Finite Group Databasebeta

← #7686467

Subgroups — #7686467

Order 512.

7143 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C22×#557C211yesmaximal, characteristic, complemented
3#59413C213yesmaximal, complemented
4#59155C216yesmaximal, complemented
5#59144C213yesmaximal, complemented
6#59127C213yesmaximal, complemented
7#45424C216yesmaximal, complemented
8#45272C216yesmaximal, complemented
9#39616C213yesmaximal, complemented
10#39599C213yesmaximal, complemented
11#37687C216yesmaximal, complemented
12#36593C211yesmaximal, characteristic, complemented
13#36577C211yesmaximal, characteristic, complemented
14Q8×C22⋊Q8C212yesmaximal, complemented
15Q8×#121C213yesmaximal, complemented
16#36445C211yesmaximal, characteristic, complemented
17D4×C4⋊Q8C213yesmaximal, complemented
18#35937C212yesmaximal, complemented
19#35816C212yesmaximal, complemented
20#34691C213yesmaximal, complemented
21#34337C211yesmaximal, characteristic, complemented
22#34294C212yesmaximal
23C4×#548C211yesmaximal, characteristic
24#3503—216no—
25C2×Q82C2212yes—
26C2×#557—216no—
27C2×#557C2213yes—
28C2×#557C2211yescharacteristic
29C2×#557C2211yescharacteristic
30C2×#557C2212yes—
31C2×#557C2216yes—
32C2×#557C2213yes—
33C2×#557C2211yescharacteristic
34C2×#554C2216yes—
35C2×D4×Q8C2213yes—
36C2×D4×Q8C2213yes—
37C2×D4×Q8C2216yes—
38C2×#548C2211yescharacteristic
39C2×#544C2216yes—
40C2×#533C2213yes—
41C22×C4⋊Q8C2213yes—
42C22×C4⋊Q8C2213yes—
43C22×#125C2216yes—
44C2×#520C2212yes—
45C2×C4×#41C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×C4×Q8C2213yes—
48C22×C4×Q8C2212yes—
49#2868C2213yes—
50#2857C2213yes—
51#2857C2213yes—
52#2857C2216yes—
53#2726C22112yes—
54#2720C22112yes—
55#2720C22112yes—
56#2713C22112yes—
57#2704C22112yes—
58#2704C22112yes—
59#2677C22112yes—
60#2660C2216yes—
61#2629C2216yes—
62#2584C2216yes—
63#2582C2213yes—
64#2582C2216yes—
65#2568C2213yes—
66#2567C2216yes—
67#2566C2216yes—
68#2556C22112yes—
69#2552C2216yes—
70#2552C2216yes—
71#2551C2216yes—
72#2551C2216yes—
73#2551C2216yes—
74#2550C2216yes—
75#2550C2216yes—
76#2546C2216yes—
77#2546C2213yes—
78#2546C2216yes—
79#2546C2213yes—
80#2542C2213yes—
81#2538C2213yes—
82#2538C2216yes—
83#2473C22112yes—
84#2473C2216yes—
85#2465C2216yes—
86#2462C2216yes—
87#2454C2216yes—
88#2454C2216yes—
89#2453C2216yes—
90#2452C2216yes—
91#2451C2216yes—
92#2451C2216yes—
93#2451C2213yes—
94#2449C2216yes—
95#2449C22112yes—
96#2446C2213yes—
97#2442C2216yes—
98#2442C2216yes—
99#2441C2216yes—
100#2440C2216yes—
101#2440C2216yes—
102#2440C2216yes—
103#2440C2216yes—
104#2440C2216yes—
105#2440C2211yescharacteristic
106#2434C2216yes—
107#2434C2216yes—
108#2434C2213yes—
109#2429C2216yes—
110#2429C22112yes—
111#2429C2213yes—
112#2429C2216yes—
113#2423C2213yes—
114#2417C22112yes—
115#2417C2213yes—
116#2409C2213yes—
117#2399C2216yes—
118#2396C2216yes—
119#2370C2216yes—
120#2367C2216yes—
121#2367C2213yes—
122#2365C2213yes—
123#2362C2213yes—
124#2361C2213yes—
125#2361C2216yes—
126#2360C2216yes—
127#2352C2213yes—
128#2351C2211yescharacteristic
129#2351C2212yes—
130Q8×C4⋊C4C2211yescharacteristic
131Q8×C4⋊C4C2213yes—
132Q8×C4⋊C4C2212yes—
133Q8×C4⋊C4C2212yes—
134Q8×C4⋊C4C2212yes—
135Q8×C4⋊C4C2212yes—
136D4×C4⋊C4C2216yes—
137D4×C4⋊C4C2216yes—
138#2341C2212yes—
139#2341C2211yescharacteristic
140Q8×C22⋊C4C2216yes—
141Q8×C22⋊C4C2211yescharacteristic
142Q8×C22⋊C4C2212yes—
143#2330C2216yes—
144#2326C2216yes—
145#2323C2216yes—
146C4×C4⋊Q8C2213yes—
147C4×C4⋊Q8C2213yes—
148C4×#124C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×C22⋊Q8C2213yes—
151C4×C22⋊Q8C2216yes—
152C4×C22⋊Q8C2213yes—
153C4×#121C2216yes—
154C4×#121C2213yes—
155#2295C2213yes—
156#2290C2216yes—
157#2276C2212yes—
158C42×Q8C2211yescharacteristic
159C42×D4C2213yes—
160C22×#41C2311yescharacteristic
161C23×Q8C2313yes—
162C23×Q8C2311yescharacteristic
163C23×Q8C2316yes—
164Q82—216no—
165#557—224no—
166#557—248no—
167#557—28no—
168#557—216no—
169#557—224no—
170#557—28no—
171#557D4116yescomplemented
172#554—248no—
173D4×Q8—224no—
174D4×Q8—224no—
175D4×Q8—424no—
176#548Q8116yescomplemented
177#544—248no—
178#533—224no—
179C2×C4⋊Q8—224no—
180C2×C4⋊Q8—224no—
181C2×C4⋊Q8C2316yes—
182C2×C4⋊Q8C2313yes—
183C2×C4⋊Q8C2313yes—
184C2×C4⋊Q8C2313yes—
185C2×C4⋊Q8C2316yes—
186C2×C4⋊Q8C2316yes—
187C2×C4⋊Q8C2316yes—
188C2×C4⋊Q8C2316yes—
189C2×C4⋊Q8C2316yes—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2316yes—
192C2×C4⋊Q8C2313yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C23112yes—
195C2×C4⋊Q8C2313yes—
196C2×#125—248no—
197C2×#125C2316yes—
198C2×#125C2316yes—
199C2×#125C2316yes—
200C2×#125C23112yes—
201C2×#125C23112yes—
202C2×#125C2316yes—
203C2×#125C2316yes—
204C2×#125C2316yes—
205C2×#124C2313yes—
206C2×C22⋊Q8C2313yes—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C2313yes—
209C2×C22⋊Q8C23112yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C23112yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C23112yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C23112yes—
217C2×C22⋊Q8C2313yes—
218C2×#121C2313yes—
219#520—216no—
220C4×#41—28no—
221C2×C4×Q8—216no—
222C2×C4×Q8—224no—
223C2×C4×Q8—28no—
224C2×C4×Q8C2313yes—
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2316yes—
227C2×C4×Q8C2313yes—
228C2×C4×Q8C2316yes—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2316yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2316yes—
239C2×C4×Q8C2313yes—
240C2×C4×Q8C2316yes—
241C2×C4×Q8C2316yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2313yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2316yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C23112yes—
253C2×C4×D4C2313yes—
254C2×#117C2316yes—
255C2×#117C2313yes—
256C22×C4⋊C4C2316yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C2316yes—
260C22×C4⋊C4C2313yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2316yes—
263C22×C42C2316yes—
264C22×C42C2313yes—
265C22×C42C2313yes—
266#400C23112yes—
267#400C2316yes—
268#399C2316yes—
269#399C23112yes—
270#398C23112yes—
271#398C23112yes—
272#398C23112yes—
273#398C23112yes—
274#398C2316yes—
275#398C23112yes—
276#398C2312yes—
277#398C2316yes—
278#398C2316yes—
279#398C2316yes—
280#398C2316yes—
281#398C23112yes—
282#398C23112yes—
283#396C2316yes—
284#396C23112yes—
285#396C23112yes—
286#396C2316yes—
287#396C23112yes—
288#395C23112yes—
289#395C23112yes—
290#395C2316yes—
291#395C2316yes—
292#395C2312yes—
293#395C2316yes—
294#395C2316yes—
295#395C23112yes—
296#395C23112yes—
297#393C2316yes—
298#391C2313yes—
299#391C2313yes—
300#391C2313yes—
301#391C2313yes—
302#391C2316yes—
303#391C2313yes—
304#391C2316yes—
305#391C2316yes—
306#391C2313yes—
307#391C2316yes—
308#391C23112yes—
309#391C23112yes—
310#391C2313yes—
311#391C2313yes—
312#390C2313yes—
313#390C2316yes—
314#390C2313yes—
315#390C2316yes—
316#389C2316yes—
317#389C2316yes—
318#389C2316yes—
319#389C2316yes—
320#389C2316yes—
321#389C23112yes—
322#389C2316yes—
323#389C23112yes—
324#389C2313yes—
325#389C2316yes—
326#389C2316yes—
327#389C2316yes—
328#389C2313yes—
329#389C23112yes—
330#389C23112yes—
331#389C2316yes—
332#389C23112yes—
333#389C2316yes—
334#389C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2313yes—
340#389C2316yes—
341#389C2313yes—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#388C23112yes—
345#388C23112yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#387C2316yes—
352#387C2316yes—
353#387C23112yes—
354#387C2316yes—
355#387C2316yes—
356#387C2316yes—
357#387C2316yes—
358#387C2316yes—
359#387C2316yes—
360#387C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#385C23112yes—
365#385C23112yes—
366#385C23112yes—
367#385C23112yes—
368#385C2316yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2312yes—
373#385C2316yes—
374#385C2316yes—
375#384C2311yescharacteristic
376#384C2313yes—
377#384C2316yes—
378#384C2316yes—
379#384C2316yes—
380#384C2316yes—
381#384C2316yes—
382#384C2316yes—
383#382C2316yes—
384#382C2313yes—
385#380C2316yes—
386#380C2313yes—
387#380C2316yes—
388#380C2313yes—
389#380C23112yes—
390#380C2313yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2311yescharacteristic
395C4×C4⋊C4C2316yes—
396C4×C4⋊C4C2316yes—
397C4×C4⋊C4C2316yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2313yes—
417C4×C22⋊C4C2313yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2311yescharacteristic
421#376C2316yes—
422C43C2313yes—
423C2×#41—24no—
424C2×#41—24no—
425C2×#41C2×Q818yescomplemented
426C22×Q8—24no—
427C22×Q8—24no—
428C22×Q8—212no—
429C22×Q8—224no—
430C22×Q8—212no—
431C22×Q8—46no—
432C22×Q8—412no—
433C22×Q8—412no—
434C22×Q8C2×Q818yescomplemented
435C22×Q8C2413yes—
436C22×Q8C2413yes—
437C22×Q8C2412yes—
438C22×Q8C2416yes—
439C22×Q8C2413yes—
440C22×Q8C2413yes—
441C22×Q8C24112yes—
442C22×Q8C2411yescharacteristic
443C22×D4C2413yes—
444C22×D4C2413yes—
445C23×C4C2413yes—
446C23×C4C2413yes—
447C23×C4C2416yes—
448C23×C4C2412yes—
449C23×C4C2413yes—
450C23×C4C2413yes—
451C23×C4C2413yes—
452C23×C4C2411yescharacteristic
453C23×C4C24112yes—
454C4⋊Q8—212no—
455C4⋊Q8—224no—
456C4⋊Q8—224no—
457C4⋊Q8—224no—
458C4⋊Q8—224no—
459C4⋊Q8—224no—
460C4⋊Q8—24no—
461C4⋊Q8—224no—
462C4⋊Q8—212no—
463C4⋊Q8—212no—
464C4⋊Q8—224no—
465C4⋊Q8—46no—
466C4⋊Q8—412no—
467C4⋊Q8—424no—
468C4⋊Q8C2×D4124yes—
469#125—248no—
470#125—224no—
471#125—224no—
472#125—248no—
473#125—224no—
474#125—224no—
475#125—224no—
476#125C2×D4148yes—
477#124C2×Q8124yescomplemented
478C22⋊Q8—212no—
479C22⋊Q8—212no—
480C22⋊Q8—212no—
481C22⋊Q8—224no—
482C22⋊Q8—248no—
483C22⋊Q8—248no—
484C22⋊Q8—28no—
485C22⋊Q8—424no—
486C22⋊Q8—424no—
487C22⋊Q8—46no—
488C22⋊Q8—412no—
489C22⋊Q8C2×Q8124yescomplemented
490#121C2×Q8124yescomplemented
491C4×Q8—28no—
492C4×Q8—212no—
493C4×Q8—24no—
494C4×Q8—24no—
495C4×Q8—28no—
496C4×Q8—24no—
497C4×Q8—28no—
498C4×Q8—224no—
499C4×Q8—224no—
500C4×Q8—212no—
501C4×Q8—212no—
502C4×Q8—212no—
503C4×Q8—224no—
504C4×Q8—224no—
505C4×Q8—212no—
506C4×Q8—212no—
507C4×Q8—224no—
508C4×Q8—412no—
509C4×Q8C2×D418yes—
510C4×Q8C2×D4116yes—
511C4×Q8C2×D4124yes—
512C4×Q8C2×Q818yescomplemented
513C4×D4—212no—
514C4×D4—212no—
515C4×D4—224no—
516C4×D4—212no—
517C4×D4—212no—
518C4×D4—224no—
519C4×D4—424no—
520C4×D4C2×Q8124yescomplemented
521#117—212no—
522#117—224no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—212no—
525C2×C4⋊C4—224no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4—224no—
529C2×C4⋊C4—224no—
530C2×C4⋊C4C2416yes—
531C2×C4⋊C4C2416yes—
532C2×C4⋊C4C2416yes—
533C2×C4⋊C4C2411yescharacteristic
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C2413yes—
537C2×C4⋊C4C2416yes—
538C2×C4⋊C4C2416yes—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C24112yes—
542C2×C4⋊C4C2416yes—
543C2×C4⋊C4C2416yes—
544C2×C4⋊C4C24112yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2413yes—
547C2×C4⋊C4C2413yes—
548C2×C4⋊C4C2413yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2416yes—
553C2×C4⋊C4C2416yes—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C24112yes—
562C2×C4⋊C4C24112yes—
563C2×C4⋊C4C24112yes—
564C2×C4⋊C4C24112yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C22⋊C4C2416yes—
580C2×C22⋊C4C2416yes—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2413yes—
584C2×C22⋊C4C2413yes—
585C2×C22⋊C4C2413yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C24112yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2411yescharacteristic
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2411yescharacteristic
595C2×C42—224no—
596C2×C42—212no—
597C2×C42—212no—
598C2×C42C2413yes—
599C2×C42C2416yes—
600C2×C42C2413yes—
601C2×C42C2413yes—
602C2×C42C2413yes—
603C2×C42C2416yes—
604C2×C42C2416yes—
605C2×C42C2416yes—
606C2×C42C2413yes—
607C2×C42C2413yes—
608C2×C42C2413yes—
609C2×C42C2413yes—
610C2×C42C2416yes—
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C24112yes—
614C2×C42C2413yes—
615C2×C42C2416yes—
616C2×C42C2413yes—
617C2×C42C2413yes—
618#95C2412yes—
619#95C2416yes—
620#95C2416yes—
621#95C2416yes—
622#95C2411yescharacteristic
623#95C2411yescharacteristic
624#95C2412yes—
625#95C2413yes—
626#95C2413yes—
627#95C2413yes—
628#95C2416yes—
629#95C2413yes—
630#95C2416yes—
631#95C24112yes—
632#95C2416yes—
633#95C2416yes—
634#95C2416yes—
635#95C2416yes—
636#95C2412yes—
637#95C2416yes—
638#95C2416yes—
639#95C2416yes—
640#95C2416yes—
641#95C2416yes—
642#95C2416yes—
643#95C2416yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C24112yes—
648C24C2513yes—
649C24C2511yescharacteristic
650#41—232no—
651C2×Q8—232no—
652C2×Q8—26no—
653C2×Q8—24no—
654C2×Q8—212no—
655C2×Q8—26no—
656C2×Q8—26no—
657C2×Q8—224no—
658C2×Q8—26no—
659C2×Q8—26no—
660C2×Q8—212no—
661C2×Q8—26no—
662C2×Q8—26no—
663C2×Q8—24no—
664C2×Q8—26no—
665C2×Q8—26no—
666C2×Q8—26no—
667C2×Q8—46no—
668C2×Q8—42no—
669C2×Q8—412no—
670C2×Q8—412no—
671C2×Q8—448no—
672C2×Q8—848no—
673C2×Q8C22×D4112yes—
674C2×Q8C22×D414yes—
675C2×Q8C22×Q8112yes—
676C2×Q8C22×Q814yes—
677C2×Q82−1+414yes—
678C2×D4—26no—
679C2×D4—26no—
680C2×D4—26no—
681C2×D4—26no—
682C2×D4C22×Q8112yes—
683C2×D4C22×Q8112yes—
684C22×C4—26no—
685C22×C4—22no—
686C22×C4—26no—
687C22×C4—26no—
688C22×C4—26no—
689C22×C4—22no—
690C22×C4—212no—
691C22×C4—26no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—26no—
695C22×C4—212no—
696C22×C4—26no—
697C22×C4—26no—
698C22×C4—26no—
699C22×C4—26no—
700C22×C4—26no—
701C22×C4—224no—
702C22×C4—43no—
703C22×C4—43no—
704C22×C4—42no—
705C22×C4—46no—
706C22×C4—412no—
707C22×C4—412no—
708C22×C4C22×Q8112yes—
709C22×C4C22×Q8112yes—
710C22×C4H(5,𝔽2)14yes—
711C22×C4C2512yes—
712C22×C4C2513yes—
713C22×C4C2516yes—
714C22×C4C2512yes—
715C22×C4C2512yes—
716C22×C4C2513yes—
717C22×C4C2513yes—
718C22×C4C2516yes—
719C22×C4C2516yes—
720C22×C4C2512yes—
721C22×C4C2513yes—
722C22×C4C2516yes—
723C22×C4C2511yescharacteristic
724C22×C4C2513yes—
725C22×C4C2513yes—
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C22×C4C2511yescharacteristic
730C22×C4C2513yes—
731C22×C4C2511yescharacteristic
732C4⋊C4—212no—
733C4⋊C4—212no—
734C4⋊C4—212no—
735C4⋊C4—24no—
736C4⋊C4—22no—
737C4⋊C4—212no—
738C4⋊C4—212no—
739C4⋊C4—212no—
740C4⋊C4—26no—
741C4⋊C4—212no—
742C4⋊C4—224no—
743C4⋊C4—212no—
744C4⋊C4—212no—
745C4⋊C4—224no—
746C4⋊C4—212no—
747C4⋊C4—24no—
748C4⋊C4—26no—
749C4⋊C4—22no—
750C4⋊C4—212no—
751C4⋊C4—212no—
752C4⋊C4—212no—
753C4⋊C4—26no—
754C4⋊C4—26no—
755C4⋊C4—212no—
756C4⋊C4—26no—
757C4⋊C4—26no—
758C4⋊C4—212no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—42no—
764C4⋊C4—46no—
765C4⋊C4—46no—
766C4⋊C4—46no—
767C4⋊C4—412no—
768C4⋊C4—412no—
769C4⋊C4—46no—
770C4⋊C4—412no—
771C4⋊C4—412no—
772C4⋊C4—46no—
773C4⋊C4—46no—
774C4⋊C4C22×D4124yes—
775C4⋊C4C22×D4124yes—
776C4⋊C4C22×D4112yes—
777C4⋊C4C22×D414yes—
778C4⋊C4C22×D4124yes—
779C4⋊C4C22×Q8112yes—
780C4⋊C4C22×Q8112yes—
781C22⋊C4—26no—
782C22⋊C4—212no—
783C22⋊C4—24no—
784C22⋊C4—212no—
785C22⋊C4—212no—
786C22⋊C4—212no—
787C22⋊C4—26no—
788C22⋊C4—26no—
789C22⋊C4—46no—
790C22⋊C4—46no—
791C22⋊C4—412no—
792C22⋊C4—46no—
793C22⋊C4C22×Q814yes—
794C22⋊C4C22×Q8112yes—
795C22⋊C4C22×Q8124yes—
796C22⋊C42−1+414yes—
797C42—22no—
798C42—26no—
799C42—26no—
800C42—212no—
801C42—212no—
802C42—212no—
803C42—26no—
804C42—26no—
805C42—26no—
806C42—212no—
807C42—26no—
808C42—26no—
809C42—26no—
810C42—212no—
811C42—22no—
812C42—43no—
813C42—412no—
814C42C22×D4112yes—
815C42C22×D4124yes—
816C42C22×Q8112yes—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—23no—
822C23—23no—
823C23—23no—
824C23—23no—
825C23—23no—
826C23—23no—
827C23C23×Q816yes—
828C23C23×Q812yes—
829C23C2×H(5,𝔽2)12yes—
830C23C2×2−1+412yes—
831C23C2611yescharacteristic
832Q8—224no—
833Q8—224no—
834Q8—48no—
835Q8—424no—
836Q8—412no—
837Q8—412no—
838Q8—824no—
839Q8D4×Q8116yescomplemented
840D4—224no—
841D4—224no—
842C2×C4—23no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—23no—
847C2×C4—26no—
848C2×C4—21no—
849C2×C4—23no—
850C2×C4—23no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—23no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—26no—
858C2×C4—21no—
859C2×C4—23no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—224no—
863C2×C4—224no—
864C2×C4—28no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—23no—
868C2×C4—23no—
869C2×C4—26no—
870C2×C4—26no—
871C2×C4—23no—
872C2×C4—26no—
873C2×C4—23no—
874C2×C4—26no—
875C2×C4—26no—
876C2×C4—22no—
877C2×C4—23no—
878C2×C4—26no—
879C2×C4—22no—
880C2×C4—23no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—26no—
885C2×C4—23no—
886C2×C4—26no—
887C2×C4—23no—
888C2×C4—22no—
889C2×C4—23no—
890C2×C4—26no—
891C2×C4—22no—
892C2×C4—412no—
893C2×C4—412no—
894C2×C4—48no—
895C2×C4—424no—
896C2×C4—412no—
897C2×C4—824no—
898C2×C4C23×D414yes—
899C2×C4C23×D416yes—
900C2×C4C23×D4112yes—
901C2×C4C23×D416yes—
902C2×C4C23×D412yes—
903C2×C4C23×Q812yes—
904C2×C4C23×Q816yes—
905C2×C4C23×Q816yes—
906C2×C4C23×Q812yes—
907C2×C4C23×Q816yes—
908C2×C4C2×H(5,𝔽2)12yes—
909C2×C4C2×H(5,𝔽2)12yes—
910C2×C4C2×2−1+412yes—
911C2×C4C2×2−1+412yes—
912C2×C4C2×2−1+416yes—
913C2×C4#58512yes—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—26no—
921C22—26no—
922C22—26no—
923C22—43no—
924C22—43no—
925C22—43no—
926C22—43no—
927C22#350314yescomplemented
928C22C24×D411yescharacteristic
929C22C24×Q811yescharacteristic
930C22C22×H(5,𝔽2)11yescharacteristic
931C22C22×2−1+411yescharacteristic
932C22C22×2−1+411yescharacteristic
933C22C2×#58511yescharacteristic
934C222−1+611yescharacteristic
935C4—22no—
936C4—26no—
937C4—24no—
938C4—22no—
939C4—22no—
940C4—22no—
941C4—212no—
942C4—26no—
943C4—22no—
944C4—26no—
945C4—42no—
946C4—43no—
947C4—42no—
948C4—42no—
949C4—46no—
950C4—43no—
951C4—46no—
952C4—43no—
953C4—46no—
954C4C2×D4×Q8112yes—
955C4#348814yes—
956C2—24no—
957C2—46no—
958C2C22×D4×Q811yescharacteristic
959C2C2×#348811yescharacteristic
960C2C2×#350311yescharacteristic
961C2#6294611yescharacteristic
962C2D4×2−1+411yescharacteristic
963C2#6300411yescharacteristic
964C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3503C2semidirect
2. C22×#557C2semidirect
3. #59413C2semidirect
4. #59155C2semidirect
5. #59144C2semidirect
6. #59127C2semidirect
7. #45424C2semidirect
8. #45272C2semidirect
9. #39616C2semidirect
10. #39599C2semidirect
11. #37687C2semidirect
12. #36593C2semidirect
13. #36577C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. Q8×#121C2semidirect
16. #36445C2semidirect
17. D4×C4⋊Q8C2semidirect
18. #35937C2semidirect
19. #35816C2semidirect
20. #34691C2semidirect
21. #34337C2semidirect
171. #557D4semidirect
176. #548Q8semidirect
425. C2×#41C2×Q8semidirect
434. C22×Q8C2×Q8semidirect
477. #124C2×Q8semidirect
489. C22⋊Q8C2×Q8semidirect
490. #121C2×Q8semidirect
512. C4×Q8C2×Q8semidirect
520. C4×D4C2×Q8semidirect
839. Q8D4×Q8semidirect
927. C22#3503semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C22×#5572
#594132
#591552
#591442
#591272
#454242
#452722
#396162
#395992
#376872
#365932
#365772
Q8×C22⋊Q82
Q8×#1212
#364452
D4×C4⋊Q82
#359372
#358162
#346912
#343372
#342942
C4×#5482