Finite Group Databasebeta

← #7732313

Subgroups — #7732313

Order 512.

6680 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic, complemented
2C2×#3536C211yesmaximal, characteristic
3#48836C218yesmaximal, complemented
4#47218C214yesmaximal, complemented
5#46815C214yesmaximal, complemented
6#43525C218yesmaximal, complemented
7#39490C212yesmaximal, complemented
8#38947C212yesmaximal, complemented
9#38094C212yesmaximal, complemented
10#38083C212yesmaximal, complemented
11#37865C212yesmaximal, complemented
12#37863C212yesmaximal, complemented
13#37747C214yesmaximal, complemented
14#37708C214yesmaximal, complemented
15#37453C211yesmaximal, characteristic, complemented
16#37423C212yesmaximal, complemented
17#37388C212yesmaximal, complemented
18#36376C212yesmaximal, complemented
19#36164C212yesmaximal, complemented
20#35669C212yesmaximal, complemented
21#35618C212yesmaximal, complemented
22#35262C211yesmaximal, characteristic, complemented
23#35019C211yesmaximal, characteristic, complemented
24C2×#2499C211yesmaximal, characteristic, complemented
25#34082C211yesmaximal, characteristic, complemented
26#3536—216no—
27C2×#562C2214yes—
28#3495—216no—
29C2×#556C2212yes—
30C2×#554C2212yes—
31C2×#554C2212yescomplemented
32C2×#552C2212yes—
33C2×#552C2212yescomplemented
34C2×#552C2214yescomplemented
35C2×#551C2214yes—
36C2×#548C2212yes—
37C2×#547C2212yes—
38C2×#546C2214yes—
39C2×#546C2212yes—
40C2×#544C2211yescharacteristic, complemented
41C2×#543C2212yes—
42C2×#542C2212yes—
43C2×#542C2212yes—
44C2×#541C2212yes—
45C2×#539C2212yes—
46C2×#538C2212yes—
47C2×#537C2212yes—
48C2×#537C2212yes—
49C2×#536C2211yescharacteristic, complemented
50C2×#533C2212yescomplemented
51C2×#529C2212yescomplemented
52C2×#525C2211yescharacteristic
53C22×C22⋊Q8C2211yescharacteristic
54C22×C22⋊Q8C2211yescharacteristic
55C22×#121C2211yescharacteristic
56C2×#520C2211yescharacteristic, complemented
57C2×#519C2211yescharacteristic, complemented
58C22×#117C2211yescharacteristic
59#2862C2212yescomplemented
60#2861C2212yescomplemented
61#2857C2212yescomplemented
62#2854C2214yes—
63#2850C2212yes—
64#2850C2212yes—
65#2850C2212yescomplemented
66#2817C2214yes—
67#2729C2218yescomplemented
68#2720C2218yescomplemented
69#2719C2218yescomplemented
70#2718C2218yescomplemented
71#2716C2218yescomplemented
72#2708C2218yescomplemented
73#2707C2218yescomplemented
74#2701C2218yescomplemented
75#2700C2218yescomplemented
76#2700C2218yescomplemented
77#2698C2218yes—
78#2697C2218yes—
79#2691C2218yescomplemented
80#2690C2218yescomplemented
81#2690C2218yescomplemented
82#2689C2218yes—
83#2689C2218yescomplemented
84#2687C2218yescomplemented
85#2686C2218yescomplemented
86#2684C2218yes—
87#2660C2212yescomplemented
88#2640C2212yescomplemented
89#2639C2214yes—
90#2627C2214yescomplemented
91#2627C2214yescomplemented
92#2624C2214yes—
93#2621C2212yes—
94#2621C2212yes—
95#2621C2212yescomplemented
96#2620C2212yescomplemented
97#2591C2214yes—
98#2568C2212yescomplemented
99#2568C2212yescomplemented
100#2567C2212yescomplemented
101#2566C2212yescomplemented
102#2565C2212yescomplemented
103#2563C2212yescomplemented
104#2561C2214yes—
105#2556C2218yescomplemented
106#2545C2212yescomplemented
107#2545C2212yescomplemented
108#2521C2218yescomplemented
109#2504C2212yes—
110#2504C2212yes—
111#2504C2212yescomplemented
112#2503C2212yes—
113#2503C2212yescomplemented
114#2503C2212yescomplemented
115#2503C2212yescomplemented
116#2503C2212yescomplemented
117#2502C2212yescomplemented
118#2501C2212yes—
119#2500C2212yes—
120#2500C2212yes—
121#2500C2212yescomplemented
122#2499C2212yes—
123#2499C2212yes—
124#2499C2214yes—
125#2499C2212yescomplemented
126#2499C2212yescomplemented
127#2499C2212yescomplemented
128#2499C2214yescomplemented
129#2489C2218yescomplemented
130#2488C2218yescomplemented
131#2488C2218yescomplemented
132#2483C2214yes—
133#2482C2214yes—
134#2480C2218yes—
135#2480C2218yes—
136#2476C2218yescomplemented
137#2474C2218yescomplemented
138#2470C2218yescomplemented
139#2469C2218yescomplemented
140#2465C2218yescomplemented
141#2458C2218yescomplemented
142#2453C2218yescomplemented
143#2450C2218yescomplemented
144#2447C2218yes—
145#2444C2218yescomplemented
146#2444C2218yescomplemented
147#2444C2218yescomplemented
148#2438C2218yescomplemented
149#2436C2212yes—
150#2435C2212yes—
151#2434C2212yescomplemented
152#2434C2212yescomplemented
153#2432C2212yescomplemented
154#2432C2212yescomplemented
155#2425C2218yescomplemented
156#2421C2218yescomplemented
157#2420C2218yescomplemented
158#2419C2218yes—
159#2413C2218yescomplemented
160#2406C2218yescomplemented
161#2405C2214yes—
162C2×#397C2214yes—
163#2359C2218yescomplemented
164#2339C2218yescomplemented
165#2335C2214yescomplemented
166#2333C2212yes—
167#2332C2212yes—
168#2329C2212yescomplemented
169#2327C2212yescomplemented
170#2326C2212yescomplemented
171#2325C2212yescomplemented
172#2321C2214yes—
173#2317C2211yescharacteristic
174#2317C2211yescharacteristic
175#2317C2212yescomplemented
176#2311C2212yescomplemented
177#2309C2211yescharacteristic
178#2309C2211yescharacteristic
179#2308C2214yes—
180C4×C4⋊Q8C2212yescomplemented
181C4×#124C2212yescomplemented
182#2298C2212yescomplemented
183#2297C2212yescomplemented
184#2297C2212yescomplemented
185C2×#391C2211yescharacteristic, complemented
186C2×#391C2211yescharacteristic, complemented
187#2293C2212yes—
188#2290C2212yes—
189#2290C2212yescomplemented
190C2×#387C2214yescomplemented
191C2×#384C2211yescharacteristic, complemented
192C2×#382C2212yescomplemented
193C2×#382C2211yescharacteristic, complemented
194#2280C2211yescharacteristic
195C42×D4C2212yescomplemented
196C2×C4×C22⋊C4C2211yescharacteristic
197C22×#41C2312yes—
198C22×#41C2314yes—
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4C2312yes—
203C23×D4C2311yescharacteristic
204C24×C4C2311yescharacteristic
205#562—232no—
206#556—216no—
207#554—216no—
208#554—216no—
209#552—232no—
210#552—216no—
211#552—216no—
212#551—232no—
213#548—216no—
214#547—216no—
215#546—232no—
216#546—216no—
217#544—28no—
218#543—216no—
219#542—216no—
220#542—216no—
221#541—216no—
222#539—216no—
223#538—216no—
224#537—216no—
225#537—216no—
226#536—28no—
227#533—216no—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234#529—216no—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125C2312yes—
241C2×#125C2312yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×#125C2314yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2314yes—
249C2×#124C2314yes—
250C2×#124C2314yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253#525D4116yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2318yes—
262C2×#123C2312yes—
263C2×C22⋊Q8—28no—
264C2×C22⋊Q8—28no—
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⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2311yescharacteristic
287C2×#121—28no—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2311yescharacteristic
299C2×#121C2311yescharacteristic
300C2×#120C2314yes—
301C2×#120C2312yes—
302#520—28no—
303#519—28no—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×#117—28no—
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2314yes—
325C2×#117C2312yes—
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2314yes—
345C22×C22⋊C4C2312yes—
346C22×C22⋊C4C2312yes—
347C22×C22⋊C4C2312yes—
348C22×C22⋊C4C2312yes—
349C22×C22⋊C4C2314yes—
350C22×C22⋊C4C2312yes—
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353C22×C42C2311yescharacteristic
354C22×C42C2312yes—
355#400C2318yes—
356#400C2318yes—
357#400C2318yes—
358#400C2318yes—
359#400C2318yes—
360#400C2318yes—
361#400C2318yes—
362#399C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#397C2318yes—
370#397C2318yes—
371#397C2318yes—
372#397C2318yes—
373#397C2318yes—
374#397C2318yes—
375#397C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#397C2318yes—
381#396C2318yes—
382#396C2318yes—
383#396C2318yes—
384#396C2318yes—
385#395C2318yes—
386#395C2318yes—
387#395C2318yes—
388#395C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2318yes—
396#393C2318yes—
397#393C2318yes—
398#393C2318yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2318yes—
409#391C2312yes—
410#391C2318yes—
411#391C2314yes—
412#391C2318yes—
413#391C2318yes—
414#391C2314yes—
415#391C2314yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2314yes—
422#390C2314yes—
423#390C2312yes—
424#390C2314yes—
425#390C2314yes—
426#389C2318yes—
427#389C2318yes—
428#389C2314yes—
429#389C2314yes—
430#389C2318yes—
431#389C2314yes—
432#389C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2318yes—
441#388C2314yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#387C2318yes—
452#387C2314yes—
453#387C2318yes—
454#387C2318yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2318yes—
459#387C2318yes—
460#387C2318yes—
461#387C2318yes—
462#387C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#385C2318yes—
477#385C2314yes—
478#385C2314yes—
479#385C2318yes—
480#385C2314yes—
481#385C2314yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#384C2312yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#384C2314yes—
493#382C2312yes—
494#382C2312yes—
495#382C2312yes—
496#382C2312yes—
497#382C2312yes—
498#382C2312yes—
499#382C2312yes—
500#382C2312yes—
501#382C2318yes—
502#382C2314yes—
503#381C2318yes—
504#381C2312yes—
505#381C2318yes—
506#381C2318yes—
507#381C2318yes—
508#381C2318yes—
509#380C2318yes—
510#380C2318yes—
511#380C2312yes—
512#380C2312yes—
513#380C2318yes—
514#379C2318yes—
515#379C2314yes—
516#379C2314yes—
517#379C2312yes—
518C4×C4⋊C4C2318yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2318yes—
527C4×C22⋊C4C2318yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534#376C2312yes—
535C2×#95C2312yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C2×#95C2314yes—
539C2×#95C2314yes—
540C43C2312yes—
541C25C2411yescharacteristic
542C25C2412yes—
543C2×#41—216no—
544C2×#41—28no—
545C2×#41—42no—
546C2×#41—42no—
547C2×#41—416no—
548C2×#41—44no—
549C2×#41—44no—
550C2×#41C2×D418yes—
551C22×Q8—24no—
552C22×Q8—24no—
553C22×Q8—42no—
554C22×Q8—42no—
555C22×Q8—42no—
556C22×Q8—42no—
557C22×Q8C2412yes—
558C22×Q8C2412yes—
559C22×Q8C2412yes—
560C22×Q8C2414yes—
561C22×Q8C2412yes—
562C22×Q8C2414yes—
563C22×Q8C2411yescharacteristic
564C22×D4—28no—
565C22×D4—24no—
566C22×D4—42no—
567C22×D4—42no—
568C22×D4—48no—
569C22×D4C2414yes—
570C22×D4C2412yes—
571C22×D4C2412yes—
572C22×D4C2414yes—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2414yes—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2411yescharacteristic
579C23×C4—42no—
580C23×C4—42no—
581C23×C4C2×D418yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2411yescharacteristic
585C23×C4C2412yes—
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2412yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2414yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—28no—
607C4⋊Q8—44no—
608C4⋊Q8—44no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126—216no—
614#125—28no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—28no—
620#124—28no—
621#124—216no—
622#124—216no—
623#124—216no—
624#124—28no—
625#124—44no—
626#124—44no—
627#123—216no—
628#123—216no—
629#123—216no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—416no—
635#123C2×D4116yes—
636C22⋊Q8—216no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8C2×D418yes—
657C22⋊Q8C2×D418yes—
658#121—216no—
659#121—216no—
660#121—216no—
661#121—216no—
662#121—28no—
663#121—28no—
664#121—28no—
665#121—28no—
666#121—28no—
667#121—216no—
668#121C2×D418yes—
669#121C2×D418yes—
670#120—216no—
671#120C2×D4116yes—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×D4—28no—
680C4×D4—216no—
681C4×D4—216no—
682C4×D4—216no—
683C4×D4—216no—
684C4×D4—28no—
685C4×D4—48no—
686C4×D4C2×D4116yes—
687C4×D4C2×D4116yes—
688#117—24no—
689#117—24no—
690#117—28no—
691#117—24no—
692#117—28no—
693#117—24no—
694#117—28no—
695#117—216no—
696#117—216no—
697#117—216no—
698#117—44no—
699#117—42no—
700#117—42no—
701#117C2×D418yes—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—24no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—48no—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2418yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C22⋊C4—28no—
756C2×C22⋊C4—28no—
757C2×C22⋊C4—28no—
758C2×C22⋊C4—28no—
759C2×C22⋊C4—216no—
760C2×C22⋊C4—44no—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C42—28no—
802C2×C42—42no—
803C2×C42—44no—
804C2×C42—42no—
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823#95C2418yes—
824#95C2414yes—
825#95C2414yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2414yes—
843#95C2418yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851C24—24no—
852C24—24no—
853C24—41no—
854C24—41no—
855C24—42no—
856C24—44no—
857C24—42no—
858C24—42no—
859C24—44no—
860C24C22×D414yes—
861C24C2514yes—
862C24C2511yescharacteristic
863C24C2511yescharacteristic
864C24C2512yes—
865C24C2511yescharacteristic
866#41—416no—
867#41—816no—
868#41—832no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—28no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—41no—
882C2×Q8—41no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—48no—
886C2×Q8—48no—
887C2×Q8—416no—
888C2×Q8—88no—
889C2×Q8C22×D414yes—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—216no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—44no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—48no—
908C2×D4—48no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—88no—
912C2×D4—816no—
913C2×D4C22×D418yes—
914C2×D4C22×D418yes—
915C2×D4C22×D418yes—
916C2×D4C22×D414yes—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—28no—
937C22×C4—24no—
938C22×C4—28no—
939C22×C4—28no—
940C22×C4—416no—
941C22×C4—42no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—48no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—44no—
963C22×C4—48no—
964C22×C4—44no—
965C22×C4—48no—
966C22×C4C22×D414yes—
967C22×C4C22×D418yes—
968C22×C4C22×D414yes—
969C22×C4C22×D414yes—
970C22×C4C22×D414yes—
971C22×C4C22×D414yes—
972C22×C4C22×D414yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2514yes—
981C22×C4C2514yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—22no—
998C4⋊C4—24no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—48no—
1022C4⋊C4—48no—
1023C4⋊C4—44no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4—48no—
1032C4⋊C4C22×D414yes—
1033C4⋊C4C22×D414yes—
1034C4⋊C4C22×D418yes—
1035C4⋊C4C22×D418yes—
1036C22⋊C4—28no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—44no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C22⋊C4—44no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—44no—
1067C22⋊C4—48no—
1068C22⋊C4—48no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4C22×D418yes—
1072C22⋊C4C22×D418yes—
1073C22⋊C4C22×D418yes—
1074C22⋊C4C22×D418yes—
1075C22⋊C4C22×D418yes—
1076C42—24no—
1077C42—24no—
1078C42—24no—
1079C42—24no—
1080C42—28no—
1081C42—28no—
1082C42—28no—
1083C42—28no—
1084C42—24no—
1085C42—24no—
1086C42—24no—
1087C42—24no—
1088C42—44no—
1089C42—42no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42C22×D418yes—
1094C23—21no—
1095C23—21no—
1096C23—22no—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—24no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—22no—
1107C23—24no—
1108C23—22no—
1109C23—28no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—28no—
1114C23—28no—
1115C23—44no—
1116C23—44no—
1117C23—48no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—164no—
1123C23—164no—
1124C23C23×D412yes—
1125C23C23×D412yes—
1126C23C23×D414yes—
1127C23C23×D412yes—
1128C23#58514yes—
1129C23C2611yescharacteristic
1130Q8—44no—
1131Q8—48no—
1132Q8—48no—
1133Q8—48no—
1134Q8—88no—
1135Q8—84no—
1136Q8—88no—
1137D4—216no—
1138D4—48no—
1139D4—44no—
1140D4—48no—
1141D4—416no—
1142D4—48no—
1143D4—84no—
1144D4—88no—
1145D4—88no—
1146D4—88no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—24no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—28no—
1160C2×C4—216no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—28no—
1183C2×C4—28no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—28no—
1192C2×C4—24no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—48no—
1197C2×C4—48no—
1198C2×C4—48no—
1199C2×C4—48no—
1200C2×C4—88no—
1201C2×C4—88no—
1202C2×C4—88no—
1203C2×C4—84no—
1204C2×C4—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4C23×D414yes—
1211C2×C4C23×D412yes—
1212C2×C4C23×D412yes—
1213C2×C4C23×D414yes—
1214C2×C4C23×D414yes—
1215C2×C4C23×D412yes—
1216C2×C4C23×D412yes—
1217C2×C4#58512yes—
1218C2×C4#58512yes—
1219C22—22no—
1220C22—22no—
1221C22—24no—
1222C22—24no—
1223C22—22no—
1224C22—22no—
1225C22—24no—
1226C22—24no—
1227C22—22no—
1228C22—22no—
1229C22—24no—
1230C22—22no—
1231C22—22no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—42no—
1237C22—42no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—48no—
1242C22—48no—
1243C22—88no—
1244C22—168no—
1245C22#350014yes—
1246C22C24×D411yescharacteristic
1247C22C2×#58511yescharacteristic
1248C22C2×#58511yescharacteristic
1249C22C2×#58512yes—
1250C222−1+612yes—
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—24no—
1255C4—24no—
1256C4—24no—
1257C4—44no—
1258C4—44no—
1259C4—42no—
1260C4—42no—
1261C4—44no—
1262C4—44no—
1263C4—42no—
1264C4—44no—
1265C4—42no—
1266C4—44no—
1267C4—44no—
1268C4—44no—
1269C4—44no—
1270C4#348514yes—
1271C2—24no—
1272C2—44no—
1273C2—42no—
1274C2—42no—
1275C2—84no—
1276C2C2×#348511yescharacteristic
1277C2C2×#350011yescharacteristic
1278C2#6285911yescharacteristic
1279C2#6291112yes—
1280C2#6293412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3536C2
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×#3495C2semidirect
3. #48836C2semidirect
4. #47218C2semidirect
5. #46815C2semidirect
6. #43525C2semidirect
7. #39490C2semidirect
8. #38947C2semidirect
9. #38094C2semidirect
10. #38083C2semidirect
11. #37865C2semidirect
12. #37863C2semidirect
13. #37747C2semidirect
14. #37708C2semidirect
15. #37453C2semidirect
16. #37423C2semidirect
17. #37388C2semidirect
18. #36376C2semidirect
19. #36164C2semidirect
20. #35669C2semidirect
21. #35618C2semidirect
22. #35262C2semidirect
23. #35019C2semidirect
24. C2×#2499C2semidirect
25. #34082C2semidirect
31. C2×#554C22semidirect
33. C2×#552C22semidirect
34. C2×#552C22semidirect
40. C2×#544C22semidirect
49. C2×#536C22semidirect
50. C2×#533C22semidirect
51. C2×#529C22semidirect
56. C2×#520C22semidirect
57. C2×#519C22semidirect
59. #2862C22semidirect
60. #2861C22semidirect
61. #2857C22semidirect
65. #2850C22semidirect
67. #2729C22semidirect
68. #2720C22semidirect
69. #2719C22semidirect
70. #2718C22semidirect
71. #2716C22semidirect
72. #2708C22semidirect
73. #2707C22semidirect
74. #2701C22semidirect
75. #2700C22semidirect
76. #2700C22semidirect
79. #2691C22semidirect
80. #2690C22semidirect
81. #2690C22semidirect
83. #2689C22semidirect
84. #2687C22semidirect
85. #2686C22semidirect
87. #2660C22semidirect
88. #2640C22semidirect
90. #2627C22semidirect
91. #2627C22semidirect
95. #2621C22semidirect
96. #2620C22semidirect
98. #2568C22semidirect
99. #2568C22semidirect
100. #2567C22semidirect
101. #2566C22semidirect
102. #2565C22semidirect
103. #2563C22semidirect
105. #2556C22semidirect
106. #2545C22semidirect
107. #2545C22semidirect
108. #2521C22semidirect
111. #2504C22semidirect
113. #2503C22semidirect
114. #2503C22semidirect
115. #2503C22semidirect
116. #2503C22semidirect
117. #2502C22semidirect
121. #2500C22semidirect
125. #2499C22semidirect
126. #2499C22semidirect
127. #2499C22semidirect
128. #2499C22semidirect
129. #2489C22semidirect
130. #2488C22semidirect
131. #2488C22semidirect
136. #2476C22semidirect
137. #2474C22semidirect
138. #2470C22semidirect
139. #2469C22semidirect
140. #2465C22semidirect
141. #2458C22semidirect
142. #2453C22semidirect
143. #2450C22semidirect
145. #2444C22semidirect
146. #2444C22semidirect
147. #2444C22semidirect
148. #2438C22semidirect
151. #2434C22semidirect
152. #2434C22semidirect
153. #2432C22semidirect
154. #2432C22semidirect
155. #2425C22semidirect
156. #2421C22semidirect
157. #2420C22semidirect
159. #2413C22semidirect
160. #2406C22semidirect
163. #2359C22semidirect
164. #2339C22semidirect
165. #2335C22semidirect
168. #2329C22semidirect
169. #2327C22semidirect
170. #2326C22semidirect
171. #2325C22semidirect
175. #2317C22semidirect
176. #2311C22semidirect
180. C4×C4⋊Q8C22semidirect
181. C4×#124C22semidirect
182. #2298C22semidirect
183. #2297C22semidirect
184. #2297C22semidirect
185. C2×#391C22semidirect
186. C2×#391C22semidirect
189. #2290C22semidirect
190. C2×#387C22semidirect
191. C2×#384C22semidirect
192. C2×#382C22semidirect
193. C2×#382C22semidirect
195. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
C2×#35362
#488362
#472182
#468152
#435252
#394902
#389472
#380942
#380832
#378652
#378632
#377472
#377082
#374532
#374232
#373882
#363762
#361642
#356692
#356182
#352622
#350192
C2×#24992
#340822