Finite Group Databasebeta

← #7654126

Subgroups — #7654126

Order 512.

6920 conjugacy classes of subgroups.

The subgroup lattice has 1245 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3475C211yesmaximal, characteristic
2C22×#554C211yesmaximal, characteristic, complemented
3#42681C212yesmaximal, complemented
4#42676C212yesmaximal, complemented
5#41411C214yesmaximal, complemented
6#41406C214yesmaximal, complemented
7#39880C214yesmaximal, complemented
8#39465C212yesmaximal, complemented
9#38919C212yesmaximal, complemented
10#38363C218yesmaximal, complemented
11#38037C214yesmaximal, complemented
12#37835C214yesmaximal, complemented
13#37540C211yesmaximal, characteristic, complemented
14#37447C212yesmaximal, complemented
15#36237C212yesmaximal, complemented
16#36219C214yesmaximal, complemented
17#36155C212yesmaximal, complemented
18#36042C212yesmaximal, complemented
19#35950C212yesmaximal, complemented
20#35311C212yesmaximal, complemented
21#35248C211yesmaximal, characteristic, complemented
22#35138C211yesmaximal, characteristic, complemented
23#35057C212yesmaximal, complemented
24#34971C211yesmaximal, characteristic, complemented
25C2×#2484C212yesmaximal, complemented
26#34190C211yesmaximal, characteristic, complemented
27#3475—216no—
28C2×#556C2211yescharacteristic
29C2×#555C2211yescharacteristic
30C2×#554—216no—
31C2×#554C2211yescharacteristic
32C2×#554C2212yes—
33C2×#554C2212yes—
34C2×#554C2212yes—
35C2×#554C2214yes—
36C2×#554C2212yes—
37C2×#554C2214yes—
38C2×#553C2212yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×#551C2214yes—
42C2×#547C2211yescharacteristic
43C2×#546C2212yes—
44C2×#533C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C2×#529C2212yes—
47C2×#529C2214yes—
48C22×#125C2211yescharacteristic
49C22×#125C2211yescharacteristic
50C2×#525C2212yes—
51C22×C22⋊Q8C2212yes—
52C22×C22⋊Q8C2212yes—
53C22×C22⋊Q8C2212yes—
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2212yes—
56C22×C4×Q8C2211yescharacteristic
57C22×C4×D4C2211yescharacteristic
58C22×C4×D4C2211yescharacteristic
59C22×C4×D4C2211yescharacteristic
60C22×#117C2212yes—
61C23×C4⋊C4C2212yes—
62#2855C2212yes—
63#2855C2212yes—
64#2855C2218yescomplemented
65#2851C2214yescomplemented
66#2849C2214yes—
67#2849C2214yes—
68#2822C2214yescomplemented
69#2817C2214yescomplemented
70#2816C2214yescomplemented
71#2721C2218yescomplemented
72#2719C2218yescomplemented
73#2716C2218yescomplemented
74#2713C2218yescomplemented
75#2700C2218yescomplemented
76#2698C2218yescomplemented
77#2698C2218yescomplemented
78#2689C2218yescomplemented
79#2689C2218yescomplemented
80#2687C2218yescomplemented
81#2680C2218yescomplemented
82#2674C2218yescomplemented
83#2660C2212yescomplemented
84#2659C2214yescomplemented
85#2642C2212yescomplemented
86#2639C2214yescomplemented
87#2638C2218yescomplemented
88#2634C2212yescomplemented
89#2634C2214yescomplemented
90#2634C2214yescomplemented
91#2633C2212yescomplemented
92#2627C2214yes—
93#2627C2214yescomplemented
94#2625C2214yescomplemented
95#2625C2214yescomplemented
96#2623C2214yes—
97#2618C2214yescomplemented
98#2614C2214yes—
99#2611C2214yescomplemented
100#2599C2214yescomplemented
101#2591C2214yescomplemented
102#2584C2212yescomplemented
103#2583C2214yescomplemented
104#2581C2214yescomplemented
105#2581C2212yescomplemented
106#2579C2218yescomplemented
107#2568C2212yescomplemented
108#2565C2214yescomplemented
109#2564C2218yescomplemented
110#2562C2212yescomplemented
111#2552C2214yescomplemented
112#2550C2214yescomplemented
113#2549C2218yescomplemented
114#2546C2212yescomplemented
115#2536C2212yescomplemented
116#2503C2212yes—
117#2503C2212yes—
118#2503C2214yescomplemented
119#2502C2212yes—
120#2502C2214yescomplemented
121#2499C2218yescomplemented
122#2492C2214yescomplemented
123#2489C2214yescomplemented
124#2488C2218yescomplemented
125#2488C2218yescomplemented
126#2487C2212yes—
127#2486C2212yes—
128#2486C2212yes—
129#2484C2214yes—
130#2484C2214yes—
131#2484C2212yes—
132#2484C2212yes—
133#2484C2212yes—
134#2484C2211yescharacteristic
135#2484C2211yescharacteristic
136#2484C2212yes—
137#2484C2212yes—
138#2484C2214yescomplemented
139#2484C2214yescomplemented
140#2484C2218yescomplemented
141#2483C2214yes—
142#2483C2214yes—
143#2453C2214yescomplemented
144#2451C2214yescomplemented
145#2450C2218yescomplemented
146#2449C2218yescomplemented
147#2447C2214yes—
148#2447C2214yes—
149#2444C2218yes—
150#2443C2218yes—
151#2441C2214yescomplemented
152#2440C2218yescomplemented
153#2439C2214yescomplemented
154#2438C2218yescomplemented
155#2438C2218yescomplemented
156#2434C2212yes—
157#2422C2214yes—
158#2420C2214yes—
159#2419C2218yes—
160#2419C2218yes—
161#2413C2214yes—
162#2413C2214yes—
163#2412C2214yes—
164#2412C2214yes—
165#2409C2212yes—
166#2406C2212yes—
167#2406C2211yescharacteristic
168#2406C2211yescharacteristic
169#2399C2212yescomplemented
170#2398C2212yescomplemented
171C2×#400C2214yescomplemented
172C2×#398C2214yescomplemented
173#2357C2212yes—
174#2353C2214yes—
175#2349C2214yes—
176#2349C2212yes—
177D4×C4⋊C4C2214yes—
178#2344C2212yes—
179#2342C2214yes—
180#2339C2214yes—
181#2339C2214yes—
182D4×C22⋊C4C2212yes—
183#2327C2214yescomplemented
184#2322C2214yes—
185#2322C2218yescomplemented
186#2319C2212yes—
187#2318C2214yes—
188#2317C2214yes—
189#2310C2214yes—
190C4×C22⋊Q8C2214yescomplemented
191C4×#123C2212yes—
192C4×#123C2212yes—
193C2×#387C2218yescomplemented
194C2×#385C2214yes—
195#2283C2211yescharacteristic
196#2283C2211yescharacteristic
197#2280C2212yes—
198C2×#381C2214yes—
199C2×#381C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C24×C4C2312yes—
207C24×C4C2312yes—
208C24×C4C2312yes—
209#556—28no—
210#555—28no—
211#554—216no—
212#554—216no—
213#554—232no—
214#554—216no—
215#554—232no—
216#554—216no—
217#554—28no—
218#553—216no—
219#552—216no—
220#552—216no—
221#551—232no—
222#547—28no—
223#546—216no—
224#533—28no—
225C2×C4⋊Q8—28no—
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232#529—232no—
233#529—216no—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125—28no—
238C2×#125—28no—
239C2×#125C2312yes—
240C2×#125C2312yes—
241C2×#125C2312yes—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#125C2312yes—
247C2×#125C2314yes—
248C2×#125C2312yes—
249C2×#124C2314yes—
250C2×#124C2312yes—
251#525—216no—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2318yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×C22⋊Q8—216no—
261C2×C22⋊Q8—216no—
262C2×C22⋊Q8—216no—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2314yes—
286C2×#120C2314yes—
287C4×#41—216no—
288C4×#41—28no—
289C2×C4×Q8—28no—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×D4—28no—
300C2×C4×D4—28no—
301C2×C4×D4D4116yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×#117—216no—
324C2×#117C2314yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2314yes—
334C22×C4⋊C4—216no—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2314yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2314yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2318yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C22⋊C4C2314yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2312yes—
356C22×C22⋊C4C2314yes—
357C22×C22⋊C4C2312yes—
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360C22×C42C2311yescharacteristic
361C22×C42C2314yes—
362C22×C42C2311yescharacteristic
363#400C2318yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2318yes—
369#400C2314yes—
370#400C2312yes—
371#400C2318yes—
372#400C2312yes—
373#400C2314yes—
374#400C2318yes—
375#400C2318yes—
376#400C2318yes—
377#399C2318yes—
378#399C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2318yes—
392#398C2312yes—
393#398C2312yes—
394#398C2318yes—
395#398C2318yes—
396#397C2318yes—
397#397C2318yes—
398#397C2314yes—
399#397C2314yes—
400#397C2318yes—
401#397C2318yes—
402#397C2318yes—
403#397C2318yes—
404#397C2318yes—
405#396C2318yes—
406#396C2318yes—
407#395C2312yes—
408#395C2318yes—
409#395C2314yes—
410#395C2312yes—
411#395C2318yes—
412#395C2314yes—
413#395C2318yes—
414#395C2318yes—
415#394C2312yes—
416#394C2314yes—
417#394C2318yes—
418#394C2318yes—
419#394C2312yes—
420#393C2318yes—
421#393C2314yes—
422#393C2318yes—
423#391C2314yes—
424#391C2314yes—
425#391C2318yes—
426#391C2318yes—
427#391C2318yes—
428#391C2318yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#390C2314yes—
435#389C2318yes—
436#389C2318yes—
437#389C2314yes—
438#389C2318yes—
439#389C2318yes—
440#389C2318yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2314yes—
452#388C2314yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2314yes—
460#387C2314yes—
461#387C2318yes—
462#387C2318yes—
463#387C2318yes—
464#387C2314yes—
465#387C2314yes—
466#387C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2314yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2312yes—
478#386C2312yes—
479#385C2314yes—
480#385C2318yes—
481#385C2312yes—
482#385C2314yes—
483#385C2314yes—
484#385C2314yes—
485#385C2318yes—
486#385C2318yes—
487#385C2314yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2314yes—
492#385C2318yes—
493#385C2318yes—
494#385C2314yes—
495#385C2312yes—
496#385C2318yes—
497#385C2318yes—
498#384C2314yes—
499#384C2318yes—
500#383C2312yes—
501#383C2312yes—
502#382C2314yes—
503#382C2312yes—
504#382C2314yes—
505#382C2318yes—
506#382C2312yes—
507#381C2314yes—
508#381C2312yes—
509#381C2314yes—
510#381C2314yes—
511#381C2314yes—
512#381C2318yes—
513#381C2314yes—
514#381C2318yes—
515#381C2318yes—
516#381C2314yes—
517#381C2314yes—
518#381C2314yes—
519#381C2311yescharacteristic
520#381C2312yes—
521#381C2311yescharacteristic
522#381C2318yes—
523#381C2318yes—
524#381C2312yes—
525#380C2314yes—
526#380C2314yes—
527#380C2318yes—
528#380C2318yes—
529#380C2314yes—
530#380C2314yes—
531#380C2312yes—
532#380C2312yes—
533#380C2314yes—
534#379C2314yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C22⋊C4C2314yes—
541C4×C22⋊C4C2312yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547#376C2312yes—
548#376C2312yes—
549C2×#95C2314yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41—24no—
558C2×#41—44no—
559C22×Q8—24no—
560C22×Q8—28no—
561C22×Q8—48no—
562C22×Q8—44no—
563C22×Q8C2412yes—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2412yes—
568C22×Q8C2414yes—
569C22×Q8C2414yes—
570C22×D4—28no—
571C22×D4C2×D418yes—
572C22×D4C2412yes—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2411yescharacteristic
576C22×D4C2411yescharacteristic
577C22×D4C2414yes—
578C22×D4C2411yescharacteristic
579C23×C4—28no—
580C23×C4—28no—
581C23×C4—48no—
582C23×C4—48no—
583C23×C4—48no—
584C23×C4C2×D4116yes—
585C23×C4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2412yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2412yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2418yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C4⋊Q8—28no—
610C4⋊Q8—28no—
611C4⋊Q8—216no—
612C4⋊Q8—24no—
613C4⋊Q8—24no—
614C4⋊Q8—48no—
615#126—216no—
616#126—216no—
617#126—216no—
618#125—28no—
619#125—28no—
620#125—216no—
621#125—216no—
622#125—28no—
623#125—28no—
624#125—28no—
625#125—28no—
626#125—28no—
627#125—28no—
628#124—28no—
629#124—216no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—416no—
635#123—44no—
636#123—48no—
637#123—44no—
638C22⋊Q8—216no—
639C22⋊Q8—216no—
640C22⋊Q8—216no—
641C22⋊Q8—216no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
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⋊Q8—48no—
657#121—216no—
658#121—28no—
659#121—28no—
660#121—28no—
661#120—216no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—28no—
671C4×D4—216no—
672C4×D4—28no—
673C4×D4—28no—
674C4×D4—216no—
675C4×D4—28no—
676C4×D4—28no—
677C4×D4—28no—
678C4×D4—216no—
679C4×D4—216no—
680C4×D4—28no—
681C4×D4—28no—
682C4×D4—216no—
683C4×D4—216no—
684C4×D4—24no—
685C4×D4—24no—
686C4×D4C2×D418yes—
687C4×D4C2×D418yes—
688C4×D4C2×D4116yes—
689C4×D4C2×D418yes—
690C4×D4C2×D4116yes—
691C4×D4C2×D418yes—
692#117—24no—
693#117—28no—
694#117—216no—
695#117—216no—
696#117—28no—
697#117—28no—
698#117—28no—
699#117—216no—
700#117—28no—
701#117—48no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—216no—
707C2×C4⋊C4—216no—
708C2×C4⋊C4—216no—
709C2×C4⋊C4—216no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—24no—
713C2×C4⋊C4—24no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—416no—
719C2×C4⋊C4C2×D418yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C22⋊C4—216no—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—28no—
773C2×C22⋊C4—48no—
774C2×C22⋊C4C2×D4116yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C42—216no—
806C2×C42—24no—
807C2×C42—24no—
808C2×C42—28no—
809C2×C42C2×D418yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2418yes—
822C2×C42C2414yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827#95C2412yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2412yes—
846#95C2414yes—
847#95C2414yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24—28no—
864C24—28no—
865C24—44no—
866C24C22×D418yes—
867C24C2512yes—
868C24C2512yes—
869C24C2512yes—
870C24C2511yescharacteristic
871#41—416no—
872#41—432no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—28no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—48no—
888C2×Q8—48no—
889C2×Q8—416no—
890C2×Q8—816no—
891C2×D4—28no—
892C2×D4—232no—
893C2×D4—24no—
894C2×D4—28no—
895C2×D4—216no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—28no—
899C2×D4—22no—
900C2×D4—24no—
901C2×D4—42no—
902C2×D4—48no—
903C2×D4C22×D418yes—
904C2×D4C22×D414yes—
905C2×D4C22×D414yes—
906C2×D42−1+418yes—
907C22×C4—22no—
908C22×C4—28no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—28no—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—28no—
919C22×C4—28no—
920C22×C4—216no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—24no—
924C22×C4—28no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—216no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—24no—
934C22×C4—432no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—48no—
947C22×C4—48no—
948C22×C4—48no—
949C22×C4—44no—
950C22×C4—48no—
951C22×C4—48no—
952C22×C4—432no—
953C22×C4—816no—
954C22×C4C22×D414yes—
955C22×C4C22×D414yes—
956C22×C4C22×D418yes—
957C22×C4C22×D418yes—
958C22×C4C22×D414yes—
959C22×C4C22×D418yes—
960C22×C4C22×D418yes—
961C22×C4C22×D418yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2518yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2514yes—
973C22×C4C2512yes—
974C22×C4C2514yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2511yescharacteristic
982C22×C4C2512yes—
983C22×C4C2511yescharacteristic
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—216no—
1021C4⋊C4—48no—
1022C4⋊C4—48no—
1023C4⋊C4—48no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—48no—
1028C4⋊C4—44no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4C22×D414yes—
1032C4⋊C4C22×D414yes—
1033C4⋊C4C22×D418yes—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—216no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—24no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—48no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—44no—
1060C22⋊C4C22×D418yes—
1061C22⋊C4C22×D418yes—
1062C22⋊C4C22×D418yes—
1063C22⋊C4C22×D418yes—
1064C42—24no—
1065C42—28no—
1066C42—28no—
1067C42—28no—
1068C42—24no—
1069C42—24no—
1070C42—24no—
1071C42—24no—
1072C42—24no—
1073C42—24no—
1074C42—28no—
1075C42—48no—
1076C42—44no—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C42C22×D414yes—
1080C42C22×D414yes—
1081C23—22no—
1082C23—24no—
1083C23—22no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—216no—
1089C23—216no—
1090C23—22no—
1091C23—24no—
1092C23—24no—
1093C23—22no—
1094C23—22no—
1095C23—48no—
1096C23—432no—
1097C23C23×D414yes—
1098C23C23×D414yes—
1099C23C23×D412yes—
1100C23C2×2−1+418yes—
1101C23#58514yes—
1102C23C2611yescharacteristic
1103Q8—48no—
1104Q8—48no—
1105Q8—44no—
1106Q8—48no—
1107Q8—84no—
1108Q8—88no—
1109Q8—88no—
1110D4—216no—
1111D4—28no—
1112D4—44no—
1113D4—416no—
1114D4—48no—
1115D4—88no—
1116D4#536116yes—
1117C2×C4—28no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—28no—
1128C2×C4—216no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—28no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—28no—
1147C2×C4—28no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—28no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—48no—
1163C2×C4—48no—
1164C2×C4—48no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—44no—
1172C2×C4—416no—
1173C2×C4—44no—
1174C2×C4—48no—
1175C2×C4—44no—
1176C2×C4—48no—
1177C2×C4—84no—
1178C2×C4—816no—
1179C2×C4—88no—
1180C2×C4—88no—
1181C2×C4—88no—
1182C2×C4C23×D412yes—
1183C2×C4C23×D412yes—
1184C2×C4C23×D414yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D412yes—
1188C2×C4C23×D414yes—
1189C2×C4C23×D412yes—
1190C2×C4C2×2−1+414yes—
1191C2×C4#58514yes—
1192C22—216no—
1193C22—28no—
1194C22—24no—
1195C22—22no—
1196C22—24no—
1197C22—22no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—432no—
1202C22—48no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22C2×#53618yes—
1209C22#348514yes—
1210C22C24×D411yescharacteristic
1211C22C22×2−1+412yes—
1212C22C2×#58512yes—
1213C22C2×#58512yes—
1214C4—22no—
1215C4—22no—
1216C4—24no—
1217C4—24no—
1218C4—24no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—44no—
1223C4—48no—
1224C4—44no—
1225C4—42no—
1226C4—44no—
1227C4—42no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—42no—
1232C4—44no—
1233C4—42no—
1234C4—44no—
1235C4C2×#53614yes—
1236C2—24no—
1237C2—28no—
1238C2—44no—
1239C2—82no—
1240C2C22×#53611yescharacteristic
1241C2C2×#348511yescharacteristic
1242C2#6281111yescharacteristic
1243C2#6302314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3475C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#554C2semidirect
3. #42681C2semidirect
4. #42676C2semidirect
5. #41411C2semidirect
6. #41406C2semidirect
7. #39880C2semidirect
8. #39465C2semidirect
9. #38919C2semidirect
10. #38363C2semidirect
11. #38037C2semidirect
12. #37835C2semidirect
13. #37540C2semidirect
14. #37447C2semidirect
15. #36237C2semidirect
16. #36219C2semidirect
17. #36155C2semidirect
18. #36042C2semidirect
19. #35950C2semidirect
20. #35311C2semidirect
21. #35248C2semidirect
22. #35138C2semidirect
23. #35057C2semidirect
24. #34971C2semidirect
25. C2×#2484C2semidirect
26. #34190C2semidirect
64. #2855C22semidirect
65. #2851C22semidirect
68. #2822C22semidirect
69. #2817C22semidirect
70. #2816C22semidirect
71. #2721C22semidirect
72. #2719C22semidirect
73. #2716C22semidirect
74. #2713C22semidirect
75. #2700C22semidirect
76. #2698C22semidirect
77. #2698C22semidirect
78. #2689C22semidirect
79. #2689C22semidirect
80. #2687C22semidirect
81. #2680C22semidirect
82. #2674C22semidirect
83. #2660C22semidirect
84. #2659C22semidirect
85. #2642C22semidirect
86. #2639C22semidirect
87. #2638C22semidirect
88. #2634C22semidirect
89. #2634C22semidirect
90. #2634C22semidirect
91. #2633C22semidirect
93. #2627C22semidirect
94. #2625C22semidirect
95. #2625C22semidirect
97. #2618C22semidirect
99. #2611C22semidirect
100. #2599C22semidirect
101. #2591C22semidirect
102. #2584C22semidirect
103. #2583C22semidirect
104. #2581C22semidirect
105. #2581C22semidirect
106. #2579C22semidirect
107. #2568C22semidirect
108. #2565C22semidirect
109. #2564C22semidirect
110. #2562C22semidirect
111. #2552C22semidirect
112. #2550C22semidirect
113. #2549C22semidirect
114. #2546C22semidirect
115. #2536C22semidirect
118. #2503C22semidirect
120. #2502C22semidirect
121. #2499C22semidirect
122. #2492C22semidirect
123. #2489C22semidirect
124. #2488C22semidirect
125. #2488C22semidirect
138. #2484C22semidirect
139. #2484C22semidirect
140. #2484C22semidirect
143. #2453C22semidirect
144. #2451C22semidirect
145. #2450C22semidirect
146. #2449C22semidirect
151. #2441C22semidirect
152. #2440C22semidirect
153. #2439C22semidirect
154. #2438C22semidirect
155. #2438C22semidirect
169. #2399C22semidirect
170. #2398C22semidirect
171. C2×#400C22semidirect
172. C2×#398C22semidirect
183. #2327C22semidirect
185. #2322C22semidirect
190. C4×C22⋊Q8C22semidirect
193. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34752
C22×#5542
#426812
#426762
#414112
#414062
#398802
#394652
#389192
#383632
#380372
#378352
#375402
#374472
#362372
#362192
#361552
#360422
#359502
#353112
#352482
#351382
#350572
#349712
C2×#24842
#341902