no—
415C2×Dic472−1+414yescomplemented
416C2×Dic47C2511yescharacteristic
417C2×Dic47C2511yescharacteristic
418C2×Dic47C2516yes—
419C2×Dic47C2514yes—
420C2×Dic47C2514yes—
421C2×Dic47C2516yes—
422C2×Dic47C2514yes—
423C2×Dic47C2511yescharacteristic
424C2×Dic47C2511yescharacteristic
425D188—212no—
426C4×D47—224no—
427C4×D47—28no—
428C4×D47—412no—
429Dic94—212no—
430Dic94—28no—
431Dic94—412no—
432#62788—471nomaximal, Sylow
433C22×C47—28no—
434C22×C47—21no—
435C22×C47—21no—
436C22×C47—21no—
437C22×C47—21no—
438C22×C47—21no—
439C22×C47—21no—
440C22×C47—24no—
441C22×C47—24no—
442C22×C47—24no—
443C22×C47C22×#4112yes—
444C22×C47C2×2−1+412yes—
445C22×C47#58512yes—
446C22×C47C2611yescharacteristic
447C2×D47—24no—
448C2×D47—24no—
449C2×D47—24no—
450C4×C47—24no—
451C4×C47—26no—
452C4×C47—24no—
453C4×C47—24no—
454C4×C47C22×#41112yes—
455Dic47—24no—
456Dic47—24no—
457Dic47—21no—
458Dic47—21no—
459Dic47—24no—
460Dic47—26no—
461Dic47—26no—
462Dic47C2×2−1+412yes—
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#3486D4711yescharacteristic, complemented
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+4—471no—
482C22×C4×Q8—471no—
483C2×C47—22no—
484C2×C47—22no—
485C2×C47—22no—
486C2×C47—44no—
487C2×C47C23×#4111yescharacteristic
488C2×C47C22×2−1+411yescharacteristic
489C2×C47C2×#58511yescharacteristic
490D47—44no—
491C2×2−1+4—471no—
492C2×2−1+4C2×D4711yescharacteristic
493C23×Q8C2×D4711yescharacteristic
494#559—4712no—
495Q82—474no—
496#557—4712no—
497#557—474no—
498#557—474no—
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×Q8C2×D4714yes—
517D4×Q8C2×D4714yes—
518#548—474no—
519#548—474no—
520#548—474no—
521#548—474no—
522#548C2×D4714yes—
523#548C2×D4714yes—
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#536C2×D4716yes—
535#533—4712no—
536#533—476no—
537#533—476no—
538#533—4712no—
539#533—476no—
540#532—476no—
541#532—476no—
542#532—476no—
543#529—4712no—
544#529—4712no—
545#529—4712no—
546#529—476no—
547#529—476no—
548#529—4712no—
549#529—476no—
550#529—476no—
551#529—4712no—
552#529—4712no—
553#525—476no—
554#525—474no—
555#525—4712no—
556#525C2×D4716yes—
557#520—476no—
558#520—474no—
559#520—474no—
560#520—476no—
561#519—471no—
562#519—474no—
563#519—474no—
564#519C2×D4711yescharacteristic
565C4×#41—476no—
566C4×#41—474no—
567C4×#41—474no—
568C4×#41—4712no—
569C4×#41—4712no—
570C4×#41—476no—
571C2×C4×Q8—471no—
572C2×C4×Q8—473no—
573C2×C4×Q8—474no—
574C2×C4×Q8—474no—
575C2×C4×Q8—471no—
576C2×C4×Q8—473no—
577C2×C4×Q8—474no—
578C2×C4×Q8—474no—
579C2×C4×Q8—474no—
580C2×C4×Q8—474no—
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—4712no—
589C2×#41—476no—
590C2×#41C22×D4716yes—
591C2×#41C22×D4714yes—
592C22×Q8—28no—
593C22×Q8—474no—
594C22×Q8C22×D4713yes—
595C22×Q8C22×D4714yes—
596C22×Q8C22×D4714yes—
597C22×Q8C22×D4714yes—
598C22×Q8C22×D4711yescharacteristic
599C23×C4—471no—
600C23×C4—473no—
601C23×C4C22×D4713yes—
602C4⋊Q8—476no—
603C4⋊Q8—4712no—
604C4⋊Q8—476no—
605C4⋊Q8—476no—
606C4⋊Q8—4712no—
607C4⋊Q8—4712no—
608C4⋊Q8C22×D47112yes—
609#127—476no—
610#126—4712no—
611#126—4712no—
612#126—4724no—
613#126—4712no—
614#126—4712no—
615#126—4724no—
616#125—4712no—
617#125—476no—
618#125—476no—
619#125—4712no—
620#125—4712no—
621#125—4724no—
622#125—4724no—
623#125—4712no—
624#124—476no—
625#124—4712no—
626#124—476no—
627#124—4712no—
628#124—4712no—
629#124C22×D47112yes—
630#123—474no—
631#123—4712no—
632#123—4712no—
633#123—474no—
634#123—4712no—
635#123—4724no—
636#123—4724no—
637#123C22×D47112yes—
638C22⋊Q8—4712no—
639C22⋊Q8—4712no—
640C22⋊Q8—4712no—
641C22⋊Q8—476no—
642C22⋊Q8—476no—
643C22⋊Q8—4712no—
644C22⋊Q8—4724no—
645C22⋊Q8—474no—
646C22⋊Q8—474no—
647C22⋊Q8—4712no—
648C22⋊Q8—4712no—
649C22⋊Q8—4724no—
650C22⋊Q8C22×D4716yes—
651C22⋊Q8C22×D4716yes—
652C22⋊Q8C22×D47112yes—
653C22⋊Q8C22×D47112yes—
654#121—474no—
655#121—474no—
656#121—4712no—
657#121—4712no—
658#121—4712no—
659#121—476no—
660#121—476no—
661#121—4712no—
662#121C22×D4716yes—
663#121C22×D4716yes—
664#120—474no—
665#120C22×D4714yes—
666C4×Q8—474no—
667C4×Q8—474no—
668C4×Q8—4712no—
669C4×Q8—4712no—
670C4×Q8—474no—
671C4×Q8—474no—
672C4×Q8—4712no—
673C4×Q8—4712no—
674C4×Q8—476no—
675C4×Q8—474no—
676C4×Q8—4712no—
677C4×Q8—476no—
678C4×Q8—474no—
679C4×Q8—476no—
680C4×Q8—476no—
681C4×Q8—4712no—
682C4×Q8—4712no—
683C4×Q8—4712no—
684C4×Q8—4712no—
685C4×Q8—4712no—
686C4×Q8C22×D4714yes—
687C4×Q8C22×D4714yes—
688C4×D4—474no—
689C4×D4—474no—
690C4×D4—476no—
691C4×D4—4712no—
692C4×D4—476no—
693C4×D4—4712no—
694C4×D4—4712no—
695C4×D4—4712no—
696C4×D4—4712no—
697C4×D4—4712no—
698C4×D4—4712no—
699C4×D4—476no—
700C4×D4—476no—
701C4×D4—474no—
702C4×D4—474no—
703C4×D4—4712no—
704C4×D4—4712no—
705C4×D4—4712no—
706C4×D4—4712no—
707C4×D4—4712no—
708C4×D4C22×D47112yes—
709C4×D4C22×D47112yes—
710#117—476no—
711#117—4712no—
712#117—4712no—
713#117—4712no—
714#117—4712no—
715#117—4712no—
716#117—474no—
717#117—4712no—
718#117—4712no—
719#117—4712no—
720#117—4712no—
721#117C22×D4716yes—
722C2×C4⋊C4—473no—
723C2×C4⋊C4—473no—
724C2×C4⋊C4—476no—
725C2×C4⋊C4—4712no—
726C2×C4⋊C4—4712no—
727C2×C4⋊C4—4712no—
728C2×C4⋊C4—4712no—
729C2×C42—473no—
730C2×C42—476no—
731C2×C42—476no—
732C2×C42—473no—
733C2×C42—476no—
734C2×C42—473no—
735C2×C42—476no—
736C2×C42—473no—
737C2×C42—4712no—
738C2×C42—4712no—
739C24C23×D4711yescharacteristic
740#41—216no—
741#41—224no—
742#41—9416no—
743#41—9416no—
744#41—9424no—
745#41—18824no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—474no—
751C2×Q8—476no—
752C2×Q8—4712no—
753C2×Q8—9416no—
754C2×Q8#1062535218yescomplemented
755C2×Q8C23×D47112yes—
756C2×Q8C23×D4716yes—
757C2×Q8C23×D4714yes—
758C2×D4—474no—
759C2×D4—474no—
760C2×D4—474no—
761C2×D4—474no—
762C2×D4—4712no—
763C2×D4—476no—
764C2×D4C23×D4714yes—
765C2×D4C23×D4716yes—
766C2×D4C23×D4714yes—
767C2×D4C23×D4714yes—
768C22×C4—212no—
769C22×C4—471no—
770C22×C4—471no—
771C22×C4—471no—
772C22×C4—471no—
773C22×C4—471no—
774C22×C4—471no—
775C22×C4—474no—
776C22×C4—476no—
777C22×C4—473no—
778C22×C4—476no—
779C22×C4—473no—
780C22×C4—4712no—
781C22×C4—474no—
782C22×C4—4712no—
783C22×C4—4712no—
784C22×C4—944no—
785C22×C4—1886no—
786C22×C4C23×D4716yes—
787C22×C4C23×D4716yes—
788C22×C4C23×D4713yes—
789C22×C4C23×D47112yes—
790C22×C4C23×D4713yes—
791C4⋊C4—4712no—
792C4⋊C4—474no—
793C4⋊C4—474no—
794C4⋊C4—474no—
795C4⋊C4—474no—
796C4⋊C4—4712no—
797C4⋊C4—4712no—
798C4⋊C4—4712no—
799C4⋊C4—4712no—
800C4⋊C4—4712no—
801C4⋊C4—4712no—
802C4⋊C4—4712no—
803C4⋊C4—4724no—
804C4⋊C4—476no—
805C4⋊C4—4712no—
806C4⋊C4—476no—
807C4⋊C4—474no—
808C4⋊C4—474no—
809C4⋊C4—4712no—
810C4⋊C4C23×D4716yes—
811C4⋊C4C23×D4716yes—
812C4⋊C4C23×D47112yes—
813C4⋊C4C23×D47112yes—
814C22⋊C4—474no—
815C22⋊C4—474no—
816C22⋊C4—4712no—
817C22⋊C4—474no—
818C22⋊C4—474no—
819C22⋊C4—474no—
820C22⋊C4—4712no—
821C22⋊C4—4712no—
822C22⋊C4—474no—
823C22⋊C4—474no—
824C22⋊C4—4712no—
825C22⋊C4—4712no—
826C22⋊C4—4712no—
827C22⋊C4C23×D4714yes—
828C22⋊C4C23×D4714yes—
829C22⋊C4C23×D47112yes—
830C22⋊C4C23×D47112yes—
831C22⋊C4C23×D4714yes—
832C42—476no—
833C42—474no—
834C42—474no—
835C42—476no—
836C42—476no—
837C42—476no—
838C42—476no—
839C42—476no—
840C42—476no—
841C42—476no—
842C42—4712no—
843C42—4712no—
844C42—4712no—
845C42C23×D47112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—474no—
850C23C24×D4714yes—
851C23C24×D4711yescharacteristic
852C23C24×D4711yescharacteristic
853C23C24×D4711yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—948no—
857Q8—9412no—
858Q8—18812no—
859Q8C2×#10625352116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—948no—
865D4—948no—
866D4—948no—
867D4—948no—
868D4—9412no—
869D4—18812no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—474no—
875C2×C4—471no—
876C2×C4—471no—
877C2×C4—471no—
878C2×C4—471no—
879C2×C4—476no—
880C2×C4—474no—
881C2×C4—474no—
882C2×C4—474no—
883C2×C4—476no—
884C2×C4—948no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—948no—
890C2×C4—942no—
891C2×C4—9412no—
892C2×C4—9424no—
893C2×C4—18812no—
894C2×C4—1883no—
895C2×C4—1886no—
896C2×C4—1883no—
897C2×C4—18812no—
898C2×C4C2×#10625352112yes—
899C2×C4C24×D4716yes—
900C2×C4C24×D4714yes—
901C2×C4C24×D4714yes—
902C2×C4C24×D4714yes—
903C2×C4C24×D4716yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—944no—
915C22—944no—
916C22—944no—
917C22C22×#1062535212yes—
918C222−1+4×D4712yes—
919C22#1568996012yes—
920C22C25×D4711yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—472no—
926C4—472no—
927C4—944no—
928C4—941no—
929C4—941no—
930C4—944no—
931C4—946no—
932C4—946no—
933C4—944no—
934C4C22×#10625352112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—1884no—
940C2C23×#1062535211yescharacteristic
941C2C2×2−1+4×D4711yescharacteristic
942C2C2×#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3486C2
hypercenter#3486D47
hypocenterC47#62788
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #20257475C2semidirect
2. #20257464C2semidirect
3. #20257382C2semidirect
4. #20257370C2semidirect
5. #20257252C2semidirect
6. #20257194C2semidirect
7. #20257155C2semidirect
8. #20257094C2semidirect
9. #20257039C2semidirect
10. #20257009C2semidirect
11. #20257004C2semidirect
12. #20256978C2semidirect
13. Q8×#10625352C2semidirect
14. #20256812C2semidirect
15. #20256680C2semidirect
16. 2−1+4×Dic47C2semidirect
17. #20256597C2semidirect
18. C22×Q8×Dic47C2semidirect
19. C47×#3486C2semidirect
21. #15689855C22semidirect
22. Q8×Dic94C22semidirect
23. #15689852C22semidirect
24. #15689849C22semidirect
25. #15689849C22semidirect
26. #15689848C22semidirect
27. #15689847C22semidirect
28. #15689844C22semidirect
29. #15689842C22semidirect
31. #15689831C22semidirect
36. #15689815C22semidirect
38. #15689807C22semidirect
39. #15689792C22semidirect
42. Q8×C22⋊D47C22semidirect
45. #15689784C22semidirect
46. #15689780C22semidirect
50. #15689746C22semidirect
51. #15689742C22semidirect
52. #15689734C22semidirect
53. #15689733C22semidirect
57. #15689678C22semidirect
61. #15689675C22semidirect
67. #15689659C22semidirect
72. #15689652C22semidirect
79. #15689606C22semidirect
80. #15689605C22semidirect
83. #15689601C22semidirect
84. #15689599C22semidirect
86. #41×Dic47C22semidirect
87. C4×#10625354C22semidirect
99. C2×Q8×Dic47C22semidirect
100. C4×Q8×D47C22semidirect
274. C2×Q8×C47#41semidirect
415. C2×Dic472−1+4semidirect
473. #3486D47semidirect
583. C47#62788semidirect
754. C2×Q8#10625352semidirect

Maximal subgroups

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

subgroupindex
#202574752
#202574642
#202573822
#202573702
#202572522
#202571942
#202571552
#202570942
#202570392
#202570092
#202570042
#202569782
Q8×#106253522
#202568122
#202566802
2−1+4×Dic472
#202565972
C22×Q8×Dic472
C47×#34862
#6278847