Finite Group Databasebeta

← #7632444

Subgroups — #7632444

Order 512.

8118 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#36580C213yesmaximal, complemented
4#36579C213yesmaximal, complemented
5#36577C211yesmaximal, characteristic, complemented
6#36576C211yesmaximal, characteristic, complemented
7#36504C213yesmaximal, complemented
8#36493C213yesmaximal, complemented
9#36455C211yesmaximal, characteristic, complemented
10#36445C211yesmaximal, characteristic, complemented
11#35801C212yesmaximal, complemented
12#35793C216yesmaximal, complemented
13#35757C212yesmaximal, complemented
14#35752C216yesmaximal, complemented
15#35664C216yesmaximal, complemented
16#35525C216yesmaximal, complemented
17#35292C213yesmaximal, complemented
18#35190C213yesmaximal, complemented
19#34976C213yesmaximal, complemented
20#34909C213yesmaximal, complemented
21#34295C212yesmaximal, complemented
22#34293C212yesmaximal, complemented
23#34196C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25#3480—216no—
26C2×#559C2213yes—
27C2×#557C2211yescharacteristic
28C2×#556C2213yes—
29C2×#553C2216yes—
30C2×#550C2212yes—
31C2×#550C2211yescharacteristic
32C2×#548C2212yes—
33C2×#548C2212yes—
34C2×#532C2213yes—
35C2×#529C2216yes—
36C4×2−1+4—216no—
37C2×#520C2213yes—
38C2×#520C2213yes—
39C2×#520C2213yes—
40C2×#520C2211yescharacteristic
41C2×#519C2213yes—
42C2×#519C2211yescharacteristic
43C2×#519C2211yescharacteristic
44C2×C4×#41C2213yes—
45C2×C4×#41C2213yes—
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2213yes—
48C2×C4×#41C2213yes—
49C2×C4×#41C2212yes—
50C22×C4×Q8C2211yescharacteristic
51C22×C4×Q8C2213yes—
52C22×C4×Q8C2211yescharacteristic
53#2857C2213yes—
54#2857C2213yes—
55#2856C2213yes—
56#2856C2213yes—
57#2850C2216yes—
58#2850C2216yes—
59#2635C22112yes—
60#2624C2216yes—
61#2615C2216yes—
62#2609C22112yes—
63#2600C2216yes—
64#2600C2216yes—
65#2599C2216yes—
66#2598C22112yes—
67#2598C2216yes—
68#2592C2216yes—
69#2582C2213yes—
70#2581C2213yes—
71#2580C2216yes—
72#2580C2213yes—
73#2568C2213yes—
74#2548C2213yes—
75#2542C2213yes—
76#2541C2213yes—
77#2540C2216yes—
78#2538C2213yes—
79#2538C2213yes—
80#2537C2213yes—
81#2536C2213yes—
82#2535C2213yes—
83#2535C2216yes—
84#2500C2216yes—
85#2485C2211yescharacteristic
86#2485C2213yes—
87#2485C2216yes—
88#2481C22112yes—
89#2479C22112yes—
90#2471C22112yes—
91#2469C22112yes—
92#2467C22112yes—
93#2458C22112yes—
94#2456C22112yes—
95#2454C2216yes—
96#2453C2216yes—
97#2448C2216yes—
98#2448C2216yes—
99#2443C22112yes—
100#2442C2216yes—
101#2441C2216yes—
102#2436C2216yes—
103#2431C2216yes—
104#2431C2216yes—
105#2428C2216yes—
106#2426C2216yes—
107#2423C2216yes—
108#2421C2216yes—
109#2416C2216yes—
110#2414C2216yes—
111#2414C2216yes—
112#2414C2216yes—
113#2409C2216yes—
114#2407C2213yes—
115#2407C2213yes—
116#2407C2216yes—
117#2407C2216yes—
118#2407C2216yes—
119#2395C2216yes—
120#2392C22112yes—
121#2388C2216yes—
122#2367C2216yes—
123#2366C2216yes—
124#2363C2216yes—
125#2363C2216yes—
126#2362C2216yes—
127#2361C2216yes—
128#2355C2213yes—
129#2355C2213yes—
130#2354C2216yes—
131#2352C2216yes—
132#2351C2212yes—
133Q8×C4⋊C4C2211yescharacteristic
134Q8×C4⋊C4C2212yes—
135Q8×C4⋊C4C2211yescharacteristic
136#2344C2216yes—
137#2341C2212yes—
138#2341C2212yes—
139#2341C2212yes—
140Q8×C22⋊C4C2212yes—
141Q8×C22⋊C4C2212yes—
142#2328C2216yes—
143#2326C2216yes—
144#2324C2216yes—
145#2324C2216yes—
146#2320C2216yes—
147C4×C22⋊Q8C2216yes—
148C4×C22⋊Q8C2213yes—
149C4×C22⋊Q8C2213yes—
150C4×C22⋊Q8C2216yes—
151C4×#121C2213yes—
152C4×#121C2213yes—
153C4×#121C2216yes—
154C4×#121C2216yes—
155#2290C2216yes—
156#2290C2216yes—
157#2285C2213yes—
158#2283C2213yes—
159#2276C2212yes—
160C2×2−1+4—28no—
161C2×2−1+4—28no—
162C2×2−1+4—28no—
163C22×#41C2313yes—
164C22×#41C2313yes—
165C22×#41C2313yes—
166C22×#41C2312yes—
167C22×#41C2311yescharacteristic
168C22×#41C2313yes—
169C23×Q8C2313yes—
170C23×Q8C2311yescharacteristic
171C23×Q8C2311yescharacteristic
172#559—224no—
173#557—28no—
174#556—224no—
175#553—248no—
176#550—216no—
177#550—28no—
178#548—216no—
179#548—216no—
180#532—224no—
181C2×C4⋊Q8C2313yes—
182C2×#127C2316yes—
183C2×#127C2313yes—
184#529—248no—
185C2×#126C23112yes—
186C2×#125C2316yes—
187C2×#124C2316yes—
188C2×#124C2316yes—
189C2×#124C2316yes—
190C2×#123C23112yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2313yes—
194C2×C22⋊Q8C2316yes—
195C2×C22⋊Q8C2313yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2316yes—
199C2×#121C2316yes—
200C2×#121C2316yes—
201C2×#121C2316yes—
202C2×#121C2313yes—
203C2×#121C2316yes—
204C2×#121C2313yes—
205C2×#121C2316yes—
206C2×#121C2316yes—
207#520—28no—
208#520—224no—
209#520—224no—
210#520—224no—
211#519—28no—
212#519—28no—
213#519—224no—
214C4×#41—28no—
215C4×#41—224no—
216C4×#41—216no—
217C4×#41—224no—
218C4×#41—224no—
219C4×#41—224no—
220C2×C4×Q8—28no—
221C2×C4×Q8—224no—
222C2×C4×Q8D4116yescomplemented
223C2×C4×Q8C2313yes—
224C2×C4×Q8C2313yes—
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2313yes—
227C2×C4×Q8C2313yes—
228C2×C4×Q8C2313yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2313yes—
235C2×C4×Q8C2313yes—
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2316yes—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2313yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2313yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2313yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2313yes—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C23112yes—
265C2×#117C2313yes—
266C2×#117C2313yes—
267C2×#117C2316yes—
268C2×#117C2316yes—
269C2×#117C2316yes—
270C2×#117C2313yes—
271C2×#117C2313yes—
272C2×#117C2311yescharacteristic
273C2×#117C2313yes—
274C2×#117C2316yes—
275C2×#117C2313yes—
276C2×#117C2316yes—
277C22×C4⋊C4C2313yes—
278C22×C4⋊C4C2313yes—
279C22×C4⋊C4C2316yes—
280C22×C4⋊C4C2313yes—
281C22×C42C2316yes—
282C22×C42C2313yes—
283C22×C42C2313yes—
284C22×C42C2316yes—
285C22×C42C2313yes—
286#400C23112yes—
287#400C2316yes—
288#399C2316yes—
289#399C23112yes—
290#399C23112yes—
291#398C23112yes—
292#398C2316yes—
293#397C23112yes—
294#397C2316yes—
295#397C2312yes—
296#397C2316yes—
297#396C23112yes—
298#396C23112yes—
299#395C2316yes—
300#394C23112yes—
301#394C2316yes—
302#394C2312yes—
303#394C2316yes—
304#394C2316yes—
305#394C2316yes—
306#394C23112yes—
307#394C23112yes—
308#393C23112yes—
309#393C2316yes—
310#392C23112yes—
311#392C2316yes—
312#392C2316yes—
313#392C2316yes—
314#392C23112yes—
315#392C23112yes—
316#391C2313yes—
317#391C2316yes—
318#391C2316yes—
319#391C2316yes—
320#391C2316yes—
321#391C2313yes—
322#391C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C23112yes—
326#390C23112yes—
327#390C2313yes—
328#390C2313yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#389C2316yes—
340#389C2311yescharacteristic
341#389C2313yes—
342#389C2316yes—
343#389C2316yes—
344#389C2311yescharacteristic
345#389C2313yes—
346#389C2316yes—
347#389C2316yes—
348#388C23112yes—
349#388C23112yes—
350#388C23112yes—
351#388C23112yes—
352#388C23112yes—
353#388C23112yes—
354#388C2312yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C23112yes—
361#387C23112yes—
362#387C23112yes—
363#387C2316yes—
364#387C2316yes—
365#387C2312yes—
366#387C2316yes—
367#387C2316yes—
368#387C2316yes—
369#387C23112yes—
370#386C2316yes—
371#386C23112yes—
372#386C2316yes—
373#386C23112yes—
374#386C23112yes—
375#386C23112yes—
376#386C23112yes—
377#386C2316yes—
378#386C2316yes—
379#386C2316yes—
380#386C2316yes—
381#386C23112yes—
382#385C2316yes—
383#385C23112yes—
384#385C2316yes—
385#385C2316yes—
386#385C2316yes—
387#385C2316yes—
388#385C2316yes—
389#385C23112yes—
390#384C2316yes—
391#384C2313yes—
392#384C2313yes—
393#383C2316yes—
394#382C2316yes—
395#382C2316yes—
396#382C2313yes—
397#382C2313yes—
398#381C2316yes—
399#380C2316yes—
400#380C2316yes—
401#380C2316yes—
402#380C2316yes—
403#380C2316yes—
404#380C2316yes—
405#380C2316yes—
406#380C2311yescharacteristic
407#380C2313yes—
408#380C2311yescharacteristic
409#380C2313yes—
410#380C2311yescharacteristic
411#380C2313yes—
412C4×C4⋊C4C2313yes—
413C4×C4⋊C4C2316yes—
414C4×C4⋊C4C2316yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2316yes—
417C4×C4⋊C4C2313yes—
418C4×C4⋊C4C2316yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C23112yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C23112yes—
427C4×C22⋊C4C23112yes—
428#376C2316yes—
4292−1+4—2128no—
430C2×#41—212no—
431C2×#41—24no—
432C2×#41—28no—
433C2×#41—212no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—212no—
438C2×#41—212no—
439C2×#41—212no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—212no—
443C2×#41—212no—
444C2×#41—212no—
445C2×#41—46no—
446C2×#41—46no—
447C2×#41#4118yescomplemented
448C22×Q8—212no—
449C22×Q8—24no—
450C22×Q8—212no—
451C22×Q8—24no—
452C22×Q8—24no—
453C22×Q8—24no—
454C22×Q8—212no—
455C22×Q8C2×D418yes—
456C22×Q8#4118yescomplemented
457C22×Q8C2413yes—
458C22×Q8C2413yes—
459C22×Q8C2413yes—
460C22×Q8C2413yes—
461C22×Q8C2411yescharacteristic
462C22×D4C2413yes—
463C22×D4C2411yescharacteristic
464C22×D4C2413yes—
465C22×D4C2416yes—
466C22×D4C2413yes—
467C22×D4C2413yes—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2416yes—
471C22×D4C24112yes—
472C22×D4C2416yes—
473C23×C4C2416yes—
474C23×C4C2416yes—
475C23×C4C2411yescharacteristic
476C23×C4C2413yes—
477C23×C4C2413yes—
478C23×C4C2411yescharacteristic
479C23×C4C2413yes—
480C23×C4C2413yes—
481C23×C4C2416yes—
482C23×C4C2413yes—
483C23×C4C2413yes—
484C23×C4C2416yes—
485C23×C4C2416yes—
486C23×C4C2413yes—
487C4⋊Q8—212no—
488#127—224no—
489#127—212no—
490#126—248no—
491#125—224no—
492#124—224no—
493#124—224no—
494#124—224no—
495#123—248no—
496C22⋊Q8—224no—
497C22⋊Q8—224no—
498C22⋊Q8—46no—
499C22⋊Q8—412no—
500C22⋊Q8—46no—
501#121—224no—
502#121—224no—
503#121—224no—
504#121—224no—
505#121—224no—
506#121—224no—
507#121—46no—
508#121—412no—
509#121—46no—
510#121—86no—
511#121—86no—
512C4×Q8—212no—
513C4×Q8—24no—
514C4×Q8—212no—
515C4×Q8—24no—
516C4×Q8—28no—
517C4×Q8—28no—
518C4×Q8—28no—
519C4×Q8—212no—
520C4×Q8—212no—
521C4×Q8—224no—
522C4×Q8—212no—
523C4×Q8—212no—
524C4×Q8—212no—
525C4×Q8—212no—
526C4×Q8—212no—
527C4×Q8—212no—
528C4×Q8C2×D418yes—
529C4×Q8C2×D4124yes—
530C4×Q8C2×D418yes—
531C4×Q8C2×D4124yes—
532C4×D4—24no—
533C4×D4—212no—
534C4×D4—212no—
535C4×D4—212no—
536C4×D4—224no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—224no—
540C4×D4—224no—
541C4×D4—212no—
542C4×D4—212no—
543C4×D4—224no—
544C4×D4—224no—
545C4×D4—212no—
546C4×D4—212no—
547C4×D4—212no—
548C4×D4—212no—
549C4×D4—224no—
550C4×D4—212no—
551C4×D4—212no—
552C4×D4—224no—
553C4×D4—812no—
554#117—24no—
555#117—212no—
556#117—212no—
557#117—212no—
558#117—212no—
559#117—224no—
560#117—224no—
561#117—212no—
562#117—212no—
563#117—224no—
564#117—224no—
565#117—86no—
566C2×C4⋊C4—212no—
567C2×C4⋊C4—212no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4C2×D4124yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2413yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2416yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2413yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C24112yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2413yes—
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2416yes—
603C2×C22⋊C4C2411yescharacteristic
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2413yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2411yescharacteristic
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C24112yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C24112yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C24112yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C24112yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2416yes—
633C2×C42—224no—
634C2×C42—212no—
635C2×C42—212no—
636C2×C42—224no—
637C2×C42C2×D4124yes—
638C2×C42C2412yes—
639C2×C42C2416yes—
640C2×C42C2413yes—
641C2×C42C2413yes—
642C2×C42C2416yes—
643C2×C42C2413yes—
644C2×C42C2413yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2413yes—
648C2×C42C2411yescharacteristic
649C2×C42C2416yes—
650C2×C42C2416yes—
651C2×C42C24112yes—
652C2×C42C2413yes—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656#95C2412yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2412yes—
662#95C2412yes—
663#95C2416yes—
664#95C2412yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C24112yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2412yes—
673#95C2416yes—
674#95C24112yes—
675#95C24112yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679C24C2516yes—
680C24C2511yescharacteristic
681C24C2511yescharacteristic
682C24C2513yes—
683#41—296no—
684#41—296no—
685#41—296no—
686#41—232no—
687#41—448no—
688#41—432no—
689C2×Q8—296no—
690C2×Q8—232no—
691C2×Q8—232no—
692C2×Q8—26no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—26no—
696C2×Q8—26no—
697C2×Q8—26no—
698C2×Q8—26no—
699C2×Q8—26no—
700C2×Q8—26no—
701C2×Q8—26no—
702C2×Q8C22×D4112yes—
703C2×Q8C22×D414yes—
704C2×Q8C2×#41112yes—
705C2×Q8C2×#4114yes—
706C2×Q8C2×#4114yes—
707C2×D4—22no—
708C2×D4—26no—
709C2×D4—26no—
710C2×D4—26no—
711C2×D4—26no—
712C2×D4—22no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—212no—
716C2×D4—224no—
717C2×D4—26no—
718C2×D4—26no—
719C2×D4—212no—
720C2×D4—26no—
721C2×D4—212no—
722C2×D4—26no—
723C2×D4—22no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—412no—
732C2×D4—46no—
733C2×D4—412no—
734C2×D4—46no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4C2×#41112yes—
740C22×C4—212no—
741C22×C4—212no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—212no—
745C22×C4—26no—
746C22×C4—26no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—26no—
753C22×C4—212no—
754C22×C4—212no—
755C22×C4—212no—
756C22×C4—212no—
757C22×C4—22no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—22no—
761C22×C4—212no—
762C22×C4—26no—
763C22×C4—26no—
764C22×C4—212no—
765C22×C4—43no—
766C22×C4—43no—
767C22×C4—46no—
768C22×C4—46no—
769C22×C4—46no—
770C22×C4—46no—
771C22×C4—43no—
772C22×C4—43no—
773C22×C4—46no—
774C22×C4—46no—
775C22×C4—43no—
776C22×C4—43no—
777C22×C4C22×D414yes—
778C22×C4C22×D4112yes—
779C22×C4C22×D4112yes—
780C22×C4C2×#41112yes—
781C22×C4C2×#41112yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2516yes—
785C22×C4C2516yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2513yes—
790C22×C4C2516yes—
791C22×C4C2511yescharacteristic
792C22×C4C2513yes—
793C22×C4C2511yescharacteristic
794C22×C4C2513yes—
795C22×C4C2513yes—
796C22×C4C2513yes—
797C22×C4C2513yes—
798C22×C4C2511yescharacteristic
799C22×C4C2513yes—
800C22×C4C2511yescharacteristic
801C4⋊C4—26no—
802C4⋊C4—26no—
803C4⋊C4—212no—
804C4⋊C4—26no—
805C4⋊C4—26no—
806C4⋊C4—22no—
807C4⋊C4—26no—
808C4⋊C4—26no—
809C4⋊C4—26no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—212no—
813C4⋊C4—212no—
814C4⋊C4—212no—
815C4⋊C4—212no—
816C4⋊C4—24no—
817C4⋊C4—212no—
818C4⋊C4—212no—
819C4⋊C4—212no—
820C4⋊C4—22no—
821C4⋊C4—26no—
822C4⋊C4—26no—
823C4⋊C4—22no—
824C4⋊C4—42no—
825C4⋊C4—46no—
826C4⋊C4—46no—
827C4⋊C4—46no—
828C4⋊C4—46no—
829C4⋊C4—412no—
830C4⋊C4—46no—
831C4⋊C4C22×D4112yes—
832C4⋊C4C22×D4112yes—
833C4⋊C4C22×D4124yes—
834C22⋊C4—22no—
835C22⋊C4—26no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—212no—
839C22⋊C4—26no—
840C22⋊C4—26no—
841C22⋊C4—212no—
842C22⋊C4—22no—
843C22⋊C4—26no—
844C22⋊C4—212no—
845C22⋊C4—224no—
846C22⋊C4—212no—
847C22⋊C4—224no—
848C22⋊C4—212no—
849C22⋊C4—212no—
850C22⋊C4—224no—
851C22⋊C4—46no—
852C22⋊C4—42no—
853C22⋊C4—42no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4—412no—
857C22⋊C4—46no—
858C22⋊C4—412no—
859C22⋊C4—46no—
860C22⋊C4—46no—
861C22⋊C4—46no—
862C22⋊C4—412no—
863C22⋊C4—46no—
864C42—24no—
865C42—26no—
866C42—22no—
867C42—212no—
868C42—26no—
869C42—26no—
870C42—212no—
871C42—26no—
872C42—26no—
873C42—212no—
874C42—212no—
875C42—212no—
876C42—212no—
877C42—412no—
878C42C22×D4112yes—
879C42C22×D4112yes—
880C42C22×D4112yes—
881C42C22×D4112yes—
882C23—23no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—23no—
887C23—21no—
888C23—21no—
889C23—23no—
890C23—23no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—23no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—23no—
900C23—26no—
901C23—26no—
902C23—26no—
903C23—26no—
904C23—26no—
905C23—26no—
906C23—26no—
907C23C23×D412yes—
908C23C22×#4116yes—
909C23C22×#4112yes—
910C23C2611yescharacteristic
911Q8—224no—
912Q8—224no—
913Q8—224no—
914Q8—412no—
915Q8#525116yes—
916D4—224no—
917D4—224no—
918D4—28no—
919D4—224no—
920D4—424no—
921D4—424no—
922D4—412no—
923D4—812no—
924D4—812no—
925D4—812no—
926D4—824no—
927C2×C4—248no—
928C2×C4—23no—
929C2×C4—21no—
930C2×C4—23no—
931C2×C4—23no—
932C2×C4—21no—
933C2×C4—23no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—23no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—23no—
940C2×C4—224no—
941C2×C4—224no—
942C2×C4—224no—
943C2×C4—28no—
944C2×C4—21no—
945C2×C4—23no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—23no—
959C2×C4—22no—
960C2×C4—26no—
961C2×C4—26no—
962C2×C4—22no—
963C2×C4—23no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—21no—
967C2×C4—26no—
968C2×C4—26no—
969C2×C4—21no—
970C2×C4—23no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—23no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—412no—
978C2×C4—424no—
979C2×C4—424no—
980C2×C4—44no—
981C2×C4—412no—
982C2×C4—812no—
983C2×C4—812no—
984C2×C4—86no—
985C2×C4—86no—
986C2×C4C23×D416yes—
987C2×C4C23×D412yes—
988C2×C4C23×D416yes—
989C2×C4C23×D416yes—
990C2×C4C23×D416yes—
991C2×C4C23×D412yes—
992C2×C4C22×#4116yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4116yes—
995C2×C4C22×#4116yes—
996C2×C4#58512yes—
997C2×C4#58512yes—
998C22—22no—
999C22—22no—
1000C22—26no—
1001C22—26no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—26no—
1006C22—22no—
1007C22—43no—
1008C22—41no—
1009C22—43no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—43no—
1017C22—43no—
1018C22—41no—
1019C22—46no—
1020C22—46no—
1021C22—46no—
1022C22—46no—
1023C22—46no—
1024C22—46no—
1025C22—46no—
1026C22C24×D411yescharacteristic
1027C22C23×#4111yescharacteristic
1028C22C23×#4111yescharacteristic
1029C22C2×#58511yescharacteristic
1030C22C2×#58511yescharacteristic
1031C22H(7,𝔽2)11yescharacteristic
1032C222−1+611yescharacteristic
1033C4—22no—
1034C4—26no—
1035C4—26no—
1036C4—26no—
1037C4—26no—
1038C4—22no—
1039C4—46no—
1040C4—42no—
1041C4—42no—
1042C4—46no—
1043C4—41no—
1044C4—43no—
1045C4—46no—
1046C4—42no—
1047C4—41no—
1048C4—43no—
1049C4—42no—
1050C4C2×#525112yes—
1051C4#348714yes—
1052C2—42no—
1053C2—46no—
1054C2—42no—
1055C2—86no—
1056C2C22×#52511yescharacteristic
1057C2C2×#348711yescharacteristic
1058C2#6285311yescharacteristic
1059C2#6300611yescharacteristic
1060C2#6300711yescharacteristic
1061C2#6300911yescharacteristic
1062C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3480C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #36580C2semidirect
4. #36579C2semidirect
5. #36577C2semidirect
6. #36576C2semidirect
7. #36504C2semidirect
8. #36493C2semidirect
9. #36455C2semidirect
10. #36445C2semidirect
11. #35801C2semidirect
12. #35793C2semidirect
13. #35757C2semidirect
14. #35752C2semidirect
15. #35664C2semidirect
16. #35525C2semidirect
17. #35292C2semidirect
18. #35190C2semidirect
19. #34976C2semidirect
20. #34909C2semidirect
21. #34295C2semidirect
22. #34293C2semidirect
23. #34196C2semidirect
222. C2×C4×Q8D4semidirect
447. C2×#41#41semidirect
456. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
C2×C4×2−1+42
#365802
#365792
#365772
#365762
#365042
#364932
#364552
#364452
#358012
#357932
#357572
#357522
#356642
#355252
#352922
#351902
#349762
#349092
#342952
#342932
#341962