Finite Group Databasebeta

← #72287288

Subgroups — #72287288

Order 2048.

Only the 62660 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 644 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72287074C211yesmaximal, characteristic, complemented
2#72287012C211yesmaximal, characteristic, complemented
3#72286972C212yesmaximal, complemented
4D8×#585C211yesmaximal, characteristic
5#72286675C2130yesmaximal, complemented
6#72286633C2115yesmaximal, complemented
7D4×#3573C212yesmaximal, complemented
8#72285875C2115yesmaximal, complemented
9#72285711C2130yesmaximal, complemented
10#72285219C2115yesmaximal, complemented
11C2×#6345807C2115yesmaximal, complemented
12D4×#585C2212yes—
13#10585809C416yes—
14#10584989C4112yes—
15D8×2−1+4C416yes—
16#10584236C4110yes—
17#10583479C4120yes—
18D8×H(5,𝔽2)C4110yes—
19#10580904C22115yes—
20#10580219C22130yes—
21C2×D8×#41C22115yes—
22C8×#585C2211yescharacteristic
23C8×#585C2211yescharacteristic
24#10574209C22130yescomplemented
25D4×#568C22130yescomplemented
26#10574205C22130yescomplemented
27C2×D4×#131C22130yescomplemented
28#10574108C2212yes—
29C4×#3573C2211yescharacteristic
30#6346071C221240yescomplemented
31#6346071C221240yescomplemented
32#6345923C221120yescomplemented
33#6345923C221120yescomplemented
34#6345807C22160yescomplemented
35#6345807C22120yescomplemented
36#6345807C221120yescomplemented
37#6345807C221120yescomplemented
38#6345807C22160yescomplemented
39#6345807C22160yescomplemented
40#6345807C221120yescomplemented
41#6345702C22190yescomplemented
42#6345612C22190yescomplemented
43#6345458C221180yescomplemented
44#6345287C221180yescomplemented
45#6345192C22190yescomplemented
46C2×#18073C22145yescomplemented
47C2×#18044C22145yescomplemented
48C2×#18001C22190yescomplemented
49C2×#17962C22145yescomplemented
50C2×#17907C22190yescomplemented
51C22×#1580C22115yescomplemented
52#6344427C22130yescomplemented
53#6344400C22115yescomplemented
54C2×#17826C22115yescomplemented
55#6343228C22130yescomplemented
56#6343174C22130yescomplemented
57#6343110C22130yescomplemented
58C2×#17507C22130yescomplemented
59#6342442C22115yescomplemented
60#6342441C22115yescomplemented
61#6342441C22115yescomplemented
62C2×#17320C22115yescomplemented
63C2×#3573D412yes—
64#63003C2×C4112yes—
65D4×2−1+4C2×C4112yes—
66#62988C2×C4120yes—
67D4×H(5,𝔽2)C2×C4120yes—
68#62812C23130yes—
69C2×D4×#41C23130yes—
70C4×#585C2311yescharacteristic
71#62529C2×C41120yes—
72#62471C2×C4160yes—
73#62415C2×C4160yes—
74#62359C2×C4130yes—
75#62359C2×C4130yes—
76#62245C2×C4190yes—
77#62245C2×C4190yes—
78#62095C2×C41120yes—
79#62095C2×C41120yes—
80#61947C2×C41120yes—
81#61947C2×C41120yes—
82#61880C2×C4160yes—
83#61817C2×C4160yes—
84#61694C2×C41180yes—
85#61559C2×C41180yes—
86D8×#41C2×C4160yes—
87D8×#41C2×C41120yes—
88D8×#41C2×C4160yes—
89D8×#41C23120yes—
90D8×#41C231120yes—
91D8×#41C23160yes—
92D8×#41C231120yes—
93C2×#3391C2×C4115yes—
94C2×Q8×D8C2×C4115yes—
95C2×#3358C2×C4130yes—
96C2×#3334C2×C4145yes—
97C2×#3294C2×C4190yes—
98C2×D4×D8C2×C4145yes—
99#60940C23190yes—
100C2×#3169C23145yes—
101C2×#3100C23190yes—
102C8×2−1+4C2×C416yes—
103C8×2−1+4C2×C416yes—
104C8×H(5,𝔽2)C2×C4110yes—
105C8×H(5,𝔽2)C2×C4110yes—
106#60276C23115yes—
107#60276C23115yes—
108C2×C8×#41C23115yes—
109C2×C8×#41C23115yes—
110C22×C4×D8C23115yes—
111#60147C231240yescomplemented
112D4×#131C23140yescomplemented
113D4×#131C231120yescomplemented
114D4×#131C231120yescomplemented
115D4×#131C231120yescomplemented
116#60144C231180yescomplemented
117C2×#2935C23190yescomplemented
118C2×D4×M16C23190yescomplemented
119C2×#2931C23190yescomplemented
120C22×C8×D4C23130yescomplemented
121#60099C23130yes—
122C2×#2906C23130yes—
123#60058D4130yes—
124C4×#568C23115yes—
125C2×C4×#131C23115yes—
126#18073C23160yescomplemented
127#18073C231360yescomplemented
128#18073C231180yescomplemented
129#18073C231360yescomplemented
130#18044C23160yes—
131#18044C231360yescomplemented
132#18044C231180yescomplemented
133#18044C231360yescomplemented
134#18001C231360yescomplemented
135#18001C231720yescomplemented
136#18001C231120yescomplemented
137#18001C231360yescomplemented
138#18001C231360yescomplemented
139#17981C231360yescomplemented
140#17962C23160yescomplemented
141#17962C231180yescomplemented
142#17962C231180yescomplemented
143#17962C231180yescomplemented
144#17935C231720yescomplemented
145#17907C231360yescomplemented
146#17907C231120yescomplemented
147#17907C231360yescomplemented
148#17907C231360yescomplemented
149C2×#1594C23190yescomplemented
150C2×#1594C23190yescomplemented
151C2×#1586C231180yescomplemented
152C2×#1586C231180yescomplemented
153C2×#1580C23115yes—
154C2×#1580C23145yes—
155C2×#1580C23145yescomplemented
156C2×#1580C23145yescomplemented
157C2×#1580C23190yescomplemented
158C2×#1580C23190yescomplemented
159C2×#1580C23190yescomplemented
160#17826C23120yescomplemented
161#17826C231120yescomplemented
162#17826C23160yescomplemented
163#17826C231120yescomplemented
164#17813C23190yescomplemented
165C2×#1570C23190yescomplemented
166C2×#1566C23145yescomplemented
167C22×#334C23115yescomplemented
168#17507C231120yescomplemented
169#17507C231240yescomplemented
170#17507C231120yescomplemented
171#17507C23140yescomplemented
172#17507C231120yescomplemented
173#17485C231180yescomplemented
174C2×#1492C23190yescomplemented
175C2×#1480C23190yescomplemented
176C2×#1486C23190yescomplemented
177C22×D4⋊C8C23130yescomplemented
178#17320C23120yescomplemented
179#17320C23160yescomplemented
180#17320C23160yescomplemented
181#17320C23160yescomplemented
182#17320C231120yescomplemented
183#17319C23190yescomplemented
184C2×#1452C23145yescomplemented
185C2×#1451C23145yescomplemented
186C2×#1451C23145yescomplemented
187C22×#322C23115yescomplemented
188C2×#585C2×D411yescharacteristic
189C23×D8C22×C4115yes—
190C2×#568C2×D4130yes—
191C22×#131C2×D4130yes—
192#3499C22×C41120yes—
193#3498C22×C41120yes—
194#3497C22×C4160yes—
195#3496C22×C41180yes—
196D4×#41C22×C41120yes—
197D4×#41C22×C41120yes—
198D4×#41C241120yes—
199D4×#41C24140yes—
200C2×#550C22×C4130yes—
201C2×D4×Q8C22×C4130yes—
202C2×#547C22×C4190yes—
203C2×D42C22×C4190yes—
204C2×#532C24190yes—
205C4×2−1+4C22×C416yes—
206C4×2−1+4#4116yes—
207C4×H(5,𝔽2)C22×C4110yes—
208C4×H(5,𝔽2)#41110yes—
209#3428C2×D4115yes—
210C2×C4×#41C24115yes—
211C22×C4×D4C24130yes—
212#3391C22×C4160yes—
213#3391C22×C41120yes—
214#3391C22×C41120yes—
215#3391C22×C4120yes—
216Q8×D8C22×C4160yes—
217Q8×D8C22×C41120yes—
218Q8×D8C22×C41120yes—
219Q8×D8C22×C4120yes—
220#3358C22×C41120yes—
221#3358C22×C41240yes—
222#3358C22×C4140yes—
223#3358C22×C41120yes—
224#3358C22×C41120yes—
225#3334C22×C41180yes—
226#3334C22×C41360yes—
227#3334C22×C4160yes—
228#3334C22×C41360yes—
229#3294C22×C41360yes—
230#3294C22×C41720yes—
231#3294C22×C41360yes—
232#3294C22×C41120yes—
233#3294C22×C41360yes—
234D4×D8C22×C41180yes—
235D4×D8C22×C41360yes—
236D4×D8C22×C4160yes—
237D4×D8C22×C41360yes—
238#3245C22×C41180yes—
239#3245C22×C41180yes—
240#3226C22×C41360yes—
241#3205C22×C41360yes—
242#3186C22×C41360yes—
243#3169C22×C41180yes—
244#3169C22×C41180yes—
245#3169C241180yes—
246#3169C24160yes—
247C2×#500C22×C4145yes—
248C2×#493C22×C4145yes—
249C2×#486C22×C4190yes—
250#3100C22×C41360yes—
251#3100C22×C41360yes—
252#3100C241360yes—
253#3100C241120yes—
254C2×#480C22×C41180yes—
255C2×#474C22×C4190yes—
256C2×#474C22×C4190yes—
257C2×#466C22×C4190yes—
258C2×#466C22×C4190yes—
259C2×#459C22×C4190yes—
260C2×#459C22×C4190yes—
261C2×#447C22×C41180yes—
262#2988C22×C4160yes—
263#2988C22×C4160yes—
264#2982C22×C4130yes—
265#2972C22×C4190yes—
266C8×#41C22×C4160yes—
267C8×#41C22×C4160yes—
268C8×#41C24120yes—
269C8×#41C24160yes—
270C8×#41C24120yes—
271C8×#41C24160yes—
272C2×C8×Q8C22×C4115yes—
273C2×C8×Q8C22×C4115yes—
274C2×C4×D8C22×C4145yes—
275C2×C4×D8C22×C4145yes—
276C2×C4×D8C22×C4190yes—
277C2×C4×D8C24190yes—
278C2×C4×D8C24190yes—
279C2×C4×D8C24115yes—
280C2×C4×D8C24145yes—
281#2935C241120yes—
282#2935C241360yes—
283D4×M16C241120yes—
284D4×M16C241360yes—
285#2931C241360yes—
286#2931C241120yes—
287C2×#436C241180yes—
288C2×C8×D4C22×C4145yes—
289C2×C8×D4C22×C4145yes—
290C2×C8×D4C24130yes—
291C2×C8×D4C24190yes—
292C2×C8×D4C24190yes—
293C2×C8×D4C24190yes—
294C2×#431C24145yes—
295C2×#431C24145yes—
296C22×#107C22×C4115yes—
297#2906C24140yes—
298#2906C241120yes—
299C2×#423C24190yes—
300C22×C4⋊C8C24130yes—
301C22×#102C22×C4130yes—
302#2875C2×D41120yes—
303C4×#131C2×D41120yes—
304C4×#131C24120yes—
305C4×#131C24160yes—
306#2873C2×D4190yes—
307C2×#405C2×D4190yes—
308C2×C4×M16C24145yes—
309C22×C4×C8C24115yes—
310C22×C4×C8C24115yes—
311C22×C4×C8C24115yes—
312#1594C241360yes—
313#1594C241360yes—
314#1594C241120yes—
315#1594C241120yes—
316#1586C241720yes—
317#1586C241720yes—
318#1586C241240yes—
319#1586C241240yes—
320#1580C24115yes—
321#1580C24190yes—
322#1580C24190yes—
323#1580C241120yes—
324#1580C24190yes—
325#1580C241360yes—
326#1580C24130yes—
327#1580C241180yes—
328#1580C241180yes—
329#1580C24115yes—
330#1580C24115yes—
331#1580C2411yescharacteristic
332#1580C24130yes—
333#1570C241360yes—
334#1570C241120yes—
335#1566C24160yes—
336#1566C241180yes—
337C2×#334C24115yes—
338C2×#334C24145yes—
339C2×#334C24190yes—
340C2×#334C24190yes—
341#1492C241120yes—
342#1492C241360yes—
343#1486C241360yes—
344#1486C241120yes—
345#1480C241360yes—
346#1480C241120yes—
347C2×D4⋊C8C24130yes—
348C2×D4⋊C8C24190yes—
349C2×D4⋊C8C24190yes—
350C2×D4⋊C8C24190yes—
351C2×D4⋊C8C241180yes—
352#1452C241180yes—
353#1452C24160yes—
354#1451C24160yes—
355#1451C241180yes—
356#1451C24160yes—
357#1451C241180yes—
358C2×#322C24115yes—
359C2×#322C24145yes—
360C2×#322C24145yes—
361C2×#322C24145yes—
362C2×#322C24190yes—
363#585AGL(1,ℤ/8)132yes—
364C2×2−1+4C4×D416yes—
365C2×H(5,𝔽2)C4×D4110yes—
366C22×#41C22×D4115yes—
367C23×D4C23×C4130yes—
368C22×D8C23×C4145yes—
369C22×D8C23×C4190yes—
370C22×D8C23×C4115yes—
371C22×D8C23×C4190yes—
372C2×#131C22×D4140yes—
373C2×#131C22×D41120yes—
374C22×M16C22×D4190yes—
375C23×C8C23×C4115yes—
376C23×C8C23×C4115yes—
377C23×C8C22×D4130yes—
378#550C23×C4140yes—
379#550C23×C41120yes—
380D4×Q8C23×C4140yes—
381D4×Q8C23×C41120yes—
382#547C23×C41120yes—
383#547C23×C41360yes—
384D42C23×C41120yes—
385D42C23×C41360yes—
386#532C23×C41360yes—
387#532C251120yes—
388C2×C4⋊Q8C23×C4190yes—
389C2×#127C23×C4190yes—
390C2×#121C23×C41180yes—
391#520C4×D4160yes—
392#520C4×D4160yes—
393#519C4×D4130yes—
394#518C4×D4190yes—
395C4×#41C23×C4160yes—
396C4×#41C22×D4160yes—
397C4×#41C2×#41160yes—
398C4×#41C25120yes—
399C2×C4×Q8C23×C4115yes—
400C2×C4×Q8C2×#41115yes—
401C2×C4×D4C23×C4145yes—
402C2×C4×D4C23×C4190yes—
403C2×C4×D4C23×C4190yes—
404C2×C4×D4C2×#41145yes—
405C2×C4×D4C25130yes—
406C2×C4×D4C25190yes—
407C2×#117C22×D4145yes—
408C22×C4⋊C4C23×C4130yes—
409C22×C42C25115yes—
410#500C23×C4160yes—
411#500C23×C41180yes—
412#493C23×C4160yes—
413#493C23×C41180yes—
414#486C23×C41120yes—
415#486C23×C41360yes—
416#480C23×C41240yes—
417#480C23×C41720yes—
418#474C23×C41120yes—
419#474C23×C41360yes—
420#474C23×C41360yes—
421#474C23×C41120yes—
422#466C23×C41120yes—
423#466C23×C41360yes—
424#466C23×C41360yes—
425#466C23×C41120yes—
426#459C23×C41120yes—
427#459C23×C41120yes—
428#459C23×C41360yes—
429#459C23×C41360yes—
430#447C23×C41240yes—
431#447C23×C41720yes—
432C8×Q8C23×C4120yes—
433C8×Q8C23×C4160yes—
434C8×Q8C23×C4160yes—
435C8×Q8C23×C4120yes—
436C4×D8C23×C4115yes—
437C4×D8C23×C41180yes—
438C4×D8C23×C4190yes—
439C4×D8C23×C41360yes—
440C4×D8C23×C41180yes—
441C4×D8C23×C4190yes—
442C4×D8C23×C4130yes—
443C4×D8C23×C4115yes—
444C4×D8C25130yes—
445C4×D8C25190yes—
446C4×D8C251120yes—
447C4×D8C2511yescharacteristic
448C4×D8C25115yes—
449#436C251240yes—
450C8×D4C23×C4160yes—
451C8×D4C23×C41180yes—
452C8×D4C23×C41180yes—
453C8×D4C23×C4160yes—
454C8×D4C2512yes—
455C8×D4C25130yes—
456C8×D4C25130yes—
457C8×D4C25130yes—
458C8×D4C251180yes—
459#431C23×C41180yes—
460#431C25160yes—
461#431C25160yes—
462C2×#107C23×C4190yes—
463C2×#107C23×C4190yes—
464C2×#107C23×C4145yes—
465C2×#107C23×C4115yes—
466#423C251120yes—
467C2×C4⋊C8C23×C4145yes—
468C2×C4⋊C8C23×C4145yes—
469C2×C4⋊C8C25130yes—
470C2×C4⋊C8C25190yes—
471C2×#102C23×C4190yes—
472C2×#102C23×C41180yes—
473C2×#102C23×C4190yes—
474C2×#102C23×C4130yes—
475C2×#102C23×C4190yes—
476C2×C22⋊C8C23×C4190yes—
477#405C22×D41120yes—
478#405C22×D41360yes—
479C4×M16C22×D41180yes—
480C4×M16C25160yes—
481C2×#97C22×D4190yes—
482C2×C4×C8C23×C4145yes—
483C2×C4×C8C23×C4145yes—
484C2×C4×C8C22×D4190yes—
485C2×C4×C8C25115yes—
486C2×C4×C8C25145yes—
487C2×C4×C8C25115yes—
488C2×C4×C8C25145yes—
489C2×C4×C8C25115yes—
490C2×C4×C8C25145yes—
491#334C2511yescharacteristic
492#334C25115yes—
493#334C25130yes—
494#334C25190yes—
495#334C251120yes—
496D4⋊C8C2512yes—
497D4⋊C8C25130yes—
498D4⋊C8C25130yes—
499D4⋊C8C25130yes—
500D4⋊C8C251180yes—
501D4⋊C8C251240yes—
502#322C2511yescharacteristic
503#322C25115yes—
504#322C25115yes—
505#322C25115yes—
506#322C25190yes—
507#322C251120yes—
5082−1+4#442196yes—
509H(5,𝔽2)#4421160yes—
510C2×#41C2×C4×D4160yes—
511C2×#41C2×AGL(1,ℤ/8)1240yes—
512C2×#41C23×D4120yes—
513C22×Q8C2×C4×D4115yes—
514C22×D4C2×C4×D4145yes—
515C22×D4C24×C4130yes—
516C22×D4C24×C4190yes—
517C23×C4C24×C4115yes—
518C23×C4C23×D4115yes—
519C23×C4C22×#41115yes—
520C2×D8C24×C411yescharacteristic
521C2×D8C24×C4130yes—
522C2×D8C24×C4115yes—
523C2×D8C24×C4190yes—
524C2×D8C24×C41120yes—
525C2×M16C23×D41120yes—
526C22×C8C24×C4115yes—
527C22×C8C24×C4115yes—
528C22×C8C24×C4145yes—
529C22×C8C24×C4145yes—
530C22×C8C23×D4130yes—
531C22×C8C23×D4190yes—
532C4⋊Q8C24×C41120yes—
533#127C24×C41120yes—
534#121C24×C41240yes—
535C4×Q8C2×C4×D4160yes—
536C4×Q8C2×C4×D4160yes—
537C4×Q8C24×C4120yes—
538C4×Q8C22×#41120yes—
539C4×D4C2×C4×D41180yes—
540C4×D4C2×C4×D41180yes—
541C4×D4C24×C4160yes—
542C4×D4C24×C4130yes—
543C4×D4C24×C4130yes—
544C4×D4C24×C41180yes—
545C4×D4C22×#41160yes—
546C4×D4C2612yes—
547C4×D4C26130yes—
548#117C2×C4×D41180yes—
549#117C23×D4160yes—
550C2×C4⋊C4C2×C4×D4145yes—
551C2×C4⋊C4C2×C4×D4145yes—
552C2×C4⋊C4C24×C4130yes—
553C2×C4⋊C4C24×C4190yes—
554C2×C22⋊C4C2×C4×D4190yes—
555C2×C42C24×C4145yes—
556C2×C42C23×D4145yes—
557C2×C42C22×#41145yes—
558C2×C42C26115yes—
559#107C24×C411yescharacteristic
560#107C24×C4115yes—
561#107C24×C4130yes—
562#107C24×C41120yes—
563#107C24×C4190yes—
564C4⋊C8C24×C4160yes—
565C4⋊C8C24×C4160yes—
566C4⋊C8C2612yes—
567C4⋊C8C26130yes—
568#102C24×C412yes—
569#102C24×C4130yes—
570#102C24×C4130yes—
571#102C24×C4130yes—
572#102C24×C41180yes—
573#102C24×C41240yes—
574C22⋊C8C24×C41120yes—
575#97C23×D41120yes—
576C4×C8C24×C4115yes—
577C4×C8C24×C4115yes—
578C4×C8C24×C4190yes—
579C4×C8C23×D4130yes—
580C4×C8C23×D4190yes—
581C4×C8C2611yescharacteristic
582C4×C8C26115yes—
583C4×C8C2611yescharacteristic
584C4×C8C26115yes—
585C4×C8C2611yescharacteristic
586C4×C8C26115yes—
587C24C22×C4×D4115yes—
588#41C2×#4421480yes—
589#41C22×AGL(1,ℤ/8)1160yes—
590C2×Q8C2×#4421120yes—
591C2×Q8C22×C4×D4120yes—
592C2×D4C2×#4421360yes—
593C2×D4C22×C4×D4160yes—
594C2×D4C25×C4130yes—
595C2×D4C25×C412yes—
596C22×C4C22×C4×D4145yes—
597C22×C4C22×C4×D4145yes—
598C22×C4C22×C4×D4145yes—
599C22×C4C22×AGL(1,ℤ/8)1120yes—
600C22×C4C25×C4115yes—
601C22×C4C24×D4115yes—
602C22×C4C23×#41115yes—
603D8#357314yescomplemented
604C2×C8C25×C411yescharacteristic
605C2×C8C25×C411yescharacteristic
606C2×C8C25×C4115yes—
607C2×C8C25×C4115yes—
608C2×C8C24×D412yes—
609C2×C8C24×D4130yes—
610C4⋊C4C22×C4×D4160yes—
611C4⋊C4C22×C4×D4160yes—
612C4⋊C4C25×C412yes—
613C4⋊C4C25×C4130yes—
614C22⋊C4C22×C4×D41120yes—
615C42C22×C4×D4190yes—
616C42C25×C4115yes—
617C42C24×D4115yes—
618C42C23×#41115yes—
619C42C2711yescharacteristic
620C23C22×#442160yes—
621C23C23×C4×D4115yes—
622Q8C22×#442180yes—
623D4C22×#4421240yes—
624D4C2×#357314yescomplemented
625C2×C4C22×#4421180yes—
626C2×C4C23×C4×D4115yes—
627C2×C4C23×C4×D4115yes—
628C2×C4C23×C4×D4115yes—
629C2×C4C23×AGL(1,ℤ/8)160yes—
630C2×C4C26×C411yescharacteristic
631C2×C4C25×D411yescharacteristic
632C2×C4C24×#4111yescharacteristic
633C8C2×#357312yescomplemented
634C22C23×#442130yes—
635C22C24×C4×D411yescharacteristic
636C4C23×#442130yes—
637C4C22×#357311yescharacteristic
638C4#1058698411yescharacteristic
639C4C24×AGL(1,ℤ/8)12yes—
640C2C24×#44211yescharacteristic
641C2D4×#357311yescharacteristic
642C2#7228661111yescharacteristic
subgroupG/H
centerC2×C4C25×D4
commutatorC2×C4C26×C4
Frattini, cosocleC42C27
socleC22C24×C4×D4
prime radicalD8×#585C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C4×#3573 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72287074C2semidirect
2. #72287012C2semidirect
3. #72286972C2semidirect
5. #72286675C2semidirect
6. #72286633C2semidirect
7. D4×#3573C2semidirect
8. #72285875C2semidirect
9. #72285711C2semidirect
10. #72285219C2semidirect
11. C2×#6345807C2semidirect
24. #10574209C22semidirect
25. D4×#568C22semidirect
26. #10574205C22semidirect
27. C2×D4×#131C22semidirect
30. #6346071C22semidirect
31. #6346071C22semidirect
32. #6345923C22semidirect
33. #6345923C22semidirect
34. #6345807C22semidirect
35. #6345807C22semidirect
36. #6345807C22semidirect
37. #6345807C22semidirect
38. #6345807C22semidirect
39. #6345807C22semidirect
40. #6345807C22semidirect
41. #6345702C22semidirect
42. #6345612C22semidirect
43. #6345458C22semidirect
44. #6345287C22semidirect
45. #6345192C22semidirect
46. C2×#18073C22semidirect
47. C2×#18044C22semidirect
48. C2×#18001C22semidirect
49. C2×#17962C22semidirect
50. C2×#17907C22semidirect
51. C22×#1580C22semidirect
52. #6344427C22semidirect
53. #6344400C22semidirect
54. C2×#17826C22semidirect
55. #6343228C22semidirect
56. #6343174C22semidirect
57. #6343110C22semidirect
58. C2×#17507C22semidirect
59. #6342442C22semidirect
60. #6342441C22semidirect
61. #6342441C22semidirect
62. C2×#17320C22semidirect
111. #60147C23semidirect
112. D4×#131C23semidirect
113. D4×#131C23semidirect
114. D4×#131C23semidirect
115. D4×#131C23semidirect
116. #60144C23semidirect
117. C2×#2935C23semidirect
118. C2×D4×M16C23semidirect
119. C2×#2931C23semidirect
120. C22×C8×D4C23semidirect
126. #18073C23semidirect
127. #18073C23semidirect
128. #18073C23semidirect
129. #18073C23semidirect
131. #18044C23semidirect
132. #18044C23semidirect
133. #18044C23semidirect
134. #18001C23semidirect
135. #18001C23semidirect
136. #18001C23semidirect
137. #18001C23semidirect
138. #18001C23semidirect
139. #17981C23semidirect
140. #17962C23semidirect
141. #17962C23semidirect
142. #17962C23semidirect
143. #17962C23semidirect
144. #17935C23semidirect
145. #17907C23semidirect
146. #17907C23semidirect
147. #17907C23semidirect
148. #17907C23semidirect
149. C2×#1594C23semidirect
150. C2×#1594C23semidirect
151. C2×#1586C23semidirect
152. C2×#1586C23semidirect
155. C2×#1580C23semidirect
156. C2×#1580C23semidirect
157. C2×#1580C23semidirect
158. C2×#1580C23semidirect
159. C2×#1580C23semidirect
160. #17826C23semidirect
161. #17826C23semidirect
162. #17826C23semidirect
163. #17826C23semidirect
164. #17813C23semidirect
165. C2×#1570C23semidirect
166. C2×#1566C23semidirect
167. C22×#334C23semidirect
168. #17507C23semidirect
169. #17507C23semidirect
170. #17507C23semidirect
171. #17507C23semidirect
172. #17507C23semidirect
173. #17485C23semidirect
174. C2×#1492C23semidirect
175. C2×#1480C23semidirect
176. C2×#1486C23semidirect
177. C22×D4⋊C8C23semidirect
178. #17320C23semidirect
179. #17320C23semidirect
180. #17320C23semidirect
181. #17320C23semidirect
182. #17320C23semidirect
183. #17319C23semidirect
184. C2×#1452C23semidirect
185. C2×#1451C23semidirect
186. C2×#1451C23semidirect
187. C22×#322C23semidirect
603. D8#3573semidirect
624. D4C2×#3573semidirect
633. C8C2×#3573semidirect

Maximal subgroups

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

subgroupindex
#722870742
#722870122
#722869722
D8×#5852
#722866752
#722866332
D4×#35732
#722858752
#722857112
#722852192
C2×#63458072