Finite Group Databasebeta

← #7658689

Subgroups — #7658689

Order 512.

6650 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C2×#3501C211yesmaximal, characteristic, complemented
3#42676C212yesmaximal, complemented
4#42647C212yesmaximal, complemented
5#42482C212yesmaximal, complemented
6#42436C214yesmaximal, complemented
7#42427C212yesmaximal, complemented
8#41411C214yesmaximal, complemented
9#41374C214yesmaximal, complemented
10#40589C214yesmaximal, complemented
11#40511C218yesmaximal, complemented
12#40495C214yesmaximal, complemented
13#37635C211yesmaximal, characteristic, complemented
14#37635C211yesmaximal, characteristic, complemented
15#37560C211yesmaximal, characteristic, complemented
16#37453C212yesmaximal, complemented
17#37447C212yesmaximal, complemented
18#37438C212yesmaximal, complemented
19#36699C211yesmaximal, characteristic, complemented
20C2×#2817C212yesmaximal, complemented
21#36042C212yesmaximal, complemented
22#36031C212yesmaximal, complemented
23#35928C212yesmaximal, complemented
24#35791C214yesmaximal, complemented
25#35739C212yesmaximal, complemented
26#34190C211yesmaximal, characteristic, complemented
27#3520—216no—
28#3501—216no—
29C2×#556C2211yescharacteristic
30C2×#554C2212yes—
31C2×#554C2214yes—
32C2×#554C2211yescharacteristic
33C2×#554C2212yes—
34C2×#554C2212yes—
35C2×#554C2211yescharacteristic
36C2×#554C2212yes—
37C2×#552C2212yes—
38C2×#551C2214yes—
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×#548C2212yes—
44C2×#547C2211yescharacteristic
45C2×#547C2211yescharacteristic
46C2×#546C2212yes—
47C2×#544C2212yes—
48C2×#543C2214yes—
49C2×#542C2212yes—
50C2×#539C2214yes—
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#533C2211yescharacteristic
54C2×#529C2211yescharacteristic
55C2×#525C2212yes—
56C22×C22⋊Q8C2212yes—
57C22×C22⋊Q8C2212yes—
58C22×C22⋊Q8C2212yes—
59C2×#520C2212yes—
60C2×#518C2212yes—
61C22×C4×D4C2211yescharacteristic
62#2822C2212yescomplemented
63#2821C2212yescomplemented
64#2821C2212yescomplemented
65#2820C2212yescomplemented
66#2817C2212yes—
67#2817C2212yes—
68#2817C2212yes—
69#2817C2212yes—
70#2817C2211yescharacteristic
71#2817C2218yes—
72#2817C2212yes—
73#2817C2211yescharacteristic
74#2817C2214yescomplemented
75#2817C2214yescomplemented
76#2817C2214yescomplemented
77#2817C2214yescomplemented
78#2816C2211yescharacteristic
79#2816C2212yes—
80#2816C2211yescharacteristic
81#2814C2214yes—
82#2719C2218yescomplemented
83#2713C2218yescomplemented
84#2700C2218yescomplemented
85#2698C2218yescomplemented
86#2698C2218yescomplemented
87#2690C2218yescomplemented
88#2689C2218yescomplemented
89#2689C2218yescomplemented
90#2687C2218yescomplemented
91#2680C2218yescomplemented
92#2677C2218yescomplemented
93#2674C2218yescomplemented
94#2663C2214yes—
95#2663C2214yescomplemented
96#2663C2214yescomplemented
97#2660C2212yescomplemented
98#2660C2212yescomplemented
99#2659C2214yescomplemented
100#2642C2212yescomplemented
101#2642C2212yescomplemented
102#2639C2214yescomplemented
103#2638C2218yes—
104#2634C2214yescomplemented
105#2634C2214yescomplemented
106#2634C2212yescomplemented
107#2632C2212yescomplemented
108#2628C2212yescomplemented
109#2628C2212yescomplemented
110#2627C2214yescomplemented
111#2627C2214yescomplemented
112#2627C2214yescomplemented
113#2627C2214yescomplemented
114#2625C2214yes—
115#2625C2214yes—
116#2625C2214yescomplemented
117#2623C2214yescomplemented
118#2622C2218yes—
119#2621C2218yes—
120#2616C2214yescomplemented
121#2614C2214yescomplemented
122#2604C2214yescomplemented
123#2591C2214yescomplemented
124#2584C2212yescomplemented
125#2583C2214yescomplemented
126#2581C2214yescomplemented
127#2581C2212yescomplemented
128#2581C2212yescomplemented
129#2568C2212yescomplemented
130#2568C2212yescomplemented
131#2567C2212yescomplemented
132#2567C2212yescomplemented
133#2564C2214yescomplemented
134#2564C2214yescomplemented
135#2562C2212yescomplemented
136#2551C2214yescomplemented
137#2550C2214yescomplemented
138#2549C2218yescomplemented
139#2503C2214yescomplemented
140#2503C2214yescomplemented
141#2499C2214yes—
142#2499C2214yes—
143#2492C2214yescomplemented
144#2489C2214yescomplemented
145#2488C2218yescomplemented
146#2488C2218yescomplemented
147#2487C2214yescomplemented
148#2485C2214yes—
149#2484C2214yescomplemented
150#2483C2218yes—
151#2453C2214yescomplemented
152#2451C2214yescomplemented
153#2450C2218yescomplemented
154#2449C2218yescomplemented
155#2447C2214yes—
156#2447C2214yes—
157#2444C2218yes—
158#2443C2218yes—
159#2442C2214yescomplemented
160#2440C2218yescomplemented
161#2440C2214yescomplemented
162#2438C2218yescomplemented
163#2438C2218yescomplemented
164#2434C2214yescomplemented
165#2434C2214yescomplemented
166#2422C2214yes—
167#2420C2214yes—
168#2419C2218yes—
169#2419C2218yes—
170#2415C2218yes—
171#2412C2218yes—
172#2409C2214yescomplemented
173#2406C2214yescomplemented
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2396C2212yescomplemented
177#2396C2212yescomplemented
178#2395C2214yes—
179C2×#400C2214yescomplemented
180C2×#400C2214yescomplemented
181C2×#397C2218yes—
182C2×#395C2214yescomplemented
183C2×#395C2214yescomplemented
184#2357C2212yes—
185#2353C2214yes—
186#2349C2214yes—
187#2349C2212yes—
188D4×C4⋊C4C2214yes—
189#2344C2212yes—
190#2342C2214yes—
191#2339C2214yes—
192#2339C2214yes—
193D4×C22⋊C4C2212yes—
194#2319C2212yes—
195#2318C2214yes—
196#2283C2211yescharacteristic
197#2283C2211yescharacteristic
198#2280C2212yes—
199C2×#381C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2312yes—
204C23×Q8C2312yes—
205C23×Q8C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2312yes—
208#556—28no—
209#554—216no—
210#554—216no—
211#554—232no—
212#554—28no—
213#554—216no—
214#554—28no—
215#554—216no—
216#552—216no—
217#551—232no—
218D4×Q8—28no—
219D4×Q8—216no—
220D4×Q8—28no—
221D4×Q8—28no—
222#548—216no—
223#547—28no—
224#547—28no—
225#546—216no—
226#544—216no—
227#543—232no—
228#542—216no—
229#539—232no—
230#533—28no—
231#533—28no—
232#533—28no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2318yes—
244#529—28no—
245C2×#126C2312yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2311yescharacteristic
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#124C2311yescharacteristic
257C2×#124C2314yes—
258C2×#124C2312yes—
259#525—216no—
260C2×#123C2314yes—
261C2×#123C2312yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2318yes—
266C2×C22⋊Q8—216no—
267C2×C22⋊Q8—216no—
268C2×C22⋊Q8—216no—
269C2×C22⋊Q8C2311yescharacteristic
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2311yescharacteristic
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2318yes—
302C2×#121C2311yescharacteristic
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#120C2314yes—
307#520—216no—
308#518—216no—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4D4116yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2311yescharacteristic
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348C22×C4⋊C4C2314yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2318yes—
353C22×C4⋊C4C2311yescharacteristic
354C22×C22⋊C4C2314yes—
355C22×C22⋊C4C2314yes—
356C22×C22⋊C4C2314yes—
357C22×C22⋊C4C2314yes—
358C22×C22⋊C4C2312yes—
359C22×C42C2311yescharacteristic
360#400C2312yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2318yes—
369#400C2318yes—
370#400C2318yes—
371#400C2318yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2318yes—
380#400C2318yes—
381#400C2314yes—
382#399C2312yes—
383#399C2314yes—
384#399C2312yes—
385#399C2314yes—
386#399C2314yes—
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2318yes—
395#398C2318yes—
396#398C2318yes—
397#398C2318yes—
398#398C2318yes—
399#398C2318yes—
400#398C2318yes—
401#397C2314yes—
402#397C2318yes—
403#397C2318yes—
404#397C2318yes—
405#397C2314yes—
406#397C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2314yes—
413#397C2314yes—
414#397C2318yes—
415#397C2318yes—
416#397C2318yes—
417#396C2314yes—
418#396C2314yes—
419#395C2312yes—
420#395C2312yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2318yes—
428#395C2318yes—
429#395C2318yes—
430#395C2318yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2318yes—
439#395C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2312yes—
443#394C2314yes—
444#394C2318yes—
445#394C2314yes—
446#394C2318yes—
447#394C2318yes—
448#393C2312yes—
449#393C2314yes—
450#393C2312yes—
451#393C2314yes—
452#393C2318yes—
453#393C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2318yes—
459#391C2314yes—
460#391C2314yes—
461#391C2318yes—
462#391C2318yes—
463#391C2318yes—
464#390C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2318yes—
468#389C2314yes—
469#389C2318yes—
470#389C2318yes—
471#389C2314yes—
472#389C2318yes—
473#389C2314yes—
474#389C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#384C2314yes—
506#384C2314yes—
507#383C2312yes—
508#383C2312yes—
509#382C2312yes—
510#382C2314yes—
511#382C2314yes—
512#382C2312yes—
513#382C2318yes—
514#381C2311yescharacteristic
515#381C2312yes—
516#381C2311yescharacteristic
517#381C2314yes—
518#381C2314yes—
519#381C2314yes—
520#381C2318yes—
521#381C2318yes—
522#381C2318yes—
523#381C2318yes—
524#381C2318yes—
525#380C2314yes—
526#380C2314yes—
527#380C2318yes—
528#380C2318yes—
529#380C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2314yes—
533#380C2318yes—
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⋊C4C2314yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547#376C2312yes—
548#376C2312yes—
549C2×#95C2314yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41—28no—
558C2×#41—84no—
559C22×Q8—28no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—84no—
563C22×Q8—84no—
564C22×Q8—84no—
565C22×Q8C2412yes—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2412yes—
572C22×Q8C2412yes—
573C22×Q8C2414yes—
574C22×Q8C2414yes—
575C22×Q8C2414yes—
576C22×D4—28no—
577C22×D4C2×D418yes—
578C22×D4C2414yes—
579C22×D4C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2412yes—
582C22×D4C2411yescharacteristic
583C22×D4C2414yes—
584C22×D4C2411yescharacteristic
585C23×C4—84no—
586C23×C4C2×D4116yes—
587C23×C4C2414yes—
588C23×C4C2412yes—
589C23×C4C2411yescharacteristic
590C23×C4C2414yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2418yes—
596C23×C4C2414yes—
597C23×C4C2411yescharacteristic
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—216no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613C4⋊Q8—24no—
614C4⋊Q8—88no—
615#126—216no—
616#126—216no—
617#126—28no—
618#125—216no—
619#125—28no—
620#125—216no—
621#125—28no—
622#125—24no—
623#125—28no—
624#125—28no—
625#125—28no—
626#124—28no—
627#124—216no—
628#124—24no—
629#123—216no—
630#123—216no—
631#123—28no—
632#123—216no—
633#123—216no—
634#123—88no—
635C22⋊Q8—24no—
636C22⋊Q8—24no—
637C22⋊Q8—28no—
638C22⋊Q8—24no—
639C22⋊Q8—28no—
640C22⋊Q8—216no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—28no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—216no—
666C22⋊Q8—216no—
667C22⋊Q8—88no—
668#121—216no—
669#121—28no—
670#121—24no—
671#121—28no—
672#120—216no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—24no—
676C4×Q8—28no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—28no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×D4—216no—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—28no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—28no—
693C4×D4—216no—
694C4×D4—24no—
695C4×D4C2×D418yes—
696C4×D4C2×D4116yes—
697C4×D4C2×D418yes—
698C4×D4C2×D418yes—
699C4×D4C2×D418yes—
700C4×D4C2×D4116yes—
701#117—28no—
702#117—28no—
703#117—28no—
704#117—28no—
705#117—216no—
706#117—28no—
707#117—84no—
708C2×C4⋊C4—216no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—216no—
711C2×C4⋊C4—216no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—88no—
716C2×C4⋊C4C2×D418yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C22⋊C4—216no—
771C2×C22⋊C4—216no—
772C2×C22⋊C4—216no—
773C2×C22⋊C4—84no—
774C2×C22⋊C4C2×D4116yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C42C2×D418yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2418yes—
818C2×C42C2414yes—
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823#95C2412yes—
824#95C2414yes—
825#95C2414yes—
826#95C2412yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2412yes—
842#95C2414yes—
843#95C2414yes—
844#95C2412yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859C24—28no—
860C24—44no—
861C24—44no—
862C24C22×D418yes—
863C24C2512yes—
864C24C2511yescharacteristic
865C24C2512yes—
866C24C2512yes—
867#41—432no—
868#41—816no—
869C2×Q8—24no—
870C2×Q8—22no—
871C2×Q8—22no—
872C2×Q8—22no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—28no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—48no—
887C2×Q8—48no—
888C2×Q8—48no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—816no—
893C2×Q8—816no—
894C2×Q8—816no—
895C2×D4—28no—
896C2×D4—232no—
897C2×D4—24no—
898C2×D4—28no—
899C2×D4—216no—
900C2×D4—28no—
901C2×D4—22no—
902C2×D4—24no—
903C2×D4—44no—
904C2×D4—42no—
905C2×D4—48no—
906C2×D4C22×D418yes—
907C2×D4C22×D414yes—
908C2×D4C22×D414yes—
909C2×D42−1+418yes—
910C22×C4—24no—
911C22×C4—28no—
912C22×C4—216no—
913C22×C4—28no—
914C22×C4—28no—
915C22×C4—28no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—216no—
919C22×C4—24no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—44no—
923C22×C4—42no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—42no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—48no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—816no—
940C22×C4C22×D414yes—
941C22×C4C22×D414yes—
942C22×C4C22×D414yes—
943C22×C4C22×D418yes—
944C22×C4C22×D418yes—
945C22×C4C22×D418yes—
946C22×C4C22×D418yes—
947C22×C4C22×D418yes—
948C22×C4C2514yes—
949C22×C4C2518yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2511yescharacteristic
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—22no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—22no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—28no—
1008C4⋊C4—44no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—48no—
1019C4⋊C4—44no—
1020C4⋊C4C22×D414yes—
1021C4⋊C4C22×D418yes—
1022C4⋊C4C22×D414yes—
1023C22⋊C4—24no—
1024C22⋊C4—28no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—216no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—24no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—42no—
1043C22⋊C4—44no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—42no—
1050C22⋊C4—44no—
1051C22⋊C4—48no—
1052C22⋊C4—44no—
1053C22⋊C4C22×D418yes—
1054C22⋊C4C22×D418yes—
1055C22⋊C4C22×D418yes—
1056C22⋊C4C22×D418yes—
1057C42—28no—
1058C42—28no—
1059C42—24no—
1060C42—28no—
1061C42—24no—
1062C42—24no—
1063C42—28no—
1064C42—44no—
1065C42—48no—
1066C42C22×D414yes—
1067C42C22×D414yes—
1068C42C22×D414yes—
1069C42C22×D414yes—
1070C23—24no—
1071C23—24no—
1072C23—22no—
1073C23—24no—
1074C23—22no—
1075C23—24no—
1076C23—24no—
1077C23—22no—
1078C23—216no—
1079C23—22no—
1080C23—24no—
1081C23—24no—
1082C23—24no—
1083C23—48no—
1084C23—48no—
1085C23—816no—
1086C23C23×D412yes—
1087C23C23×D414yes—
1088C23C23×D414yes—
1089C23C2×2−1+418yes—
1090C23C2611yescharacteristic
1091Q8—44no—
1092Q8—44no—
1093Q8—48no—
1094Q8—44no—
1095Q8—48no—
1096Q8—48no—
1097Q8—84no—
1098Q8—84no—
1099Q8—88no—
1100Q8—88no—
1101Q8—88no—
1102D4—216no—
1103D4—28no—
1104D4—44no—
1105D4—48no—
1106D4—416no—
1107D4—88no—
1108D4#536116yes—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—28no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—28no—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—28no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—24no—
1141C2×C4—28no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—44no—
1152C2×C4—48no—
1153C2×C4—48no—
1154C2×C4—48no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—44no—
1158C2×C4—416no—
1159C2×C4—48no—
1160C2×C4—88no—
1161C2×C4—816no—
1162C2×C4—88no—
1163C2×C4—88no—
1164C2×C4—88no—
1165C2×C4—88no—
1166C2×C4—88no—
1167C2×C4C23×D412yes—
1168C2×C4C23×D412yes—
1169C2×C4C23×D414yes—
1170C2×C4C23×D412yes—
1171C2×C4C23×D412yes—
1172C2×C4C23×D412yes—
1173C2×C4C23×D414yes—
1174C2×C4C23×D412yes—
1175C2×C4C2×2−1+414yes—
1176C22—216no—
1177C22—24no—
1178C22—24no—
1179C22—22no—
1180C22—24no—
1181C22—22no—
1182C22—24no—
1183C22—22no—
1184C22—24no—
1185C22—48no—
1186C22—44no—
1187C22—48no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—816no—
1192C22C2×#53618yes—
1193C22C24×D411yescharacteristic
1194C22C22×2−1+412yes—
1195C22H(7,𝔽2)12yes—
1196C222−1+612yes—
1197C4—22no—
1198C4—22no—
1199C4—24no—
1200C4—24no—
1201C4—22no—
1202C4—22no—
1203C4—22no—
1204C4—44no—
1205C4—48no—
1206C4—44no—
1207C4—44no—
1208C4—42no—
1209C4—42no—
1210C4—44no—
1211C4—42no—
1212C4—42no—
1213C4—44no—
1214C4—42no—
1215C4—42no—
1216C4—42no—
1217C4—44no—
1218C4C2×#53614yes—
1219C2—28no—
1220C2—44no—
1221C2—42no—
1222C2—82no—
1223C2C22×#53611yescharacteristic
1224C2#6284211yescharacteristic
1225C2#6285911yescharacteristic
1226C2#6305814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3520C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3501C2semidirect
3. #42676C2semidirect
4. #42647C2semidirect
5. #42482C2semidirect
6. #42436C2semidirect
7. #42427C2semidirect
8. #41411C2semidirect
9. #41374C2semidirect
10. #40589C2semidirect
11. #40511C2semidirect
12. #40495C2semidirect
13. #37635C2semidirect
14. #37635C2semidirect
15. #37560C2semidirect
16. #37453C2semidirect
17. #37447C2semidirect
18. #37438C2semidirect
19. #36699C2semidirect
20. C2×#2817C2semidirect
21. #36042C2semidirect
22. #36031C2semidirect
23. #35928C2semidirect
24. #35791C2semidirect
25. #35739C2semidirect
26. #34190C2semidirect
62. #2822C22semidirect
63. #2821C22semidirect
64. #2821C22semidirect
65. #2820C22semidirect
74. #2817C22semidirect
75. #2817C22semidirect
76. #2817C22semidirect
77. #2817C22semidirect
82. #2719C22semidirect
83. #2713C22semidirect
84. #2700C22semidirect
85. #2698C22semidirect
86. #2698C22semidirect
87. #2690C22semidirect
88. #2689C22semidirect
89. #2689C22semidirect
90. #2687C22semidirect
91. #2680C22semidirect
92. #2677C22semidirect
93. #2674C22semidirect
95. #2663C22semidirect
96. #2663C22semidirect
97. #2660C22semidirect
98. #2660C22semidirect
99. #2659C22semidirect
100. #2642C22semidirect
101. #2642C22semidirect
102. #2639C22semidirect
104. #2634C22semidirect
105. #2634C22semidirect
106. #2634C22semidirect
107. #2632C22semidirect
108. #2628C22semidirect
109. #2628C22semidirect
110. #2627C22semidirect
111. #2627C22semidirect
112. #2627C22semidirect
113. #2627C22semidirect
116. #2625C22semidirect
117. #2623C22semidirect
120. #2616C22semidirect
121. #2614C22semidirect
122. #2604C22semidirect
123. #2591C22semidirect
124. #2584C22semidirect
125. #2583C22semidirect
126. #2581C22semidirect
127. #2581C22semidirect
128. #2581C22semidirect
129. #2568C22semidirect
130. #2568C22semidirect
131. #2567C22semidirect
132. #2567C22semidirect
133. #2564C22semidirect
134. #2564C22semidirect
135. #2562C22semidirect
136. #2551C22semidirect
137. #2550C22semidirect
138. #2549C22semidirect
139. #2503C22semidirect
140. #2503C22semidirect
143. #2492C22semidirect
144. #2489C22semidirect
145. #2488C22semidirect
146. #2488C22semidirect
147. #2487C22semidirect
149. #2484C22semidirect
151. #2453C22semidirect
152. #2451C22semidirect
153. #2450C22semidirect
154. #2449C22semidirect
159. #2442C22semidirect
160. #2440C22semidirect
161. #2440C22semidirect
162. #2438C22semidirect
163. #2438C22semidirect
164. #2434C22semidirect
165. #2434C22semidirect
172. #2409C22semidirect
173. #2406C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
179. C2×#400C22semidirect
180. C2×#400C22semidirect
182. C2×#395C22semidirect
183. C2×#395C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#35012
#426762
#426472
#424822
#424362
#424272
#414112
#413742
#405892
#405112
#404952
#376352
#375602
#374532
#374472
#374382
#366992
C2×#28172
#360422
#360312
#359282
#357912
#357392
#341902