Finite Group Databasebeta

← #26005144

Subgroups — #26005144

Order 11008.

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×#14583736C212yesmaximal, complemented
2#19148386C218yesmaximal, complemented
3#19148379C214yesmaximal, complemented
4#19148372C214yesmaximal, complemented
5#19148366C211yesmaximal, characteristic, complemented
6#19148362C212yesmaximal, complemented
7#19148358C216yesmaximal, complemented
8#19148357C216yesmaximal, complemented
9D4×#10621902C214yesmaximal, complemented
10#19148085C214yesmaximal, complemented
11#19148084C218yesmaximal, complemented
12#19147923C216yesmaximal, complemented
13#532×D43C216yesmaximal, complemented
14C2×C4×#10621902C211yesmaximal, characteristic, complemented
15C43×#3497C211yesmaximal, characteristic, complemented
16#14583736—232no—
17C2×#13063373C2212yescomplemented
18C2×#13063373C2218yescomplemented
19C2×#13063371C22112yescomplemented
20C2×#13063371C2218yescomplemented
21C22×#10621902C2211yescharacteristic
22C22×#10621902C2218yescomplemented
23C2×#41×D43C2218yescomplemented
24C2×#41×D43C22112yescomplemented
25#14583571C2214yescomplemented
26#14583568C2218yescomplemented
27Q8×D172C2214yescomplemented
28Q8×C22⋊D43C2218yescomplemented
29#14583561C2218yescomplemented
30#14583560C2218yescomplemented
31#14583556C2218yescomplemented
32#14583554C22112yescomplemented
33#14583552C22112yescomplemented
34#14583551C22124yescomplemented
35#14583546C22124yescomplemented
36#14583545C22124yescomplemented
37#14583542C22124yescomplemented
38#14583540C22124yescomplemented
39D4×D172C22112yescomplemented
40#14583534C22112yescomplemented
41#14583533C22124yescomplemented
42#14583480C2216yescomplemented
43#14583477C22112yescomplemented
44#14583472C22124yescomplemented
45#14583465C22124yescomplemented
46#14583457C22124yescomplemented
47#14583450C2216yescomplemented
48#14583449C2216yescomplemented
49#14583448C22112yescomplemented
50#14583447C2216yescomplemented
51#14583446C22112yescomplemented
52#14583446C22112yescomplemented
53#14583445C22112yescomplemented
54#14583444C2214yescomplemented
55#14583444C22112yescomplemented
56C4⋊Q8×D43C2216yescomplemented
57#127×D43C2216yescomplemented
58#124×D43C22112yescomplemented
59#14583412C22124yescomplemented
60#14583409C22124yescomplemented
61#121×D43C22112yescomplemented
62#121×D43C22112yescomplemented
63C4×#10621902C2214yescomplemented
64C4×#10621902C2214yescomplemented
65C4×#10621902C2214yescomplemented
66C4×#10621902C2214yescomplemented
67C2×Q8×Dic43C2211yescharacteristic, complemented
68C2×C4×D172C2213yescomplemented
69C2×#13063287C2213yescomplemented
70C4×D4×D43C22112yescomplemented
71C4×D4×D43C22112yescomplemented
72C2×#13063283C2213yescomplemented
73C2×C42×D43C2213yescomplemented
74C2×2−1+4×C43C2212yescomplemented
75C43×#550C2214yescomplemented
76D4×Q8×C43C2214yescomplemented
77C43×#548C2218yescomplemented
78C43×#537C2216yescomplemented
79C43×#532C2216yescomplemented
80C2×C4×Q8×C43C2211yescharacteristic, complemented
81#13063373—216no—
82#13063373—264no—
83#13063371—264no—
84#13063371—296no—
85C2×#10621902—264no—
86C2×#10621902D4116yescomplemented
87C2×#10621902C23124yes—
88C2×#10621902C2318yes—
89C2×#10621902C23112yes—
90C2×#10621902C2314yes—
91C2×#10621902C2314yes—
92C2×#10621898C23124yes—
93C2×#10621898C23112yes—
94C2×#10621898C23124yes—
95C2×#10621900C23112yes—
96C2×#10621900C2318yes—
97#41×D43—264no—
98#41×D43—296no—
99C2×Q8×D43C2318yes—
100C2×Q8×D43C23112yes—
101C22×D172C23124yes—
102C22×D172C2313yes—
103C2×D4×D43C23124yes—
104C2×D4×D43C23112yes—
105C2×D4×D43C23124yes—
106C2×D4×D43C23112yes—
107C2×D4×D43C23112yes—
108C22×C4×D43C23124yes—
109C22×C4×D43C2313yes—
110C22×C4×D43C2313yes—
111C22×C4×D43C2313yes—
112#13063325C2316yes—
113#13063324C2314yes—
114#13063324C23112yes—
115#13063323C23112yes—
116#13063322C2316yes—
117#13063321C23112yes—
118#13063321C2314yes—
119#13063321C23112yes—
120#13063314C23112yes—
121#13063313C23112yes—
122#13063312C23112yes—
123#13063311C2318yes—
124#13063311C23124yes—
125#13063310C23148yes—
126#13063307C23148yes—
127#13063305C23124yes—
128#13063304C23124yes—
129#13063301C23124yes—
130#13063300C23112yes—
131#13063300C23124yes—
132#13063300C23112yes—
133#13063299C23124yes—
134#13063299C2314yes—
135#13063299C23112yes—
136#13063298C23124yes—
137#13063298C23124yes—
138#13063297C2318yes—
139#13063297C23124yes—
140#13063296C23112yes—
141#13063296C23124yes—
142#13063296C23112yes—
143#13063295C23148yes—
144#13063293C23148yes—
145Q8×Dic43C2314yes—
146Q8×Dic43C2314yes—
147C4×D172C23112yes—
148C4×D172C23112yes—
149C4×D172C23112yes—
150C4×D172C23112yes—
151D4×Dic43C2314yes—
152D4×Dic43C23112yes—
153#13063287C2314yes—
154#13063287C23112yes—
155#13063287C23112yes—
156#13063287C23112yes—
157C4×C22⋊D43C23124yes—
158C4×C22⋊D43C23124yes—
159(C22⋊D43)⋊C4C2318yes—
160(C22⋊D43)⋊C4C23124yes—
161#13063283C23112yes—
162#13063283C23112yes—
163C2×C4⋊Dic43C2313yes—
164C4⋊C4×D43C23112yes—
165C4⋊C4×D43C23112yes—
166C2×(C2×D43)⋊C4C2316yes—
167C22⋊C4×D43C23124yes—
168C22⋊C4×D43C23124yes—
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2313yes—
171C2×C4×Dic43C2313yes—
172C42×D43C2316yes—
173C42×D43C2316yes—
174C42×D43C2316yes—
175C42×D43C2316yes—
1762−1+4×C43—216no—
177C2×#41×C43C2318yes—
178C2×#41×C43C23112yes—
179C22×Q8×C43C2318yes—
180C22×Q8×C43C2311yescharacteristic
181C4⋊Q8×C43C2316yes—
182#127×C43C2316yes—
183#124×C43C23112yes—
184C22⋊Q8×C43C23124yes—
185#121×C43C2314yes—
186#121×C43C23112yes—
187#121×C43C23124yes—
188C4×Q8×C43C2314yes—
189C4×Q8×C43C2314yes—
190C4×D4×C43C23112yes—
191C4×D4×C43C23112yes—
192C2×C4⋊C4×C43C2313yes—
193C2×C42×C43C2313yes—
194C23×D43C24124yes—
195C23×D43C2413yes—
196#41×C43—232no—
197#41×C43—248no—
198C2×Q8×C43—232no—
199C2×Q8×C43C2×D418yescomplemented
200C2×Q8×C43C24112yes—
201C2×Q8×C43C2414yes—
202C2×D4×C43C2414yes—
203C2×D4×C43C2418yes—
204C2×D4×C43C24112yes—
205C2×D4×C43C24112yes—
206C22×C4×C43C2411yescharacteristic
207C22×C4×C43C24124yes—
208C22×C4×C43C2413yes—
209C22×C4×C43C2413yes—
210C2×C22⋊D43C2418yes—
211C2×C22⋊D43C24124yes—
212C2×C22⋊D43C2418yes—
213C2×C22⋊D43C2418yes—
214C2×C22⋊D43C24124yes—
215C22×Dic43C2411yescharacteristic
216C22×Dic43C2418yes—
217C22×Dic43C2413yes—
218C22×Dic43C2411yescharacteristic
219#10621902—232no—
220#10621902—296no—
221#10621902—248no—
222#10621902C2×D4132yescomplemented
223#10621902C2×D4132yescomplemented
224Q8×D43—232no—
225Q8×D43—248no—
226#10621900—232no—
227#10621900—248no—
228D4×D43—296no—
229D4×D43—248no—
230D4×D43—296no—
231D4×D43—424no—
232D4×D43—424no—
233#10621898—248no—
234#10621898—296no—
235#10621898—296no—
236C2×D172—296no—
237C2×D172C2×D4124yescomplemented
238C2×D172C2414yes—
239C2×D172C24124yes—
240C2×D172C24112yes—
241C2×D172C24112yes—
242C2×D172C24112yes—
243C2×C4×D43—296no—
244C2×C4×D43—46no—
245C2×C4×D43—46no—
246C2×C4×D43C2×D4124yescomplemented
247C2×C4×D43C2416yes—
248C2×C4×D43C2416yes—
249C2×C4×D43C24124yes—
250C2×C4×D43C2418yes—
251C2×C4×D43C24124yes—
252C2×C4×D43C2416yes—
253C2×C4×D43C2416yes—
254C2×C4×D43C2416yes—
255C2×C4×D43C2416yes—
256C2×Dic86C24112yes—
257C2×Dic86C2418yes—
258C4⋊C4×C43C24112yes—
259C4⋊C4×C43C2414yes—
260C4⋊C4×C43C24112yes—
261C22⋊C4×C43C2418yes—
262C22⋊C4×C43C24124yes—
263C42×C43C2416yes—
264C42×C43C2416yes—
265C22⋊Dic43C2418yes—
266C22⋊Dic43C24124yes—
267(C2×D43)⋊C4C2418yes—
268(C2×D43)⋊C4C2418yes—
269(C2×D43)⋊C4C24124yes—
270(C2×D43)⋊C4C24124yes—
271(C2×D43)⋊C4C24124yes—
272C4⋊Dic43C2414yes—
273C4⋊Dic43C24112yes—
274C4⋊Dic43C24112yes—
275Dic43⋊C4C2418yes—
276Dic43⋊C4C24124yes—
277C4×Dic43C2411yescharacteristic
278C4×Dic43C2411yescharacteristic
279C4×Dic43C2411yescharacteristic
280C4×Dic43C2411yescharacteristic
281C4×Dic43C2416yes—
282C4×Dic43C2416yes—
283C4×Dic43C2416yes—
284C4×Dic43C2416yes—
285C23×C43C2518yes—
286C23×C43C2511yescharacteristic
287C22×D43—248no—
288C22×D43—43no—
289C22×D43—43no—
290C22×D43—424no—
291C22×D43—424no—
292C22×D43C22×D4112yes—
293C22×D43C2518yes—
294C22×D43C2516yes—
295Q8×C43—224no—
296Q8×C43C22×D4116yes—
297D4×C43—216no—
298D4×C43—224no—
299D4×C43—28no—
300D4×C43—412no—
301C2×C4×C43—248no—
302C2×C4×C43—22no—
303C2×C4×C43—43no—
304C2×C4×C43C22×D4112yes—
305C2×C4×C43C2516yes—
306C2×C4×C43C2511yescharacteristic
307C2×C4×C43C2518yes—
308C2×C4×C43C2516yes—
309C2×C4×C43C2511yescharacteristic
310C22⋊D43—216no—
311C22⋊D43—248no—
312C22⋊D43—216no—
313C22⋊D43—216no—
314C22⋊D43—424no—
315C2×Dic43—216no—
316C2×Dic43—22no—
317C2×Dic43—43no—
318C2×Dic43C22×D414yes—
319C2×Dic43C2511yescharacteristic
320C2×Dic43C2516yes—
321C2×Dic43C2518yes—
322C2×Dic43C2511yescharacteristic
323C2×Dic43C2511yescharacteristic
324C2×Dic43C2511yescharacteristic
325D172—248no—
326D172—224no—
327D172—28no—
328D172—412no—
329D172C22×D4148yes—
330C4×D43—248no—
331C4×D43—248no—
332C4×D43—212no—
333C4×D43—216no—
334C4×D43—212no—
335C4×D43—46no—
336C4×D43—46no—
337C4×D43C22×D4124yes—
338C4×D43C22×D4124yes—
339Dic86—224no—
340Dic86—216no—
341#62812—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—28no—
345C22×C43—28no—
346C22×C43—28no—
347C22×C43C23×D412yes—
348C22×C43C2611yescharacteristic
349C2×D43—26no—
350C2×D43—26no—
351C2×D43—28no—
352C2×D43—28no—
353C2×D43—28no—
354C2×D43—412no—
355C2×D43—848no—
356C2×D43C23×D4112yes—
357C4×C43—28no—
358C4×C43—26no—
359C4×C43—21no—
360C4×C43C23×D4112yes—
361C4×C43#58512yescomplemented
362Dic43—28no—
363Dic43—26no—
364Dic43—21no—
365Dic43C23×D412yes—
366Dic43C23×D412yes—
367Dic43#58512yescomplemented
368C2×#585—432no—
369#3500—438no—
370#3499—434no—
371#3498—434no—
372#3497—432no—
373#3497—431no—
374#3497D4311yescharacteristic, complemented
375#3496—436no—
376#3496—436no—
377D4×#41—434no—
378D4×#41—434no—
379D4×#41—438no—
380#3449—436no—
381C2×#532—436no—
382C2×C4×#41—431no—
383C2×C43—22no—
384C2×C43—48no—
385C2×C43C24×D411yescharacteristic
386C2×C43C2×#58511yescharacteristic
387C2×C43C2×#58511yescharacteristic
388D43—212no—
389D43—48no—
390#585—8632no—
391C2×2−1+4—432no—
392C2×2−1+4—438no—
393C2×2−1+4C2×D4312yescomplemented
394C2×H(5,𝔽2)—4312no—
395C2×H(5,𝔽2)—438no—
396C22×#41—4312no—
397C22×#41—438no—
398C22×#41—431no—
399C22×#41—438no—
400#550—438no—
401#550—434no—
402#550C2×D4314yescomplemented
403D4×Q8—438no—
404D4×Q8—434no—
405D4×Q8C2×D4314yescomplemented
406#548—438no—
407#548—438no—
408#548—438no—
409#548C2×D4318yescomplemented
410#547—4312no—
411#547—4324no—
412#547—4312no—
413#546—4324no—
414#546—4324no—
415#546—4324no—
416#546—4324no—
417D42—4312no—
418D42—4324no—
419D42—4312no—
420#537—4312no—
421#537—436no—
422#537C2×D4316yescomplemented
423#536—4324no—
424#535—4324no—
425#534—4324no—
426#532—4312no—
427#532—436no—
428#532—436no—
429#532—4312no—
430#532—434no—
431#532—4312no—
432#532—4312no—
433#532—4312no—
434#532—436no—
435#532C2×D4316yescomplemented
436C2×C4⋊Q8—436no—
437C2×#127—436no—
438C2×#124—4312no—
439#525—4324no—
440#525—4324no—
441C2×#121—4312no—
442C2×#121—4312no—
443C4×#41—434no—
444C4×#41—434no—
445C4×#41—434no—
446C4×#41—434no—
447C2×C4×Q8—431no—
448C2×C4×Q8C2×D4311yescharacteristic, complemented
449C2×C4×D4—4312no—
450C2×C4×D4—4312no—
451C2×C4×D4—433no—
452C2×C4×D4—433no—
453C2×#117—433no—
454C22×C42—433no—
455C43#6281211yescharacteristic, complemented, Sylow
4562−1+4—216no—
4572−1+4—8664no—
4582−1+4—8616no—
459H(5,𝔽2)—8696no—
460H(5,𝔽2)—8664no—
461C2×#41—4316no—
462C2×#41—434no—
463C2×#41—434no—
464C2×#41—4312no—
465C2×#41—4324no—
466C2×#41—438no—
467C2×#41—4312no—
468C2×#41—438no—
469C2×#41—4324no—
470C2×#41—4312no—
471C2×#41—4324no—
472C2×#41—8696no—
473C2×#41—8664no—
474C2×#41—8664no—
475C2×#41C22×D43112yes—
476C2×#41C22×D4318yes—
477C22×Q8—4312no—
478C22×Q8—438no—
479C22×Q8C22×D4318yes—
480C22×Q8C22×D4311yescharacteristic
481C22×D4—4324no—
482C22×D4—4312no—
483C22×D4—4324no—
484C22×D4—4312no—
485C22×D4—4312no—
486C22×D4—433no—
487C22×D4—4324no—
488C23×C4—433no—
489C23×C4—4324no—
490C23×C4—433no—
491C23×C4—433no—
492C4⋊Q8—4312no—
493C4⋊Q8—434no—
494C4⋊Q8—4312no—
495C4⋊Q8—436no—
496C4⋊Q8C22×D4316yes—
497#127—434no—
498#127—4312no—
499#127—4312no—
500#127—436no—
501#127C22×D4316yes—
502#124—4312no—
503#124—4312no—
504#124—438no—
505#124—4324no—
506#124—4312no—
507#124C22×D43112yes—
508#123—4348no—
509#123—4348no—
510C22⋊Q8—4324no—
511C22⋊Q8—4324no—
512C22⋊Q8—4324no—
513C22⋊Q8C22×D43124yes—
514#121—438no—
515#121—4324no—
516#121—4312no—
517#121—4312no—
518#121—4324no—
519#121—434no—
520#121—4312no—
521#121—4324no—
522#121—4312no—
523#121—4312no—
524#121—4324no—
525#121—4324no—
526#121—4324no—
527#121C22×D4314yes—
528#121C22×D43112yes—
529#121C22×D43124yes—
530#120—4348no—
531#120—4348no—
532C4×Q8—434no—
533C4×Q8—434no—
534C4×Q8C22×D4314yes—
535C4×Q8C22×D4314yes—
536C4×D4—434no—
537C4×D4—4312no—
538C4×D4—4324no—
539C4×D4—4324no—
540C4×D4—434no—
541C4×D4—4312no—
542C4×D4—4312no—
543C4×D4—4312no—
544C4×D4—438no—
545C4×D4—4324no—
546C4×D4—4312no—
547C4×D4—4312no—
548C4×D4—4312no—
549C4×D4—4312no—
550C4×D4C22×D43112yes—
551C4×D4C22×D43112yes—
552#117—4312no—
553#117—4312no—
554C2×C4⋊C4—433no—
555C2×C4⋊C4—4312no—
556C2×C4⋊C4—4312no—
557C2×C4⋊C4C22×D4313yes—
558C2×C22⋊C4—436no—
559C2×C22⋊C4—4324no—
560C2×C22⋊C4—4324no—
561C2×C42—433no—
562C2×C42—433no—
563C2×C42—431no—
564C2×C42—436no—
565C2×C42—436no—
566C2×C42—436no—
567C2×C42—436no—
568C2×C42C22×D4313yes—
569C24—433no—
570C24—4324no—
571#41—232no—
572#41—248no—
573#41—4332no—
574#41—4332no—
575#41—8696no—
576#41—8696no—
577#41—8632no—
578#41—8648no—
579#41—8648no—
580#41—8696no—
581#41—8632no—
582#41—8648no—
583C2×Q8—232no—
584C2×Q8—4312no—
585C2×Q8—438no—
586C2×Q8—8648no—
587C2×Q8—8632no—
588C2×Q8D4×D4318yescomplemented
589C2×Q8C23×D43112yes—
590C2×Q8C23×D4314yes—
591C2×D4—438no—
592C2×D4—4324no—
593C2×D4—438no—
594C2×D4—438no—
595C2×D4—4324no—
596C2×D4—4324no—
597C2×D4—4312no—
598C2×D4—434no—
599C2×D4—4324no—
600C2×D4—4312no—
601C2×D4—4312no—
602C2×D4—8696no—
603C2×D4—8648no—
604C2×D4—8696no—
605C2×D4—8696no—
606C2×D4—17224no—
607C2×D4—17224no—
608C2×D4C23×D4314yes—
609C2×D4C23×D4318yes—
610C2×D4C23×D43112yes—
611C2×D4C23×D43112yes—
612C22×C4—431no—
613C22×C4—4324no—
614C22×C4—436no—
615C22×C4—436no—
616C22×C4—431no—
617C22×C4—438no—
618C22×C4—433no—
619C22×C4—436no—
620C22×C4—436no—
621C22×C4—4324no—
622C22×C4—438no—
623C22×C4—4324no—
624C22×C4—436no—
625C22×C4—436no—
626C22×C4—8696no—
627C22×C4—1726no—
628C22×C4—1726no—
629C22×C4C23×D4311yescharacteristic
630C22×C4C23×D43124yes—
631C22×C4C23×D4313yes—
632C22×C4C23×D4313yes—
633C4⋊C4—438no—
634C4⋊C4—434no—
635C4⋊C4—4312no—
636C4⋊C4—4324no—
637C4⋊C4—4312no—
638C4⋊C4C23×D4314yes—
639C4⋊C4C23×D43112yes—
640C4⋊C4C23×D43112yes—
641C22⋊C4—438no—
642C22⋊C4—4324no—
643C22⋊C4—438no—
644C22⋊C4—438no—
645C22⋊C4—4324no—
646C22⋊C4—4324no—
647C22⋊C4—4324no—
648C22⋊C4C23×D4318yes—
649C22⋊C4C23×D43124yes—
650C42—431no—
651C42—431no—
652C42—431no—
653C42—431no—
654C42—436no—
655C42—436no—
656C42—436no—
657C42—436no—
658C42C23×D4316yes—
659C42C23×D4316yes—
660C23—436no—
661C23—4312no—
662C23—438no—
663C23—8648no—
664C23—17224no—
665C23—17224no—
666C23—1723no—
667C23—1723no—
668C23C24×D4318yes—
669C23C24×D4311yescharacteristic
670Q8—224no—
671Q8—8616no—
672Q8—8624no—
673Q8C2×D4×D43116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—4348no—
679D4—8648no—
680D4—8616no—
681D4—8616no—
682D4—8648no—
683D4—8616no—
684D4—8624no—
685D4—868no—
686D4—17212no—
687D4—17224no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—434no—
692C2×C4—431no—
693C2×C4—431no—
694C2×C4—431no—
695C2×C4—4324no—
696C2×C4—4324no—
697C2×C4—431no—
698C2×C4—436no—
699C2×C4—438no—
700C2×C4—8616no—
701C2×C4—8612no—
702C2×C4—8648no—
703C2×C4—8616no—
704C2×C4—862no—
705C2×C4—8648no—
706C2×C4—8612no—
707C2×C4—1726no—
708C2×C4—1726no—
709C2×C4—1723no—
710C2×C4C2×D4×D43112yes—
711C2×C4C24×D4311yescharacteristic
712C2×C4C24×D4316yes—
713C2×C4C24×D4318yes—
714C2×C4C24×D4316yes—
715C2×C4C24×D4311yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—4312no—
722C22—866no—
723C22—866no—
724C22—868no—
725C22—868no—
726C22—868no—
727C22—34448no—
728C22—17212no—
729C22C22×D4×D4312yes—
730C22C25×D4311yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—432no—
735C4—432no—
736C4—432no—
737C4—868no—
738C4—861no—
739C4—866no—
740C4C22×D4×D43112yes—
741C4#1458373612yescomplemented
742C2—22no—
743C2—48no—
744C2—8612no—
745C2—1728no—
746C2C23×D4×D4311yescharacteristic
747C2#585×D4311yescharacteristic
748C2C2×#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3497C2
hypercenter#3497D43
hypocenterC43#62812
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#14583736C2semidirect
2. #19148386C2semidirect
3. #19148379C2semidirect
4. #19148372C2semidirect
5. #19148366C2semidirect
6. #19148362C2semidirect
7. #19148358C2semidirect
8. #19148357C2semidirect
9. D4×#10621902C2semidirect
10. #19148085C2semidirect
11. #19148084C2semidirect
12. #19147923C2semidirect
13. #532×D43C2semidirect
14. C2×C4×#10621902C2semidirect
15. C43×#3497C2semidirect
17. C2×#13063373C22semidirect
18. C2×#13063373C22semidirect
19. C2×#13063371C22semidirect
20. C2×#13063371C22semidirect
22. C22×#10621902C22semidirect
23. C2×#41×D43C22semidirect
24. C2×#41×D43C22semidirect
25. #14583571C22semidirect
26. #14583568C22semidirect
27. Q8×D172C22semidirect
28. Q8×C22⋊D43C22semidirect
29. #14583561C22semidirect
30. #14583560C22semidirect
31. #14583556C22semidirect
32. #14583554C22semidirect
33. #14583552C22semidirect
34. #14583551C22semidirect
35. #14583546C22semidirect
36. #14583545C22semidirect
37. #14583542C22semidirect
38. #14583540C22semidirect
39. D4×D172C22semidirect
40. #14583534C22semidirect
41. #14583533C22semidirect
42. #14583480C22semidirect
43. #14583477C22semidirect
44. #14583472C22semidirect
45. #14583465C22semidirect
46. #14583457C22semidirect
47. #14583450C22semidirect
48. #14583449C22semidirect
49. #14583448C22semidirect
50. #14583447C22semidirect
51. #14583446C22semidirect
52. #14583446C22semidirect
53. #14583445C22semidirect
54. #14583444C22semidirect
55. #14583444C22semidirect
56. C4⋊Q8×D43C22semidirect
57. #127×D43C22semidirect
58. #124×D43C22semidirect
59. #14583412C22semidirect
60. #14583409C22semidirect
61. #121×D43C22semidirect
62. #121×D43C22semidirect
63. C4×#10621902C22semidirect
64. C4×#10621902C22semidirect
65. C4×#10621902C22semidirect
66. C4×#10621902C22semidirect
67. C2×Q8×Dic43C22semidirect
68. C2×C4×D172C22semidirect
69. C2×#13063287C22semidirect
70. C4×D4×D43C22semidirect
71. C4×D4×D43C22semidirect
72. C2×#13063283C22semidirect
73. C2×C42×D43C22semidirect
74. C2×2−1+4×C43C22semidirect
75. C43×#550C22semidirect
76. D4×Q8×C43C22semidirect
77. C43×#548C22semidirect
78. C43×#537C22semidirect
79. C43×#532C22semidirect
80. C2×C4×Q8×C43C22semidirect
86. C2×#10621902D4semidirect
199. C2×Q8×C43C2×D4semidirect
222. #10621902C2×D4semidirect
223. #10621902C2×D4semidirect
237. C2×D172C2×D4semidirect
246. C2×C4×D43C2×D4semidirect
361. C4×C43#585semidirect
367. Dic43#585semidirect
374. #3497D43semidirect
393. C2×2−1+4C2×D43semidirect
402. #550C2×D43semidirect
405. D4×Q8C2×D43semidirect
409. #548C2×D43semidirect
422. #537C2×D43semidirect
435. #532C2×D43semidirect
448. C2×C4×Q8C2×D43semidirect
455. C43#62812semidirect
588. C2×Q8D4×D43semidirect
741. C4#14583736semidirect

Maximal subgroups

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

subgroupindex
C2×#145837362
#191483862
#191483792
#191483722
#191483662
#191483622
#191483582
#191483572
D4×#106219022
#191480852
#191480842
#191479232
#532×D432
C2×C4×#106219022
C43×#34972
#6281243