Finite Group Databasebeta

← #7656009

Subgroups — #7656009

Order 512.

6914 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C22×#554C211yesmaximal, characteristic, complemented
3#42676C212yesmaximal, complemented
4#42482C212yesmaximal, complemented
5#42442C214yesmaximal, complemented
6#41411C214yesmaximal, complemented
7#40589C214yesmaximal, complemented
8#40516C218yesmaximal, complemented
9#39592C212yesmaximal, complemented
10#39122C212yesmaximal, complemented
11#38037C214yesmaximal, complemented
12#37835C214yesmaximal, complemented
13#37549C211yesmaximal, characteristic, complemented
14#37540C211yesmaximal, characteristic, complemented
15#37453C212yesmaximal, complemented
16#37442C212yesmaximal, complemented
17#36237C212yesmaximal, complemented
18#36155C212yesmaximal, complemented
19#36042C212yesmaximal, complemented
20#35928C212yesmaximal, complemented
21#35806C214yesmaximal, complemented
22#35179C211yesmaximal, characteristic, complemented
23#35057C212yesmaximal, complemented
24#34602C211yesmaximal, characteristic, complemented
25C2×#2627C212yesmaximal, complemented
26#34194C211yesmaximal, characteristic, complemented
27#3520—216no—
28C2×#556C2211yescharacteristic
29C2×#554—216no—
30C2×#554C2212yes—
31C2×#554C2214yes—
32C2×#554C2212yes—
33C2×#554C2214yes—
34C2×#554C2212yes—
35C2×#554C2212yes—
36C2×#554C2212yes—
37C2×#552C2212yes—
38C2×#551C2214yes—
39C2×D4×Q8C2211yescharacteristic
40C2×#548C2212yes—
41C2×#547C2211yescharacteristic
42C2×#547C2211yescharacteristic
43C2×#546C2212yes—
44C2×#542C2212yes—
45C2×#539C2214yes—
46C2×#533C2211yescharacteristic
47C22×C4⋊Q8C2211yescharacteristic
48C2×#529C2211yescharacteristic
49C22×#125C2211yescharacteristic
50C22×#125C2211yescharacteristic
51C2×#525C2212yes—
52C22×C22⋊Q8C2212yes—
53C22×C22⋊Q8C2212yes—
54C22×C22⋊Q8C2212yes—
55C22×C22⋊Q8C2212yes—
56C2×#520C2212yes—
57C22×C4×Q8C2211yescharacteristic
58C22×C4×D4C2211yescharacteristic
59C22×C4×D4C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic
61C23×C4⋊C4C2212yes—
62#2855C2212yes—
63#2855C2212yes—
64#2849C2214yes—
65#2849C2214yes—
66#2822C2214yescomplemented
67#2822C2212yescomplemented
68#2820C2212yescomplemented
69#2817C2214yescomplemented
70#2817C2214yescomplemented
71#2814C2218yescomplemented
72#2719C2218yescomplemented
73#2713C2218yescomplemented
74#2700C2218yescomplemented
75#2698C2218yescomplemented
76#2698C2218yescomplemented
77#2690C2218yescomplemented
78#2689C2218yescomplemented
79#2689C2218yescomplemented
80#2687C2218yescomplemented
81#2680C2218yescomplemented
82#2677C2218yescomplemented
83#2674C2218yescomplemented
84#2664C2214yescomplemented
85#2660C2212yescomplemented
86#2659C2214yescomplemented
87#2642C2212yescomplemented
88#2639C2214yescomplemented
89#2637C2214yescomplemented
90#2634C2212yescomplemented
91#2634C2214yescomplemented
92#2632C2212yescomplemented
93#2629C2214yescomplemented
94#2627C2211yescharacteristic
95#2627C2211yescharacteristic
96#2627C2212yes—
97#2627C2212yes—
98#2627C2212yes—
99#2627C2212yes—
100#2627C2212yes—
101#2627C2214yes—
102#2627C2214yes—
103#2627C2218yescomplemented
104#2627C2218yescomplemented
105#2627C2214yescomplemented
106#2627C2214yescomplemented
107#2625C2214yescomplemented
108#2623C2212yes—
109#2621C2218yescomplemented
110#2618C2211yescharacteristic
111#2618C2211yescharacteristic
112#2618C2212yes—
113#2616C2214yescomplemented
114#2614C2212yes—
115#2591C2214yescomplemented
116#2584C2212yescomplemented
117#2583C2214yescomplemented
118#2582C2214yescomplemented
119#2581C2214yescomplemented
120#2579C2218yescomplemented
121#2568C2212yescomplemented
122#2567C2212yescomplemented
123#2565C2214yescomplemented
124#2565C2214yescomplemented
125#2562C2212yescomplemented
126#2551C2214yescomplemented
127#2550C2214yescomplemented
128#2549C2218yescomplemented
129#2503C2212yes—
130#2503C2214yes—
131#2503C2214yescomplemented
132#2502C2212yes—
133#2492C2214yescomplemented
134#2489C2214yescomplemented
135#2488C2218yescomplemented
136#2488C2218yescomplemented
137#2487C2212yes—
138#2486C2212yes—
139#2486C2214yes—
140#2484C2214yes—
141#2484C2214yescomplemented
142#2483C2214yes—
143#2483C2214yes—
144#2453C2214yescomplemented
145#2451C2214yescomplemented
146#2450C2218yescomplemented
147#2449C2218yescomplemented
148#2447C2214yes—
149#2447C2214yes—
150#2444C2218yes—
151#2443C2218yes—
152#2442C2214yescomplemented
153#2440C2218yescomplemented
154#2440C2214yescomplemented
155#2438C2218yescomplemented
156#2438C2218yescomplemented
157#2434C2214yes—
158#2434C2214yescomplemented
159#2422C2214yes—
160#2420C2214yes—
161#2419C2218yes—
162#2419C2218yes—
163#2417C2218yescomplemented
164#2413C2214yes—
165#2413C2218yescomplemented
166#2412C2214yes—
167#2412C2214yes—
168#2409C2214yes—
169#2406C2214yescomplemented
170#2399C2212yescomplemented
171#2398C2212yescomplemented
172#2396C2214yescomplemented
173C2×#400C2214yescomplemented
174C2×#398C2218yescomplemented
175C2×#395C2214yescomplemented
176#2354C2212yes—
177#2352C2214yes—
178#2349C2214yes—
179D4×C4⋊C4C2214yes—
180D4×C4⋊C4C2212yes—
181#2345C2212yes—
182#2342C2214yes—
183#2339C2214yes—
184#2339C2214yes—
185D4×C22⋊C4C2212yes—
186#2322C2214yes—
187#2322C2214yes—
188#2319C2212yes—
189#2318C2214yes—
190#2317C2212yes—
191#2310C2212yes—
192C4×#123C2212yes—
193C4×#123C2212yes—
194C2×#385C2214yes—
195#2285C2211yescharacteristic
196#2283C2211yescharacteristic
197#2280C2212yes—
198C2×#381C2214yes—
199C2×#380C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C23×Q8C2311yescharacteristic
204C23×Q8C2312yes—
205C23×Q8C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2312yes—
208C24×C4C2312yes—
209C24×C4C2312yes—
210#556—28no—
211#554—216no—
212#554—232no—
213#554—216no—
214#554—216no—
215#554—216no—
216#554—232no—
217#554—216no—
218#552—216no—
219#551—232no—
220D4×Q8—28no—
221#548—216no—
222#547—28no—
223#547—28no—
224#546—216no—
225#542—216no—
226#539—232no—
227#533—28no—
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2318yes—
236#529—28no—
237C2×#126C2312yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#125—28no—
241C2×#125—28no—
242C2×#125C2312yes—
243C2×#125C2312yes—
244C2×#125C2312yes—
245C2×#125C2312yes—
246C2×#125C2311yescharacteristic
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#124C2311yescharacteristic
253C2×#124C2314yes—
254C2×#124C2312yes—
255#525—216no—
256C2×#123C2312yes—
257C2×#123C2312yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2312yes—
264C2×#123C2318yes—
265C2×C22⋊Q8—216no—
266C2×C22⋊Q8—216no—
267C2×C22⋊Q8—216no—
268C2×C22⋊Q8—216no—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2311yescharacteristic
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2318yes—
293C2×#121C2312yes—
294C2×#121C2311yescharacteristic
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#120C2314yes—
298#520—216no—
299C2×C4×Q8—28no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×D4—28no—
309C2×C4×D4—28no—
310C2×C4×D4D4116yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2314yes—
334C2×#117C2312yes—
335C2×#117C2314yes—
336C22×C4⋊C4—216no—
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2314yes—
341C22×C4⋊C4C2314yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2314yes—
347C22×C4⋊C4C2314yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2318yes—
356C22×C4⋊C4C2311yescharacteristic
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2312yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2314yes—
361C22×C22⋊C4C2312yes—
362C22×C42C2311yescharacteristic
363C22×C42C2311yescharacteristic
364C22×C42C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2318yes—
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2318yes—
379#400C2318yes—
380#399C2314yes—
381#399C2314yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2314yes—
387#398C2318yes—
388#398C2318yes—
389#398C2318yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2318yes—
395#398C2314yes—
396#398C2314yes—
397#398C2318yes—
398#398C2318yes—
399#398C2318yes—
400#398C2318yes—
401#398C2318yes—
402#397C2318yes—
403#397C2318yes—
404#397C2318yes—
405#397C2318yes—
406#397C2314yes—
407#397C2314yes—
408#397C2318yes—
409#397C2318yes—
410#397C2318yes—
411#396C2318yes—
412#396C2314yes—
413#396C2318yes—
414#396C2314yes—
415#395C2312yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2318yes—
420#395C2318yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2312yes—
426#395C2318yes—
427#395C2318yes—
428#395C2318yes—
429#394C2314yes—
430#394C2312yes—
431#394C2312yes—
432#394C2318yes—
433#394C2318yes—
434#393C2314yes—
435#393C2314yes—
436#393C2318yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2318yes—
442#391C2314yes—
443#391C2314yes—
444#391C2318yes—
445#391C2318yes—
446#391C2318yes—
447#390C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2318yes—
451#389C2314yes—
452#389C2318yes—
453#389C2318yes—
454#389C2314yes—
455#389C2314yes—
456#389C2318yes—
457#389C2318yes—
458#388C2318yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2314yes—
464#388C2314yes—
465#387C2318yes—
466#387C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2314yes—
473#387C2314yes—
474#386C2318yes—
475#386C2312yes—
476#386C2314yes—
477#386C2318yes—
478#386C2318yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2312yes—
483#385C2314yes—
484#385C2314yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2314yes—
489#385C2318yes—
490#385C2318yes—
491#385C2318yes—
492#385C2318yes—
493#385C2318yes—
494#385C2312yes—
495#385C2312yes—
496#385C2314yes—
497#385C2314yes—
498#385C2318yes—
499#385C2318yes—
500#384C2314yes—
501#384C2314yes—
502#384C2312yes—
503#383C2312yes—
504#382C2312yes—
505#382C2314yes—
506#382C2314yes—
507#382C2312yes—
508#382C2318yes—
509#381C2314yes—
510#381C2314yes—
511#381C2314yes—
512#381C2314yes—
513#381C2318yes—
514#381C2318yes—
515#381C2318yes—
516#381C2312yes—
517#381C2312yes—
518#381C2312yes—
519#381C2314yes—
520#381C2314yes—
521#381C2318yes—
522#381C2318yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2312yes—
528#380C2314yes—
529#380C2318yes—
530#380C2318yes—
531#380C2314yes—
532#380C2318yes—
533#380C2311yescharacteristic
534#380C2312yes—
535#380C2311yescharacteristic
536#379C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549#376C2312yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41—28no—
558C2×#41—84no—
559C22×Q8—24no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—24no—
563C22×Q8—42no—
564C22×Q8—84no—
565C22×Q8—84no—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2411yescharacteristic
570C22×Q8C2412yes—
571C22×Q8C2414yes—
572C22×Q8C2414yes—
573C22×Q8C2414yes—
574C22×D4—28no—
575C22×D4C2×D418yes—
576C22×D4C2412yes—
577C22×D4C2414yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2411yescharacteristic
581C22×D4C2414yes—
582C22×D4C2411yescharacteristic
583C23×C4—28no—
584C23×C4—28no—
585C23×C4—28no—
586C23×C4—44no—
587C23×C4—84no—
588C23×C4—84no—
589C23×C4C2×D4116yes—
590C23×C4C2411yescharacteristic
591C23×C4C2412yes—
592C23×C4C2414yes—
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2412yes—
601C23×C4C2414yes—
602C23×C4C2418yes—
603C23×C4C2414yes—
604C23×C4C2411yescharacteristic
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C4⋊Q8—28no—
614C4⋊Q8—216no—
615C4⋊Q8—28no—
616C4⋊Q8—28no—
617C4⋊Q8—24no—
618C4⋊Q8—24no—
619C4⋊Q8—88no—
620#126—216no—
621#126—216no—
622#126—28no—
623#125—28no—
624#125—216no—
625#125—28no—
626#125—216no—
627#125—28no—
628#125—28no—
629#125—28no—
630#125—28no—
631#125—24no—
632#125—28no—
633#124—28no—
634#124—216no—
635#124—24no—
636#123—216no—
637#123—216no—
638#123—28no—
639#123—28no—
640#123—216no—
641#123—216no—
642#123—44no—
643#123—48no—
644#123—88no—
645C22⋊Q8—24no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—216no—
658C22⋊Q8—28no—
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—216no—
668C22⋊Q8—88no—
669#121—216no—
670#121—28no—
671#121—24no—
672#121—28no—
673#120—216no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—24no—
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—216no—
704#117—28no—
705#117—44no—
706#117—84no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—216no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—24no—
717C2×C4⋊C4—24no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—216no—
720C2×C4⋊C4—28no—
721C2×C4⋊C4—28no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—28no—
724C2×C4⋊C4—84no—
725C2×C4⋊C4—88no—
726C2×C4⋊C4C2×D418yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2418yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2418yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C22⋊C4—28no—
783C2×C22⋊C4—28no—
784C2×C22⋊C4—216no—
785C2×C22⋊C4—48no—
786C2×C22⋊C4C2×D4116yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C42—24no—
819C2×C42—24no—
820C2×C42C2×D418yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2418yes—
830C2×C42C2414yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835#95C2412yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2412yes—
851#95C2414yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868C24—24no—
869C24—28no—
870C24—24no—
871C24—44no—
872C24C22×D418yes—
873C24C2512yes—
874C24C2512yes—
875C24C2512yes—
876C24C2511yescharacteristic
877#41—432no—
878#41—816no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—22no—
883C2×Q8—24no—
884C2×Q8—28no—
885C2×Q8—28no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—28no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—48no—
895C2×Q8—48no—
896C2×Q8—48no—
897C2×Q8—416no—
898C2×Q8—816no—
899C2×Q8—816no—
900C2×D4—28no—
901C2×D4—232no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—216no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—22no—
909C2×D4—24no—
910C2×D4—42no—
911C2×D4—48no—
912C2×D4C22×D418yes—
913C2×D4C22×D414yes—
914C2×D4C22×D414yes—
915C2×D42−1+418yes—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—28no—
929C22×C4—24no—
930C22×C4—22no—
931C22×C4—216no—
932C22×C4—24no—
933C22×C4—22no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—28no—
937C22×C4—216no—
938C22×C4—24no—
939C22×C4—28no—
940C22×C4—28no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—42no—
954C22×C4—48no—
955C22×C4—48no—
956C22×C4—48no—
957C22×C4—48no—
958C22×C4—48no—
959C22×C4—48no—
960C22×C4—432no—
961C22×C4—816no—
962C22×C4—816no—
963C22×C4C22×D414yes—
964C22×C4C22×D414yes—
965C22×C4C22×D414yes—
966C22×C4C22×D418yes—
967C22×C4C22×D418yes—
968C22×C4C22×D418yes—
969C22×C4C22×D418yes—
970C22×C4C22×D418yes—
971C22×C42−1+414yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2518yes—
977C22×C4C2512yes—
978C22×C4C2514yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—22no—
1005C4⋊C4—24no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—22no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—24no—
1028C4⋊C4—28no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—42no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—48no—
1036C4⋊C4—48no—
1037C4⋊C4—48no—
1038C4⋊C4—48no—
1039C4⋊C4—44no—
1040C4⋊C4—42no—
1041C4⋊C4—48no—
1042C4⋊C4—48no—
1043C4⋊C4—44no—
1044C4⋊C4—48no—
1045C4⋊C4—44no—
1046C4⋊C4C22×D414yes—
1047C4⋊C4C22×D418yes—
1048C4⋊C4C22×D414yes—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—216no—
1060C22⋊C4—24no—
1061C22⋊C4—24no—
1062C22⋊C4—28no—
1063C22⋊C4—24no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—24no—
1068C22⋊C4—28no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—44no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4C22×D418yes—
1077C22⋊C4C22×D418yes—
1078C22⋊C4C22×D418yes—
1079C22⋊C4C22×D418yes—
1080C42—24no—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—28no—
1085C42—28no—
1086C42—24no—
1087C42—28no—
1088C42—44no—
1089C42—48no—
1090C42C22×D414yes—
1091C42C22×D414yes—
1092C42C22×D414yes—
1093C42C22×D414yes—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—24no—
1098C23—22no—
1099C23—22no—
1100C23—24no—
1101C23—22no—
1102C23—24no—
1103C23—216no—
1104C23—216no—
1105C23—22no—
1106C23—22no—
1107C23—24no—
1108C23—22no—
1109C23—24no—
1110C23—48no—
1111C23—416no—
1112C23—416no—
1113C23C23×D414yes—
1114C23C23×D414yes—
1115C23C23×D412yes—
1116C23C2×2−1+418yes—
1117C23C2×2−1+412yes—
1118C23#58512yes—
1119C23C2611yescharacteristic
1120Q8—48no—
1121Q8—48no—
1122Q8—44no—
1123Q8—48no—
1124Q8—48no—
1125Q8—88no—
1126Q8—88no—
1127Q8—88no—
1128D4—216no—
1129D4—28no—
1130D4—44no—
1131D4—416no—
1132D4—48no—
1133D4—88no—
1134D4#536116yes—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—28no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—28no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—28no—
1167C2×C4—22no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—28no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—24no—
1179C2×C4—28no—
1180C2×C4—24no—
1181C2×C4—44no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—48no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—416no—
1188C2×C4—416no—
1189C2×C4—44no—
1190C2×C4—48no—
1191C2×C4—44no—
1192C2×C4—416no—
1193C2×C4—48no—
1194C2×C4—44no—
1195C2×C4—48no—
1196C2×C4—88no—
1197C2×C4—816no—
1198C2×C4—88no—
1199C2×C4—88no—
1200C2×C4—88no—
1201C2×C4C23×D412yes—
1202C2×C4C23×D412yes—
1203C2×C4C23×D414yes—
1204C2×C4C23×D412yes—
1205C2×C4C23×D412yes—
1206C2×C4C23×D412yes—
1207C2×C4C23×D414yes—
1208C2×C4C23×D412yes—
1209C2×C4C2×2−1+414yes—
1210C2×C4C2×2−1+414yes—
1211C22—24no—
1212C22—22no—
1213C22—24no—
1214C22—22no—
1215C22—24no—
1216C22—28no—
1217C22—28no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—432no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22C2×#53618yes—
1231C22#348914yes—
1232C22C24×D411yescharacteristic
1233C22C22×2−1+411yescharacteristic
1234C22C22×2−1+412yes—
1235C22C2×#58511yescharacteristic
1236C22H(7,𝔽2)12yes—
1237C4—24no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—24no—
1243C4—24no—
1244C4—22no—
1245C4—44no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—44no—
1250C4—42no—
1251C4—44no—
1252C4—42no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4—48no—
1257C4—44no—
1258C4C2×#53614yes—
1259C2—24no—
1260C2—28no—
1261C2—44no—
1262C2—82no—
1263C2C22×#53611yescharacteristic
1264C2C2×#348911yescharacteristic
1265C2#6284211yescharacteristic
1266C2#6294512yes—
1267C2#6294812yes—
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. C22×#554C2semidirect
3. #42676C2semidirect
4. #42482C2semidirect
5. #42442C2semidirect
6. #41411C2semidirect
7. #40589C2semidirect
8. #40516C2semidirect
9. #39592C2semidirect
10. #39122C2semidirect
11. #38037C2semidirect
12. #37835C2semidirect
13. #37549C2semidirect
14. #37540C2semidirect
15. #37453C2semidirect
16. #37442C2semidirect
17. #36237C2semidirect
18. #36155C2semidirect
19. #36042C2semidirect
20. #35928C2semidirect
21. #35806C2semidirect
22. #35179C2semidirect
23. #35057C2semidirect
24. #34602C2semidirect
25. C2×#2627C2semidirect
26. #34194C2semidirect
66. #2822C22semidirect
67. #2822C22semidirect
68. #2820C22semidirect
69. #2817C22semidirect
70. #2817C22semidirect
71. #2814C22semidirect
72. #2719C22semidirect
73. #2713C22semidirect
74. #2700C22semidirect
75. #2698C22semidirect
76. #2698C22semidirect
77. #2690C22semidirect
78. #2689C22semidirect
79. #2689C22semidirect
80. #2687C22semidirect
81. #2680C22semidirect
82. #2677C22semidirect
83. #2674C22semidirect
84. #2664C22semidirect
85. #2660C22semidirect
86. #2659C22semidirect
87. #2642C22semidirect
88. #2639C22semidirect
89. #2637C22semidirect
90. #2634C22semidirect
91. #2634C22semidirect
92. #2632C22semidirect
93. #2629C22semidirect
103. #2627C22semidirect
104. #2627C22semidirect
105. #2627C22semidirect
106. #2627C22semidirect
107. #2625C22semidirect
109. #2621C22semidirect
113. #2616C22semidirect
115. #2591C22semidirect
116. #2584C22semidirect
117. #2583C22semidirect
118. #2582C22semidirect
119. #2581C22semidirect
120. #2579C22semidirect
121. #2568C22semidirect
122. #2567C22semidirect
123. #2565C22semidirect
124. #2565C22semidirect
125. #2562C22semidirect
126. #2551C22semidirect
127. #2550C22semidirect
128. #2549C22semidirect
131. #2503C22semidirect
133. #2492C22semidirect
134. #2489C22semidirect
135. #2488C22semidirect
136. #2488C22semidirect
141. #2484C22semidirect
144. #2453C22semidirect
145. #2451C22semidirect
146. #2450C22semidirect
147. #2449C22semidirect
152. #2442C22semidirect
153. #2440C22semidirect
154. #2440C22semidirect
155. #2438C22semidirect
156. #2438C22semidirect
158. #2434C22semidirect
163. #2417C22semidirect
165. #2413C22semidirect
169. #2406C22semidirect
170. #2399C22semidirect
171. #2398C22semidirect
172. #2396C22semidirect
173. C2×#400C22semidirect
174. C2×#398C22semidirect
175. C2×#395C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C22×#5542
#426762
#424822
#424422
#414112
#405892
#405162
#395922
#391222
#380372
#378352
#375492
#375402
#374532
#374422
#362372
#361552
#360422
#359282
#358062
#351792
#350572
#346022
C2×#26272
#341942