Finite Group Databasebeta

← #7655277

Subgroups — #7655277

Order 512.

6714 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42891C212yesmaximal, complemented
4#42811C212yesmaximal, complemented
5#41411C214yesmaximal, complemented
6#40589C214yesmaximal, complemented
7#39867C214yesmaximal, complemented
8#39724C212yesmaximal, complemented
9#39597C212yesmaximal, complemented
10#38371C218yesmaximal, complemented
11#38040C214yesmaximal, complemented
12#38027C214yesmaximal, complemented
13#37635C211yesmaximal, characteristic, complemented
14#37555C212yesmaximal, complemented
15#36275C212yesmaximal, complemented
16#36274C212yesmaximal, complemented
17#36217C214yesmaximal, complemented
18#36042C212yesmaximal, complemented
19#35928C212yesmaximal, complemented
20#35297C211yesmaximal, characteristic, complemented
21#35248C212yesmaximal, complemented
22#35245C212yesmaximal, complemented
23#35179C211yesmaximal, characteristic, complemented
24#34971C211yesmaximal, characteristic, complemented
25C2×#2581C212yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3482—216no—
28Q8×#41—216no—
29C2×Q82C2211yescharacteristic
30C2×#557C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2212yes—
33C2×#556C2211yescharacteristic
34C2×#556C2212yes—
35C2×#554C2212yes—
36C2×#554C2214yes—
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic
39C2×#552C2212yes—
40C2×#552C2214yes—
41C2×D4×Q8C2211yescharacteristic
42C2×D4×Q8C2212yes—
43C2×D4×Q8C2211yescharacteristic
44C2×#548C2212yes—
45C2×#547C2212yes—
46C2×#547C2211yescharacteristic
47C2×#533C2211yescharacteristic
48C2×#533C2211yescharacteristic
49C2×#533C2212yes—
50C2×#533C2212yes—
51C2×#533C2212yes—
52C2×#533C2214yes—
53C2×#529C2214yes—
54C2×#529C2212yes—
55C2×C4×#41C2212yes—
56C2×C4×#41C2211yescharacteristic
57C2×C4×#41C2212yes—
58C2×C4×#41C2211yescharacteristic
59C22×C4×Q8C2212yes—
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2855C2214yes—
65#2855C2214yes—
66#2855C2214yes—
67#2853C2218yes—
68#2822C2214yes—
69#2820C2214yes—
70#2817C2214yes—
71#2721C2218yes—
72#2719C2218yes—
73#2719C2218yes—
74#2716C2218yes—
75#2713C2218yes—
76#2713C2218yes—
77#2700C2218yes—
78#2698C2218yes—
79#2690C2218yes—
80#2689C2218yes—
81#2677C2218yes—
82#2674C2218yes—
83#2660C2212yes—
84#2659C2214yes—
85#2642C2212yes—
86#2639C2214yes—
87#2637C2218yes—
88#2634C2214yes—
89#2634C2214yes—
90#2634C2214yes—
91#2634C2214yes—
92#2632C2214yes—
93#2628C2214yes—
94#2627C2214yes—
95#2625C2214yes—
96#2625C2212yes—
97#2621C2214yes—
98#2616C2212yes—
99#2604C2218yes—
100#2599C2214yes—
101#2591C2214yes—
102#2584C2212yes—
103#2583C2214yes—
104#2582C2212yes—
105#2582C2212yes—
106#2581C2212yes—
107#2581C2212yes—
108#2581C2214yes—
109#2581C2214yes—
110#2581C2211yescharacteristic
111#2581C2212yes—
112#2581C2214yes—
113#2581C2214yes—
114#2581C2212yes—
115#2581C2218yes—
116#2581C2212yes—
117#2581C2211yescharacteristic
118#2568C2212yes—
119#2568C2214yes—
120#2568C2212yes—
121#2567C2212yes—
122#2567C2212yes—
123#2565C2214yes—
124#2562C2212yes—
125#2551C2214yes—
126#2550C2214yes—
127#2549C2218yes—
128#2546C2214yes—
129#2536C2211yescharacteristic
130#2536C2211yescharacteristic
131#2536C2212yes—
132#2503C2214yes—
133#2499C2214yes—
134#2498C2218yes—
135#2492C2214yes—
136#2489C2214yes—
137#2488C2218yes—
138#2488C2218yes—
139#2487C2214yes—
140#2486C2212yes—
141#2485C2214yes—
142#2484C2218yes—
143#2484C2212yes—
144#2453C2214yes—
145#2451C2214yes—
146#2450C2218yes—
147#2449C2218yes—
148#2446C2214yes—
149#2446C2214yes—
150#2444C2218yes—
151#2443C2218yes—
152#2441C2214yes—
153#2440C2218yes—
154#2439C2214yes—
155#2438C2218yes—
156#2438C2218yes—
157#2434C2214yes—
158#2423C2214yes—
159#2421C2214yes—
160#2419C2218yes—
161#2419C2218yes—
162#2417C2214yes—
163#2417C2214yes—
164#2415C2214yes—
165#2409C2212yes—
166#2409C2214yes—
167#2406C2212yes—
168#2399C2212yes—
169#2398C2212yes—
170C2×#400C2214yes—
171C2×#395C2214yes—
172#2355C2212yes—
173#2352C2214yes—
174#2349C2214yes—
175D4×C4⋊C4C2214yes—
176D4×C4⋊C4C2212yes—
177#2346C2212yes—
178#2343C2214yes—
179#2339C2212yes—
180#2339C2214yes—
181#2339C2214yes—
182#2327C2218yes—
183#2323C2214yes—
184#2323C2214yes—
185#2323C2214yes—
186#2320C2212yes—
187#2318C2214yes—
188#2317C2212yes—
189#2310C2212yes—
190C4×C22⋊Q8C2212yes—
191C4×C22⋊Q8C2212yes—
192C4×#123C2214yes—
193C2×#391C2214yes—
194C2×#389C2214yes—
195C2×#387C2218yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199C2×#382C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×Q8C2312yes—
206C23×Q8C2312yes—
207Q82—28no—
208#557—28no—
209#557—216no—
210#557—28no—
211#556—28no—
212#556—216no—
213#554—216no—
214#554—232no—
215#554—28no—
216#554—216no—
217#552—216no—
218#552—232no—
219D4×Q8—28no—
220D4×Q8—216no—
221D4×Q8—28no—
222#548—216no—
223#547—216no—
224#547—28no—
225#533—216no—
226#533—232no—
227#533—216no—
228#533—216no—
229#533—28no—
230#533—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2318yes—
244#529—232no—
245#529—216no—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2312yes—
250C2×#125C2314yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2312yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C4×#41—216no—
290C4×#41—216no—
291C4×#41—28no—
292C4×#41D4116yes—
293C2×C4×Q8—216no—
294C2×C4×Q8—28no—
295C2×C4×Q8—216no—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2311yescharacteristic
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2318yes—
357C22×C42C2314yes—
358C22×C42C2314yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2312yes—
362C22×C42C2311yescharacteristic
363#400C2314yes—
364#400C2318yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2318yes—
369#400C2314yes—
370#400C2318yes—
371#400C2318yes—
372#400C2312yes—
373#400C2318yes—
374#400C2318yes—
375#400C2312yes—
376#400C2318yes—
377#400C2318yes—
378#399C2318yes—
379#399C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2312yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#398C2312yes—
388#398C2314yes—
389#398C2318yes—
390#398C2318yes—
391#398C2318yes—
392#398C2318yes—
393#397C2318yes—
394#397C2318yes—
395#397C2318yes—
396#397C2314yes—
397#397C2318yes—
398#397C2318yes—
399#396C2318yes—
400#396C2318yes—
401#395C2314yes—
402#395C2318yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2314yes—
408#395C2318yes—
409#395C2318yes—
410#395C2312yes—
411#395C2314yes—
412#395C2318yes—
413#395C2318yes—
414#394C2314yes—
415#394C2312yes—
416#394C2312yes—
417#394C2318yes—
418#393C2314yes—
419#393C2318yes—
420#393C2318yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2318yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2318yes—
438#391C2318yes—
439#391C2318yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2318yes—
448#389C2318yes—
449#389C2318yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#389C2312yes—
456#389C2314yes—
457#389C2314yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2314yes—
466#388C2314yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2314yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2314yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2314yes—
487#387C2314yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2314yes—
494#385C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#385C2314yes—
499#385C2314yes—
500#385C2318yes—
501#385C2318yes—
502#385C2314yes—
503#384C2314yes—
504#384C2314yes—
505#384C2312yes—
506#383C2314yes—
507#383C2312yes—
508#382C2314yes—
509#382C2314yes—
510#382C2318yes—
511#382C2314yes—
512#382C2311yescharacteristic
513#382C2312yes—
514#382C2311yescharacteristic
515#382C2314yes—
516#382C2314yes—
517#381C2312yes—
518#381C2318yes—
519#381C2314yes—
520#381C2318yes—
521#381C2318yes—
522#381C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2312yes—
527#380C2314yes—
528#380C2314yes—
529#380C2312yes—
530#380C2314yes—
531#380C2318yes—
532#380C2318yes—
533#380C2312yes—
534#380C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547#376C2312yes—
548#376C2314yes—
549C2×#95C2314yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—24no—
559C2×#41—44no—
560C2×#41C2×D418yes—
561C22×Q8—24no—
562C22×Q8—28no—
563C22×Q8—28no—
564C22×Q8—28no—
565C22×Q8—24no—
566C22×Q8—44no—
567C22×Q8—42no—
568C22×Q8—48no—
569C22×Q8C2411yescharacteristic
570C22×Q8C2412yes—
571C22×Q8C2411yescharacteristic
572C22×Q8C2412yes—
573C22×Q8C2414yes—
574C22×Q8C2412yes—
575C22×Q8C2414yes—
576C22×Q8C2411yescharacteristic
577C22×Q8C2411yescharacteristic
578C22×Q8C2412yes—
579C22×Q8C2412yes—
580C22×Q8C2414yes—
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C22×D4C2411yescharacteristic
586C23×C4C2414yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2414yes—
598C23×C4C2412yes—
599C23×C4C2418yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—216no—
606C4⋊Q8—216no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614C4⋊Q8—416no—
615#126—216no—
616#126—216no—
617#126—216no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—216no—
622#125—28no—
623#125—216no—
624#125—28no—
625#125—28no—
626#125—28no—
627#125—216no—
628#124—216no—
629#124—28no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—48no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—48no—
654C22⋊Q8—44no—
655C22⋊Q8—48no—
656#121—216no—
657#121—28no—
658C4×Q8—28no—
659C4×Q8—28no—
660C4×Q8—28no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—216no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—216no—
667C4×Q8—28no—
668C4×Q8—24no—
669C4×Q8—28no—
670C4×Q8—24no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—216no—
674C4×Q8—24no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—216no—
678C4×Q8—28no—
679C4×Q8—24no—
680C4×Q8—28no—
681C4×Q8—216no—
682C4×Q8C2×D418yes—
683C4×Q8C2×D418yes—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—28no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—216no—
692C4×D4—28no—
693C4×D4—216no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4C2×D418yes—
697C4×D4C2×D4116yes—
698C4×D4C2×D418yes—
699C4×D4C2×D4116yes—
700#117—216no—
701#117—28no—
702#117—24no—
703#117—28no—
704#117—28no—
705#117—216no—
706#117—28no—
707#117—216no—
708#117—44no—
709#117C2×D4116yes—
710#117C2×D418yes—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4—24no—
717C2×C4⋊C4—48no—
718C2×C4⋊C4—416no—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C42—216no—
800C2×C42—216no—
801C2×C42—28no—
802C2×C42—28no—
803C2×C42C2×D4116yes—
804C2×C42C2×D418yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2418yes—
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2412yes—
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828#95C2412yes—
829#95C2414yes—
830#95C2412yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2418yes—
846#95C2412yes—
847#95C2414yes—
848#95C2412yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864C24C2512yes—
865C24C2511yescharacteristic
866C24C2512yes—
867#41—232no—
868#41—416no—
869#41—432no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—28no—
875C2×Q8—24no—
876C2×Q8—22no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—28no—
884C2×Q8—22no—
885C2×Q8—24no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—22no—
889C2×Q8—24no—
890C2×Q8—22no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—42no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×Q8—48no—
899C2×Q8—432no—
900C2×Q8—416no—
901C2×Q8—432no—
902C2×Q8C22×D414yes—
903C2×Q82−1+414yes—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—22no—
910C2×D4—24no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4C22×D418yes—
914C2×D4C22×D414yes—
915C2×D42−1+418yes—
916C22×C4—28no—
917C22×C4—24no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—216no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—28no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—48no—
949C22×C4—48no—
950C22×C4—48no—
951C22×C4—44no—
952C22×C4C22×D418yes—
953C22×C4C22×D418yes—
954C22×C4C22×D414yes—
955C22×C4C22×D414yes—
956C22×C4C22×D418yes—
957C22×C4C22×D414yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2518yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2511yescharacteristic
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C4⋊C4—24no—
982C4⋊C4—22no—
983C4⋊C4—24no—
984C4⋊C4—22no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—24no—
996C4⋊C4—22no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—24no—
1001C4⋊C4—22no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—24no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—216no—
1025C4⋊C4—28no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—44no—
1030C4⋊C4—48no—
1031C4⋊C4—44no—
1032C4⋊C4—48no—
1033C4⋊C4—48no—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D418yes—
1036C4⋊C4C22×D414yes—
1037C4⋊C4C22×D418yes—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—216no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4C22×D418yes—
1059C22⋊C4C22×D418yes—
1060C22⋊C4C22×D418yes—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—28no—
1065C42—28no—
1066C42—24no—
1067C42—28no—
1068C42—24no—
1069C42—28no—
1070C42—28no—
1071C42—24no—
1072C42—28no—
1073C42—24no—
1074C42—28no—
1075C42—44no—
1076C42—48no—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C42C22×D414yes—
1080C42C22×D418yes—
1081C42C22×D418yes—
1082C42C22×D414yes—
1083C42C22×D418yes—
1084C23—22no—
1085C23—22no—
1086C23—24no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23C23×D412yes—
1099C23C23×D414yes—
1100C23C2×2−1+418yes—
1101C23C2611yescharacteristic
1102Q8—28no—
1103Q8—28no—
1104Q8—28no—
1105Q8—48no—
1106Q8—416no—
1107Q8—416no—
1108Q8—48no—
1109Q8—48no—
1110Q8—48no—
1111Q8—44no—
1112Q8—84no—
1113Q8—88no—
1114D4—216no—
1115D4—48no—
1116D4—44no—
1117D4—416no—
1118D4#536116yes—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—216no—
1133C2×C4—28no—
1134C2×C4—216no—
1135C2×C4—28no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—28no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—48no—
1170C2×C4—44no—
1171C2×C4—48no—
1172C2×C4—416no—
1173C2×C4—48no—
1174C2×C4—416no—
1175C2×C4—416no—
1176C2×C4—48no—
1177C2×C4—48no—
1178C2×C4—816no—
1179C2×C4—88no—
1180C2×C4—84no—
1181C2×C4C23×D412yes—
1182C2×C4C23×D414yes—
1183C2×C4C23×D414yes—
1184C2×C4C23×D412yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D414yes—
1188C2×C4C23×D412yes—
1189C2×C4C23×D412yes—
1190C2×C4C2×2−1+414yes—
1191C2×C4C2×2−1+414yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4#58514yes—
1194C2×C4#58512yes—
1195C22—28no—
1196C22—28no—
1197C22—24no—
1198C22—24no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22C2×#53618yes—
1212C22C24×D411yescharacteristic
1213C22C22×2−1+412yes—
1214C22C22×2−1+411yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22C2×#58512yes—
1217C4—22no—
1218C4—24no—
1219C4—24no—
1220C4—22no—
1221C4—22no—
1222C4—24no—
1223C4—24no—
1224C4—22no—
1225C4—24no—
1226C4—48no—
1227C4—44no—
1228C4—44no—
1229C4—42no—
1230C4—44no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—44no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4C2×#53614yes—
1239C4#348914yes—
1240C2—28no—
1241C2—42no—
1242C2—82no—
1243C2C22×#53611yescharacteristic
1244C2C2×#348911yescharacteristic
1245C2#6281111yescharacteristic
1246C2#6302512yes—
1247C2#6303212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3482C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×Q8×#41C2semidirect
3. #42891C2semidirect
4. #42811C2semidirect
5. #41411C2semidirect
6. #40589C2semidirect
7. #39867C2semidirect
8. #39724C2semidirect
9. #39597C2semidirect
10. #38371C2semidirect
11. #38040C2semidirect
12. #38027C2semidirect
13. #37635C2semidirect
14. #37555C2semidirect
15. #36275C2semidirect
16. #36274C2semidirect
17. #36217C2semidirect
18. #36042C2semidirect
19. #35928C2semidirect
20. #35297C2semidirect
21. #35248C2semidirect
22. #35245C2semidirect
23. #35179C2semidirect
24. #34971C2semidirect
25. C2×#2581C2semidirect
26. #34191C2semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×Q8×#412
#428912
#428112
#414112
#405892
#398672
#397242
#395972
#383712
#380402
#380272
#376352
#375552
#362752
#362742
#362172
#360422
#359282
#352972
#352482
#352452
#351792
#349712
C2×#25812
#341912