Finite Group Databasebeta

← #7626947

Subgroups — #7626947

Order 512.

7970 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic
2#34487C212yesmaximal, complemented
3#34475C214yesmaximal, complemented
4#34469C218yesmaximal, complemented
5#34460C214yesmaximal, complemented
6#34412C214yesmaximal, complemented
7#34409C218yesmaximal, complemented
8#34398C212yesmaximal, complemented
9#34371C211yesmaximal, characteristic, complemented
10#34367C211yesmaximal, characteristic, complemented
11#34365C212yesmaximal, complemented
12#34334C212yesmaximal, complemented
13#34308C212yesmaximal, complemented
14#34298C214yesmaximal, complemented
15#34289C214yesmaximal, complemented
16#34259C214yesmaximal, complemented
17#34222C212yesmaximal, complemented
18#34216C211yesmaximal, characteristic, complemented
19#34191C211yesmaximal, characteristic, complemented
20C4×#547C212yesmaximal, complemented
21#34123C211yesmaximal, characteristic, complemented
22#34086C211yesmaximal, characteristic, complemented
23C2×#2331C212yesmaximal, complemented
24C22×2−1+4C2212yes—
25#3499C4132yescomplemented
26C2×D4×Q8C2212yes—
27C2×D4×Q8C2212yes—
28C2×#547C2212yes—
29C2×#547C2214yes—
30C2×#547C2214yes—
31C2×#547C2212yes—
32C2×#536C2214yes—
33C2×#536C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C22×C4⋊Q8C2212yes—
37C22×C4⋊Q8C2211yescharacteristic
38C2×#520C2214yes—
39C2×C4×#41C2214yes—
40C2×C4×#41C2211yescharacteristic
41#2381C2218yes—
42#2381C2214yes—
43#2379C2218yes—
44#2378C2218yes—
45#2378C2218yes—
46#2377C2214yes—
47#2376C2218yes—
48#2374C2218yes—
49#2372C2218yes—
50#2369C2214yes—
51#2369C2214yes—
52#2369C2214yes—
53#2368C2218yes—
54#2368C2218yes—
55#2365C2212yes—
56#2365C2212yes—
57#2365C2214yes—
58#2364C2218yes—
59#2363C2214yes—
60#2362C2214yes—
61#2362C2214yes—
62#2361C2214yes—
63#2361C2214yes—
64#2360C2214yes—
65#2360C2214yes—
66#2359C2218yes—
67#2359C2218yes—
68#2359C2218yes—
69#2359C2218yes—
70#2357C2214yes—
71#2356C2212yes—
72#2355C2212yes—
73#2354C2212yes—
74#2353C2214yes—
75#2353C2218yes—
76#2352C2214yes—
77#2352C2214yes—
78#2349C2214yes—
79#2349C2212yes—
80D4×C4⋊C4C2212yes—
81D4×C4⋊C4C2212yes—
82#2346C2212yes—
83#2346C2212yes—
84#2345C2214yes—
85#2345C2214yes—
86#2344C2214yes—
87#2344C2214yes—
88#2344C2218yes—
89#2343C2214yes—
90#2343C2214yes—
91Q8×C22⋊C4C2214yes—
92Q8×C22⋊C4C2214yes—
93Q8×C22⋊C4C2214yes—
94Q8×C22⋊C4C2214yes—
95#2339C2214yes—
96#2339C2212yes—
97#2339C2218yes—
98#2339C2218yes—
99#2339C2214yes—
100#2339C2212yes—
101#2339C2218yes—
102#2339C2218yes—
103#2337C2214yes—
104#2337C2214yes—
105#2335C2218yes—
106#2335C2218yes—
107#2333C2214yes—
108#2332C2218yes—
109#2332C2218yes—
110#2331C2211yescharacteristic
111#2331C2214yes—
112#2331C2212yes—
113#2331C2212yes—
114#2331C2218yes—
115#2331C2214yes—
116#2331C2218yes—
117#2331C2212yes—
118#2331C2211yescharacteristic
119#2331C2212yes—
120#2331C2212yes—
121#2331C2218yes—
122#2329C2218yes—
123#2329C2218yes—
124#2328C2211yescharacteristic
125#2328C2211yescharacteristic
126#2328C2212yes—
127#2327C2214yes—
128#2325C2218yes—
129#2324C2212yes—
130#2324C2212yes—
131#2323C2214yes—
132#2323C2214yes—
133#2322C2218yes—
134#2322C2218yes—
135#2320C2212yes—
136#2319C2214yes—
137#2318C2218yes—
138#2318C2214yes—
139#2316C2212yes—
140#2313C2214yes—
141#2311C2214yes—
142#2311C2218yes—
143#2310C2218yes—
144#2310C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2212yes—
147C4×C22⋊Q8C2214yes—
148C4×C22⋊Q8C2214yes—
149C4×#123C2218yes—
150C4×#123C2218yes—
151C4×#121C2214yes—
152C4×#121C2214yes—
153#2297C2214yes—
154#2297C2218yes—
155#2295C2211yescharacteristic
156#2295C2211yescharacteristic
157C2×#391C2218yes—
158C2×#391C2214yes—
159#2293C2212yes—
160C2×#389C2214yes—
161#2290C2214yes—
162#2290C2212yes—
163#2290C2212yes—
164C2×#387C2218yes—
165#2285C2211yescharacteristic
166#2283C2211yescharacteristic
167#2283C2212yes—
168#2283C2212yes—
169#2283C2211yescharacteristic
170C2×#382C2212yes—
171#2275C2214yes—
172#2275C2212yes—
173#2274C2212yes—
174C42×D4C2211yescharacteristic
175C42×D4C2212yes—
176C42×D4C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C2×C4×C4⋊C4C2214yes—
179C2×#376C2212yes—
180C2×2−1+4—416no—
181C2×2−1+4C2×C4132yescomplemented
182C22×#41C2311yescharacteristic
183C22×#41C2314yes—
184C22×#41C2312yes—
185C22×#41C2318yes—
186C22×#41C2314yes—
187C23×Q8C2314yes—
188C23×Q8C2314yes—
189C23×Q8C2312yes—
190D4×Q8C2×C4132yescomplemented
191D4×Q8C2×C4132yescomplemented
192#547C2×C4132yescomplemented
193#547C2×C4132yescomplemented
194#547C2×C4164yescomplemented
195#547C2×C4164yescomplemented
196#536C2×C4164yescomplemented
197#536C2×C4132yescomplemented
198#532C2×C4116yescomplemented
199#532C2×C4132yescomplemented
200C2×C4⋊Q8C2×C4132yescomplemented
201C2×C4⋊Q8C2×C4116yescomplemented
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#124C2312yes—
212C2×#124C2314yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2312yes—
223C2×#121C2314yes—
224#520—416no—
225C4×#41—416no—
226C4×#41C2×C4116yescomplemented
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2318yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2318yes—
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2312yes—
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2318yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C42C2312yes—
268C22×C42C2318yes—
269C22×C42C2314yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2311yescharacteristic
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2312yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2318yes—
287#391C2314yes—
288#391C2318yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#391C2318yes—
293#391C2318yes—
294#391C2312yes—
295#390C2314yes—
296#390C2318yes—
297#390C2312yes—
298#390C2314yes—
299#390C2312yes—
300#390C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#389C2318yes—
310#389C2312yes—
311#389C2318yes—
312#389C2312yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#389C2318yes—
317#389C2312yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2314yes—
328#388C2314yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#387C2314yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2314yes—
357#387C2318yes—
358#387C2314yes—
359#387C2314yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2314yes—
367#386C2318yes—
368#386C2318yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2314yes—
374#386C2314yes—
375#386C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2318yes—
385#385C2314yes—
386#384C2312yes—
387#383C2314yes—
388#383C2314yes—
389#383C2312yes—
390#383C2312yes—
391#382C2314yes—
392#382C2312yes—
393#382C2311yescharacteristic
394#382C2312yes—
395#382C2311yescharacteristic
396#382C2314yes—
397#382C2314yes—
398#382C2314yes—
399#381C2314yes—
400#381C2314yes—
401#381C2318yes—
402#381C2318yes—
403#381C2318yes—
404#381C2318yes—
405#381C2312yes—
406#381C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2318yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2312yes—
417#380C2314yes—
418#380C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2312yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2312yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2318yes—
469#376C2312yes—
470#376C2312yes—
471#376C2311yescharacteristic
472#376C2312yes—
473#376C2311yescharacteristic
474#376C2314yes—
475#376C2314yes—
476#376C2314yes—
477#376C2312yes—
478C2×#95C2314yes—
479C2×#95C2318yes—
480C2×#95C2318yes—
481C2×#95C2314yes—
482C2×#95C2314yes—
483C2×#95C2318yes—
484C2×#95C2318yes—
485C2×#95C2314yes—
486C43C2311yescharacteristic
487C43C2311yescharacteristic
4882−1+4—4128no—
489C2×#41—216no—
490C2×#41—216no—
491C2×#41—28no—
492C2×#41—48no—
493C2×#41—416no—
494C2×#41—416no—
495C2×#41—416no—
496C2×#41C22×C418yes—
497C2×#41C22×C4132yes—
498C2×#41C22×C4116yes—
499C2×#41C22×C4132yes—
500C2×#41C22×C4164yes—
501C22×Q8—416no—
502C22×Q8—48no—
503C22×Q8—48no—
504C22×Q8—48no—
505C22×Q8C22×C4132yes—
506C22×Q8C22×C4116yes—
507C22×Q8C22×C4132yes—
508C22×Q8C2414yes—
509C22×Q8C2411yescharacteristic
510C22×Q8C2418yes—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×D4C2412yes—
514C22×D4C2418yes—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C23×C4C2414yes—
521C23×C4C2412yes—
522C23×C4C2418yes—
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2412yes—
526C23×C4C2411yescharacteristic
527C23×C4C2418yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2418yes—
531C23×C4C2414yes—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2414yes—
535C23×C4C2418yes—
536C4⋊Q8C22×C418yes—
537C4⋊Q8C22×C4116yes—
538C4⋊Q8C22×C4132yes—
539C4⋊Q8C22×C4116yes—
540C4⋊Q8C22×C4116yes—
541C4⋊Q8C22×C4116yes—
542C4⋊Q8C22×C4132yes—
543C4⋊Q8C22×C4132yes—
544#127C22×C418yes—
545#124C22×C4116yes—
546#124C22×C4132yes—
547#123C22×C4164yes—
548#123C22×C4164yes—
549#123C22×C4164yes—
550C22⋊Q8C22×C4132yes—
551C22⋊Q8C22×C4132yes—
552C22⋊Q8C22×C4164yes—
553C22⋊Q8C22×C4164yes—
554#121C22×C4132yes—
555#121C22×C4116yes—
556#121C22×C4132yes—
557#121C22×C4116yes—
558C4×Q8—48no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×Q8—48no—
562C4×Q8C22×C418yes—
563C4×Q8C22×C418yes—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—48no—
569C4×D4—44no—
570C4×D4—416no—
571C4×D4—416no—
572C4×D4—416no—
573C4×D4—416no—
574C4×D4C22×C4116yes—
575C4×D4C22×C418yes—
576C4×D4C22×C4116yes—
577C4×D4C22×C418yes—
578C4×D4C22×C4116yes—
579C4×D4C22×C4116yes—
580C4×D4C22×C4132yes—
581C4×D4C22×C4132yes—
582#117—24no—
583#117—42no—
584#117—48no—
585#117—416no—
586#117—416no—
587#117—44no—
588#117—48no—
589#117C22×C4116yes—
590#117C22×C418yes—
591C2×C4⋊C4—48no—
592C2×C4⋊C4—48no—
593C2×C4⋊C4—416no—
594C2×C4⋊C4C22×C4132yes—
595C2×C4⋊C4C22×C4116yes—
596C2×C4⋊C4C22×C4132yes—
597C2×C4⋊C4C22×C4116yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C42—28no—
654C2×C42—48no—
655C2×C42—44no—
656C2×C42—416no—
657C2×C42C22×C4116yes—
658C2×C42C22×C418yes—
659C2×C42C2412yes—
660C2×C42C2411yescharacteristic
661C2×C42C2414yes—
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2418yes—
671C2×C42C2418yes—
672C2×C42C2414yes—
673C2×C42C2418yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#95C2414yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2414yes—
693#95C2418yes—
694#95C2418yes—
695#95C2412yes—
696#95C2418yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2412yes—
715#95C2414yes—
716#95C2418yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2412yes—
725#95C2414yes—
726#95C2412yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731C24C2514yes—
732C24C2511yescharacteristic
733C24C2512yes—
734#41—2128no—
735#41—232no—
736#41—432no—
737#41—464no—
738#41—4128no—
739C2×Q8—28no—
740C2×Q8—28no—
741C2×Q8—24no—
742C2×Q8—48no—
743C2×Q8—44no—
744C2×Q8—48no—
745C2×Q8—48no—
746C2×Q8—464no—
747C2×Q8—432no—
748C2×Q8—464no—
749C2×Q8C23×C414yes—
750C2×Q8C23×C4116yes—
751C2×Q8C23×C4132yes—
752C2×Q8C23×C418yes—
753C2×Q8C23×C4116yes—
754C2×D4—216no—
755C2×D4—216no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4C23×C418yes—
764C2×D4C23×C418yes—
765C2×D4C23×C4132yes—
766C2×D4C23×C418yes—
767C2×D4C23×C4116yes—
768C2×D4C23×C418yes—
769C2×D4C23×C414yes—
770C2×D4H(5,𝔽2)18yes—
771C22×C4—216no—
772C22×C4—216no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—48no—
800C22×C4—44no—
801C22×C4—48no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4C23×C414yes—
805C22×C4C23×C418yes—
806C22×C4C23×C418yes—
807C22×C4C23×C414yes—
808C22×C4C23×C4132yes—
809C22×C4C23×C4116yes—
810C22×C4C23×C414yes—
811C22×C4C23×C418yes—
812C22×C4C23×C4116yes—
813C22×C4C23×C4132yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2518yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2514yes—
830C22×C4C2518yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—42no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4C23×C418yes—
854C4⋊C4C23×C4116yes—
855C4⋊C4C23×C418yes—
856C4⋊C4C23×C4116yes—
857C4⋊C4C23×C4132yes—
858C4⋊C4C23×C4116yes—
859C4⋊C4C23×C4132yes—
860C4⋊C4C23×C4116yes—
861C4⋊C4C23×C418yes—
862C4⋊C4C23×C418yes—
863C4⋊C4C23×C414yes—
864C4⋊C4C23×C414yes—
865C22⋊C4—28no—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—24no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—42no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4C23×C418yes—
883C22⋊C4C23×C418yes—
884C22⋊C4C23×C418yes—
885C22⋊C4C23×C4116yes—
886C22⋊C4C23×C4132yes—
887C22⋊C4C23×C4116yes—
888C22⋊C4C23×C4132yes—
889C42—24no—
890C42—28no—
891C42—24no—
892C42—28no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—22no—
898C42—44no—
899C42—44no—
900C42—44no—
901C42—48no—
902C42—48no—
903C42—48no—
904C42—42no—
905C42—48no—
906C42—42no—
907C42—44no—
908C42—48no—
909C42—48no—
910C42C23×C414yes—
911C42C23×C418yes—
912C42C23×C414yes—
913C42C23×C418yes—
914C42C23×C414yes—
915C42C23×C418yes—
916C42C23×C414yes—
917C422−1+414yescomplemented
918C23—22no—
919C23—22no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—21no—
925C23—24no—
926C23—21no—
927C23—24no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23C24×C418yes—
932C23C24×C412yes—
933C23C24×C414yes—
934C23C2×H(5,𝔽2)18yes—
935C23C2611yescharacteristic
936Q8—28no—
937Q8—232no—
938Q8—48no—
939Q8—416no—
940Q8—432no—
941D4—264no—
942D4—216no—
943D4—216no—
944D4—48no—
945D4—48no—
946D4—416no—
947D4#518116yes—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—28no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—216no—
964C2×C4—264no—
965C2×C4—28no—
966C2×C4—232no—
967C2×C4—216no—
968C2×C4—28no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—48no—
994C2×C4—44no—
995C2×C4—432no—
996C2×C4—416no—
997C2×C4—416no—
998C2×C4—88no—
999C2×C4—88no—
1000C2×C4—816no—
1001C2×C4—88no—
1002C2×C4—168no—
1003C2×C4C24×C412yes—
1004C2×C4C24×C412yes—
1005C2×C4C24×C414yes—
1006C2×C4C24×C412yes—
1007C2×C4C24×C414yes—
1008C2×C4C24×C412yes—
1009C2×C4C24×C414yes—
1010C2×C4C24×C418yes—
1011C2×C4C24×C4116yes—
1012C2×C4C24×C412yes—
1013C2×C4C24×C412yes—
1014C2×C4C2×H(5,𝔽2)14yes—
1015C2×C4C2×2−1+414yes—
1016C2×C4C2×2−1+412yes—
1017C2×C4#58512yes—
1018C22—24no—
1019C22—24no—
1020C22—28no—
1021C22—28no—
1022C22—22no—
1023C22—28no—
1024C22—22no—
1025C22—28no—
1026C22—22no—
1027C22—28no—
1028C22—44no—
1029C22—44no—
1030C22—42no—
1031C22—44no—
1032C22—44no—
1033C22—42no—
1034C22C2×#51818yes—
1035C22C25×C411yescharacteristic
1036C22C22×H(5,𝔽2)12yes—
1037C22C22×2−1+411yescharacteristic
1038C22C2×#58511yescharacteristic
1039C222−1+612yes—
1040C4—22no—
1041C4—28no—
1042C4—24no—
1043C4—216no—
1044C4—24no—
1045C4—22no—
1046C4—22no—
1047C4—24no—
1048C4—22no—
1049C4—24no—
1050C4—42no—
1051C4—44no—
1052C4—44no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—48no—
1057C4—44no—
1058C4C2×#51814yes—
1059C4C4×2−1+414yes—
1060C2—28no—
1061C2—42no—
1062C2—48no—
1063C2C22×#51811yescharacteristic
1064C2C2×C4×2−1+411yescharacteristic
1065C2#6265311yescharacteristic
1066C2#6291512yes—
1067C2#6292112yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3499C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34487C2semidirect
3. #34475C2semidirect
4. #34469C2semidirect
5. #34460C2semidirect
6. #34412C2semidirect
7. #34409C2semidirect
8. #34398C2semidirect
9. #34371C2semidirect
10. #34367C2semidirect
11. #34365C2semidirect
12. #34334C2semidirect
13. #34308C2semidirect
14. #34298C2semidirect
15. #34289C2semidirect
16. #34259C2semidirect
17. #34222C2semidirect
18. #34216C2semidirect
19. #34191C2semidirect
20. C4×#547C2semidirect
21. #34123C2semidirect
22. #34086C2semidirect
23. C2×#2331C2semidirect
25. #3499C4semidirect
181. C2×2−1+4C2×C4semidirect
190. D4×Q8C2×C4semidirect
191. D4×Q8C2×C4semidirect
192. #547C2×C4semidirect
193. #547C2×C4semidirect
194. #547C2×C4semidirect
195. #547C2×C4semidirect
196. #536C2×C4semidirect
197. #536C2×C4semidirect
198. #532C2×C4semidirect
199. #532C2×C4semidirect
200. C2×C4⋊Q8C2×C4semidirect
201. C2×C4⋊Q8C2×C4semidirect
226. C4×#41C2×C4semidirect
917. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
#344872
#344752
#344692
#344602
#344122
#344092
#343982
#343712
#343672
#343652
#343342
#343082
#342982
#342892
#342592
#342222
#342162
#341912
C4×#5472
#341232
#340862
C2×#23312