Finite Group Databasebeta

← #7657152

Subgroups — #7657152

Order 512.

6600 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#42929C214yesmaximal, complemented
4#42915C212yesmaximal, complemented
5#42911C212yesmaximal, complemented
6#42315C214yesmaximal, complemented
7#42179C218yesmaximal, complemented
8#42156C214yesmaximal, complemented
9#39465C212yesmaximal, complemented
10#39461C214yesmaximal, complemented
11#38917C212yesmaximal, complemented
12#38913C214yesmaximal, complemented
13#37548C212yesmaximal, complemented
14#37538C212yesmaximal, complemented
15#37453C211yesmaximal, characteristic, complemented
16#37442C211yesmaximal, characteristic, complemented
17#36547C212yesmaximal, complemented
18#36516C212yesmaximal, complemented
19#36007C212yesmaximal, complemented
20#35834C214yesmaximal, complemented
21#35759C212yesmaximal, complemented
22#35179C212yesmaximal, complemented
23#35010C211yesmaximal, characteristic, complemented
24#34602C212yesmaximal, complemented
25#34562C211yesmaximal, characteristic
26#34180C211yesmaximal, characteristic, complemented
27#3495—216no—
28C2×#556—216no—
29C2×#556C2214yes—
30C2×#556C2212yes—
31C2×#556C2212yes—
32C2×#556C2212yes—
33C2×#556C2214yes—
34C2×#556C2212yes—
35C2×#556C2212yescomplemented
36C2×#554C2212yes—
37C2×#552C2212yes—
38C2×#552C2214yescomplemented
39C2×#552C2212yescomplemented
40C2×#551C2214yes—
41C2×#544C2211yescharacteristic, complemented
42C2×#542C2212yescomplemented
43C2×#541C2212yescomplemented
44C2×#536C2211yescharacteristic, complemented
45C2×#533C2212yes—
46C22×C4⋊Q8C2211yescharacteristic
47C2×#529C2212yes—
48C22×#126C2212yes—
49C22×#126C2212yes—
50C22×#124C2212yes—
51C2×#525C2211yescharacteristic
52C22×C22⋊Q8C2211yescharacteristic
53C22×C22⋊Q8C2211yescharacteristic
54C22×C22⋊Q8C2211yescharacteristic
55C2×#520C2211yescharacteristic, complemented
56C2×#519C2211yescharacteristic, complemented
57C22×C4×Q8C2212yes—
58C22×C4×Q8C2211yescharacteristic
59C22×C4×D4C2211yescharacteristic
60C22×#117C2211yescharacteristic
61C22×#117C2211yescharacteristic
62#2855C2214yes—
63#2855C2214yes—
64#2855C2212yes—
65#2848C2212yes—
66#2823C2218yescomplemented
67#2821C2214yescomplemented
68#2821C2214yescomplemented
69#2817C2214yescomplemented
70#2814C2214yescomplemented
71#2723C2218yescomplemented
72#2722C2218yescomplemented
73#2720C2218yescomplemented
74#2718C2218yescomplemented
75#2716C2218yescomplemented
76#2715C2218yes—
77#2715C2218yescomplemented
78#2713C2218yescomplemented
79#2712C2218yes—
80#2710C2218yes—
81#2700C2218yes—
82#2698C2218yescomplemented
83#2664C2214yescomplemented
84#2664C2218yescomplemented
85#2662C2214yescomplemented
86#2659C2212yescomplemented
87#2639C2212yescomplemented
88#2638C2212yes—
89#2637C2218yescomplemented
90#2637C2214yescomplemented
91#2637C2218yescomplemented
92#2636C2214yescomplemented
93#2635C2212yes—
94#2634C2214yescomplemented
95#2632C2214yescomplemented
96#2630C2214yes—
97#2627C2211yescharacteristic
98#2627C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2627C2212yes—
102#2627C2214yescomplemented
103#2626C2211yescharacteristic
104#2626C2212yes—
105#2625C2212yescomplemented
106#2623C2214yes—
107#2622C2212yes—
108#2621C2214yescomplemented
109#2618C2211yescharacteristic
110#2618C2212yes—
111#2617C2211yescharacteristic
112#2616C2212yescomplemented
113#2614C2214yes—
114#2613C2212yes—
115#2604C2214yescomplemented
116#2604C2214yescomplemented
117#2601C2218yescomplemented
118#2583C2214yes—
119#2582C2218yescomplemented
120#2581C2214yescomplemented
121#2581C2214yescomplemented
122#2579C2214yes—
123#2579C2214yes—
124#2568C2214yescomplemented
125#2567C2214yescomplemented
126#2565C2218yescomplemented
127#2564C2214yes—
128#2561C2214yes—
129#2557C2218yes—
130#2553C2218yescomplemented
131#2550C2214yescomplemented
132#2542C2214yescomplemented
133#2534C2214yes—
134#2521C2218yes—
135#2503C2212yes—
136#2503C2212yescomplemented
137#2496C2218yescomplemented
138#2492C2214yescomplemented
139#2489C2214yescomplemented
140#2487C2212yes—
141#2486C2212yes—
142#2484C2214yes—
143#2483C2214yes—
144#2482C2214yes—
145#2478C2218yescomplemented
146#2477C2218yescomplemented
147#2475C2218yescomplemented
148#2474C2218yes—
149#2466C2218yescomplemented
150#2465C2218yescomplemented
151#2462C2218yescomplemented
152#2459C2218yes—
153#2451C2214yescomplemented
154#2451C2214yescomplemented
155#2439C2214yescomplemented
156#2439C2214yescomplemented
157#2434C2212yes—
158#2434C2212yescomplemented
159#2429C2214yescomplemented
160#2429C2214yescomplemented
161#2417C2214yes—
162#2417C2214yescomplemented
163#2415C2214yescomplemented
164#2415C2214yescomplemented
165#2413C2214yes—
166#2412C2214yes—
167#2411C2214yes—
168#2409C2212yes—
169#2409C2212yes—
170#2399C2214yescomplemented
171#2398C2214yescomplemented
172#2396C2218yescomplemented
173#2395C2212yes—
174#2392C2214yes—
175#2388C2212yes—
176#2365C2214yescomplemented
177#2362C2214yescomplemented
178#2360C2214yescomplemented
179#2352C2214yescomplemented
180#2347C2212yescomplemented
181#2346C2212yescomplemented
182#2345C2212yes—
183#2344C2212yes—
184#2343C2214yescomplemented
185#2342C2214yes—
186#2317C2214yes—
187#2317C2212yescomplemented
188#2315C2212yes—
189#2314C2214yescomplemented
190#2310C2214yes—
191#2308C2212yes—
192C4×#123C2214yes—
193C4×#123C2212yes—
194C4×#123C2214yes—
195C4×#120C2212yes—
196#2285C2212yes—
197#2283C2212yes—
198#2280C2211yescharacteristic
199C2×#380C2211yescharacteristic
200#2274C2212yescomplemented
201C22×#41C2311yescharacteristic
202C23×Q8C2312yes—
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207C24×C4C2311yescharacteristic
208#556—216no—
209#556—216no—
210#556—232no—
211#556—232no—
212#556—216no—
213#556—216no—
214#556—216no—
215#554—216no—
216#552—232no—
217#552—216no—
218#552—216no—
219#551—232no—
220#544—28no—
221#542—216no—
222#541—216no—
223#536—28no—
224#533—216no—
225C2×C4⋊Q8—28no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233#529—216no—
234C2×#126—216no—
235C2×#126—216no—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#124—216no—
254C2×#124C2312yes—
255C2×#124C2314yes—
256C2×#124C2314yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260#525—28no—
261C2×#123C2312yes—
262C2×#123C2314yes—
263C2×#123C2312yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8—28no—
268C2×C22⋊Q8—28no—
269C2×C22⋊Q8—28no—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×#121C2311yescharacteristic
291C2×#121C2311yescharacteristic
292C2×#120C2312yes—
293C2×#120C2312yes—
294#520—28no—
295#519—28no—
296C2×C4×Q8—28no—
297C2×C4×Q8—216no—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×D4—28no—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×#117—28no—
323C2×#117D4116yescomplemented
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2312yes—
327C2×#117C2311yescharacteristic
328C2×#117C2312yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2312yes—
332C2×#117C2314yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2311yescharacteristic
336C2×#117C2312yes—
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2311yescharacteristic
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2311yescharacteristic
352C22×C22⋊C4C2312yes—
353C22×C22⋊C4C2312yes—
354C22×C22⋊C4C2311yescharacteristic
355C22×C22⋊C4C2311yescharacteristic
356C22×C22⋊C4C2312yes—
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2312yes—
359C22×C22⋊C4C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2312yes—
363C22×C42C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2318yes—
367#400C2314yes—
368#400C2314yes—
369#400C2318yes—
370#400C2312yes—
371#400C2318yes—
372#399C2314yes—
373#399C2312yes—
374#399C2318yes—
375#399C2318yes—
376#398C2314yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2314yes—
385#398C2312yes—
386#398C2318yes—
387#398C2318yes—
388#398C2314yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#397C2312yes—
394#397C2314yes—
395#397C2314yes—
396#397C2318yes—
397#397C2318yes—
398#397C2314yes—
399#396C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#396C2318yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2318yes—
410#395C2314yes—
411#395C2314yes—
412#395C2318yes—
413#395C2312yes—
414#395C2318yes—
415#395C2318yes—
416#395C2314yes—
417#394C2314yes—
418#394C2318yes—
419#394C2318yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2318yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#393C2318yes—
428#393C2314yes—
429#393C2312yes—
430#393C2318yes—
431#393C2318yes—
432#393C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2312yes—
436#391C2318yes—
437#391C2318yes—
438#391C2318yes—
439#391C2318yes—
440#391C2318yes—
441#391C2318yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#390C2318yes—
447#389C2318yes—
448#389C2318yes—
449#389C2318yes—
450#389C2318yes—
451#389C2314yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#389C2314yes—
456#389C2318yes—
457#389C2314yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2314yes—
468#388C2318yes—
469#388C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2314yes—
481#387C2318yes—
482#387C2318yes—
483#386C2318yes—
484#386C2314yes—
485#386C2314yes—
486#386C2312yes—
487#386C2314yes—
488#386C2318yes—
489#386C2312yes—
490#386C2314yes—
491#386C2318yes—
492#385C2318yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2312yes—
498#385C2314yes—
499#385C2314yes—
500#385C2318yes—
501#385C2318yes—
502#385C2312yes—
503#385C2314yes—
504#385C2318yes—
505#385C2314yes—
506#384C2318yes—
507#384C2314yes—
508#383C2314yes—
509#382C2318yes—
510#382C2314yes—
511#382C2314yes—
512#382C2314yes—
513#381C2314yes—
514#381C2314yes—
515#381C2312yes—
516#381C2314yes—
517#381C2312yes—
518#381C2314yes—
519#381C2314yes—
520#381C2318yes—
521#380C2318yes—
522#380C2312yes—
523#380C2312yes—
524#380C2314yes—
525#380C2312yes—
526#380C2314yes—
527#380C2312yes—
528#380C2314yes—
529#380C2311yescharacteristic
530#380C2312yes—
531#380C2311yescharacteristic
532#380C2318yes—
533#379C2312yes—
534#379C2314yes—
535#379C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2318yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2318yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552#376C2314yes—
553C2×#95C2312yes—
554C25C2411yescharacteristic
555C25C2411yescharacteristic
556C2×#41—24no—
557C2×#41—44no—
558C22×Q8—24no—
559C22×Q8—28no—
560C22×Q8—24no—
561C22×Q8—28no—
562C22×Q8—44no—
563C22×Q8—44no—
564C22×Q8—44no—
565C22×Q8C2412yes—
566C22×Q8C2412yes—
567C22×Q8C2414yes—
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2411yescharacteristic
572C22×Q8C2414yes—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—42no—
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2412yes—
582C22×D4C2414yes—
583C23×C4—24no—
584C23×C4—44no—
585C23×C4—44no—
586C23×C4C2×D418yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2412yes—
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2412yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2411yescharacteristic
607C4⋊Q8—28no—
608C4⋊Q8—28no—
609C4⋊Q8—216no—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—28no—
613C4⋊Q8—48no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—216no—
625#126—216no—
626#125—216no—
627#125—216no—
628#125—28no—
629#125—28no—
630#125—216no—
631#124—216no—
632#124—216no—
633#124—216no—
634#124—216no—
635#124—216no—
636#124—28no—
637#123—28no—
638#123—216no—
639#123—28no—
640#123—216no—
641#123—216no—
642#123—48no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—24no—
652C22⋊Q8—24no—
653C22⋊Q8—216no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—48no—
662C22⋊Q8—48no—
663#121—24no—
664#121—24no—
665#120—28no—
666#120—44no—
667C4×Q8—28no—
668C4×Q8—216no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—216no—
673C4×Q8—216no—
674C4×Q8—216no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—216no—
680C4×D4—28no—
681C4×D4—28no—
682C4×D4—28no—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—48no—
690#117—24no—
691#117—216no—
692#117—28no—
693#117—216no—
694#117—28no—
695#117—28no—
696#117—216no—
697#117—216no—
698#117—44no—
699#117—48no—
700#117C2×D418yes—
701#117C2×D418yes—
702#117C2×D4116yes—
703#117C2×D418yes—
704#117C2×D4116yes—
705#117C2×D418yes—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—44no—
716C2×C4⋊C4C2×D418yes—
717C2×C4⋊C4C2×D418yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C22⋊C4—24no—
768C2×C22⋊C4—28no—
769C2×C22⋊C4—28no—
770C2×C22⋊C4—28no—
771C2×C22⋊C4—24no—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—44no—
774C2×C22⋊C4C2×D4116yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C42—28no—
816C2×C42—24no—
817C2×C42—28no—
818C2×C42C2×D4116yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2418yes—
831C2×C42C2418yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2412yes—
839#95C2418yes—
840#95C2412yes—
841#95C2418yes—
842#95C2418yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2414yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865C24—22no—
866C24—22no—
867C24—22no—
868C24—22no—
869C24—22no—
870C24—42no—
871C24—42no—
872C24—42no—
873C24—42no—
874C24C22×D414yes—
875C24C2512yes—
876C24C2512yes—
877C24C2511yescharacteristic
878C24C2511yescharacteristic
879C24C2511yescharacteristic
880#41—416no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—22no—
886C2×Q8—28no—
887C2×Q8—28no—
888C2×Q8—28no—
889C2×Q8—28no—
890C2×Q8—28no—
891C2×Q8—28no—
892C2×Q8—28no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×Q8—48no—
899C2×Q8—432no—
900C2×Q8—416no—
901C2×Q8—416no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—22no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—416no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—22no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—28no—
940C22×C4—28no—
941C22×C4—28no—
942C22×C4—416no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—44no—
947C22×C4—42no—
948C22×C4—44no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—48no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—416no—
958C22×C4C22×D414yes—
959C22×C4C22×D418yes—
960C22×C4C22×D414yes—
961C22×C4C22×D414yes—
962C22×C4C22×D418yes—
963C22×C4C22×D414yes—
964C22×C4C22×D414yes—
965C22×C4C22×D414yes—
966C22×C42−1+414yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2518yes—
970C22×C4C2512yes—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2512yes—
987C22×C4C2511yescharacteristic
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—44no—
1019C4⋊C4—48no—
1020C4⋊C4—44no—
1021C4⋊C4—48no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—48no—
1025C4⋊C4—44no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4C22×D414yes—
1032C4⋊C4C22×D418yes—
1033C4⋊C4C22×D414yes—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D414yes—
1036C4⋊C4C22×D418yes—
1037C22⋊C4—28no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—28no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4C22×D418yes—
1074C22⋊C4C22×D418yes—
1075C22⋊C4C22×D418yes—
1076C22⋊C4C22×D418yes—
1077C42—28no—
1078C42—28no—
1079C42—24no—
1080C42—24no—
1081C42—28no—
1082C42—28no—
1083C42—28no—
1084C42—28no—
1085C42—28no—
1086C42—24no—
1087C42—28no—
1088C42—48no—
1089C42—48no—
1090C42C22×D418yes—
1091C42C22×D418yes—
1092C42C22×D418yes—
1093C42C22×D418yes—
1094C23—22no—
1095C23—22no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—22no—
1101C23—21no—
1102C23—22no—
1103C23—22no—
1104C23—28no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—24no—
1111C23—24no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—44no—
1116C23—44no—
1117C23—44no—
1118C23—44no—
1119C23—44no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23C23×D412yes—
1125C23C23×D412yes—
1126C23C23×D412yes—
1127C23C2×2−1+412yes—
1128C23#58512yes—
1129C23C2611yescharacteristic
1130Q8—416no—
1131Q8—416no—
1132Q8—48no—
1133Q8—48no—
1134Q8—44no—
1135Q8—48no—
1136Q8—48no—
1137Q8—88no—
1138D4—48no—
1139D4—48no—
1140D4—44no—
1141D4—48no—
1142D4—48no—
1143D4—84no—
1144D4—88no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—216no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—28no—
1160C2×C4—28no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—28no—
1177C2×C4—28no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—28no—
1183C2×C4—28no—
1184C2×C4—24no—
1185C2×C4—28no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—28no—
1189C2×C4—24no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—48no—
1194C2×C4—48no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—48no—
1198C2×C4—48no—
1199C2×C4—48no—
1200C2×C4—48no—
1201C2×C4—48no—
1202C2×C4—88no—
1203C2×C4—84no—
1204C2×C4—164no—
1205C2×C4C23×D414yes—
1206C2×C4C23×D414yes—
1207C2×C4C23×D414yes—
1208C2×C4C23×D412yes—
1209C2×C4C23×D412yes—
1210C2×C4C23×D412yes—
1211C2×C4C23×D414yes—
1212C2×C4C23×D412yes—
1213C2×C4C2×2−1+414yes—
1214C2×C4#58514yes—
1215C22—22no—
1216C22—24no—
1217C22—24no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—88no—
1240C22—88no—
1241C22#348914yes—
1242C22C24×D411yescharacteristic
1243C22C22×2−1+411yescharacteristic
1244C22C2×#58511yescharacteristic
1245C22C2×#58512yes—
1246C222−1+612yes—
1247C4—24no—
1248C4—24no—
1249C4—24no—
1250C4—24no—
1251C4—24no—
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—44no—
1256C4—42no—
1257C4—42no—
1258C4—44no—
1259C4—42no—
1260C4—48no—
1261C4—44no—
1262C4—44no—
1263C4—42no—
1264C4—42no—
1265C4—44no—
1266C4—44no—
1267C4#344914yes—
1268C2—24no—
1269C2—42no—
1270C2—42no—
1271C2—82no—
1272C2—82no—
1273C2C2×#344911yescharacteristic
1274C2C2×#348911yescharacteristic
1275C2#6285911yescharacteristic
1276C2#6291112yes—
1277C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34562C2
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
2. C22×#556C2semidirect
3. #42929C2semidirect
4. #42915C2semidirect
5. #42911C2semidirect
6. #42315C2semidirect
7. #42179C2semidirect
8. #42156C2semidirect
9. #39465C2semidirect
10. #39461C2semidirect
11. #38917C2semidirect
12. #38913C2semidirect
13. #37548C2semidirect
14. #37538C2semidirect
15. #37453C2semidirect
16. #37442C2semidirect
17. #36547C2semidirect
18. #36516C2semidirect
19. #36007C2semidirect
20. #35834C2semidirect
21. #35759C2semidirect
22. #35179C2semidirect
23. #35010C2semidirect
24. #34602C2semidirect
26. #34180C2semidirect
35. C2×#556C22semidirect
38. C2×#552C22semidirect
39. C2×#552C22semidirect
41. C2×#544C22semidirect
42. C2×#542C22semidirect
43. C2×#541C22semidirect
44. C2×#536C22semidirect
55. C2×#520C22semidirect
56. C2×#519C22semidirect
66. #2823C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
69. #2817C22semidirect
70. #2814C22semidirect
71. #2723C22semidirect
72. #2722C22semidirect
73. #2720C22semidirect
74. #2718C22semidirect
75. #2716C22semidirect
77. #2715C22semidirect
78. #2713C22semidirect
82. #2698C22semidirect
83. #2664C22semidirect
84. #2664C22semidirect
85. #2662C22semidirect
86. #2659C22semidirect
87. #2639C22semidirect
89. #2637C22semidirect
90. #2637C22semidirect
91. #2637C22semidirect
92. #2636C22semidirect
94. #2634C22semidirect
95. #2632C22semidirect
102. #2627C22semidirect
105. #2625C22semidirect
108. #2621C22semidirect
112. #2616C22semidirect
115. #2604C22semidirect
116. #2604C22semidirect
117. #2601C22semidirect
119. #2582C22semidirect
120. #2581C22semidirect
121. #2581C22semidirect
124. #2568C22semidirect
125. #2567C22semidirect
126. #2565C22semidirect
130. #2553C22semidirect
131. #2550C22semidirect
132. #2542C22semidirect
136. #2503C22semidirect
137. #2496C22semidirect
138. #2492C22semidirect
139. #2489C22semidirect
145. #2478C22semidirect
146. #2477C22semidirect
147. #2475C22semidirect
149. #2466C22semidirect
150. #2465C22semidirect
151. #2462C22semidirect
153. #2451C22semidirect
154. #2451C22semidirect
155. #2439C22semidirect
156. #2439C22semidirect
158. #2434C22semidirect
159. #2429C22semidirect
160. #2429C22semidirect
162. #2417C22semidirect
163. #2415C22semidirect
164. #2415C22semidirect
170. #2399C22semidirect
171. #2398C22semidirect
172. #2396C22semidirect
176. #2365C22semidirect
177. #2362C22semidirect
178. #2360C22semidirect
179. #2352C22semidirect
180. #2347C22semidirect
181. #2346C22semidirect
184. #2343C22semidirect
187. #2317C22semidirect
189. #2314C22semidirect
200. #2274C22semidirect
323. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
C22×#5562
#429292
#429152
#429112
#423152
#421792
#421562
#394652
#394612
#389172
#389132
#375482
#375382
#374532
#374422
#365472
#365162
#360072
#358342
#357592
#351792
#350102
#346022
#345622
#341802