Finite Group Databasebeta

← #27124825

Subgroups — #27124825

Order 12032.

11346 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689960C212yesmaximal, complemented
2#20257179C218yesmaximal, complemented
3#20257172C214yesmaximal, complemented
4#20257165C214yesmaximal, complemented
5#20257159C211yesmaximal, characteristic, complemented
6#20257155C212yesmaximal, complemented
7#20257151C216yesmaximal, complemented
8#20257150C216yesmaximal, complemented
9D4×#10625354C214yesmaximal, complemented
10#20256878C214yesmaximal, complemented
11#20256877C218yesmaximal, complemented
12#20256716C216yesmaximal, complemented
13#532×D47C216yesmaximal, complemented
14C2×C4×#10625354C211yesmaximal, characteristic, complemented
15C47×#3497C211yesmaximal, characteristic, complemented
16#15689960—232no—
17C2×#13094072C2212yescomplemented
18C2×#13094072C2218yescomplemented
19C2×#13094070C22112yescomplemented
20C2×#13094070C2218yescomplemented
21C22×#10625354C2211yescharacteristic
22C22×#10625354C2218yescomplemented
23C2×#41×D47C2218yescomplemented
24C2×#41×D47C22112yescomplemented
25#15689795C2214yescomplemented
26#15689792C2218yescomplemented
27Q8×D188C2214yescomplemented
28Q8×C22⋊D47C2218yescomplemented
29#15689785C2218yescomplemented
30#15689784C2218yescomplemented
31#15689780C2218yescomplemented
32#15689778C22112yescomplemented
33#15689776C22112yescomplemented
34#15689775C22124yescomplemented
35#15689770C22124yescomplemented
36#15689769C22124yescomplemented
37#15689766C22124yescomplemented
38#15689764C22124yescomplemented
39D4×D188C22112yescomplemented
40#15689758C22112yescomplemented
41#15689757C22124yescomplemented
42#15689704C2216yescomplemented
43#15689701C22112yescomplemented
44#15689696C22124yescomplemented
45#15689689C22124yescomplemented
46#15689681C22124yescomplemented
47#15689674C2216yescomplemented
48#15689673C2216yescomplemented
49#15689672C22112yescomplemented
50#15689671C2216yescomplemented
51#15689670C22112yescomplemented
52#15689670C22112yescomplemented
53#15689669C22112yescomplemented
54#15689668C2214yescomplemented
55#15689668C22112yescomplemented
56C4⋊Q8×D47C2216yescomplemented
57#127×D47C2216yescomplemented
58#124×D47C22112yescomplemented
59#15689636C22124yescomplemented
60#15689633C22124yescomplemented
61#121×D47C22112yescomplemented
62#121×D47C22112yescomplemented
63C4×#10625354C2214yescomplemented
64C4×#10625354C2214yescomplemented
65C4×#10625354C2214yescomplemented
66C4×#10625354C2214yescomplemented
67C2×Q8×Dic47C2211yescharacteristic, complemented
68C2×C4×D188C2213yescomplemented
69C2×#13093986C2213yescomplemented
70C4×D4×D47C22112yescomplemented
71C4×D4×D47C22112yescomplemented
72C2×#13093982C2213yescomplemented
73C2×C42×D47C2213yescomplemented
74C2×2−1+4×C47C2212yescomplemented
75C47×#550C2214yescomplemented
76D4×Q8×C47C2214yescomplemented
77C47×#548C2218yescomplemented
78C47×#537C2216yescomplemented
79C47×#532C2216yescomplemented
80C2×C4×Q8×C47C2211yescharacteristic, complemented
81#13094072—216no—
82#13094072—264no—
83#13094070—264no—
84#13094070—296no—
85C2×#10625354—264no—
86C2×#10625354D4116yescomplemented
87C2×#10625354C23124yes—
88C2×#10625354C2318yes—
89C2×#10625354C23112yes—
90C2×#10625354C2314yes—
91C2×#10625354C2314yes—
92C2×#10625350C23124yes—
93C2×#10625350C23112yes—
94C2×#10625350C23124yes—
95C2×#10625352C23112yes—
96C2×#10625352C2318yes—
97#41×D47—264no—
98#41×D47—296no—
99C2×Q8×D47C2318yes—
100C2×Q8×D47C23112yes—
101C22×D188C23124yes—
102C22×D188C2313yes—
103C2×D4×D47C23124yes—
104C2×D4×D47C23124yes—
105C2×D4×D47C23112yes—
106C2×D4×D47C23112yes—
107C2×D4×D47C23112yes—
108C22×C4×D47C23124yes—
109C22×C4×D47C2313yes—
110C22×C4×D47C2313yes—
111C22×C4×D47C2313yes—
112#13094024C2316yes—
113#13094023C2314yes—
114#13094023C23112yes—
115#13094022C23112yes—
116#13094021C2316yes—
117#13094020C23112yes—
118#13094020C2314yes—
119#13094020C23112yes—
120#13094013C23112yes—
121#13094012C23112yes—
122#13094011C23112yes—
123#13094010C2318yes—
124#13094010C23124yes—
125#13094009C23148yes—
126#13094006C23148yes—
127#13094004C23124yes—
128#13094003C23124yes—
129#13094000C23124yes—
130#13093999C23124yes—
131#13093999C23112yes—
132#13093999C23112yes—
133#13093998C23124yes—
134#13093998C2314yes—
135#13093998C23112yes—
136#13093997C23124yes—
137#13093997C23124yes—
138#13093996C2318yes—
139#13093996C23124yes—
140#13093995C23112yes—
141#13093995C23124yes—
142#13093995C23112yes—
143#13093994C23148yes—
144#13093992C23148yes—
145Q8×Dic47C2314yes—
146Q8×Dic47C2314yes—
147C4×D188C23112yes—
148C4×D188C23112yes—
149C4×D188C23112yes—
150C4×D188C23112yes—
151D4×Dic47C2314yes—
152D4×Dic47C23112yes—
153#13093986C23112yes—
154#13093986C23112yes—
155#13093986C2314yes—
156#13093986C23112yes—
157C4×C22⋊D47C23124yes—
158C4×C22⋊D47C23124yes—
159(C22⋊D47)⋊C4C2318yes—
160(C22⋊D47)⋊C4C23124yes—
161#13093982C23112yes—
162#13093982C23112yes—
163C2×C4⋊Dic47C2313yes—
164C4⋊C4×D47C23112yes—
165C4⋊C4×D47C23112yes—
166C2×(C2×D47)⋊C4C2316yes—
167C22⋊C4×D47C23124yes—
168C22⋊C4×D47C23124yes—
169C2×C4×Dic47C2311yescharacteristic
170C2×C4×Dic47C2313yes—
171C2×C4×Dic47C2313yes—
172C42×D47C2316yes—
173C42×D47C2316yes—
174C42×D47C2316yes—
175C42×D47C2316yes—
1762−1+4×C47—216no—
177C2×#41×C47C2318yes—
178C2×#41×C47C23112yes—
179C22×Q8×C47C2318yes—
180C22×Q8×C47C2311yescharacteristic
181C4⋊Q8×C47C2316yes—
182#127×C47C2316yes—
183#124×C47C23112yes—
184C22⋊Q8×C47C23124yes—
185#121×C47C23124yes—
186#121×C47C2314yes—
187#121×C47C23112yes—
188C4×Q8×C47C2314yes—
189C4×Q8×C47C2314yes—
190C4×D4×C47C23112yes—
191C4×D4×C47C23112yes—
192C2×C4⋊C4×C47C2313yes—
193C2×C42×C47C2313yes—
194C23×D47C24124yes—
195C23×D47C2413yes—
196#41×C47—232no—
197#41×C47—248no—
198C2×Q8×C47—232no—
199C2×Q8×C47C2×D418yescomplemented
200C2×Q8×C47C24112yes—
201C2×Q8×C47C2414yes—
202C2×D4×C47C2414yes—
203C2×D4×C47C2418yes—
204C2×D4×C47C24112yes—
205C2×D4×C47C24112yes—
206C22×C4×C47C2411yescharacteristic
207C22×C4×C47C24124yes—
208C22×C4×C47C2413yes—
209C22×C4×C47C2413yes—
210C2×C22⋊D47C2418yes—
211C2×C22⋊D47C24124yes—
212C2×C22⋊D47C2418yes—
213C2×C22⋊D47C2418yes—
214C2×C22⋊D47C24124yes—
215C22×Dic47C2411yescharacteristic
216C22×Dic47C2418yes—
217C22×Dic47C2413yes—
218C22×Dic47C2411yescharacteristic
219#10625354—232no—
220#10625354—296no—
221#10625354—248no—
222#10625354C2×D4132yescomplemented
223#10625354C2×D4132yescomplemented
224Q8×D47—232no—
225Q8×D47—248no—
226#10625352—232no—
227#10625352—248no—
228D4×D47—296no—
229D4×D47—296no—
230D4×D47—248no—
231D4×D47—424no—
232D4×D47—424no—
233#10625350—248no—
234#10625350—296no—
235#10625350—296no—
236C2×D188—296no—
237C2×D188C2×D4124yescomplemented
238C2×D188C2414yes—
239C2×D188C24124yes—
240C2×D188C24112yes—
241C2×D188C24112yes—
242C2×D188C24112yes—
243C2×C4×D47—296no—
244C2×C4×D47—46no—
245C2×C4×D47—46no—
246C2×C4×D47C2×D4124yescomplemented
247C2×C4×D47C2416yes—
248C2×C4×D47C2416yes—
249C2×C4×D47C24124yes—
250C2×C4×D47C2418yes—
251C2×C4×D47C24124yes—
252C2×C4×D47C2416yes—
253C2×C4×D47C2416yes—
254C2×C4×D47C2416yes—
255C2×C4×D47C2416yes—
256C2×Dic94C24112yes—
257C2×Dic94C2418yes—
258C4⋊C4×C47C24112yes—
259C4⋊C4×C47C2414yes—
260C4⋊C4×C47C24112yes—
261C22⋊C4×C47C2418yes—
262C22⋊C4×C47C24124yes—
263C42×C47C2416yes—
264C42×C47C2416yes—
265C22⋊Dic47C2418yes—
266C22⋊Dic47C24124yes—
267(C2×D47)⋊C4C2418yes—
268(C2×D47)⋊C4C2418yes—
269(C2×D47)⋊C4C24124yes—
270(C2×D47)⋊C4C24124yes—
271(C2×D47)⋊C4C24124yes—
272C4⋊Dic47C2414yes—
273C4⋊Dic47C24112yes—
274C4⋊Dic47C24112yes—
275Dic47⋊C4C2418yes—
276Dic47⋊C4C24124yes—
277C4×Dic47C2411yescharacteristic
278C4×Dic47C2411yescharacteristic
279C4×Dic47C2411yescharacteristic
280C4×Dic47C2411yescharacteristic
281C4×Dic47C2416yes—
282C4×Dic47C2416yes—
283C4×Dic47C2416yes—
284C4×Dic47C2416yes—
285C23×C47C2518yes—
286C23×C47C2511yescharacteristic
287C22×D47—248no—
288C22×D47—43no—
289C22×D47—43no—
290C22×D47—424no—
291C22×D47—424no—
292C22×D47C22×D4112yes—
293C22×D47C2518yes—
294C22×D47C2516yes—
295Q8×C47—224no—
296Q8×C47C22×D4116yes—
297D4×C47—216no—
298D4×C47—224no—
299D4×C47—28no—
300D4×C47—412no—
301C2×C4×C47—248no—
302C2×C4×C47—22no—
303C2×C4×C47—43no—
304C2×C4×C47C22×D4112yes—
305C2×C4×C47C2516yes—
306C2×C4×C47C2511yescharacteristic
307C2×C4×C47C2518yes—
308C2×C4×C47C2516yes—
309C2×C4×C47C2511yescharacteristic
310C22⋊D47—216no—
311C22⋊D47—248no—
312C22⋊D47—216no—
313C22⋊D47—216no—
314C22⋊D47—424no—
315C2×Dic47—216no—
316C2×Dic47—22no—
317C2×Dic47—43no—
318C2×Dic47C22×D414yes—
319C2×Dic47C2511yescharacteristic
320C2×Dic47C2516yes—
321C2×Dic47C2518yes—
322C2×Dic47C2511yescharacteristic
323C2×Dic47C2511yescharacteristic
324C2×Dic47C2511yescharacteristic
325D188—248no—
326D188—224no—
327D188—28no—
328D188—412no—
329D188C22×D4148yes—
330C4×D47—248no—
331C4×D47—248no—
332C4×D47—212no—
333C4×D47—216no—
334C4×D47—212no—
335C4×D47—46no—
336C4×D47—46no—
337C4×D47C22×D4124yes—
338C4×D47C22×D4124yes—
339Dic94—224no—
340Dic94—216no—
341#62812—471nomaximal, Sylow
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—28no—
345C22×C47—28no—
346C22×C47—28no—
347C22×C47C23×D412yes—
348C22×C47C2611yescharacteristic
349C2×D47—26no—
350C2×D47—26no—
351C2×D47—28no—
352C2×D47—28no—
353C2×D47—28no—
354C2×D47—412no—
355C2×D47—848no—
356C2×D47C23×D4112yes—
357C4×C47—28no—
358C4×C47—26no—
359C4×C47—21no—
360C4×C47C23×D4112yes—
361C4×C47#58512yescomplemented
362Dic47—28no—
363Dic47—26no—
364Dic47—21no—
365Dic47C23×D412yes—
366Dic47C23×D412yes—
367Dic47#58512yescomplemented
368C2×#585—472no—
369#3500—478no—
370#3499—474no—
371#3498—474no—
372#3497—472no—
373#3497—471no—
374#3497D4711yescharacteristic, complemented
375#3496—476no—
376#3496—476no—
377D4×#41—474no—
378D4×#41—474no—
379D4×#41—478no—
380#3449—476no—
381C2×#532—476no—
382C2×C4×#41—471no—
383C2×C47—22no—
384C2×C47—48no—
385C2×C47C24×D411yescharacteristic
386C2×C47C2×#58511yescharacteristic
387C2×C47C2×#58511yescharacteristic
388D47—212no—
389D47—48no—
390#585—9432no—
391C2×2−1+4—472no—
392C2×2−1+4—478no—
393C2×2−1+4C2×D4712yescomplemented
394C2×H(5,𝔽2)—4712no—
395C2×H(5,𝔽2)—478no—
396C22×#41—4712no—
397C22×#41—478no—
398C22×#41—471no—
399C22×#41—478no—
400#550—478no—
401#550—474no—
402#550C2×D4714yescomplemented
403D4×Q8—478no—
404D4×Q8—474no—
405D4×Q8C2×D4714yescomplemented
406#548—478no—
407#548—478no—
408#548—478no—
409#548C2×D4718yescomplemented
410#547—4712no—
411#547—4724no—
412#547—4712no—
413#546—4724no—
414#546—4724no—
415#546—4724no—
416#546—4724no—
417D42—4712no—
418D42—4724no—
419D42—4712no—
420#537—4712no—
421#537—476no—
422#537C2×D4716yescomplemented
423#536—4724no—
424#535—4724no—
425#534—4724no—
426#532—4712no—
427#532—476no—
428#532—476no—
429#532—4712no—
430#532—474no—
431#532—4712no—
432#532—4712no—
433#532—4712no—
434#532—476no—
435#532C2×D4716yescomplemented
436C2×C4⋊Q8—476no—
437C2×#127—476no—
438C2×#124—4712no—
439#525—4724no—
440#525—4724no—
441C2×#121—4712no—
442C2×#121—4712no—
443C4×#41—474no—
444C4×#41—474no—
445C4×#41—474no—
446C4×#41—474no—
447C2×C4×Q8—471no—
448C2×C4×Q8C2×D4711yescharacteristic, complemented
449C2×C4×D4—4712no—
450C2×C4×D4—4712no—
451C2×C4×D4—473no—
452C2×C4×D4—473no—
453C2×#117—473no—
454C22×C42—473no—
455C47#6281211yescharacteristic, complemented, Sylow
4562−1+4—216no—
4572−1+4—9464no—
4582−1+4—9416no—
459H(5,𝔽2)—9496no—
460H(5,𝔽2)—9464no—
461C2×#41—4716no—
462C2×#41—474no—
463C2×#41—474no—
464C2×#41—4712no—
465C2×#41—4724no—
466C2×#41—478no—
467C2×#41—4712no—
468C2×#41—478no—
469C2×#41—4724no—
470C2×#41—4712no—
471C2×#41—4724no—
472C2×#41—9496no—
473C2×#41—9464no—
474C2×#41—9464no—
475C2×#41C22×D47112yes—
476C2×#41C22×D4718yes—
477C22×Q8—4712no—
478C22×Q8—478no—
479C22×Q8C22×D4718yes—
480C22×Q8C22×D4711yescharacteristic
481C22×D4—4724no—
482C22×D4—4712no—
483C22×D4—4724no—
484C22×D4—4712no—
485C22×D4—4712no—
486C22×D4—473no—
487C22×D4—4724no—
488C23×C4—473no—
489C23×C4—4724no—
490C23×C4—473no—
491C23×C4—473no—
492C4⋊Q8—4712no—
493C4⋊Q8—474no—
494C4⋊Q8—4712no—
495C4⋊Q8—476no—
496C4⋊Q8C22×D4716yes—
497#127—474no—
498#127—4712no—
499#127—4712no—
500#127—476no—
501#127C22×D4716yes—
502#124—4712no—
503#124—4712no—
504#124—478no—
505#124—4724no—
506#124—4712no—
507#124C22×D47112yes—
508#123—4748no—
509#123—4748no—
510C22⋊Q8—4724no—
511C22⋊Q8—4724no—
512C22⋊Q8—4724no—
513C22⋊Q8C22×D47124yes—
514#121—478no—
515#121—4724no—
516#121—4712no—
517#121—4712no—
518#121—4724no—
519#121—474no—
520#121—4712no—
521#121—4724no—
522#121—4712no—
523#121—4712no—
524#121—4724no—
525#121—4724no—
526#121—4724no—
527#121C22×D4714yes—
528#121C22×D47112yes—
529#121C22×D47124yes—
530#120—4748no—
531#120—4748no—
532C4×Q8—474no—
533C4×Q8—474no—
534C4×Q8C22×D4714yes—
535C4×Q8C22×D4714yes—
536C4×D4—474no—
537C4×D4—4712no—
538C4×D4—4724no—
539C4×D4—4724no—
540C4×D4—474no—
541C4×D4—4712no—
542C4×D4—4712no—
543C4×D4—4712no—
544C4×D4—478no—
545C4×D4—4724no—
546C4×D4—4712no—
547C4×D4—4712no—
548C4×D4—4712no—
549C4×D4—4712no—
550C4×D4C22×D47112yes—
551C4×D4C22×D47112yes—
552#117—4712no—
553#117—4712no—
554C2×C4⋊C4—473no—
555C2×C4⋊C4—4712no—
556C2×C4⋊C4—4712no—
557C2×C4⋊C4C22×D4713yes—
558C2×C22⋊C4—476no—
559C2×C22⋊C4—4724no—
560C2×C22⋊C4—4724no—
561C2×C42—473no—
562C2×C42—473no—
563C2×C42—471no—
564C2×C42—476no—
565C2×C42—476no—
566C2×C42—476no—
567C2×C42—476no—
568C2×C42C22×D4713yes—
569C24—473no—
570C24—4724no—
571#41—232no—
572#41—248no—
573#41—4732no—
574#41—4732no—
575#41—9496no—
576#41—9496no—
577#41—9432no—
578#41—9448no—
579#41—9448no—
580#41—9496no—
581#41—9432no—
582#41—9448no—
583C2×Q8—232no—
584C2×Q8—4712no—
585C2×Q8—478no—
586C2×Q8—9448no—
587C2×Q8—9432no—
588C2×Q8D4×D4718yescomplemented
589C2×Q8C23×D47112yes—
590C2×Q8C23×D4714yes—
591C2×D4—478no—
592C2×D4—4724no—
593C2×D4—478no—
594C2×D4—478no—
595C2×D4—4724no—
596C2×D4—4724no—
597C2×D4—4712no—
598C2×D4—474no—
599C2×D4—4724no—
600C2×D4—4712no—
601C2×D4—4712no—
602C2×D4—9496no—
603C2×D4—9448no—
604C2×D4—9496no—
605C2×D4—9496no—
606C2×D4—18824no—
607C2×D4—18824no—
608C2×D4C23×D4714yes—
609C2×D4C23×D4718yes—
610C2×D4C23×D47112yes—
611C2×D4C23×D47112yes—
612C22×C4—471no—
613C22×C4—4724no—
614C22×C4—476no—
615C22×C4—476no—
616C22×C4—471no—
617C22×C4—478no—
618C22×C4—473no—
619C22×C4—476no—
620C22×C4—476no—
621C22×C4—4724no—
622C22×C4—478no—
623C22×C4—4724no—
624C22×C4—476no—
625C22×C4—476no—
626C22×C4—9496no—
627C22×C4—1886no—
628C22×C4—1886no—
629C22×C4C23×D4711yescharacteristic
630C22×C4C23×D47124yes—
631C22×C4C23×D4713yes—
632C22×C4C23×D4713yes—
633C4⋊C4—478no—
634C4⋊C4—4724no—
635C4⋊C4—474no—
636C4⋊C4—4712no—
637C4⋊C4—4712no—
638C4⋊C4C23×D4714yes—
639C4⋊C4C23×D47112yes—
640C4⋊C4C23×D47112yes—
641C22⋊C4—478no—
642C22⋊C4—4724no—
643C22⋊C4—478no—
644C22⋊C4—478no—
645C22⋊C4—4724no—
646C22⋊C4—4724no—
647C22⋊C4—4724no—
648C22⋊C4C23×D4718yes—
649C22⋊C4C23×D47124yes—
650C42—471no—
651C42—471no—
652C42—471no—
653C42—471no—
654C42—476no—
655C42—476no—
656C42—476no—
657C42—476no—
658C42C23×D4716yes—
659C42C23×D4716yes—
660C23—476no—
661C23—4712no—
662C23—478no—
663C23—9448no—
664C23—18824no—
665C23—18824no—
666C23—1883no—
667C23—1883no—
668C23C24×D4718yes—
669C23C24×D4711yescharacteristic
670Q8—224no—
671Q8—9416no—
672Q8—9424no—
673Q8C2×D4×D47116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—4748no—
679D4—9448no—
680D4—9416no—
681D4—9416no—
682D4—9448no—
683D4—9416no—
684D4—9424no—
685D4—948no—
686D4—18812no—
687D4—18824no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—474no—
692C2×C4—471no—
693C2×C4—471no—
694C2×C4—471no—
695C2×C4—4724no—
696C2×C4—4724no—
697C2×C4—471no—
698C2×C4—476no—
699C2×C4—478no—
700C2×C4—9416no—
701C2×C4—9412no—
702C2×C4—9448no—
703C2×C4—9416no—
704C2×C4—942no—
705C2×C4—9448no—
706C2×C4—9412no—
707C2×C4—1886no—
708C2×C4—1886no—
709C2×C4—1883no—
710C2×C4C2×D4×D47112yes—
711C2×C4C24×D4711yescharacteristic
712C2×C4C24×D4716yes—
713C2×C4C24×D4718yes—
714C2×C4C24×D4716yes—
715C2×C4C24×D4711yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—4712no—
722C22—946no—
723C22—946no—
724C22—948no—
725C22—948no—
726C22—948no—
727C22—37648no—
728C22—18812no—
729C22C22×D4×D4712yes—
730C22C25×D4711yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—472no—
735C4—472no—
736C4—472no—
737C4—948no—
738C4—941no—
739C4—946no—
740C4C22×D4×D47112yes—
741C4#1568996012yescomplemented
742C2—22no—
743C2—48no—
744C2—9412no—
745C2—1888no—
746C2C23×D4×D4711yescharacteristic
747C2#585×D4711yescharacteristic
748C2C2×#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3497C2
hypercenter#3497D47
hypocenterC47#62812
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#15689960C2semidirect
2. #20257179C2semidirect
3. #20257172C2semidirect
4. #20257165C2semidirect
5. #20257159C2semidirect
6. #20257155C2semidirect
7. #20257151C2semidirect
8. #20257150C2semidirect
9. D4×#10625354C2semidirect
10. #20256878C2semidirect
11. #20256877C2semidirect
12. #20256716C2semidirect
13. #532×D47C2semidirect
14. C2×C4×#10625354C2semidirect
15. C47×#3497C2semidirect
17. C2×#13094072C22semidirect
18. C2×#13094072C22semidirect
19. C2×#13094070C22semidirect
20. C2×#13094070C22semidirect
22. C22×#10625354C22semidirect
23. C2×#41×D47C22semidirect
24. C2×#41×D47C22semidirect
25. #15689795C22semidirect
26. #15689792C22semidirect
27. Q8×D188C22semidirect
28. Q8×C22⋊D47C22semidirect
29. #15689785C22semidirect
30. #15689784C22semidirect
31. #15689780C22semidirect
32. #15689778C22semidirect
33. #15689776C22semidirect
34. #15689775C22semidirect
35. #15689770C22semidirect
36. #15689769C22semidirect
37. #15689766C22semidirect
38. #15689764C22semidirect
39. D4×D188C22semidirect
40. #15689758C22semidirect
41. #15689757C22semidirect
42. #15689704C22semidirect
43. #15689701C22semidirect
44. #15689696C22semidirect
45. #15689689C22semidirect
46. #15689681C22semidirect
47. #15689674C22semidirect
48. #15689673C22semidirect
49. #15689672C22semidirect
50. #15689671C22semidirect
51. #15689670C22semidirect
52. #15689670C22semidirect
53. #15689669C22semidirect
54. #15689668C22semidirect
55. #15689668C22semidirect
56. C4⋊Q8×D47C22semidirect
57. #127×D47C22semidirect
58. #124×D47C22semidirect
59. #15689636C22semidirect
60. #15689633C22semidirect
61. #121×D47C22semidirect
62. #121×D47C22semidirect
63. C4×#10625354C22semidirect
64. C4×#10625354C22semidirect
65. C4×#10625354C22semidirect
66. C4×#10625354C22semidirect
67. C2×Q8×Dic47C22semidirect
68. C2×C4×D188C22semidirect
69. C2×#13093986C22semidirect
70. C4×D4×D47C22semidirect
71. C4×D4×D47C22semidirect
72. C2×#13093982C22semidirect
73. C2×C42×D47C22semidirect
74. C2×2−1+4×C47C22semidirect
75. C47×#550C22semidirect
76. D4×Q8×C47C22semidirect
77. C47×#548C22semidirect
78. C47×#537C22semidirect
79. C47×#532C22semidirect
80. C2×C4×Q8×C47C22semidirect
86. C2×#10625354D4semidirect
199. C2×Q8×C47C2×D4semidirect
222. #10625354C2×D4semidirect
223. #10625354C2×D4semidirect
237. C2×D188C2×D4semidirect
246. C2×C4×D47C2×D4semidirect
361. C4×C47#585semidirect
367. Dic47#585semidirect
374. #3497D47semidirect
393. C2×2−1+4C2×D47semidirect
402. #550C2×D47semidirect
405. D4×Q8C2×D47semidirect
409. #548C2×D47semidirect
422. #537C2×D47semidirect
435. #532C2×D47semidirect
448. C2×C4×Q8C2×D47semidirect
455. C47#62812semidirect
588. C2×Q8D4×D47semidirect
741. C4#15689960semidirect

Maximal subgroups

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

subgroupindex
C2×#156899602
#202571792
#202571722
#202571652
#202571592
#202571552
#202571512
#202571502
D4×#106253542
#202568782
#202568772
#202567162
#532×D472
C2×C4×#106253542
C47×#34972
#6281247