Finite Group Databasebeta

← #7629626

Subgroups — #7629626

Order 512.

8032 conjugacy classes of subgroups.

The subgroup lattice has 1019 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#41C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#35749C213yesmaximal, complemented
4#35748C211yesmaximal, characteristic, complemented
5#35738C213yesmaximal, complemented
6#35737C211yesmaximal, characteristic, complemented
7#35724C216yesmaximal, complemented
8#35723C212yesmaximal, complemented
9#35712C213yesmaximal, complemented
10#35711C211yesmaximal, characteristic, complemented
11#35701C213yesmaximal, complemented
12#35700C211yesmaximal, characteristic, complemented
13#35688C216yesmaximal, complemented
14#35687C212yesmaximal, complemented
15#34979C213yesmaximal, complemented
16#34909C213yesmaximal, complemented
17#34720C216yesmaximal, complemented
18#34691C216yesmaximal, complemented
19#34627C213yesmaximal, complemented
20#34547C213yesmaximal, complemented
21C4×D4×Q8C212yesmaximal, complemented
22C4×#548C212yesmaximal, complemented
23#34128C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25Q8×#41—216no—
26C2×Q82C2211yescharacteristic
27C2×#557C2213yes—
28C2×#554C2216yes—
29C2×#554C2213yes—
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2211yescharacteristic
33C2×#548C2212yes—
34C2×#533C2213yes—
35C2×#533C2216yes—
36C4×2−1+4—216no—
37C2×#520C2213yes—
38C2×#520C2213yes—
39C2×#520C2213yes—
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×#519C2213yes—
44C2×C4×#41C2213yes—
45C2×C4×#41C2213yes—
46C2×C4×#41C2213yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2213yes—
49C22×C4×Q8C2212yes—
50C22×C4×Q8C2211yescharacteristic
51C22×C4×Q8C2213yes—
52C22×C4×Q8C2211yescharacteristic
53#2638C2216yes—
54#2638C2216yes—
55#2634C2216yes—
56#2633C2216yes—
57#2628C2213yes—
58#2628C2213yes—
59#2625C2216yes—
60#2621C2213yes—
61#2621C2213yes—
62#2616C2216yes—
63#2611C2216yes—
64#2611C2216yes—
65#2600C22112yes—
66#2599C2216yes—
67#2598C2216yes—
68#2581C2213yes—
69#2580C2213yes—
70#2568C2213yes—
71#2547C2213yes—
72#2546C2213yes—
73#2542C2213yes—
74#2536C2213yes—
75#2535C2213yes—
76#2499C2216yes—
77#2485C2216yes—
78#2477C22112yes—
79#2475C22112yes—
80#2473C22112yes—
81#2465C22112yes—
82#2463C22112yes—
83#2462C22112yes—
84#2460C22112yes—
85#2452C2216yes—
86#2451C2216yes—
87#2449C22112yes—
88#2446C2216yes—
89#2446C2216yes—
90#2440C2216yes—
91#2439C2216yes—
92#2434C2216yes—
93#2432C2216yes—
94#2432C2216yes—
95#2429C2216yes—
96#2427C2216yes—
97#2423C2216yes—
98#2421C2216yes—
99#2417C2216yes—
100#2415C2216yes—
101#2415C22112yes—
102#2409C2216yes—
103#2407C2216yes—
104#2407C2216yes—
105#2399C2216yes—
106#2399C2213yes—
107#2398C2216yes—
108#2398C2213yes—
109#2398C2213yes—
110#2397C2213yes—
111#2396C2213yes—
112#2396C2216yes—
113#2396C2213yes—
114#2395C2213yes—
115#2395C2216yes—
116#2395C2216yes—
117#2395C2213yes—
118#2392C2216yes—
119#2392C2213yes—
120#2392C2216yes—
121#2392C2213yes—
122#2392C2216yes—
123#2388C2213yes—
124#2388C2216yes—
125#2388C2211yescharacteristic
126#2367C2216yes—
127#2365C2216yes—
128#2362C2216yes—
129#2361C2216yes—
130#2360C2216yes—
131#2360C2216yes—
132#2356C2213yes—
133#2356C2213yes—
134#2352C2216yes—
135#2351C2211yescharacteristic
136#2351C2211yescharacteristic
137#2351C2212yes—
138Q8×C4⋊C4C2212yes—
139D4×C4⋊C4C2216yes—
140#2344C2216yes—
141#2341C2212yes—
142Q8×C22⋊C4C2212yes—
143Q8×C22⋊C4C2212yes—
144Q8×C22⋊C4C2212yes—
145Q8×C22⋊C4C2212yes—
146C4×C4⋊Q8C2216yes—
147C4×#124C2216yes—
148C4×C22⋊Q8C2216yes—
149C4×C22⋊Q8C2216yes—
150C4×C22⋊Q8C2216yes—
151C4×C22⋊Q8C22112yes—
152C4×#121C2216yes—
153#2295C2216yes—
154#2290C22112yes—
155#2283C2213yes—
156C42×Q8C2212yes—
157C42×D4C2216yes—
158C42×D4C2216yes—
159C4×#117C2213yes—
160C2×2−1+4—28no—
161C2×2−1+4—28no—
162C2×2−1+4—28no—
163C22×#41C2313yes—
164C22×#41C2313yes—
165C22×#41C2313yes—
166C22×#41C2311yescharacteristic
167C22×#41C2311yescharacteristic
168C23×Q8C2313yes—
169C23×Q8C2312yes—
170C23×Q8C2311yescharacteristic
171C23×Q8C2311yescharacteristic
172Q82—28no—
173#557—224no—
174#554—224no—
175#554—248no—
176D4×Q8—216no—
177D4×Q8—216no—
178D4×Q8—28no—
179#548—216no—
180#533—248no—
181#533—224no—
182C2×C4⋊Q8C2316yes—
183C2×C4⋊Q8C2313yes—
184C2×C4⋊Q8C2313yes—
185C2×C4⋊Q8C2316yes—
186C2×C4⋊Q8C2316yes—
187C2×#125C2316yes—
188C2×#125C23112yes—
189C2×#124C2316yes—
190C2×C22⋊Q8C2316yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2316yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2316yes—
196C2×C22⋊Q8C2316yes—
197C2×C22⋊Q8C23112yes—
198C2×C22⋊Q8C23112yes—
199C2×#121C2316yes—
200#520—28no—
201#520—224no—
202#520—224no—
203#520—224no—
204#519—28no—
205#519—28no—
206#519—224no—
207C4×#41—28no—
208C4×#41—224no—
209C4×#41—224no—
210C4×#41—224no—
211C4×#41—224no—
212C2×C4×Q8—28no—
213C2×C4×Q8—224no—
214C2×C4×Q8—216no—
215C2×C4×Q8D4116yescomplemented
216C2×C4×Q8C2313yes—
217C2×C4×Q8C2316yes—
218C2×C4×Q8C2313yes—
219C2×C4×Q8C2313yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2313yes—
227C2×C4×Q8C2316yes—
228C2×C4×Q8C2313yes—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2316yes—
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2313yes—
233C2×C4×Q8C2316yes—
234C2×C4×Q8C2313yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2313yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2313yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2316yes—
254C2×C4×D4C2313yes—
255C2×C4×D4C2313yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×#117C2316yes—
262C2×#117C2313yes—
263C2×#117C2313yes—
264C2×#117C2313yes—
265C2×#117C2313yes—
266C2×#117C2316yes—
267C2×#117C2313yes—
268C2×#117C2313yes—
269C2×#117C2316yes—
270C2×#117C2313yes—
271C2×#117C2316yes—
272C22×C4⋊C4C2313yes—
273C22×C4⋊C4C2316yes—
274C22×C4⋊C4C2313yes—
275C22×C4⋊C4C2316yes—
276C22×C4⋊C4C2313yes—
277C22×C42C2313yes—
278C22×C42C2313yes—
279C22×C42C2316yes—
280C22×C42C2316yes—
281C22×C42C2313yes—
282#400C2313yes—
283#400C2316yes—
284#400C23112yes—
285#400C2313yes—
286#400C2316yes—
287#399C2316yes—
288#399C2313yes—
289#399C2313yes—
290#399C2316yes—
291#398C2316yes—
292#398C2313yes—
293#398C2313yes—
294#398C2316yes—
295#398C2316yes—
296#398C23112yes—
297#398C2316yes—
298#398C2316yes—
299#398C2316yes—
300#397C2316yes—
301#397C23112yes—
302#397C2313yes—
303#397C2313yes—
304#397C2316yes—
305#397C2316yes—
306#397C2316yes—
307#397C2316yes—
308#397C2316yes—
309#396C2316yes—
310#396C2316yes—
311#396C2316yes—
312#396C2316yes—
313#395C2313yes—
314#395C23112yes—
315#395C2316yes—
316#395C2316yes—
317#395C2311yescharacteristic
318#395C2316yes—
319#394C2313yes—
320#394C2316yes—
321#394C23112yes—
322#394C2316yes—
323#394C23112yes—
324#394C2312yes—
325#394C2311yescharacteristic
326#394C2316yes—
327#394C2316yes—
328#394C2316yes—
329#394C2316yes—
330#393C2313yes—
331#393C2316yes—
332#393C2316yes—
333#393C2311yescharacteristic
334#393C2316yes—
335#392C2313yes—
336#392C2316yes—
337#392C2312yes—
338#392C2311yescharacteristic
339#392C2316yes—
340#391C2316yes—
341#391C2316yes—
342#391C23112yes—
343#391C2316yes—
344#391C2316yes—
345#391C2316yes—
346#391C2316yes—
347#391C2316yes—
348#391C2316yes—
349#390C2316yes—
350#390C2316yes—
351#389C23112yes—
352#389C23112yes—
353#389C2316yes—
354#389C2316yes—
355#389C2316yes—
356#389C2316yes—
357#389C2316yes—
358#389C2316yes—
359#389C23112yes—
360#388C23112yes—
361#388C23112yes—
362#388C23112yes—
363#388C23112yes—
364#388C23112yes—
365#387C23112yes—
366#387C23112yes—
367#387C23112yes—
368#387C23112yes—
369#387C23112yes—
370#387C23112yes—
371#387C23112yes—
372#387C23112yes—
373#387C23112yes—
374#386C23112yes—
375#386C23112yes—
376#386C23112yes—
377#385C23112yes—
378#385C23112yes—
379#385C23112yes—
380#385C23112yes—
381#385C23112yes—
382#385C23112yes—
383#385C23112yes—
384#384C2316yes—
385#383C2316yes—
386#382C2316yes—
387#382C2313yes—
388#382C2313yes—
389#381C2316yes—
390#380C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C23112yes—
396C4×C4⋊C4C2316yes—
397C4×C4⋊C4C23112yes—
398C4×C4⋊C4C2313yes—
399C4×C4⋊C4C2316yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C2316yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2311yescharacteristic
419C4×C22⋊C4C2313yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C23112yes—
425#376C2313yes—
426#376C2313yes—
427#376C2316yes—
428C43C2316yes—
4292−1+4—2128no—
430C2×#41—212no—
431C2×#41—24no—
432C2×#41—212no—
433C2×#41—24no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41—24no—
437C2×#41—212no—
438C2×#41—212no—
439C2×#41—212no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—28no—
443C2×#41#4118yescomplemented
444C22×Q8—212no—
445C22×Q8—24no—
446C22×Q8—212no—
447C22×Q8—24no—
448C22×Q8—24no—
449C22×Q8—24no—
450C22×Q8—28no—
451C22×Q8—28no—
452C22×Q8—28no—
453C22×Q8—212no—
454C22×Q8C2×D418yes—
455C22×Q8#4118yescomplemented
456C22×Q8C2411yescharacteristic
457C22×Q8C2413yes—
458C22×Q8C2416yes—
459C22×Q8C2413yes—
460C22×Q8C2413yes—
461C22×Q8C2416yes—
462C22×Q8C2411yescharacteristic
463C22×D4C2412yes—
464C22×D4C2411yescharacteristic
465C22×D4C2412yes—
466C22×D4C2413yes—
467C22×D4C2413yes—
468C22×D4C2411yescharacteristic
469C22×D4C2416yes—
470C22×D4C2413yes—
471C23×C4C2416yes—
472C23×C4C2416yes—
473C23×C4C2411yescharacteristic
474C23×C4C2413yes—
475C23×C4C2413yes—
476C23×C4C2411yescharacteristic
477C23×C4C2413yes—
478C23×C4C2413yes—
479C23×C4C2412yes—
480C23×C4C2413yes—
481C23×C4C2413yes—
482C23×C4C2416yes—
483C23×C4C2416yes—
484C23×C4C2413yes—
485C4⋊Q8—224no—
486C4⋊Q8—224no—
487C4⋊Q8—224no—
488C4⋊Q8—212no—
489C4⋊Q8—212no—
490#125—248no—
491#125—224no—
492#124—224no—
493C22⋊Q8—224no—
494C22⋊Q8—224no—
495C22⋊Q8—224no—
496C22⋊Q8—224no—
497C22⋊Q8—224no—
498C22⋊Q8—224no—
499C22⋊Q8—224no—
500C22⋊Q8—248no—
501C22⋊Q8—424no—
502#121—224no—
503C4×Q8—212no—
504C4×Q8—24no—
505C4×Q8—28no—
506C4×Q8—212no—
507C4×Q8—24no—
508C4×Q8—28no—
509C4×Q8—28no—
510C4×Q8—212no—
511C4×Q8—224no—
512C4×Q8—212no—
513C4×Q8—224no—
514C4×Q8—212no—
515C4×Q8—212no—
516C4×Q8—224no—
517C4×Q8—212no—
518C4×Q8—212no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8—224no—
522C4×Q8C2×D418yes—
523C4×Q8C2×D4124yes—
524C4×Q8C2×D418yes—
525C4×Q8C2×D4124yes—
526C4×D4—212no—
527C4×D4—24no—
528C4×D4—224no—
529C4×D4—212no—
530C4×D4—212no—
531C4×D4—224no—
532C4×D4—224no—
533C4×D4—224no—
534C4×D4—224no—
535C4×D4—28no—
536C4×D4—224no—
537C4×D4—212no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—212no—
541C4×D4—212no—
542C4×D4—212no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—412no—
547C4×D4—412no—
548#117—212no—
549#117—212no—
550#117—212no—
551#117—212no—
552#117—224no—
553#117—212no—
554#117—224no—
555#117—212no—
556#117—212no—
557#117—224no—
558#117—412no—
559C2×C4⋊C4—212no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—212no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4C2×D4124yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C24112yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C24112yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C24112yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C24112yes—
593C2×C4⋊C4C2413yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2413yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2411yescharacteristic
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2411yescharacteristic
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C24112yes—
622C2×C42—212no—
623C2×C42—212no—
624C2×C42—224no—
625C2×C42—224no—
626C2×C42C2×D4124yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2416yes—
632C2×C42C2416yes—
633C2×C42C2416yes—
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2416yes—
637C2×C42C2416yes—
638C2×C42C2416yes—
639C2×C42C2413yes—
640C2×C42C2411yescharacteristic
641C2×C42C2412yes—
642C2×C42C2416yes—
643C2×C42C2416yes—
644C2×C42C2413yes—
645C2×C42C2413yes—
646C2×C42C2413yes—
647C2×C42C2413yes—
648#95C2411yescharacteristic
649#95C2411yescharacteristic
650#95C2413yes—
651#95C2413yes—
652#95C2416yes—
653#95C2416yes—
654#95C24112yes—
655#95C2416yes—
656#95C2416yes—
657#95C2412yes—
658#95C2412yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C24112yes—
670#95C24112yes—
671#95C24112yes—
672#95C24112yes—
673#95C24112yes—
674C24C2511yescharacteristic
675C24C2513yes—
676C24C2511yescharacteristic
677C24C2512yes—
678#41—232no—
679#41—296no—
680#41—296no—
681#41—296no—
682#41—232no—
683C2×Q8—296no—
684C2×Q8—232no—
685C2×Q8—232no—
686C2×Q8—22no—
687C2×Q8—26no—
688C2×Q8—26no—
689C2×Q8—212no—
690C2×Q8—212no—
691C2×Q8—26no—
692C2×Q8—26no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—26no—
696C2×Q8—212no—
697C2×Q8—212no—
698C2×Q8—24no—
699C2×Q8—412no—
700C2×Q8—432no—
701C2×Q8C22×D4112yes—
702C2×Q8C22×D414yes—
703C2×Q8C2×#41112yes—
704C2×Q8C2×#4114yes—
705C2×Q8C2×#4114yes—
706C2×D4—24no—
707C2×D4—26no—
708C2×D4—22no—
709C2×D4—24no—
710C2×D4—26no—
711C2×D4—26no—
712C2×D4—26no—
713C2×D4—22no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—22no—
720C2×D4—26no—
721C2×D4—26no—
722C2×D4—26no—
723C2×D4—22no—
724C2×D4—26no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—46no—
728C2×D4C2×#41112yes—
729C22×C4—212no—
730C22×C4—24no—
731C22×C4—212no—
732C22×C4—26no—
733C22×C4—26no—
734C22×C4—212no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—26no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—22no—
742C22×C4—26no—
743C22×C4—212no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—24no—
747C22×C4—212no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—212no—
751C22×C4—212no—
752C22×C4—46no—
753C22×C4—46no—
754C22×C4—46no—
755C22×C4—46no—
756C22×C4—46no—
757C22×C4—412no—
758C22×C4C22×D414yes—
759C22×C4C22×D4112yes—
760C22×C4C22×D4112yes—
761C22×C4C2×#41112yes—
762C22×C4C2×#41112yes—
763C22×C42−1+418yescomplemented
764C22×C4C2516yes—
765C22×C4C2512yes—
766C22×C4C2516yes—
767C22×C4C2513yes—
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C22×C4C2513yes—
771C22×C4C2516yes—
772C22×C4C2516yes—
773C22×C4C2511yescharacteristic
774C22×C4C2513yes—
775C22×C4C2513yes—
776C22×C4C2513yes—
777C22×C4C2513yes—
778C22×C4C2511yescharacteristic
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2513yes—
782C22×C4C2511yescharacteristic
783C4⋊C4—212no—
784C4⋊C4—26no—
785C4⋊C4—26no—
786C4⋊C4—26no—
787C4⋊C4—26no—
788C4⋊C4—224no—
789C4⋊C4—212no—
790C4⋊C4—26no—
791C4⋊C4—22no—
792C4⋊C4—26no—
793C4⋊C4—26no—
794C4⋊C4—212no—
795C4⋊C4—212no—
796C4⋊C4—26no—
797C4⋊C4—26no—
798C4⋊C4—212no—
799C4⋊C4—224no—
800C4⋊C4—212no—
801C4⋊C4—212no—
802C4⋊C4—212no—
803C4⋊C4—212no—
804C4⋊C4—224no—
805C4⋊C4—24no—
806C4⋊C4—212no—
807C4⋊C4—212no—
808C4⋊C4—212no—
809C4⋊C4—46no—
810C4⋊C4—46no—
811C4⋊C4—412no—
812C4⋊C4C22×D4112yes—
813C4⋊C4C22×D4124yes—
814C4⋊C4C22×D4112yes—
815C22⋊C4—22no—
816C22⋊C4—26no—
817C22⋊C4—212no—
818C22⋊C4—212no—
819C22⋊C4—212no—
820C22⋊C4—224no—
821C22⋊C4—24no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—26no—
825C22⋊C4—26no—
826C22⋊C4—26no—
827C22⋊C4—22no—
828C22⋊C4—212no—
829C22⋊C4—212no—
830C22⋊C4—24no—
831C22⋊C4—212no—
832C22⋊C4—24no—
833C22⋊C4—212no—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—212no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—412no—
841C42—22no—
842C42—26no—
843C42—26no—
844C42—26no—
845C42—212no—
846C42—212no—
847C42—26no—
848C42—26no—
849C42—212no—
850C42—212no—
851C42—212no—
852C42—212no—
853C42—212no—
854C42—24no—
855C42—212no—
856C42—212no—
857C42—46no—
858C42C22×D4112yes—
859C42C22×D4112yes—
860C42C22×D4112yes—
861C42C22×D4112yes—
862C23—22no—
863C23—23no—
864C23—21no—
865C23—22no—
866C23—22no—
867C23—21no—
868C23—21no—
869C23—23no—
870C23—21no—
871C23—22no—
872C23—26no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—26no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23C23×D412yes—
881C23C22×#4116yes—
882C23C22×#4112yes—
883C23C2×2−1+414yes—
884C23C2611yescharacteristic
885Q8—224no—
886Q8—28no—
887Q8—224no—
888Q8—224no—
889Q8—424no—
890Q8—812no—
891Q8#525116yes—
892D4—216no—
893D4—28no—
894D4—216no—
895D4—224no—
896D4—224no—
897D4—28no—
898D4—224no—
899D4—424no—
900C2×C4—248no—
901C2×C4—22no—
902C2×C4—23no—
903C2×C4—21no—
904C2×C4—22no—
905C2×C4—23no—
906C2×C4—23no—
907C2×C4—21no—
908C2×C4—23no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—26no—
913C2×C4—26no—
914C2×C4—224no—
915C2×C4—224no—
916C2×C4—224no—
917C2×C4—28no—
918C2×C4—216no—
919C2×C4—21no—
920C2×C4—23no—
921C2×C4—21no—
922C2×C4—23no—
923C2×C4—26no—
924C2×C4—26no—
925C2×C4—22no—
926C2×C4—26no—
927C2×C4—26no—
928C2×C4—26no—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—22no—
932C2×C4—26no—
933C2×C4—22no—
934C2×C4—26no—
935C2×C4—26no—
936C2×C4—22no—
937C2×C4—26no—
938C2×C4—22no—
939C2×C4—26no—
940C2×C4—26no—
941C2×C4—26no—
942C2×C4—412no—
943C2×C4—424no—
944C2×C4—44no—
945C2×C4—412no—
946C2×C4—86no—
947C2×C4—86no—
948C2×C4—812no—
949C2×C4—812no—
950C2×C4C23×D416yes—
951C2×C4C23×D416yes—
952C2×C4C23×D416yes—
953C2×C4C23×D412yes—
954C2×C4C23×D416yes—
955C2×C4C23×D412yes—
956C2×C4C22×#4116yes—
957C2×C4C22×#4112yes—
958C2×C4C22×#4116yes—
959C2×C4C22×#4116yes—
960C2×C4C2×2−1+414yes—
961C2×C4C2×2−1+414yes—
962C2×C4#58514yes—
963C22—22no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—212no—
969C22—22no—
970C22—22no—
971C22—26no—
972C22—22no—
973C22—41no—
974C22—43no—
975C22—42no—
976C22—46no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—43no—
983C22—41no—
984C22—42no—
985C22C24×D411yescharacteristic
986C22C23×#4111yescharacteristic
987C22C23×#4111yescharacteristic
988C22C22×2−1+412yes—
989C22C2×#58512yes—
990C4—22no—
991C4—24no—
992C4—24no—
993C4—26no—
994C4—26no—
995C4—26no—
996C4—26no—
997C4—22no—
998C4—41no—
999C4—43no—
1000C4—46no—
1001C4—42no—
1002C4—46no—
1003C4—41no—
1004C4—43no—
1005C4—46no—
1006C4—46no—
1007C4C2×#525112yes—
1008C4#348614yes—
1009C2—42no—
1010C2—44no—
1011C2—42no—
1012C2—46no—
1013C2C22×#52511yescharacteristic
1014C2C2×#348611yescharacteristic
1015C2#6278812yes—
1016C2#6280512yes—
1017C2#6281211yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#41C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #35749C2semidirect
4. #35748C2semidirect
5. #35738C2semidirect
6. #35737C2semidirect
7. #35724C2semidirect
8. #35723C2semidirect
9. #35712C2semidirect
10. #35711C2semidirect
11. #35701C2semidirect
12. #35700C2semidirect
13. #35688C2semidirect
14. #35687C2semidirect
15. #34979C2semidirect
16. #34909C2semidirect
17. #34720C2semidirect
18. #34691C2semidirect
19. #34627C2semidirect
20. #34547C2semidirect
21. C4×D4×Q8C2semidirect
22. C4×#548C2semidirect
23. #34128C2semidirect
215. C2×C4×Q8D4semidirect
443. C2×#41#41semidirect
455. C22×Q8#41semidirect
763. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#412
C2×C4×2−1+42
#357492
#357482
#357382
#357372
#357242
#357232
#357122
#357112
#357012
#357002
#356882
#356872
#349792
#349092
#347202
#346912
#346272
#345472
C4×D4×Q82
C4×#5482
#341282