Finite Group Databasebeta

← #7658916

Subgroups — #7658916

Order 512.

6716 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3514C211yesmaximal, characteristic
3#42968C212yesmaximal, complemented
4#42965C212yesmaximal, complemented
5#42891C212yesmaximal, complemented
6#42886C212yesmaximal, complemented
7#42804C214yesmaximal, complemented
8#41953C214yesmaximal, complemented
9#41938C214yesmaximal, complemented
10#40592C214yesmaximal, complemented
11#40589C214yesmaximal, complemented
12#40513C218yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#37549C211yesmaximal, characteristic, complemented
17#37539C211yesmaximal, characteristic, complemented
18#37537C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20C2×#2820C212yesmaximal, complemented
21#35987C212yesmaximal, complemented
22#35976C212yesmaximal, complemented
23#35928C212yesmaximal, complemented
24#35903C212yesmaximal, complemented
25#35776C214yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3514—216no—
28#3504—216no—
29C2×#559C2211yescharacteristic
30C2×#557C2212yescomplemented
31C2×#557C2212yescomplemented
32C2×#556C2211yescharacteristic
33C2×#555C2212yes—
34C2×#554C2212yes—
35C2×#554C2212yes—
36C2×#554C2214yescomplemented
37C2×#554C2214yescomplemented
38C2×#551C2214yes—
39C2×D4×Q8C2211yescharacteristic
40C2×#548C2212yes—
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic
44C2×#544C2212yescomplemented
45C2×#544C2211yescharacteristic, complemented
46C2×#544C2211yescharacteristic, complemented
47C2×#544C2212yescomplemented
48C2×#542C2212yes—
49C2×#538C2214yes—
50C2×#533C2211yescharacteristic, complemented
51C2×#533C2212yescomplemented
52C2×#532C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C22×#125C2212yescomplemented
56C22×#125C2211yescharacteristic, complemented
57C22×#124C2212yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#518C2212yes—
61C2×C4×#41C2211yescharacteristic
62#2822C2211yescharacteristic, complemented
63#2822C2211yescharacteristic, complemented
64#2822C2212yescomplemented
65#2821C2212yescomplemented
66#2821C2212yescomplemented
67#2820C2211yescharacteristic
68#2820C2214yes—
69#2820C2212yes—
70#2820C2211yescharacteristic
71#2820C2212yescomplemented
72#2820C2212yescomplemented
73#2820C2218yescomplemented
74#2820C2214yescomplemented
75#2820C2212yescomplemented
76#2820C2214yescomplemented
77#2820C2214yescomplemented
78#2820C2212yescomplemented
79#2817C2212yescomplemented
80#2816C2212yes—
81#2814C2214yescomplemented
82#2721C2218yescomplemented
83#2716C2218yescomplemented
84#2700C2218yescomplemented
85#2694C2218yescomplemented
86#2694C2218yescomplemented
87#2690C2218yescomplemented
88#2681C2218yescomplemented
89#2677C2218yescomplemented
90#2674C2218yescomplemented
91#2674C2218yescomplemented
92#2674C2218yescomplemented
93#2672C2218yescomplemented
94#2664C2218yescomplemented
95#2664C2214yescomplemented
96#2660C2212yescomplemented
97#2659C2214yescomplemented
98#2658C2214yescomplemented
99#2641C2212yes—
100#2640C2214yescomplemented
101#2639C2214yes—
102#2637C2218yescomplemented
103#2634C2214yescomplemented
104#2633C2214yescomplemented
105#2633C2214yescomplemented
106#2632C2214yes—
107#2632C2214yescomplemented
108#2629C2214yescomplemented
109#2628C2214yescomplemented
110#2627C2212yescomplemented
111#2626C2218yescomplemented
112#2624C2212yescomplemented
113#2624C2212yescomplemented
114#2623C2214yescomplemented
115#2623C2214yescomplemented
116#2621C2214yescomplemented
117#2620C2214yescomplemented
118#2618C2212yes—
119#2618C2214yescomplemented
120#2616C2214yescomplemented
121#2611C2214yescomplemented
122#2611C2214yescomplemented
123#2591C2214yes—
124#2584C2212yescomplemented
125#2583C2214yescomplemented
126#2581C2214yescomplemented
127#2579C2218yescomplemented
128#2567C2212yescomplemented
129#2566C2214yescomplemented
130#2562C2212yes—
131#2551C2214yescomplemented
132#2550C2214yescomplemented
133#2549C2218yescomplemented
134#2548C2212yes—
135#2547C2212yescomplemented
136#2545C2218yescomplemented
137#2542C2212yescomplemented
138#2538C2214yescomplemented
139#2536C2214yescomplemented
140#2504C2212yescomplemented
141#2501C2212yescomplemented
142#2498C2214yescomplemented
143#2498C2214yescomplemented
144#2491C2214yes—
145#2490C2214yes—
146#2487C2212yescomplemented
147#2486C2212yescomplemented
148#2482C2214yescomplemented
149#2482C2214yescomplemented
150#2472C2218yes—
151#2472C2218yes—
152#2454C2214yescomplemented
153#2452C2214yescomplemented
154#2450C2218yescomplemented
155#2449C2218yescomplemented
156#2448C2214yescomplemented
157#2448C2214yescomplemented
158#2444C2218yescomplemented
159#2443C2218yescomplemented
160#2441C2214yescomplemented
161#2440C2218yescomplemented
162#2439C2214yescomplemented
163#2437C2218yescomplemented
164#2437C2218yescomplemented
165#2435C2214yes—
166#2434C2214yescomplemented
167#2423C2214yescomplemented
168#2421C2214yescomplemented
169#2418C2218yescomplemented
170#2418C2218yescomplemented
171#2417C2218yescomplemented
172#2413C2214yescomplemented
173#2406C2214yescomplemented
174#2399C2212yescomplemented
175#2398C2212yes—
176#2396C2214yescomplemented
177#2395C2212yescomplemented
178#2395C2212yescomplemented
179C2×#399C2214yescomplemented
180C2×#397C2214yescomplemented
181C2×#396C2218yescomplemented
182C2×#395C2214yescomplemented
183C2×#394C2214yes—
184#2355C2212yescomplemented
185#2352C2214yescomplemented
186#2349C2214yes—
187D4×C4⋊C4C2214yes—
188D4×C4⋊C4C2212yes—
189#2346C2212yescomplemented
190#2343C2214yescomplemented
191#2339C2212yes—
192D4×C22⋊C4C2214yes—
193D4×C22⋊C4C2214yes—
194#2320C2212yescomplemented
195#2318C2214yescomplemented
196#2285C2211yescharacteristic, complemented
197#2283C2211yescharacteristic, complemented
198#2283C2212yescomplemented
199C2×#382C2212yescomplemented
200#2275C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C23×Q8C2312yes—
204C23×D4C2312yes—
205C23×D4C2312yes—
206#559—28no—
207#557—216no—
208#557—216no—
209#556—28no—
210#555—216no—
211#554—216no—
212#554—216no—
213#554—232no—
214#554—232no—
215#551—232no—
216D4×Q8—28no—
217#548—216no—
218#546—216no—
219#546—216no—
220D42—28no—
221#544—216no—
222#544—216no—
223#544—28no—
224#544—28no—
225#542—216no—
226#538—232no—
227#533—216no—
228#533—28no—
229#532—28no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2318yes—
241C2×#127C2311yescharacteristic
242#529—216no—
243#529—28no—
244C2×#126C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125—216no—
248C2×#125—28no—
249C2×#125C2312yes—
250C2×#125C2311yescharacteristic
251C2×#125C2312yes—
252C2×#125C2311yescharacteristic
253C2×#125C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2311yescharacteristic
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#124—216no—
265C2×#124C2311yescharacteristic
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#124C2318yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2318yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#120C2314yes—
306C2×#120C2314yes—
307#520—28no—
308#520—28no—
309#518—216no—
310C4×#41D4116yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×#117C2314yes—
340C2×#117C2311yescharacteristic
341C2×#117C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2311yescharacteristic
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2318yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2314yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2318yes—
363C22×C22⋊C4C2318yes—
364C22×C42C2312yes—
365C22×C42C2311yescharacteristic
366#400C2314yes—
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#400C2314yes—
373#400C2318yes—
374#399C2314yes—
375#399C2312yes—
376#399C2314yes—
377#399C2318yes—
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2318yes—
382#399C2314yes—
383#399C2314yes—
384#399C2318yes—
385#399C2318yes—
386#399C2318yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2318yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2318yes—
398#398C2318yes—
399#398C2318yes—
400#398C2318yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2314yes—
405#397C2318yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2318yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2318yes—
414#397C2318yes—
415#396C2314yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2314yes—
420#396C2318yes—
421#396C2318yes—
422#396C2318yes—
423#396C2318yes—
424#396C2318yes—
425#396C2318yes—
426#396C2318yes—
427#395C2312yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2318yes—
434#395C2318yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2318yes—
439#394C2312yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2318yes—
447#394C2318yes—
448#394C2314yes—
449#394C2314yes—
450#394C2318yes—
451#394C2318yes—
452#394C2318yes—
453#393C2314yes—
454#393C2314yes—
455#393C2318yes—
456#393C2318yes—
457#393C2318yes—
458#391C2314yes—
459#391C2314yes—
460#391C2318yes—
461#391C2318yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2318yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2318yes—
472#389C2318yes—
473#389C2318yes—
474#389C2314yes—
475#389C2314yes—
476#389C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2314yes—
510#384C2314yes—
511#384C2314yes—
512#384C2312yes—
513#383C2312yes—
514#383C2314yes—
515#382C2311yescharacteristic
516#382C2312yes—
517#382C2311yescharacteristic
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#381C2312yes—
523#381C2314yes—
524#381C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2314yes—
529#380C2312yes—
530#380C2318yes—
531#380C2318yes—
532#380C2312yes—
533#380C2318yes—
534#380C2318yes—
535#379C2318yes—
536#379C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549#376C2312yes—
550#376C2314yes—
551C2×#95C2314yes—
552C2×#95C2314yes—
553C2×#95C2318yes—
554C25C2414yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—84no—
558C2×#41C2×D418yes—
559C22×Q8—28no—
560C22×Q8—84no—
561C22×Q8C2411yescharacteristic
562C22×Q8C2412yes—
563C22×Q8C2414yes—
564C22×Q8C2414yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2412yes—
568C22×Q8C2414yes—
569C22×D4—28no—
570C22×D4—216no—
571C22×D4—28no—
572C22×D4—84no—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2412yes—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2411yescharacteristic
579C22×D4C2412yes—
580C22×D4C2414yes—
581C22×D4C2414yes—
582C22×D4C2411yescharacteristic
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2411yescharacteristic
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2418yes—
590C23×C4C2414yes—
591C23×C4C2414yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C4⋊Q8—28no—
599C4⋊Q8—28no—
600C4⋊Q8—28no—
601C4⋊Q8—216no—
602C4⋊Q8—216no—
603C4⋊Q8—24no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—24no—
607C4⋊Q8—24no—
608C4⋊Q8—88no—
609#127—24no—
610#126—216no—
611#126—216no—
612#126—28no—
613#125—28no—
614#125—28no—
615#125—216no—
616#125—216no—
617#125—24no—
618#125—28no—
619#125—28no—
620#125—28no—
621#125—28no—
622#125—28no—
623#125—216no—
624#125—28no—
625#125—216no—
626#125—24no—
627#125—24no—
628#124—28no—
629#124—216no—
630#124—24no—
631#124—28no—
632#124—216no—
633#124—28no—
634#124—28no—
635#124—216no—
636#124—84no—
637#124—88no—
638#123—28no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—84no—
643#123—88no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—24no—
647C22⋊Q8—216no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—88no—
660C22⋊Q8—88no—
661#121—216no—
662#121—28no—
663#121—24no—
664#121—28no—
665#121—28no—
666#121—28no—
667#121—216no—
668#120—216no—
669#120—216no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—24no—
674C4×Q8—28no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8—216no—
678C4×Q8C2×D418yes—
679C4×Q8C2×D418yes—
680C4×D4—28no—
681C4×D4—216no—
682C4×D4—216no—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—24no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4C2×D418yes—
695C4×D4C2×D4116yes—
696C4×D4C2×D418yes—
697C4×D4C2×D4116yes—
698#117—28no—
699#117—28no—
700#117—24no—
701#117—24no—
702#117—28no—
703#117—28no—
704#117—216no—
705#117—82no—
706#117C2×D4116yes—
707#117C2×D418yes—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4—84no—
717C2×C4⋊C4—88no—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—216no—
776C2×C22⋊C4—216no—
777C2×C22⋊C4—88no—
778C2×C22⋊C4—88no—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C42C2×D4116yes—
818C2×C42C2×D418yes—
819C2×C42C2414yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2418yes—
828C2×C42C2412yes—
829C2×C42C2411yescharacteristic
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833C2×C42C2412yes—
834C2×C42C2411yescharacteristic
835#95C2412yes—
836#95C2412yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2412yes—
846#95C2414yes—
847#95C2412yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24—28no—
864C24—216no—
865C24—44no—
866C24—48no—
867C24—44no—
868C24C2512yes—
869C24C2514yes—
870C24C2511yescharacteristic
871C24C2512yes—
872#41—232no—
873#41—816no—
874C2×Q8—22no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—42no—
887C2×Q8—48no—
888C2×Q8—48no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—816no—
892C2×Q8C22×D414yes—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—216no—
896C2×D4—24no—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—22no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—42no—
905C2×D4—44no—
906C2×D4—42no—
907C2×D4—48no—
908C2×D4—42no—
909C2×D4—48no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—432no—
913C2×D4—816no—
914C2×D4C22×D418yes—
915C2×D4C22×D414yes—
916C2×D42−1+418yes—
917C22×C4—28no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—216no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—28no—
929C22×C4—42no—
930C22×C4—41no—
931C22×C4—42no—
932C22×C4—41no—
933C22×C4—44no—
934C22×C4—42no—
935C22×C4—44no—
936C22×C4—48no—
937C22×C4—48no—
938C22×C4—48no—
939C22×C4—48no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—42no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—42no—
946C22×C4—44no—
947C22×C4C22×D418yes—
948C22×C4C22×D414yes—
949C22×C4C22×D418yes—
950C22×C4C22×D414yes—
951C22×C4C22×D418yes—
952C22×C4C22×D414yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2518yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2512yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C4⋊C4—22no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—42no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—48no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—48no—
1019C4⋊C4—42no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—48no—
1024C4⋊C4—48no—
1025C4⋊C4—48no—
1026C4⋊C4—44no—
1027C4⋊C4C22×D414yes—
1028C4⋊C4C22×D414yes—
1029C4⋊C4C22×D418yes—
1030C4⋊C4C22×D418yes—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—24no—
1037C22⋊C4—216no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—44no—
1066C22⋊C4C22×D418yes—
1067C22⋊C4C22×D418yes—
1068C22⋊C4C22×D418yes—
1069C42—28no—
1070C42—24no—
1071C42—28no—
1072C42—28no—
1073C42—24no—
1074C42—24no—
1075C42—28no—
1076C42—44no—
1077C42—48no—
1078C42C22×D414yes—
1079C42C22×D418yes—
1080C42C22×D414yes—
1081C42C22×D414yes—
1082C42C22×D418yes—
1083C42C22×D414yes—
1084C42C22×D418yes—
1085C23—22no—
1086C23—24no—
1087C23—22no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—22no—
1093C23—24no—
1094C23—24no—
1095C23—28no—
1096C23—24no—
1097C23—22no—
1098C23—28no—
1099C23—24no—
1100C23—24no—
1101C23—22no—
1102C23—416no—
1103C23—88no—
1104C23—816no—
1105C23—816no—
1106C23—88no—
1107C23C23×D412yes—
1108C23C23×D414yes—
1109C23C2×2−1+418yes—
1110C23C2611yescharacteristic
1111Q8—28no—
1112Q8—44no—
1113Q8—48no—
1114Q8—84no—
1115Q8—88no—
1116Q8—88no—
1117Q8—84no—
1118Q8—88no—
1119D4—216no—
1120D4—44no—
1121D4—48no—
1122D4—416no—
1123D4—48no—
1124D4—84no—
1125D4—88no—
1126D4—84no—
1127D4—88no—
1128D4#536116yes—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—21no—
1132C2×C4—24no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—216no—
1141C2×C4—28no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—28no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—48no—
1176C2×C4—44no—
1177C2×C4—48no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—88no—
1181C2×C4—88no—
1182C2×C4—816no—
1183C2×C4—88no—
1184C2×C4—84no—
1185C2×C4—88no—
1186C2×C4—84no—
1187C2×C4—88no—
1188C2×C4C23×D414yes—
1189C2×C4C23×D414yes—
1190C2×C4C23×D412yes—
1191C2×C4C23×D412yes—
1192C2×C4C23×D412yes—
1193C2×C4C23×D412yes—
1194C2×C4C23×D412yes—
1195C2×C4C23×D414yes—
1196C2×C4C23×D412yes—
1197C2×C4C2×2−1+414yes—
1198C22—28no—
1199C22—28no—
1200C22—24no—
1201C22—24no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—42no—
1206C22—42no—
1207C22—48no—
1208C22—44no—
1209C22—48no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—1616no—
1218C22C2×#53618yes—
1219C22C24×D411yescharacteristic
1220C22C22×2−1+412yes—
1221C22H(7,𝔽2)11yescharacteristic
1222C22H(7,𝔽2)12yes—
1223C222−1+611yescharacteristic
1224C4—22no—
1225C4—22no—
1226C4—24no—
1227C4—22no—
1228C4—24no—
1229C4—22no—
1230C4—22no—
1231C4—24no—
1232C4—48no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4—42no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4C2×#53614yes—
1246C2—28no—
1247C2—42no—
1248C2—84no—
1249C2—82no—
1250C2C22×#53611yescharacteristic
1251C2#6285211yescharacteristic
1252C2#6285311yescharacteristic
1253C2#6305412yes—
1254C2#6305812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3514C2
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×#3504C2semidirect
3. #42968C2semidirect
4. #42965C2semidirect
5. #42891C2semidirect
6. #42886C2semidirect
7. #42804C2semidirect
8. #41953C2semidirect
9. #41938C2semidirect
10. #40592C2semidirect
11. #40589C2semidirect
12. #40513C2semidirect
13. #37640C2semidirect
14. #37607C2semidirect
15. #37555C2semidirect
16. #37549C2semidirect
17. #37539C2semidirect
18. #37537C2semidirect
19. #36699C2semidirect
20. C2×#2820C2semidirect
21. #35987C2semidirect
22. #35976C2semidirect
23. #35928C2semidirect
24. #35903C2semidirect
25. #35776C2semidirect
26. #34191C2semidirect
30. C2×#557C22semidirect
31. C2×#557C22semidirect
36. C2×#554C22semidirect
37. C2×#554C22semidirect
44. C2×#544C22semidirect
45. C2×#544C22semidirect
46. C2×#544C22semidirect
47. C2×#544C22semidirect
50. C2×#533C22semidirect
51. C2×#533C22semidirect
55. C22×#125C22semidirect
56. C22×#125C22semidirect
62. #2822C22semidirect
63. #2822C22semidirect
64. #2822C22semidirect
65. #2821C22semidirect
66. #2821C22semidirect
71. #2820C22semidirect
72. #2820C22semidirect
73. #2820C22semidirect
74. #2820C22semidirect
75. #2820C22semidirect
76. #2820C22semidirect
77. #2820C22semidirect
78. #2820C22semidirect
79. #2817C22semidirect
81. #2814C22semidirect
82. #2721C22semidirect
83. #2716C22semidirect
84. #2700C22semidirect
85. #2694C22semidirect
86. #2694C22semidirect
87. #2690C22semidirect
88. #2681C22semidirect
89. #2677C22semidirect
90. #2674C22semidirect
91. #2674C22semidirect
92. #2674C22semidirect
93. #2672C22semidirect
94. #2664C22semidirect
95. #2664C22semidirect
96. #2660C22semidirect
97. #2659C22semidirect
98. #2658C22semidirect
100. #2640C22semidirect
102. #2637C22semidirect
103. #2634C22semidirect
104. #2633C22semidirect
105. #2633C22semidirect
107. #2632C22semidirect
108. #2629C22semidirect
109. #2628C22semidirect
110. #2627C22semidirect
111. #2626C22semidirect
112. #2624C22semidirect
113. #2624C22semidirect
114. #2623C22semidirect
115. #2623C22semidirect
116. #2621C22semidirect
117. #2620C22semidirect
119. #2618C22semidirect
120. #2616C22semidirect
121. #2611C22semidirect
122. #2611C22semidirect
124. #2584C22semidirect
125. #2583C22semidirect
126. #2581C22semidirect
127. #2579C22semidirect
128. #2567C22semidirect
129. #2566C22semidirect
131. #2551C22semidirect
132. #2550C22semidirect
133. #2549C22semidirect
135. #2547C22semidirect
136. #2545C22semidirect
137. #2542C22semidirect
138. #2538C22semidirect
139. #2536C22semidirect
140. #2504C22semidirect
141. #2501C22semidirect
142. #2498C22semidirect
143. #2498C22semidirect
146. #2487C22semidirect
147. #2486C22semidirect
148. #2482C22semidirect
149. #2482C22semidirect
152. #2454C22semidirect
153. #2452C22semidirect
154. #2450C22semidirect
155. #2449C22semidirect
156. #2448C22semidirect
157. #2448C22semidirect
158. #2444C22semidirect
159. #2443C22semidirect
160. #2441C22semidirect
161. #2440C22semidirect
162. #2439C22semidirect
163. #2437C22semidirect
164. #2437C22semidirect
166. #2434C22semidirect
167. #2423C22semidirect
168. #2421C22semidirect
169. #2418C22semidirect
170. #2418C22semidirect
171. #2417C22semidirect
172. #2413C22semidirect
173. #2406C22semidirect
174. #2399C22semidirect
176. #2396C22semidirect
177. #2395C22semidirect
178. #2395C22semidirect
179. C2×#399C22semidirect
180. C2×#397C22semidirect
181. C2×#396C22semidirect
182. C2×#395C22semidirect
184. #2355C22semidirect
185. #2352C22semidirect
189. #2346C22semidirect
190. #2343C22semidirect
194. #2320C22semidirect
195. #2318C22semidirect
196. #2285C22semidirect
197. #2283C22semidirect
198. #2283C22semidirect
199. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#35142
#429682
#429652
#428912
#428862
#428042
#419532
#419382
#405922
#405892
#405132
#376402
#376072
#375552
#375492
#375392
#375372
#366992
C2×#28202
#359872
#359762
#359282
#359032
#357762
#341912