Finite Group Databasebeta

← #7626959

Subgroups — #7626959

Order 512.

6982 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#34506C218yesmaximal, complemented
3#34496C214yesmaximal, complemented
4#34480C212yesmaximal, complemented
5#34464C214yesmaximal, complemented
6#34453C218yesmaximal, complemented
7#34410C214yesmaximal, complemented
8#34402C212yesmaximal, complemented
9#34399C212yesmaximal, complemented
10#34371C211yesmaximal, characteristic, complemented
11#34367C211yesmaximal, characteristic, complemented
12#34322C212yesmaximal, complemented
13#34312C214yesmaximal, complemented
14#34308C212yesmaximal, complemented
15#34306C214yesmaximal, complemented
16#34253C214yesmaximal, complemented
17#34209C211yesmaximal, characteristic, complemented
18#34208C212yesmaximal, complemented
19#34191C211yesmaximal, characteristic, complemented
20C4×#556C212yesmaximal, complemented
21#34125C211yesmaximal, characteristic, complemented
22#34086C211yesmaximal, characteristic, complemented
23#34085C212yesmaximal, complemented
24#3511C4132yescomplemented
25C2×#556C2212yes—
26C2×#555C2212yes—
27C2×#554C2212yes—
28C2×#553C2214yes—
29C2×#548C2214yes—
30C2×#547C2212yes—
31C2×#542C2214yes—
32C2×#537C2212yes—
33C2×#533C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C22×C4⋊Q8C2211yescharacteristic
37C2×#520C2214yes—
38C2×#520C2212yes—
39C2×#519C2212yes—
40C2×C4×#41C2211yescharacteristic
41#2382C2218yes—
42#2381C2214yes—
43#2378C2218yes—
44#2377C2214yes—
45#2377C2218yes—
46#2377C2218yes—
47#2376C2218yes—
48#2373C2218yes—
49#2373C2218yes—
50#2372C2218yes—
51#2367C2218yes—
52#2367C2214yes—
53#2367C2214yes—
54#2365C2214yes—
55#2365C2212yes—
56#2365C2212yes—
57#2365C2214yes—
58#2364C2218yes—
59#2364C2218yes—
60#2363C2214yes—
61#2363C2214yes—
62#2363C2218yes—
63#2362C2214yes—
64#2361C2214yes—
65#2360C2214yes—
66#2360C2214yes—
67#2360C2218yes—
68#2360C2214yes—
69#2359C2218yes—
70#2357C2212yes—
71#2357C2214yes—
72#2356C2214yes—
73#2355C2212yes—
74#2354C2212yes—
75#2353C2218yes—
76#2353C2218yes—
77#2352C2214yes—
78#2352C2214yes—
79#2352C2218yes—
80#2352C2218yes—
81#2352C2218yes—
82#2351C2214yes—
83#2351C2212yes—
84D4×C4⋊C4C2212yes—
85D4×C4⋊C4C2212yes—
86#2347C2214yes—
87#2347C2214yes—
88#2347C2212yes—
89#2346C2214yes—
90#2346C2212yes—
91#2345C2214yes—
92#2345C2214yes—
93#2344C2214yes—
94#2344C2214yes—
95#2344C2214yes—
96#2343C2218yes—
97#2343C2214yes—
98#2341C2214yes—
99#2341C2212yes—
100Q8×C22⋊C4C2214yes—
101#2339C2214yes—
102#2339C2212yes—
103#2337C2218yes—
104#2337C2214yes—
105#2337C2214yes—
106#2336C2218yes—
107#2335C2218yes—
108#2334C2218yes—
109#2333C2218yes—
110#2333C2214yes—
111#2333C2218yes—
112#2332C2218yes—
113#2331C2214yes—
114#2331C2211yescharacteristic
115#2331C2212yes—
116#2331C2211yescharacteristic
117#2329C2218yes—
118#2329C2218yes—
119#2328C2211yescharacteristic
120#2328C2211yescharacteristic
121#2328C2212yes—
122#2327C2212yes—
123#2327C2212yes—
124#2327C2212yes—
125#2327C2212yes—
126#2324C2214yes—
127#2324C2212yes—
128#2324C2218yes—
129#2324C2212yes—
130#2323C2214yes—
131#2323C2218yes—
132#2323C2214yes—
133#2323C2214yes—
134#2322C2218yes—
135#2320C2218yes—
136#2320C2212yes—
137#2319C2218yes—
138#2318C2218yes—
139#2318C2214yes—
140#2316C2214yes—
141#2313C2214yes—
142#2311C2214yes—
143#2311C2214yes—
144#2310C2212yes—
145C4×C4⋊Q8C2212yes—
146C4×C4⋊Q8C2212yes—
147C4×#126C2218yes—
148C4×#124C2218yes—
149C4×#124C2214yes—
150C4×#124C2214yes—
151C4×C22⋊Q8C2214yes—
152C4×#121C2214yes—
153#2298C2218yes—
154#2297C2214yes—
155#2295C2214yes—
156#2295C2218yes—
157#2293C2211yescharacteristic
158#2293C2212yes—
159#2293C2218yes—
160#2293C2212yes—
161#2293C2211yescharacteristic
162#2293C2212yes—
163C2×#389C2214yes—
164#2290C2214yes—
165#2285C2211yescharacteristic
166#2283C2212yes—
167#2283C2211yescharacteristic
168#2283C2211yescharacteristic
169#2283C2212yes—
170C2×#382C2212yes—
171#2275C2212yes—
172#2274C2214yes—
173C42×Q8C2214yes—
174C42×Q8C2211yescharacteristic
175C42×Q8C2211yescharacteristic
176C42×D4C2212yes—
177C4×#117C2214yes—
178C4×#117C2212yes—
179C4×#117C2211yescharacteristic
180C22×#41C2312yes—
181C22×#41C2314yes—
182C22×#41C2311yescharacteristic
183C23×Q8C2312yes—
184#556C2×C4132yescomplemented
185#555C2×C4132yescomplemented
186#554C2×C4132yescomplemented
187#553C2×C4164yescomplemented
188#548C2×C4164yescomplemented
189#547C2×C4132yescomplemented
190#542C2×C4164yescomplemented
191#537C2×C4132yescomplemented
192#533C2×C4132yescomplemented
193#532C2×C4116yescomplemented
194#532C2×C4132yescomplemented
195C2×C4⋊Q8C2×C4116yescomplemented
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#127C2311yescharacteristic
202C2×#126C2318yes—
203C2×#125C2314yes—
204C2×#124C2312yes—
205C2×#124C2318yes—
206C2×#124C2314yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×#121C2312yes—
213C2×#121C2318yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218#520—416no—
219#520C2×C4132yescomplemented
220#519—48no—
221C4×#41C2×C4116yescomplemented
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2318yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2312yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2318yes—
256C2×#117C2318yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2311yescharacteristic
260C2×#117C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2318yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2312yes—
267C22×C42C2314yes—
268C22×C42C2311yescharacteristic
269C22×C42C2312yes—
270#391C2314yes—
271#391C2314yes—
272#391C2318yes—
273#391C2318yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#391C2314yes—
280#391C2318yes—
281#390C2312yes—
282#390C2318yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2312yes—
287#390C2314yes—
288#390C2312yes—
289#390C2318yes—
290#390C2318yes—
291#390C2314yes—
292#390C2312yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2312yes—
298#389C2318yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2312yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2312yes—
311#389C2314yes—
312#389C2312yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2314yes—
319#388C2318yes—
320#388C2314yes—
321#388C2318yes—
322#388C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2314yes—
331#388C2318yes—
332#388C2314yes—
333#388C2314yes—
334#388C2314yes—
335#388C2314yes—
336#388C2318yes—
337#388C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2314yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2314yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2314yes—
374#386C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2314yes—
383#384C2312yes—
384#383C2318yes—
385#383C2314yes—
386#383C2314yes—
387#383C2312yes—
388#383C2312yes—
389#382C2314yes—
390#382C2314yes—
391#382C2314yes—
392#382C2318yes—
393#382C2311yescharacteristic
394#382C2312yes—
395#382C2311yescharacteristic
396#382C2312yes—
397#382C2314yes—
398#381C2318yes—
399#381C2312yes—
400#381C2312yes—
401#381C2318yes—
402#381C2314yes—
403#381C2314yes—
404#380C2312yes—
405#380C2312yes—
406#380C2318yes—
407#380C2318yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2318yes—
412#380C2312yes—
413#380C2314yes—
414#380C2312yes—
415#380C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2312yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472#376C2318yes—
473#376C2312yes—
474#376C2311yescharacteristic
475#376C2312yes—
476#376C2311yescharacteristic
477#376C2314yes—
478#376C2318yes—
479C2×#95C2318yes—
480C2×#95C2314yes—
481C2×#95C2314yes—
482C43C2318yes—
483C43C2311yescharacteristic
484C43C2311yescharacteristic
485C43C2312yes—
486C43C2312yes—
487C2×#41—48no—
488C2×#41—48no—
489C2×#41—48no—
490C2×#41—44no—
491C2×#41C22×C418yes—
492C2×#41C22×C4116yes—
493C2×#41C22×C4132yes—
494C22×Q8—44no—
495C22×Q8—44no—
496C22×Q8C22×C4116yes—
497C22×Q8C2411yescharacteristic
498C22×Q8C2414yes—
499C22×Q8C2414yes—
500C22×Q8C2412yes—
501C22×D4C2411yescharacteristic
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2418yes—
505C22×D4C2412yes—
506C22×D4C2414yes—
507C22×D4C2412yes—
508C23×C4C2414yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2414yes—
513C23×C4C2418yes—
514C23×C4C2418yes—
515C23×C4C2414yes—
516C23×C4C2414yes—
517C23×C4C2418yes—
518C23×C4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2412yes—
521C4⋊Q8C22×C4116yes—
522C4⋊Q8C22×C4116yes—
523C4⋊Q8C22×C4116yes—
524C4⋊Q8C22×C4116yes—
525C4⋊Q8C22×C418yes—
526#127C22×C418yes—
527#126C22×C4164yes—
528#125C22×C4132yes—
529#124C22×C4116yes—
530#124C22×C4132yes—
531#124C22×C4164yes—
532#123C22×C4164yes—
533C22⋊Q8C22×C4132yes—
534C22⋊Q8C22×C4132yes—
535C22⋊Q8C22×C4132yes—
536C22⋊Q8C22×C4164yes—
537#121C22×C4132yes—
538#121C22×C4116yes—
539#121C22×C4116yes—
540#121C22×C4132yes—
541#121C22×C4132yes—
542#121C22×C4164yes—
543C4×Q8—216no—
544C4×Q8—416no—
545C4×Q8—44no—
546C4×Q8—44no—
547C4×Q8—48no—
548C4×Q8—48no—
549C4×Q8—48no—
550C4×Q8C22×C418yes—
551C4×Q8C22×C418yes—
552C4×Q8C22×C4132yes—
553C4×Q8C22×C4132yes—
554C4×D4—28no—
555C4×D4—416no—
556C4×D4—48no—
557C4×D4—44no—
558C4×D4—48no—
559C4×D4—416no—
560C4×D4C22×C418yes—
561C4×D4C22×C4116yes—
562C4×D4C22×C4116yes—
563C4×D4C22×C418yes—
564C4×D4C22×C4132yes—
565C4×D4C22×C4164yes—
566C4×D4C22×C4116yes—
567C4×D4C22×C4132yes—
568C4×D4C22×C4116yes—
569#117—24no—
570#117—28no—
571#117—48no—
572#117—42no—
573#117—44no—
574#117—416no—
575#117—416no—
576#117—48no—
577#117—44no—
578#117C22×C418yes—
579#117C22×C4116yes—
580#117C22×C4132yes—
581#117C22×C4132yes—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—416no—
584C2×C4⋊C4—48no—
585C2×C4⋊C4C22×C4116yes—
586C2×C4⋊C4C22×C4132yes—
587C2×C4⋊C4C22×C4116yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C42—48no—
649C2×C42C22×C418yes—
650C2×C42C22×C4116yes—
651C2×C42C2411yescharacteristic
652C2×C42C2418yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2411yescharacteristic
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2418yes—
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2418yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2414yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2418yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2412yes—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#95C2412yes—
684#95C2414yes—
685#95C2412yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2418yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2412yes—
695#95C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2418yes—
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2412yes—
706#95C2414yes—
707#95C2418yes—
708#95C2414yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2412yes—
720#95C2418yes—
721#95C2412yes—
722C24C2511yescharacteristic
723C24C2512yes—
724C24C2514yes—
725#41—432no—
726#41—416no—
727#41—464no—
728C2×Q8—28no—
729C2×Q8—24no—
730C2×Q8—28no—
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—44no—
734C2×Q8—432no—
735C2×Q8C23×C414yes—
736C2×Q8C23×C4116yes—
737C2×Q8C23×C418yes—
738C2×Q8C23×C4116yes—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4C23×C414yes—
750C2×D4C23×C418yes—
751C2×D4C23×C418yes—
752C2×D4C23×C418yes—
753C2×D4C23×C4116yes—
754C2×D4C23×C418yes—
755C2×D4C23×C4132yes—
756C22×C4—24no—
757C22×C4—22no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—48no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—42no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—48no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4C23×C414yes—
783C22×C4C23×C414yes—
784C22×C4C23×C418yes—
785C22×C4C23×C4116yes—
786C22×C4C23×C414yes—
787C22×C4C23×C418yes—
788C22×C4C23×C418yes—
789C22×C4C23×C4116yes—
790C22×C4C23×C4132yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2518yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2518yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—42no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4C23×C414yes—
833C4⋊C4C23×C4116yes—
834C4⋊C4C23×C4116yes—
835C4⋊C4C23×C4116yes—
836C4⋊C4C23×C4132yes—
837C4⋊C4C23×C4116yes—
838C4⋊C4C23×C414yes—
839C4⋊C4C23×C418yes—
840C4⋊C4C23×C418yes—
841C4⋊C4C23×C418yes—
842C4⋊C4C23×C418yes—
843C4⋊C4C23×C4132yes—
844C22⋊C4—24no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—42no—
858C22⋊C4—48no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4C23×C418yes—
864C22⋊C4C23×C4132yes—
865C22⋊C4C23×C418yes—
866C22⋊C4C23×C418yes—
867C22⋊C4C23×C4132yes—
868C22⋊C4C23×C4132yes—
869C22⋊C4C23×C4116yes—
870C22⋊C4C23×C4116yes—
871C42—24no—
872C42—22no—
873C42—216no—
874C42—24no—
875C42—28no—
876C42—22no—
877C42—24no—
878C42—22no—
879C42—24no—
880C42—44no—
881C42—44no—
882C42—44no—
883C42—44no—
884C42—48no—
885C42—42no—
886C42—42no—
887C42—48no—
888C42—48no—
889C42—48no—
890C42—44no—
891C42—44no—
892C42—44no—
893C42—48no—
894C42C23×C414yes—
895C42C23×C418yes—
896C42C23×C414yes—
897C42C23×C418yes—
898C42C23×C414yes—
899C42C23×C414yes—
900C42C23×C418yes—
901C42C23×C4132yes—
902C42H(5,𝔽2)14yes—
903C23—21no—
904C23—22no—
905C23—24no—
906C23—24no—
907C23—21no—
908C23—22no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—22no—
913C23—22no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23C24×C418yes—
918C23C24×C414yes—
919C23C24×C412yes—
920C23C2611yescharacteristic
921Q8—28no—
922Q8—232no—
923Q8—416no—
924Q8—48no—
925D4—28no—
926D4—216no—
927D4—48no—
928D4—48no—
929D4—416no—
930D4—48no—
931D4—432no—
932C2×C4—28no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—232no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—216no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—24no—
975C2×C4—44no—
976C2×C4—48no—
977C2×C4—416no—
978C2×C4—48no—
979C2×C4—432no—
980C2×C4—88no—
981C2×C4—88no—
982C2×C4—168no—
983C2×C4—168no—
984C2×C4C24×C414yes—
985C2×C4C24×C412yes—
986C2×C4C24×C412yes—
987C2×C4C24×C412yes—
988C2×C4C24×C412yes—
989C2×C4C24×C418yes—
990C2×C4C24×C414yes—
991C2×C4C24×C414yes—
992C2×C4C24×C4116yes—
993C2×C4C24×C412yes—
994C2×C4C24×C412yes—
995C2×C4C2×H(5,𝔽2)14yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4#58514yes—
998C2×C4#58512yes—
999C22—22no—
1000C22—28no—
1001C22—24no—
1002C22—22no—
1003C22—24no—
1004C22—28no—
1005C22—22no—
1006C22—24no—
1007C22—28no—
1008C22—44no—
1009C22—44no—
1010C22—42no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—42no—
1015C22—44no—
1016C22C25×C411yescharacteristic
1017C22C22×H(5,𝔽2)11yescharacteristic
1018C22C2×#58512yes—
1019C22C2×#58511yescharacteristic
1020C222−1+612yes—
1021C4—22no—
1022C4—28no—
1023C4—24no—
1024C4—24no—
1025C4—22no—
1026C4—216no—
1027C4—22no—
1028C4—24no—
1029C4—22no—
1030C4—24no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—48no—
1035C4—42no—
1036C4—44no—
1037C4—44no—
1038C4—42no—
1039C4#342814yes—
1040C4C4×H(5,𝔽2)14yes—
1041C2—42no—
1042C2—48no—
1043C2—44no—
1044C2C2×#342811yescharacteristic
1045C2C2×C4×H(5,𝔽2)11yescharacteristic
1046C2#6265311yescharacteristic
1047C2#6293112yes—
1048C2#6293912yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3511C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34506C2semidirect
3. #34496C2semidirect
4. #34480C2semidirect
5. #34464C2semidirect
6. #34453C2semidirect
7. #34410C2semidirect
8. #34402C2semidirect
9. #34399C2semidirect
10. #34371C2semidirect
11. #34367C2semidirect
12. #34322C2semidirect
13. #34312C2semidirect
14. #34308C2semidirect
15. #34306C2semidirect
16. #34253C2semidirect
17. #34209C2semidirect
18. #34208C2semidirect
19. #34191C2semidirect
20. C4×#556C2semidirect
21. #34125C2semidirect
22. #34086C2semidirect
23. #34085C2semidirect
24. #3511C4semidirect
184. #556C2×C4semidirect
185. #555C2×C4semidirect
186. #554C2×C4semidirect
187. #553C2×C4semidirect
188. #548C2×C4semidirect
189. #547C2×C4semidirect
190. #542C2×C4semidirect
191. #537C2×C4semidirect
192. #533C2×C4semidirect
193. #532C2×C4semidirect
194. #532C2×C4semidirect
195. C2×C4⋊Q8C2×C4semidirect
219. #520C2×C4semidirect
221. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#345062
#344962
#344802
#344642
#344532
#344102
#344022
#343992
#343712
#343672
#343222
#343122
#343082
#343062
#342532
#342092
#342082
#341912
C4×#5562
#341252
#340862
#340852