Finite Group Databasebeta

← #41×#10625354 #27123392

Subgroups — #41×#10625354 #27123392

Order 12032.

7812 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257015C211yesmaximal, characteristic, complemented
2#20257009C213yesmaximal, complemented
3#20257008C213yesmaximal, complemented
4#20256999C219yesmaximal, complemented
5#20256988C213yesmaximal, complemented
6#20256983C213yesmaximal, complemented
7Q8×#10625354C211yesmaximal, characteristic, complemented
8#20256955C219yesmaximal, complemented
9#20256954C219yesmaximal, complemented
10D4×#10625354C213yesmaximal, complemented
11#41×D188C213yesmaximal, complemented
12#20256685C219yesmaximal, complemented
13C2×C4×#10625354C213yesmaximal, complemented
14C4×#41×D47C213yesmaximal, complemented
15Q8×#41×C47C211yesmaximal, characteristic, complemented
16C22×#10625354C2213yes—
17C2×#41×D47C2213yes—
18#15689858C2219yescomplemented
19#15689852C2213yescomplemented
20#15689847C2219yescomplemented
21#15689846C2219yescomplemented
22#15689839C2219yescomplemented
23#15689834C2219yescomplemented
24#15689826C22118yescomplemented
25#15689821C22118yescomplemented
26#15689815C22118yescomplemented
27#15689811C22118yescomplemented
28#15689800C22136yescomplemented
29#15689795C2213yescomplemented
30#15689795C2213yescomplemented
31Q8×D188C2213yescomplemented
32#15689785C2216yescomplemented
33#15689784C2216yescomplemented
34#15689777C2219yescomplemented
35#15689776C2219yescomplemented
36#15689768C22118yescomplemented
37#15689764C22118yescomplemented
38D4×D188C2219yescomplemented
39#15689678C2219yescomplemented
40#15689678C2219yescomplemented
41#15689674C2219yescomplemented
42#15689674C2219yescomplemented
43#15689673C2219yescomplemented
44#15689660C22118yescomplemented
45#15689660C22118yescomplemented
46#15689659C22118yescomplemented
47#15689659C22118yescomplemented
48#15689658C22118yescomplemented
49#15689658C22118yescomplemented
50#15689636C22118yescomplemented
51#15689636C22118yescomplemented
52#15689635C22118yescomplemented
53#41×Dic47C2211yescharacteristic
54C4×#10625354C2211yescharacteristic
55C4×#10625354C2213yes—
56C4×#10625354C2213yescomplemented
57C4×#10625354C2213yescomplemented
58C4×#10625354C2219yescomplemented
59C4×#10625354C2219yescomplemented
60C4×#10625354C2219yescomplemented
61C4×#10625354C2213yescomplemented
62C4×#10625354C2219yescomplemented
63C4×#10625354C2213yescomplemented
64C4×#10625354C2216yescomplemented
65C4×#10625350C2219yescomplemented
66#15689591C2219yescomplemented
67C4×#10625352C2219yescomplemented
68C4×#10625352C2219yescomplemented
69C2×Q8×Dic47C2213yescomplemented
70C4×Q8×D47C2213yescomplemented
71C4×Q8×D47C2213yescomplemented
72C2×C4×D188C2219yescomplemented
73C2×#13093986C2219yescomplemented
74C4×D4×D47C2219yescomplemented
75C4×D4×D47C2219yescomplemented
76C2×#13093982C2219yescomplemented
77#117×D47C2219yescomplemented
78C2×C42×D47C2219yescomplemented
79Q82×C47C2211yescharacteristic, complemented
80C47×#557C2213yescomplemented
81C47×#554C2219yescomplemented
82D4×Q8×C47C2213yescomplemented
83C47×#533C2219yescomplemented
84C4×#41×C47C2213yes—
85C2×C4×Q8×C47C2213yescomplemented
86C2×#10625354—224no—
87C2×#10625354C2319yes—
88C2×#10625354C2313yes—
89C2×#10625354C2313yes—
90C2×#10625354C2319yes—
91C2×#10625354C2316yes—
92C2×#10625354C2311yescharacteristic
93C2×#10625350C2319yes—
94C2×#10625352C2319yes—
95#41×D47—224no—
96C2×Q8×D47C2313yes—
97C22×D188C2319yes—
98C2×D4×D47C2319yes—
99C22×C4×D47C2319yes—
100C22×C4×D47C2319yes—
101C22×C4×D47C2319yes—
102#13094024C2319yes—
103#13094021C2319yes—
104#13094019C23136yes—
105#13094019C23136yes—
106#13094015C23118yes—
107#13094015C23118yes—
108#13094013C23118yes—
109#13094013C23118yes—
110#13094012C23118yes—
111#13094009C23136yes—
112#13094009C23136yes—
113#13094008C23136yes—
114#13094004C23118yes—
115#13094004C23118yes—
116#13094000C23118yes—
117#13094000C23118yes—
118#13093999C23118yes—
119#13093999C23118yes—
120#13093999C23118yes—
121#13093999C23118yes—
122#13093998C23118yes—
123#13093998C23118yes—
124#13093994C23136yes—
125Q8×Dic47C2313yes—
126Q8×Dic47C2319yes—
127Q8×Dic47C2311yescharacteristic
128Q8×Dic47C2311yescharacteristic
129Q8×Dic47C2311yescharacteristic
130Q8×Dic47C2319yes—
131Q8×Dic47C2316yes—
132C4×Dic94C2319yes—
133C4×Dic94C2319yes—
134#13093989C2319yes—
135#13093989C2319yes—
136C4×D188C2319yes—
137C4×D188C23118yes—
138C4×D188C2319yes—
139C4×D188C2319yes—
140C4×D188C2319yes—
141C4×D188C2313yes—
142C4×D188C23118yes—
143C4×D188C2319yes—
144C4×D188C23118yes—
145D4×Dic47C2313yes—
146D4×Dic47C2313yes—
147#13093986C2319yes—
148#13093986C23118yes—
149#13093986C2319yes—
150#13093986C2319yes—
151#13093986C2319yes—
152#13093986C2313yes—
153#13093986C23118yes—
154#13093986C2319yes—
155#13093986C23118yes—
156C4×C22⋊D47C23118yes—
157C4×C22⋊D47C23118yes—
158(C22⋊D47)⋊C4C23118yes—
159(C22⋊D47)⋊C4C23118yes—
160#13093983C2313yes—
161#13093982C23118yes—
162#13093982C2319yes—
163#13093982C2319yes—
164#13093982C2319yes—
165#13093982C2319yes—
166#13093982C2313yes—
167#13093982C2319yes—
168#13093982C23118yes—
169#13093982C23118yes—
170#13093981C23118yes—
171#13093980C23118yes—
172C2×C4⋊Dic47C2319yes—
173C4⋊C4×D47C2319yes—
174C4⋊C4×D47C2319yes—
175C2×(C2×D47)⋊C4C23118yes—
176C22⋊C4×D47C23118yes—
177C2×C4×Dic47C2313yes—
178C2×C4×Dic47C2319yes—
179C2×C4×Dic47C2319yes—
180C42×D47C2313yes—
181C42×D47C2319yes—
182C42×D47C2319yes—
183C42×D47C2319yes—
184C42×D47C2319yes—
185C42×D47C2319yes—
186C42×D47C2319yes—
187C42×D47C2319yes—
188C2×#41×C47C2311yescharacteristic
189C22×Q8×C47C2313yes—
190C4⋊Q8×C47C2319yes—
191C4⋊Q8×C47C2319yes—
192#125×C47C23118yes—
193C22⋊Q8×C47C23118yes—
194C22⋊Q8×C47C23118yes—
195C4×Q8×C47C2313yes—
196C4×Q8×C47C2313yes—
197C4×Q8×C47C2311yescharacteristic
198C4×Q8×C47C2313yes—
199C4×Q8×C47C2319yes—
200C4×Q8×C47C2319yes—
201C4×Q8×C47C2316yes—
202C4×D4×C47C2319yes—
203C4×D4×C47C2319yes—
204#117×C47C2319yes—
205C2×C4⋊C4×C47C2319yes—
206C2×C42×C47C2319yes—
207C23×D47C2419yes—
208#41×C47#4118yescomplemented
209C2×Q8×C47—212no—
210C2×Q8×C47C2419yes—
211C2×Q8×C47C2416yes—
212C2×Q8×C47C2411yescharacteristic
213C2×Q8×C47C2411yescharacteristic
214C2×D4×C47C2413yes—
215C22×C4×C47C2419yes—
216C22×C4×C47C2419yes—
217C22×C4×C47C2413yes—
218C2×C22⋊D47C24118yes—
219C22×Dic47C2413yes—
220C22×Dic47C2413yes—
221C22×Dic47C2419yes—
222#10625354—212no—
223#10625354—212no—
224#10625354—236no—
225#10625354—236no—
226#10625354—412no—
227#10625354#4118yesdirect product factor
228Q8×D47—212no—
229#10625352—236no—
230D4×D47—236no—
231#10625350—236no—
232C2×D188—236no—
233C2×D188C24118yes—
234C2×D188C2419yes—
235C2×D188C2419yes—
236C2×D188C24118yes—
237C2×D188C2413yes—
238C2×C4×D47—236no—
239C2×C4×D47—236no—
240C2×C4×D47—418no—
241C2×C4×D47C2413yes—
242C2×C4×D47C2413yes—
243C2×C4×D47C2419yes—
244C2×C4×D47C2419yes—
245C2×C4×D47C2419yes—
246C2×C4×D47C2419yes—
247C2×C4×D47C2419yes—
248C2×C4×D47C2419yes—
249C2×C4×D47C2419yes—
250C2×C4×D47C2419yes—
251C2×C4×D47C2419yes—
252C2×C4×D47C2413yes—
253C2×Dic94C2419yes—
254C4⋊C4×C47C2413yes—
255C4⋊C4×C47C24118yes—
256C4⋊C4×C47C2419yes—
257C4⋊C4×C47C2419yes—
258C4⋊C4×C47C2419yes—
259C4⋊C4×C47C24118yes—
260C22⋊C4×C47C24118yes—
261C42×C47C2413yes—
262C42×C47C2419yes—
263C42×C47C2419yes—
264C42×C47C2419yes—
265C22⋊Dic47C2416yes—
266(C2×D47)⋊C4C24118yes—
267(C2×D47)⋊C4C24118yes—
268(C2×D47)⋊C4C2416yes—
269(C2×D47)⋊C4C24118yes—
270(C2×D47)⋊C4C24118yes—
271(C2×D47)⋊C4C24118yes—
272(C2×D47)⋊C4C24136yes—
273C4⋊Dic47C2413yes—
274C4⋊Dic47C2413yes—
275C4⋊Dic47C2413yes—
276C4⋊Dic47C2419yes—
277C4⋊Dic47C24118yes—
278C4⋊Dic47C24118yes—
279Dic47⋊C4C24118yes—
280Dic47⋊C4C24118yes—
281C4×Dic47C2411yescharacteristic
282C4×Dic47C2413yes—
283C4×Dic47C2413yes—
284C4×Dic47C2413yes—
285C4×Dic47C2413yes—
286C4×Dic47C2413yes—
287C4×Dic47C2419yes—
288C4×Dic47C2419yes—
289C4×Dic47C2419yes—
290C4×Dic47C2419yes—
291C4×Dic47C2419yes—
292C4×Dic47C2419yes—
293C23×C47C2513yes—
294C22×D47—218no—
295C22×D47—218no—
296C22×D47—49no—
297C22×D47C2519yes—
298C22×D47C2513yes—
299Q8×C47—218no—
300Q8×C47—46no—
301Q8×C47C2×#4114yescomplemented
302Q8×C47C2×#4114yescomplemented
303D4×C47C2×#41112yescomplemented
304C2×C4×C47—218no—
305C2×C4×C47—49no—
306C2×C4×C47C2×#41112yescomplemented
307C2×C4×C47C2513yes—
308C2×C4×C47C2519yes—
309C2×C4×C47C2519yes—
310C2×C4×C47C2513yes—
311C2×C4×C47C2513yes—
312C2×C4×C47C2511yescharacteristic
313C22⋊D47—236no—
314C2×Dic47—218no—
315C2×Dic47—26no—
316C2×Dic47—26no—
317C2×Dic47C2513yes—
318C2×Dic47C2513yes—
319C2×Dic47C2513yes—
320C2×Dic47C2519yes—
321C2×Dic47C2511yescharacteristic
322C2×Dic47C2511yescharacteristic
323D188—236no—
324D188—218no—
325D188—218no—
326D188—418no—
327D188C2×#41112yescomplemented
328C4×D47—218no—
329C4×D47—26no—
330C4×D47—218no—
331C4×D47—218no—
332C4×D47—218no—
333C4×D47—218no—
334C4×D47—218no—
335C4×D47—26no—
336C4×D47—218no—
337C4×D47—49no—
338C4×D47—49no—
339C4×D47C2×#41112yescomplemented
340Dic94—218no—
341#412—471nomaximal, Sylow
342C22×C47—23no—
343C22×C47—23no—
344C22×C47C22×#4116yes—
345C22×C47C2611yescharacteristic
346C2×D47—23no—
347C2×D47—23no—
348C2×D47—29no—
349C2×D47—29no—
350C2×D47—29no—
351C2×D47—436no—
352C2×D47C22×#4116yes—
353C4×C47—29no—
354C4×C47—23no—
355C4×C47—29no—
356C4×C47C22×#4116yes—
357C4×C47C22×#4116yes—
358C4×C47C22×#4112yes—
359Dic47—29no—
360Dic47—23no—
361Dic47—23no—
362Dic47—23no—
363Dic47C22×#4112yes—
364Dic47#58512yes—
365#3483—471no—
366#3482—473no—
367#3482—473no—
368#3481—479no—
369#3480—473no—
370#3480—473no—
371Q8×#41—471no—
372Q8×#41D4711yescharacteristic, complemented
373#3475—479no—
374#3475—479no—
375D4×#41—473no—
376D4×#41—473no—
377#3444—479no—
378C2×C4×#41—473no—
379C2×C4×#41—473no—
380C2×C47—26no—
381C2×C47C23×#4111yescharacteristic
382C2×C47C23×#4111yescharacteristic
383C2×C47C2×#58511yescharacteristic
384D47—26no—
385D47—49no—
386C22×#41—473no—
387C22×#41—473no—
388#559—479no—
389Q82C2×D4711yescharacteristic, complemented
390#557—473no—
391#557C2×D4713yescomplemented
392#556—479no—
393#556—479no—
394#555—479no—
395#554—479no—
396#554C2×D4719yescomplemented
397#553—4718no—
398#553—4718no—
399#552—4718no—
400#552—4718no—
401#551—4736no—
402#550—473no—
403#550—473no—
404D4×Q8—473no—
405D4×Q8C2×D4713yescomplemented
406#548—476no—
407#548—476no—
408#547—479no—
409#547—479no—
410#546—4718no—
411#546—4718no—
412D42—479no—
413#533—479no—
414#533—479no—
415#533C2×D4719yescomplemented
416#532—479no—
417#532—479no—
418#532—479no—
419#529—4718no—
420#529—4718no—
421#529—4718no—
422#529—4718no—
423#529—4718no—
424#529—4718no—
425#525—4718no—
426#525—4718no—
427#525—4718no—
428C4×#41—471no—
429C4×#41—471no—
430C4×#41—479no—
431C4×#41—473no—
432C4×#41—479no—
433C4×#41—479no—
434C4×#41—473no—
435C4×#41—473no—
436C4×#41—479no—
437C4×#41—473no—
438C4×#41—473no—
439C4×#41—476no—
440C4×#41—479no—
441C4×#41—479no—
442C4×#41—479no—
443C4×#41—479no—
444C4×#41C2×D4713yes—
445C2×C4×Q8—473no—
446C2×C4×Q8—473no—
447C2×C4×Q8—473no—
448C2×C4×Q8C2×D4713yescomplemented
449C2×C4×D4—479no—
450C2×C4×D4—479no—
451C2×C4×D4—479no—
452C2×C4×D4—479no—
453C2×#117—479no—
454C2×#117—479no—
455C22×C42—479no—
456C47#41211yescharacteristic, complemented, Sylow
457C2×#41—471no—
458C2×#41—479no—
459C2×#41—479no—
460C2×#41—473no—
461C2×#41—473no—
462C2×#41—476no—
463C2×#41—479no—
464C2×#41—479no—
465C2×#41—9424no—
466C2×#41—9424no—
467C2×#41C22×D4711yescharacteristic
468C22×Q8—473no—
469C22×Q8C22×D4713yes—
470C22×D4—479no—
471C22×D4—479no—
472C23×C4—479no—
473C23×C4—479no—
474C23×C4—479no—
475C4⋊Q8—479no—
476C4⋊Q8C22×D4719yes—
477C4⋊Q8C22×D4719yes—
478#127—479no—
479#126—4736no—
480#126—4736no—
481#125—4718no—
482#125—4718no—
483#125C22×D47118yes—
484#124—4718no—
485#124—4718no—
486#124—4718no—
487#123—4736no—
488#123—4736no—
489#123—4736no—
490C22⋊Q8—4718no—
491C22⋊Q8—4718no—
492C22⋊Q8—4718no—
493C22⋊Q8—4718no—
494C22⋊Q8C22×D47118yes—
495C22⋊Q8C22×D47118yes—
496#121—4718no—
497#121—4718no—
498#121—4718no—
499#121—4718no—
500#121—4718no—
501#121—4718no—
502#120—4736no—
503C4×Q8—471no—
504C4×Q8—471no—
505C4×Q8—471no—
506C4×Q8—479no—
507C4×Q8—473no—
508C4×Q8—479no—
509C4×Q8—476no—
510C4×Q8—479no—
511C4×Q8—479no—
512C4×Q8—479no—
513C4×Q8—479no—
514C4×Q8C22×D4713yes—
515C4×Q8C22×D4713yes—
516C4×Q8C22×D4711yescharacteristic
517C4×Q8C22×D4719yes—
518C4×Q8C22×D4713yes—
519C4×Q8C22×D4719yes—
520C4×Q8C22×D4716yes—
521C4×D4—473no—
522C4×D4—473no—
523C4×D4—4718no—
524C4×D4—4718no—
525C4×D4—473no—
526C4×D4—4718no—
527C4×D4—479no—
528C4×D4—479no—
529C4×D4—479no—
530C4×D4—479no—
531C4×D4—4718no—
532C4×D4—479no—
533C4×D4—4718no—
534C4×D4—4718no—
535C4×D4—4718no—
536C4×D4—473no—
537C4×D4—4718no—
538C4×D4—479no—
539C4×D4—479no—
540C4×D4—4718no—
541C4×D4—479no—
542C4×D4—479no—
543C4×D4—479no—
544C4×D4—4718no—
545C4×D4C22×D4719yes—
546C4×D4C22×D4719yes—
547#117—473no—
548#117—473no—
549#117—479no—
550#117—4718no—
551#117—4718no—
552#117—479no—
553#117—479no—
554#117—479no—
555#117—479no—
556#117—4718no—
557#117—4718no—
558#117—4718no—
559#117C22×D4719yes—
560C2×C4⋊C4—479no—
561C2×C4⋊C4—479no—
562C2×C4⋊C4—479no—
563C2×C4⋊C4C22×D4719yes—
564C2×C22⋊C4—4718no—
565C2×C22⋊C4—4718no—
566C2×C42—479no—
567C2×C42—479no—
568C2×C42—473no—
569C2×C42—479no—
570C2×C42—479no—
571C2×C42—479no—
572C2×C42—479no—
573C2×C42—479no—
574C2×C42—479no—
575C2×C42—479no—
576C2×C42—473no—
577C2×C42C22×D4719yes—
578C24—479no—
579#41—478no—
580#41—9436no—
581#41—9436no—
582#41—9412no—
583#41—9412no—
584#41—9436no—
585#41—9436no—
586#41—18812no—
587#41#1062535418yesdirect product factor
588C2×Q8—212no—
589C2×Q8—479no—
590C2×Q8—9412no—
591C2×Q8C23×D4719yes—
592C2×Q8C23×D4716yes—
593C2×Q8C23×D4711yescharacteristic
594C2×Q8C23×D4711yescharacteristic
595C2×D4—4718no—
596C2×D4—473no—
597C2×D4—4718no—
598C2×D4—479no—
599C2×D4—479no—
600C2×D4—4718no—
601C2×D4—9436no—
602C2×D4—9436no—
603C2×D4C23×D4713yes—
604C22×C4—473no—
605C22×C4—473no—
606C22×C4—473no—
607C22×C4—479no—
608C22×C4—473no—
609C22×C4—479no—
610C22×C4—479no—
611C22×C4—479no—
612C22×C4—479no—
613C22×C4—479no—
614C22×C4—479no—
615C22×C4—473no—
616C22×C4—479no—
617C22×C4—479no—
618C22×C4—479no—
619C22×C4—9436no—
620C22×C4—9436no—
621C22×C4—18818no—
622C22×C4C23×D4719yes—
623C22×C4C23×D4719yes—
624C22×C4C23×D4713yes—
625C4⋊C4—4718no—
626C4⋊C4—4718no—
627C4⋊C4—473no—
628C4⋊C4—473no—
629C4⋊C4—473no—
630C4⋊C4—479no—
631C4⋊C4—4718no—
632C4⋊C4—4718no—
633C4⋊C4C23×D4719yes—
634C4⋊C4C23×D4719yes—
635C4⋊C4C23×D4713yes—
636C4⋊C4C23×D4719yes—
637C4⋊C4C23×D47118yes—
638C4⋊C4C23×D47118yes—
639C22⋊C4—476no—
640C22⋊C4—476no—
641C22⋊C4—4718no—
642C22⋊C4—4718no—
643C22⋊C4—4718no—
644C22⋊C4—4718no—
645C22⋊C4—4718no—
646C22⋊C4—4736no—
647C22⋊C4C23×D47118yes—
648C42—473no—
649C42—473no—
650C42—473no—
651C42—473no—
652C42—479no—
653C42—479no—
654C42—479no—
655C42—479no—
656C42—479no—
657C42—479no—
658C42—471no—
659C42—473no—
660C42C23×D4719yes—
661C42C23×D4719yes—
662C42C23×D4713yes—
663C42C23×D4719yes—
664C23—473no—
665C23—479no—
666C23—9418no—
667C23—9418no—
668C23—1889no—
669C23C24×D4713yes—
670Q8—218no—
671Q8—46no—
672Q8—9418no—
673Q8#41×D4714yescomplemented
674Q8C2×#1062535414yescomplemented
675D4—4712no—
676D4—9436no—
677D4—9436no—
678D4—9418no—
679D4—9418no—
680D4—18818no—
681D4C2×#10625354112yescomplemented
682C2×C4—218no—
683C2×C4—49no—
684C2×C4—471no—
685C2×C4—471no—
686C2×C4—4712no—
687C2×C4—473no—
688C2×C4—473no—
689C2×C4—473no—
690C2×C4—479no—
691C2×C4—9418no—
692C2×C4—946no—
693C2×C4—9418no—
694C2×C4—9418no—
695C2×C4—946no—
696C2×C4—946no—
697C2×C4—9418no—
698C2×C4—9418no—
699C2×C4—946no—
700C2×C4—9418no—
701C2×C4—9418no—
702C2×C4—9418no—
703C2×C4—1889no—
704C2×C4—1889no—
705C2×C4C2×#10625354112yescomplemented
706C2×C4C24×D4713yes—
707C2×C4C24×D4719yes—
708C2×C4C24×D4719yes—
709C2×C4C24×D4713yes—
710C2×C4C24×D4713yes—
711C2×C4C24×D4711yescharacteristic
712C22—23no—
713C22—23no—
714C22—476no—
715C22—943no—
716C22—943no—
717C22—949no—
718C22—949no—
719C22—949no—
720C22—18836no—
721C22C22×#1062535416yes—
722C22C25×D4711yescharacteristic
723C4—29no—
724C4—23no—
725C4—29no—
726C4—472no—
727C4—472no—
728C4—943no—
729C4—943no—
730C4—949no—
731C4—943no—
732C4C2×#41×D4716yes—
733C4C22×#1062535412yes—
734C4C22×#1062535416yes—
735C2—26no—
736C2—946no—
737C2—1889no—
738C2C22×#41×D4711yescharacteristic
739C2C23×#1062535411yescharacteristic
740C2#585×D4711yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingQ8×#41×C47C2
hypercenterQ8×#41D47
hypocenterC47#412
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. #20257015C2semidirect
2. #20257009C2semidirect
3. #20257008C2semidirect
4. #20256999C2semidirect
5. #20256988C2semidirect
6. #20256983C2semidirect
7. Q8×#10625354C2semidirect
8. #20256955C2semidirect
9. #20256954C2semidirect
10. D4×#10625354C2semidirect
11. #41×D188C2semidirect
12. #20256685C2semidirect
13. C2×C4×#10625354C2semidirect
14. C4×#41×D47C2semidirect
15. Q8×#41×C47C2semidirect
18. #15689858C22semidirect
19. #15689852C22semidirect
20. #15689847C22semidirect
21. #15689846C22semidirect
22. #15689839C22semidirect
23. #15689834C22semidirect
24. #15689826C22semidirect
25. #15689821C22semidirect
26. #15689815C22semidirect
27. #15689811C22semidirect
28. #15689800C22semidirect
29. #15689795C22semidirect
30. #15689795C22semidirect
31. Q8×D188C22semidirect
32. #15689785C22semidirect
33. #15689784C22semidirect
34. #15689777C22semidirect
35. #15689776C22semidirect
36. #15689768C22semidirect
37. #15689764C22semidirect
38. D4×D188C22semidirect
39. #15689678C22semidirect
40. #15689678C22semidirect
41. #15689674C22semidirect
42. #15689674C22semidirect
43. #15689673C22semidirect
44. #15689660C22semidirect
45. #15689660C22semidirect
46. #15689659C22semidirect
47. #15689659C22semidirect
48. #15689658C22semidirect
49. #15689658C22semidirect
50. #15689636C22semidirect
51. #15689636C22semidirect
52. #15689635C22semidirect
56. C4×#10625354C22semidirect
57. C4×#10625354C22semidirect
58. C4×#10625354C22semidirect
59. C4×#10625354C22semidirect
60. C4×#10625354C22semidirect
61. C4×#10625354C22semidirect
62. C4×#10625354C22semidirect
63. C4×#10625354C22semidirect
64. C4×#10625354C22semidirect
65. C4×#10625350C22semidirect
66. #15689591C22semidirect
67. C4×#10625352C22semidirect
68. C4×#10625352C22semidirect
69. C2×Q8×Dic47C22semidirect
70. C4×Q8×D47C22semidirect
71. C4×Q8×D47C22semidirect
72. C2×C4×D188C22semidirect
73. C2×#13093986C22semidirect
74. C4×D4×D47C22semidirect
75. C4×D4×D47C22semidirect
76. C2×#13093982C22semidirect
77. #117×D47C22semidirect
78. C2×C42×D47C22semidirect
79. Q82×C47C22semidirect
80. C47×#557C22semidirect
81. C47×#554C22semidirect
82. D4×Q8×C47C22semidirect
83. C47×#533C22semidirect
85. C2×C4×Q8×C47C22semidirect
208. #41×C47#41semidirect
227. #10625354#41direct (N × H)
301. Q8×C47C2×#41semidirect
302. Q8×C47C2×#41semidirect
303. D4×C47C2×#41semidirect
306. C2×C4×C47C2×#41semidirect
327. D188C2×#41semidirect
339. C4×D47C2×#41semidirect
372. Q8×#41D47semidirect
389. Q82C2×D47semidirect
391. #557C2×D47semidirect
396. #554C2×D47semidirect
405. D4×Q8C2×D47semidirect
415. #533C2×D47semidirect
448. C2×C4×Q8C2×D47semidirect
456. C47#412semidirect
587. #41#10625354direct (N × H)
673. Q8#41×D47semidirect
674. Q8C2×#10625354semidirect
681. D4C2×#10625354semidirect
705. C2×C4C2×#10625354semidirect

Maximal subgroups

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

subgroupindex
#202570152
#202570092
#202570082
#202569992
#202569882
#202569832
Q8×#106253542
#202569552
#202569542
D4×#106253542
#41×D1882
#202566852
C2×C4×#106253542
C4×#41×D472
Q8×#41×C472
#41247