Finite Group Databasebeta

← C2×#24910914 #35572360

Subgroups — C2×#24910914 #35572360

Order 21248.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581771C211yesmaximal, characteristic, complemented
2C22×#14581771C211yesmaximal, characteristic, complemented
3C23×C4⋊Dic83C211yesmaximal, characteristic, complemented
4#24910914C2116yesmaximal, direct product factor
5C2×#19127634C212yesmaximal, complemented
6C2×#19127624C212yesmaximal, complemented
7C2×#19127607C211yesmaximal, characteristic, complemented
8C2×#19127599C211yesmaximal, characteristic, complemented
9C2×#19127581C212yesmaximal
10C2×#19127561C211yesmaximal, characteristic, complemented
11C2×#19127559C212yesmaximal, complemented
12C22×C4×D4×C83C211yesmaximal, characteristic
13C23×Dic166C2211yescharacteristic
14C24×Dic83C2212yes—
15C2×#14581771—28no—
16C2×#14581771—28no—
17C2×#14581771C2218yescomplemented
18C2×#14581771C2218yescomplemented
19C22×C4⋊Dic83—28no—
20C22×C4⋊Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2212yes—
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2218yescomplemented
25C22×Dic83⋊C4C2212yes—
26C22×Dic83⋊C4C2212yes—
27C22×Dic83⋊C4C2212yes—
28C22×C22⋊Dic83C2212yes—
29C22×C22⋊Dic83C2212yes—
30C22×C22⋊Dic83C2212yes—
31#19127634C22116yescomplemented
32#19127624C22116yescomplemented
33#19127607C2218yescomplemented
34#19127599C2218yescomplemented
35#19127581C22116yes—
36#19127561C2218yescomplemented
37#19127559C22116yescomplemented
38C2×C83⋊#95C2212yes—
39C2×C83⋊#95C2212yes—
40C2×C83⋊#95C2212yes—
41C2×C83⋊#95C2212yes—
42C23×D4×C83C2211yescharacteristic
43C24×C4×C83C2211yescharacteristic
44C24×C4×C83C2211yescharacteristic
45C2×C4×D4×C83—28no—
46C2×C4×D4×C83C2218yes—
47C22×C4⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51C22×Dic166—24no—
52C22×Dic166—24no—
53C22×Dic166—24no—
54C22×Dic166C2314yes—
55C23×Dic83—28no—
56C23×Dic83—28no—
57C23×Dic83—44no—
58C23×Dic83C2312yes—
59C23×Dic83C2312yes—
60C23×Dic83C2312yes—
61C23×Dic83C2318yes—
62C23×Dic83C2312yes—
63#14581771—232no—
64#14581771—232no—
65C2×C4⋊Dic83—28no—
66C2×C4⋊Dic83—232no—
67C2×C4⋊Dic83—24no—
68C2×C4⋊Dic83—24no—
69C2×C4⋊Dic83D418yescomplemented
70C2×C4⋊Dic83C2314yes—
71C2×C4⋊Dic83C2314yes—
72C2×C4⋊Dic83C2318yes—
73C2×C4⋊Dic83C2314yes—
74C2×Dic83⋊C4—28no—
75C2×Dic83⋊C4—28no—
76C2×Dic83⋊C4—44no—
77C2×Dic83⋊C4C2318yes—
78C2×Dic83⋊C4C2318yes—
79C2×Dic83⋊C4C2318yes—
80C2×C22⋊Dic83—28no—
81C2×C22⋊Dic83—28no—
82C2×C22⋊Dic83—44no—
83C2×C22⋊Dic83C2318yes—
84C2×C22⋊Dic83C2318yes—
85C2×C22⋊Dic83C2318yes—
86C83⋊#95C2318yes—
87C83⋊#95C2318yes—
88C83⋊#95C2318yes—
89C83⋊#95C2318yes—
90C25×C83C2311yescharacteristic
91C25×C83C2311yescharacteristic
92C22×D4×C83—24no—
93C22×D4×C83—24no—
94C22×D4×C83Q818yescomplemented
95C22×D4×C83C2314yes—
96C23×C4×C83—24no—
97C23×C4×C83—24no—
98C23×C4×C83—24no—
99C23×C4×C83—24no—
100C23×C4×C83—24no—
101C23×C4×C83D418yes—
102C23×C4×C83C2314yes—
103C23×C4×C83C2311yescharacteristic
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2314yes—
107C23×C4×C83C2311yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C4×D4×C83—232no—
110C2×C4⋊C4×C83—24no—
111C2×C4⋊C4×C83C2314yes—
112C2×C22⋊C4×C83—24no—
113C2×C22⋊C4×C83—24no—
114C2×C22⋊C4×C83C2314yes—
115C2×C22⋊C4×C83C2314yes—
116C2×C42×C83—24no—
117C2×C42×C83C2314yes—
118C2×Dic166—28no—
119C2×Dic166—28no—
120C2×Dic166—28no—
121C2×Dic166—416no—
122C22×Dic83—24no—
123C22×Dic83—24no—
124C22×Dic83—24no—
125C22×Dic83—24no—
126C22×Dic83—24no—
127C22×Dic83—24no—
128C22×Dic83—216no—
129C22×Dic83—24no—
130C22×Dic83—24no—
131C22×Dic83—24no—
132C22×Dic83—24no—
133C22×Dic83—24no—
134C22×Dic83—216no—
135C22×Dic83—48no—
136C22×Dic83—432no—
137C22×Dic83C2×D418yes—
138C22×Dic83C2414yes—
139C22×Dic83C2414yes—
140C22×Dic83C2414yes—
141C22×Dic83C2414yes—
142C4⋊Dic83—28no—
143C4⋊Dic83—28no—
144C4⋊Dic83—216no—
145C4⋊Dic83C2×D4116yescomplemented
146Dic83⋊C4—216no—
147Dic83⋊C4—216no—
148Dic83⋊C4—48no—
149C22⋊Dic83—216no—
150C22⋊Dic83—216no—
151C22⋊Dic83—48no—
152C24×C83—22no—
153C24×C83—22no—
154C24×C83—22no—
155C24×C83—22no—
156C24×C83—22no—
157C24×C83—22no—
158C24×C83—22no—
159C24×C83—22no—
160C24×C83—22no—
161C24×C83—22no—
162C24×C83C2×D414yes—
163C24×C83C2×Q814yes—
164C24×C83C2×Q814yes—
165C24×C83#4114yes—
166C24×C83C2412yes—
167C24×C83C2412yes—
168C24×C83C2411yescharacteristic
169C2×D4×C83—232no—
170C2×D4×C83—28no—
171C2×D4×C83—28no—
172C2×D4×C83C2×Q8116yescomplemented
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83—22no—
176C22×C4×C83—22no—
177C22×C4×C83—232no—
178C22×C4×C83—28no—
179C22×C4×C83—28no—
180C22×C4×C83—22no—
181C22×C4×C83—22no—
182C22×C4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—28no—
187C22×C4×C83—28no—
188C22×C4×C83—28no—
189C22×C4×C83—416no—
190C22×C4×C83C2×D414yes—
191C22×C4×C83C2×D4116yes—
192C22×C4×C83C2×D414yes—
193C22×C4×C83C2×D414yes—
194C22×C4×C83C2×Q814yes—
195C22×C4×C83#4114yes—
196C22×C4×C83C2412yes—
197C22×C4×C83C2412yes—
198C22×C4×C83C2412yes—
199C22×C4×C83C2412yes—
200C22×C4×C83C2412yes—
201C4⋊C4×C83—28no—
202C22⋊C4×C83—28no—
203C22⋊C4×C83—28no—
204C42×C83—28no—
205C23×C83—28no—
206C23×C83—28no—
207C23×C83—28no—
208C23×C83—28no—
209C23×C83—28no—
210C23×C83—28no—
211C23×C83—22no—
212C23×C83—22no—
213C23×C83—22no—
214C23×C83—22no—
215C23×C83—28no—
216C23×C83—28no—
217C23×C83—28no—
218C23×C83—22no—
219C23×C83—22no—
220C23×C83—22no—
221C23×C83—22no—
222C23×C83—22no—
223C23×C83—22no—
224C23×C83—44no—
225C23×C83—44no—
226C23×C83—44no—
227C23×C83—44no—
228C23×C83C22⋊Q8116yescomplemented
229C23×C83C22×D412yes—
230C23×C83C22×D414yes—
231C23×C83C22×D412yes—
232C23×C83C22×Q814yes—
233C23×C83C22×Q814yes—
234C23×C83C22×Q812yes—
235C23×C83C2×#4112yes—
236C23×C83C2×#4114yes—
237C23×C83C2×#4112yes—
238C23×C83H(5,𝔽2)12yes—
239C23×C832−1+412yes—
240C23×C83C2511yescharacteristic
241D4×C83—232no—
242C2×C4×C83—28no—
243C2×C4×C83—28no—
244C2×C4×C83—22no—
245C2×C4×C83—22no—
246C2×C4×C83—22no—
247C2×C4×C83—22no—
248C2×C4×C83—232no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—44no—
256C2×C4×C83—44no—
257C2×C4×C83—416no—
258C2×C4×C83#121116yes—
259C2×C4×C83C22×D414yes—
260C2×C4×C83C22×D414yes—
261C2×C4×C83C22×D414yes—
262C2×C4×C83C22×Q814yes—
263C2×C4×C83C2×#4114yes—
264C2×Dic83—216no—
265C2×Dic83—24no—
266C2×Dic83—24no—
267C2×Dic83—24no—
268C2×Dic83—24no—
269C2×Dic83—24no—
270C2×Dic83—24no—
271C2×Dic83—24no—
272C2×Dic83—24no—
273C2×Dic83—24no—
274C2×Dic83—24no—
275C2×Dic83—24no—
276C2×Dic83—432no—
277C2×Dic83—48no—
278C2×Dic83—48no—
279C2×Dic83—48no—
280C2×Dic83C22×D418yes—
281Dic166—416no—
282C22×C83—24no—
283C22×C83—232no—
284C22×C83—24no—
285C22×C83—24no—
286C22×C83—24no—
287C22×C83—24no—
288C22×C83—24no—
289C22×C83—24no—
290C22×C83—24no—
291C22×C83—24no—
292C22×C83—42no—
293C22×C83—416no—
294C22×C83—42no—
295C22×C83—42no—
296C22×C83—42no—
297C22×C83C2×#12114yes—
298C22×C83C2×C22⋊Q814yes—
299C22×C83C2×C22⋊Q818yescomplemented
300C22×C83#53714yes—
301C22×C83#54614yes—
302C22×C83D4×Q814yes—
303C22×C83#55214yes—
304C22×C83#55414yes—
305C22×C83C23×D411yescharacteristic
306C22×C83C23×D411yescharacteristic
307C22×C83C23×Q811yescharacteristic
308C22×C83C22×#4111yescharacteristic
309C22×C83C22×#4111yescharacteristic
310C22×C83C2×H(5,𝔽2)11yescharacteristic
311C22×C83C2×2−1+411yescharacteristic
312C4×C83—24no—
313C4×C83—24no—
314C4×C83—42no—
315C4×C83—42no—
316C4×C83C2×#12118yes—
317Dic83—28no—
318Dic83—44no—
319Dic83—44no—
320Dic83—44no—
321C2×#2417—831nomaximal, Sylow
322C2×C83—28no—
323C2×C83—44no—
324C2×C83#241718yescomplemented
325C2×C83C22×#12111yescharacteristic
326C2×C83C22×C22⋊Q811yescharacteristic
327C2×C83C2×#53711yescharacteristic
328C2×C83C2×#54611yescharacteristic
329C2×C83C2×D4×Q811yescharacteristic
330C2×C83C2×#55211yescharacteristic
331C2×C83C2×#55411yescharacteristic
332C22×C22⋊Q8—831no—
333C22×C22⋊Q8—831no—
334C22×C4×D4D8311yescharacteristic
335C23×C4⋊C4—831no—
336#2417—8316no—
337C2×#398—832no—
338C2×#396—832no—
339C2×#391—831no—
340C2×#389—831no—
341C2×#386—832no—
342C2×#380—831no—
343C2×#380—832no—
344C83C2×#241711yescharacteristic, complemented, Sylow
345C23×Q8—831no—
346C23×D4C2×D8311yescharacteristic
347C24×C4—832no—
348C24×C4C2×D8311yescharacteristic
349C24×C4C2×D8311yescharacteristic
350C2×C22⋊Q8—838no—
351C2×C22⋊Q8—838no—
352C2×C22⋊Q8—1668no—
353C2×C22⋊Q8—1668no—
354C2×C4×D4—28no—
355C2×C4×D4C2×D8318yes—
356C22×C4⋊C4—832no—
357C22×C4⋊C4—831no—
358C22×C4⋊C4—832no—
359C22×C4⋊C4—832no—
360C22×C4⋊C4—832no—
361C22×C4⋊C4—831no—
362C22×C4⋊C4—831no—
363C22×C4⋊C4—838no—
364C22×C4⋊C4—1668no—
365C22×C4⋊C4C2×D8311yescharacteristic
366C22×C22⋊C4—832no—
367C22×C22⋊C4—832no—
368C22×C22⋊C4—832no—
369C22×C22⋊C4C2×D8311yescharacteristic
370C22×C22⋊C4C2×D8311yescharacteristic
371C22×C42C2×D8311yescharacteristic
372#398—8316no—
373#396—8316no—
374#391—838no—
375#389—838no—
376#386—8316no—
377#380—838no—
378#380—8316no—
379C2×#95—832no—
380C2×#95—832no—
381C2×#95—832no—
382C2×#95—832no—
383C25C22×D8311yescharacteristic
384C25C22×D8311yescharacteristic
385C22×Q8—834no—
386C22×Q8—1664no—
387C22×Q8—1664no—
388C22×Q8—1664no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4Dic16618yescomplemented
392C22×D4C22×D8314yes—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—3324no—
399C23×C4—838no—
400C23×C4—832no—
401C23×C4—832no—
402C23×C4—832no—
403C23×C4—832no—
404C23×C4—1668no—
405C23×C4—1668no—
406C23×C4C22⋊D8318yes—
407C23×C4C22×D8314yes—
408C23×C4C22×D8311yescharacteristic
409C23×C4C22×D8311yescharacteristic
410C23×C4C22×D8314yes—
411C23×C4C22×D8311yescharacteristic
412C23×C4C22×D8311yescharacteristic
413C23×C4C22×D8311yescharacteristic
414C22⋊Q8—16632no—
415C22⋊Q8—16632no—
416C4×D4—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—3324no—
419C2×C4⋊C4—838no—
420C2×C4⋊C4—838no—
421C2×C4⋊C4—834no—
422C2×C4⋊C4—834no—
423C2×C4⋊C4—838no—
424C2×C4⋊C4—834no—
425C2×C4⋊C4—838no—
426C2×C4⋊C4—838no—
427C2×C4⋊C4—16632no—
428C2×C4⋊C4—1668no—
429C2×C4⋊C4—1668no—
430C2×C4⋊C4—1664no—
431C2×C4⋊C4—1668no—
432C2×C4⋊C4—1664no—
433C2×C4⋊C4C22×D8314yes—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—3324no—
437C2×C22⋊C4—838no—
438C2×C22⋊C4—838no—
439C2×C22⋊C4—838no—
440C2×C22⋊C4—1668no—
441C2×C22⋊C4—1668no—
442C2×C22⋊C4C22×D8314yes—
443C2×C22⋊C4C22×D8314yes—
444C2×C42—24no—
445C2×C42C22×D8314yes—
446#95—838no—
447#95—838no—
448#95—838no—
449#95—838no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×C22⋊D8314yes—
461C24C2×Dic16614yes—
462C24C2×Dic16614yes—
463C24#1305059014yes—
464C24C23×D8312yes—
465C24C23×D8312yes—
466C24C23×D8311yescharacteristic
467C2×Q8—33216no—
468C2×Q8—1668no—
469C2×Q8—1668no—
470C2×Q8—1668no—
471C2×D4—232no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4C2×Dic166116yescomplemented
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—232no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—416no—
492C22×C4—33232no—
493C22×C4—3328no—
494C22×C4—838no—
495C22×C4—834no—
496C22×C4—834no—
497C22×C4—834no—
498C22×C4—834no—
499C22×C4—16616no—
500C22×C4—1664no—
501C22×C4—1664no—
502C22×C4—1664no—
503C22×C4—1664no—
504C22×C4—1664no—
505C22×C4—1664no—
506C22×C4—16616no—
507C22×C4—1664no—
508C22×C4—1664no—
509C22×C4—1664no—
510C22×C4—1664no—
511C22×C4—1664no—
512C22×C4D4×D8314yes—
513C22×C4C2×C22⋊D8314yes—
514C22×C4C2×C22⋊D83116yes—
515C22×C4C2×C22⋊D8314yes—
516C22×C4C2×Dic16614yes—
517C22×C4#1305058914yes—
518C22×C4C23×D8312yes—
519C22×C4C23×D8312yes—
520C22×C4C23×D8312yes—
521C22×C4C23×D8312yes—
522C22×C4C23×D8312yes—
523C4⋊C4—28no—
524C4⋊C4—3328no—
525C4⋊C4—8316no—
526C4⋊C4—16616no—
527C4⋊C4—16616no—
528C4⋊C4—1668no—
529C4⋊C4—16616no—
530C4⋊C4—1668no—
531C22⋊C4—28no—
532C22⋊C4—28no—
533C22⋊C4—3328no—
534C22⋊C4—16616no—
535C22⋊C4—16616no—
536C42—28no—
537C23—28no—
538C23—28no—
539C23—28no—
540C23—28no—
541C23—28no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—28no—
547C23—28no—
548C23—28no—
549C23—28no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23#14581771116yescomplemented
561C23C2×D4×D8312yes—
562C23C22×C22⋊D8314yes—
563C23C22×C22⋊D8312yes—
564C23C22×Dic16614yes—
565C23C22×Dic16614yes—
566C23C22×Dic16612yes—
567C23C2×#1305058912yes—
568C23C2×#1305059014yes—
569C23C2×#1305059012yes—
570C23#1458183812yes—
571C23#1458183912yes—
572C23C24×D8311yescharacteristic
573Q8—33216no—
574D4—232no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—232no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—416no—
591C2×C4—3328no—
592C2×C4—3328no—
593C2×C4—3328no—
594C2×C4—33232no—
595C2×C4—838no—
596C2×C4—1664no—
597C2×C4—1664no—
598C2×C4—1664no—
599C2×C4—1664no—
600C2×C4—1664no—
601C2×C4—1664no—
602C2×C4—1664no—
603C2×C4—1664no—
604C2×C4—1664no—
605C2×C4—16616no—
606C2×C4—1664no—
607C2×C4—1664no—
608C2×C4#14581764116yes—
609C2×C4C2×D4×D8314yes—
610C2×C4C22×C22⋊D8314yes—
611C2×C4C22×C22⋊D8314yes—
612C2×C4C22×Dic16614yes—
613C2×C4C2×#1305058914yes—
614C22—232no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—416no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22C2×#1458176414yes—
630C22C2×#1458177114yes—
631C22C2×#1458177118yescomplemented
632C22#1912827914yes—
633C22#1912834714yes—
634C22D4×Dic16614yes—
635C22#1912839114yes—
636C22#1912840814yes—
637C22C22×D4×D8311yescharacteristic
638C22C23×C22⋊D8311yescharacteristic
639C22C23×Dic16611yescharacteristic
640C22C22×#1305058911yescharacteristic
641C22C22×#1305059011yescharacteristic
642C22C2×#1458183811yescharacteristic
643C22C2×#1458183911yescharacteristic
644C4—24no—
645C4—24no—
646C4—42no—
647C4—42no—
648C4—3324no—
649C4—3324no—
650C4—3324no—
651C4—1668no—
652C4C2×#1458176418yes—
653C2—28no—
654C2—44no—
655C2#2491091418yesdirect product factor
656C2C22×#1458176411yescharacteristic
657C2C22×#1458177111yescharacteristic
658C2C2×#1912827911yescharacteristic
659C2C2×#1912834711yescharacteristic
660C2C2×D4×Dic16611yescharacteristic
661C2C2×#1912839111yescharacteristic
662C2C2×#1912840811yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×C4×D4×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
hypercenterC22×C4×D4D83
hypocenterC83C2×#2417
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14581771C2semidirect
2. C22×#14581771C2semidirect
3. C23×C4⋊Dic83C2semidirect
4. #24910914C2direct (N × H)
5. C2×#19127634C2semidirect
6. C2×#19127624C2semidirect
7. C2×#19127607C2semidirect
8. C2×#19127599C2semidirect
10. C2×#19127561C2semidirect
11. C2×#19127559C2semidirect
17. C2×#14581771C22semidirect
18. C2×#14581771C22semidirect
24. C22×C4⋊Dic83C22semidirect
31. #19127634C22semidirect
32. #19127624C22semidirect
33. #19127607C22semidirect
34. #19127599C22semidirect
36. #19127561C22semidirect
37. #19127559C22semidirect
69. C2×C4⋊Dic83D4semidirect
94. C22×D4×C83Q8semidirect
145. C4⋊Dic83C2×D4semidirect
172. C2×D4×C83C2×Q8semidirect
228. C23×C83C22⋊Q8semidirect
299. C22×C83C2×C22⋊Q8semidirect
324. C2×C83#2417semidirect
344. C83C2×#2417semidirect
391. C22×D4Dic166semidirect
474. C2×D4C2×Dic166semidirect
560. C23#14581771semidirect
631. C22C2×#14581771semidirect
655. C2#24910914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817712
C23×C4⋊Dic832
#249109142
C2×#191276342
C2×#191276242
C2×#191276072
C2×#191275992
C2×#191275812
C2×#191275612
C2×#191275592
C22×C4×D4×C832
C2×#241783