Finite Group Databasebeta

← #7632777

Subgroups — #7632777

Order 512.

7962 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3428C211yesmaximal, characteristic, complemented
3#36505C214yesmaximal, complemented
4#36229C214yesmaximal, complemented
5#36223C218yesmaximal, complemented
6#35787C214yesmaximal, complemented
7#35753C218yesmaximal, complemented
8#35712C214yesmaximal, complemented
9#35674C211yesmaximal, characteristic, complemented
10#35673C211yesmaximal, characteristic, complemented
11#35625C214yesmaximal, complemented
12#35617C211yesmaximal, characteristic, complemented
13#35526C214yesmaximal, complemented
14#35515C211yesmaximal, characteristic, complemented
15#35306C211yesmaximal, characteristic, complemented
16#35205C214yesmaximal, complemented
17#35149C211yesmaximal, characteristic
18#34739C211yesmaximal, characteristic, complemented
19#34720C214yesmaximal, complemented
20C2×#2432C211yesmaximal, characteristic, complemented
21#34269C211yesmaximal, characteristic, complemented
22#34254C211yesmaximal, characteristic, complemented
23#34211C211yesmaximal, characteristic, complemented
24#34203C211yesmaximal, characteristic, complemented
25#34136C211yesmaximal, characteristic, complemented
26C23×#41C2211yescharacteristic
27#3509—216no—
28C2×#557C2214yescomplemented
29C2×#556C2214yescomplemented
30C2×#552C2218yes—
31C2×#541C2214yescomplemented
32C2×#536C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C2×#535C2211yescharacteristic
35C2×#533C2211yescharacteristic
36C2×#533C2214yescomplemented
37C22×C4⋊Q8C2211yescharacteristic
38C22×#124C2211yescharacteristic
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41#3428—216no—
42C2×#520C2214yes—
43C2×#520C2214yes—
44C2×#519C2211yescharacteristic
45C2×#519C2211yescharacteristic
46C2×#519C2211yescharacteristic
47C2×#518C2211yescharacteristic
48C2×#518C2211yescharacteristic
49C2×#518C2214yes—
50C2×C4×#41C2211yescharacteristic
51C2×C4×#41C2214yes—
52C2×C4×#41C2214yes—
53C22×#117C2211yescharacteristic
54C22×#117C2214yes—
55C22×#117C2211yescharacteristic
56#2857C2212yescomplemented
57#2852C2218yescomplemented
58#2851C2218yescomplemented
59#2850C2212yescomplemented
60#2849C2214yes—
61#2636C2218yescomplemented
62#2633C2218yescomplemented
63#2621C2212yescomplemented
64#2620C2212yescomplemented
65#2613C2214yes—
66#2611C2218yescomplemented
67#2609C2218yescomplemented
68#2603C2218yescomplemented
69#2601C2218yescomplemented
70#2599C2218yescomplemented
71#2598C2218yescomplemented
72#2580C2214yescomplemented
73#2562C2218yescomplemented
74#2547C2214yescomplemented
75#2544C2214yescomplemented
76#2538C2214yescomplemented
77#2536C2218yescomplemented
78#2498C2218yes—
79#2484C2218yes—
80#2481C2218yescomplemented
81#2479C2218yescomplemented
82#2477C2218yescomplemented
83#2475C2218yescomplemented
84#2475C2218yescomplemented
85#2473C2218yescomplemented
86#2473C2218yescomplemented
87#2467C2218yescomplemented
88#2467C2218yescomplemented
89#2463C2218yescomplemented
90#2463C2218yescomplemented
91#2460C2218yescomplemented
92#2460C2218yescomplemented
93#2460C2218yescomplemented
94#2460C2218yescomplemented
95#2454C2214yescomplemented
96#2452C2214yescomplemented
97#2449C2218yescomplemented
98#2448C2214yescomplemented
99#2446C2214yescomplemented
100#2446C2214yescomplemented
101#2446C2214yescomplemented
102#2446C2214yescomplemented
103#2446C2214yescomplemented
104#2442C2212yescomplemented
105#2441C2212yescomplemented
106#2440C2212yescomplemented
107#2439C2212yescomplemented
108#2438C2214yes—
109#2437C2218yes—
110#2437C2214yes—
111#2432C2212yes—
112#2432C2212yes—
113#2432C2212yes—
114#2432C2214yes—
115#2432C2212yes—
116#2432C2214yes—
117#2432C2212yes—
118#2432C2212yes—
119#2431C2212yes—
120#2431C2212yes—
121#2427C2214yescomplemented
122#2427C2214yescomplemented
123#2423C2214yescomplemented
124#2421C2214yescomplemented
125#2417C2214yescomplemented
126#2415C2214yescomplemented
127#2413C2214yes—
128#2412C2218yes—
129#2412C2214yes—
130#2407C2214yes—
131#2407C2214yes—
132#2398C2218yescomplemented
133#2396C2214yescomplemented
134#2392C2218yescomplemented
135C2×#394C2214yes—
136#2367C2214yescomplemented
137#2367C2214yescomplemented
138#2367C2214yescomplemented
139#2366C2214yescomplemented
140#2363C2212yescomplemented
141#2362C2212yescomplemented
142#2362C2214yescomplemented
143#2361C2212yescomplemented
144#2360C2212yescomplemented
145#2360C2214yescomplemented
146#2359C2214yes—
147#2358C2214yes—
148#2358C2218yes—
149#2356C2214yescomplemented
150#2355C2214yescomplemented
151#2344C2214yes—
152#2343C2218yes—
153#2342C2218yes—
154#2342C2214yes—
155#2326C2214yescomplemented
156#2324C2214yescomplemented
157#2323C2214yescomplemented
158#2320C2214yescomplemented
159#2317C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2309C2211yescharacteristic
166C4×#124C2214yescomplemented
167C4×C22⋊Q8C2218yescomplemented
168C4×C22⋊Q8C2214yescomplemented
169C4×C22⋊Q8C2214yescomplemented
170C4×#121C2214yescomplemented
171#2297C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2295C2214yescomplemented
176C2×#391C2211yescharacteristic
177#2293C2212yescomplemented
178C2×#390C2211yescharacteristic
179#2290C2212yescomplemented
180#2290C2212yescomplemented
181#2290C2218yescomplemented
182C2×#385C2214yes—
183#2285C2211yescharacteristic
184#2280C2211yescharacteristic
185#2274C2211yescharacteristic
186C42×D4C2212yescomplemented
187C4×#117C2211yescharacteristic
188C2×C4×C22⋊C4C2211yescharacteristic
189C22×#41—28no—
190C22×#41—28no—
191C22×#41—28no—
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C22×#41C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2311yescharacteristic
199C23×D4C2312yes—
200C23×D4C2311yescharacteristic
201C24×C4C2312yes—
202C24×C4C2311yescharacteristic
203#557—232no—
204#556—232no—
205#552—264no—
206#541—232no—
207#536—28no—
208#536—28no—
209#535—28no—
210#533—232no—
211#533—28no—
212C2×C4⋊Q8—28no—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×#127C2312yes—
220C2×#126C2318yes—
221C2×#126C2318yes—
222C2×#125C2318yes—
223C2×#125C2312yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#124—28no—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#124C2312yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233#525—28no—
234C2×#123C2312yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×C22⋊Q8—28no—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2318yes—
250C2×#121C2314yes—
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#120C2314yes—
254C2×#120C2312yes—
255#520—232no—
256#520—232no—
257#519—28no—
258#519—28no—
259#519D4116yescomplemented
260#518—28no—
261#518—28no—
262#518—232no—
263C4×#41—232no—
264C4×#41—232no—
265C4×#41—28no—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2318yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2314yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2314yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2318yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2318yes—
284C2×C4×D4C2318yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2318yes—
289C2×#117—28no—
290C2×#117—28no—
291C2×#117—232no—
292C2×#117C2311yescharacteristic
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2318yes—
301C2×#117C2318yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2312yes—
306C2×#117C2312yes—
307C2×#117C2318yes—
308C2×#117C2314yes—
309C2×#117C2311yescharacteristic
310C2×#117C2314yes—
311C2×#117C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2318yes—
318C22×C22⋊C4C2314yes—
319C22×C22⋊C4C2312yes—
320C22×C22⋊C4C2312yes—
321C22×C22⋊C4C2314yes—
322C22×C22⋊C4C2314yes—
323C22×C22⋊C4C2312yes—
324C22×C22⋊C4C2312yes—
325C22×C22⋊C4C2314yes—
326C22×C42C2312yes—
327C22×C42C2318yes—
328C22×C42C2312yes—
329C22×C42C2311yescharacteristic
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2314yes—
336#399C2318yes—
337#399C2318yes—
338#399C2314yes—
339#398C2318yes—
340#398C2314yes—
341#398C2318yes—
342#398C2314yes—
343#398C2318yes—
344#398C2318yes—
345#397C2318yes—
346#397C2318yes—
347#397C2318yes—
348#397C2318yes—
349#396C2318yes—
350#396C2318yes—
351#396C2318yes—
352#396C2314yes—
353#396C2314yes—
354#395C2314yes—
355#394C2318yes—
356#394C2318yes—
357#394C2318yes—
358#394C2318yes—
359#394C2318yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2318yes—
364#393C2318yes—
365#393C2314yes—
366#392C2318yes—
367#392C2318yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2312yes—
374#391C2312yes—
375#391C2314yes—
376#391C2312yes—
377#391C2312yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#391C2314yes—
382#390C2312yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2312yes—
387#390C2318yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2318yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2318yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#388C2314yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2314yes—
418#388C2318yes—
419#388C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2314yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2314yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2314yes—
436#386C2314yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2314yes—
443#386C2318yes—
444#386C2318yes—
445#386C2314yes—
446#386C2314yes—
447#385C2314yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2314yes—
463#385C2314yes—
464#385C2314yes—
465#385C2314yes—
466#385C2318yes—
467#384C2312yes—
468#384C2312yes—
469#383C2318yes—
470#382C2312yes—
471#382C2318yes—
472#382C2312yes—
473#381C2314yes—
474#381C2314yes—
475#381C2314yes—
476#381C2312yes—
477#380C2314yes—
478#380C2318yes—
479#380C2318yes—
480#380C2318yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2318yes—
485#380C2314yes—
486#380C2312yes—
487#379C2314yes—
488#379C2312yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2311yescharacteristic
516C4×C22⋊C4C2311yescharacteristic
517C4×C22⋊C4C2311yescharacteristic
518C4×C22⋊C4C2311yescharacteristic
519#376C2312yes—
520#376C2318yes—
521C2×#95C2314yes—
522C2×#95C2312yes—
523C43C2312yes—
524C25C2412yes—
525C25C2411yescharacteristic
526C2×#41—2128no—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—28no—
532C2×#41—28no—
533C2×#41—28no—
534C2×#41—28no—
535C2×#41—24no—
536C2×#41—28no—
537C2×#41—28no—
538C2×#41—28no—
539C2×#41—28no—
540C2×#41—24no—
541C2×#41—24no—
542C22×Q8—24no—
543C22×Q8—24no—
544C22×Q8—24no—
545C22×Q8—24no—
546C22×Q8—24no—
547C22×Q8C2×D418yes—
548C22×Q8C2412yes—
549C22×Q8C2412yes—
550C22×Q8C2411yescharacteristic
551C22×Q8C2414yes—
552C22×Q8C2412yes—
553C22×Q8C2412yes—
554C22×D4—28no—
555C22×D4—28no—
556C22×D4—28no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4#4118yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2412yes—
563C22×D4C2411yescharacteristic
564C22×D4C2412yes—
565C22×D4C2412yes—
566C22×D4C2412yes—
567C22×D4C2418yes—
568C22×D4C2412yes—
569C23×C4—28no—
570C23×C4—28no—
571C23×C4—24no—
572C23×C4—28no—
573C23×C4—24no—
574C23×C4#4118yes—
575C23×C4C2412yes—
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2412yes—
579C23×C4C2412yes—
580C23×C4C2414yes—
581C23×C4C2412yes—
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2411yescharacteristic
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2418yes—
591C23×C4C2414yes—
592C23×C4C2418yes—
593C23×C4C2411yescharacteristic
594C4⋊Q8—28no—
595C4⋊Q8—28no—
596C4⋊Q8—216no—
597C4⋊Q8—28no—
598C4⋊Q8—28no—
599C4⋊Q8—28no—
600#127—28no—
601#126—232no—
602#126—232no—
603#125—28no—
604#125—232no—
605#125—232no—
606#125—232no—
607#124—28no—
608#124—28no—
609#124—28no—
610#124—216no—
611#124—28no—
612#124—28no—
613#123—216no—
614#123—28no—
615#123—216no—
616C22⋊Q8—216no—
617C22⋊Q8—28no—
618C22⋊Q8—28no—
619C22⋊Q8—28no—
620C22⋊Q8—28no—
621C22⋊Q8—24no—
622C22⋊Q8—24no—
623C22⋊Q8—216no—
624C22⋊Q8—232no—
625C22⋊Q8—216no—
626C22⋊Q8—416no—
627C22⋊Q8—48no—
628#121—216no—
629#121—24no—
630#121—24no—
631#120—28no—
632#120—216no—
633C4×Q8—216no—
634C4×Q8—216no—
635C4×Q8—28no—
636C4×Q8—216no—
637C4×Q8—216no—
638C4×Q8—232no—
639C4×Q8—216no—
640C4×Q8C2×D4132yes—
641C4×Q8C2×D4132yes—
642C4×D4—28no—
643C4×D4—28no—
644C4×D4—216no—
645C4×D4—216no—
646C4×D4—232no—
647C4×D4—232no—
648C4×D4—28no—
649C4×D4—216no—
650C4×D4—216no—
651C4×D4—232no—
652C4×D4—232no—
653C4×D4—216no—
654C4×D4—48no—
655C4×D4—416no—
656#117—216no—
657#117—24no—
658#117—24no—
659#117—24no—
660#117—24no—
661#117—24no—
662#117—28no—
663#117—28no—
664#117—232no—
665#117—28no—
666#117—28no—
667#117—216no—
668#117—28no—
669#117—232no—
670#117—28no—
671#117—28no—
672#117—232no—
673#117C2×D418yes—
674#117C2×D418yes—
675#117C2×D4132yes—
676C2×C4⋊C4—216no—
677C2×C4⋊C4—28no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—28no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—232no—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2418yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2418yes—
719C2×C22⋊C4—28no—
720C2×C22⋊C4—216no—
721C2×C22⋊C4—216no—
722C2×C22⋊C4—28no—
723C2×C22⋊C4—216no—
724C2×C22⋊C4—28no—
725C2×C22⋊C4—44no—
726C2×C22⋊C4—48no—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2412yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2418yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2418yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C42—24no—
764C2×C42—24no—
765C2×C42—28no—
766C2×C42—232no—
767C2×C42—28no—
768C2×C42—28no—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2418yes—
774C2×C42C2418yes—
775C2×C42C2411yescharacteristic
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2414yes—
780C2×C42C2412yes—
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2412yes—
784C2×C42C2411yescharacteristic
785C2×C42C2414yes—
786C2×C42C2418yes—
787C2×C42C2414yes—
788C2×C42C2412yes—
789C2×C42C2418yes—
790C2×C42C2412yes—
791#95C2418yes—
792#95C2412yes—
793#95C2412yes—
794#95C2412yes—
795#95C2412yes—
796#95C2418yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2418yes—
801#95C2418yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2418yes—
809#95C2414yes—
810#95C2418yes—
811#95C2418yes—
812#95C2414yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816#95C2414yes—
817#95C2418yes—
818#95C2414yes—
819#95C2418yes—
820#95C2414yes—
821C24—24no—
822C24—22no—
823C24—22no—
824C24—24no—
825C24—42no—
826C24—44no—
827C24—42no—
828C24—44no—
829C24C2×#4118yes—
830C24C2×#4114yes—
831C24C2512yes—
832C24C2511yescharacteristic
833C24C2514yes—
834C24C2511yescharacteristic
835C24C2511yescharacteristic
836#41—264no—
837#41—264no—
838#41—264no—
839#41—264no—
840#41—416no—
841C2×Q8—232no—
842C2×Q8—28no—
843C2×Q8—24no—
844C2×Q8—24no—
845C2×Q8—22no—
846C2×Q8—24no—
847C2×Q8—24no—
848C2×Q8—24no—
849C2×Q8—24no—
850C2×Q8—24no—
851C2×Q8—24no—
852C2×Q8—22no—
853C2×Q8—24no—
854C2×Q8—24no—
855C2×Q8—22no—
856C2×Q8—28no—
857C2×Q8—44no—
858C2×Q8—416no—
859C2×Q8C22×D418yes—
860C2×Q8C22×D418yes—
861C2×D4—264no—
862C2×D4—28no—
863C2×D4—28no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—24no—
867C2×D4—24no—
868C2×D4—24no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—216no—
872C2×D4—232no—
873C2×D4—28no—
874C2×D4—28no—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—44no—
883C2×D4—48no—
884C2×D4—44no—
885C2×D4—48no—
886C2×D4C2×#4118yes—
887C2×D4C2×#4118yes—
888C22×C4—264no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—232no—
896C22×C4—28no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—28no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—28no—
903C22×C4—28no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—28no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—216no—
922C22×C4—216no—
923C22×C4—28no—
924C22×C4—44no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—48no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—44no—
936C22×C4—42no—
937C22×C4C22×D418yes—
938C22×C4C22×D414yes—
939C22×C4C2×#4114yes—
940C22×C4C2×#4114yes—
941C22×C4C2×#4114yes—
942C22×C4C2×#4114yes—
943C22×C4C2×#4114yes—
944C22×C4C2×#4114yes—
945C22×C4C2×#4114yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2512yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—216no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—216no—
972C4⋊C4—216no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—216no—
977C4⋊C4—216no—
978C4⋊C4—216no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—48no—
998C4⋊C4—48no—
999C4⋊C4—44no—
1000C4⋊C4C22×D418yes—
1001C4⋊C4C22×D418yes—
1002C4⋊C4C22×D4132yes—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—216no—
1009C22⋊C4—216no—
1010C22⋊C4—24no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—24no—
1014C22⋊C4—216no—
1015C22⋊C4—28no—
1016C22⋊C4—216no—
1017C22⋊C4—216no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—216no—
1021C22⋊C4—216no—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—216no—
1026C22⋊C4—24no—
1027C22⋊C4—42no—
1028C22⋊C4—48no—
1029C22⋊C4—42no—
1030C22⋊C4—48no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—48no—
1035C22⋊C4—44no—
1036C22⋊C4—48no—
1037C22⋊C4C22×D418yes—
1038C22⋊C4C22×D418yes—
1039C42—28no—
1040C42—28no—
1041C42—22no—
1042C42—216no—
1043C42—24no—
1044C42—24no—
1045C42—22no—
1046C42—28no—
1047C42—24no—
1048C42—216no—
1049C42—24no—
1050C42—24no—
1051C42—22no—
1052C42—22no—
1053C42—24no—
1054C42—24no—
1055C42—44no—
1056C42—44no—
1057C42—48no—
1058C42C22×D418yes—
1059C42C22×D4132yes—
1060C42C22×D418yes—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—24no—
1069C23—22no—
1070C23—28no—
1071C23—22no—
1072C23—22no—
1073C23—28no—
1074C23—22no—
1075C23—216no—
1076C23—28no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—24no—
1081C23—24no—
1082C23—416no—
1083C23—44no—
1084C23—44no—
1085C23—84no—
1086C23—84no—
1087C23—88no—
1088C23—84no—
1089C23—84no—
1090C23C23×D412yes—
1091C23C22×#4118yes—
1092C23C22×#4112yes—
1093C23C22×#4112yes—
1094C23C22×#4112yes—
1095C23C22×#4112yes—
1096C23C2611yescharacteristic
1097Q8—216no—
1098Q8—216no—
1099Q8—416no—
1100Q8—48no—
1101Q8—48no—
1102Q8—44no—
1103D4—232no—
1104D4—232no—
1105D4—216no—
1106D4—216no—
1107D4—48no—
1108D4—48no—
1109D4—44no—
1110D4—816no—
1111D4—84no—
1112C2×C4—232no—
1113C2×C4—232no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—28no—
1127C2×C4—216no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—28no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—28no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—416no—
1166C2×C4—48no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—816no—
1170C2×C4—88no—
1171C2×C4—88no—
1172C2×C4—816no—
1173C2×C4—84no—
1174C2×C4—84no—
1175C2×C4#525116yes—
1176C2×C4C23×D418yes—
1177C2×C4C23×D418yes—
1178C2×C4C23×D418yes—
1179C2×C4C23×D412yes—
1180C2×C4C23×D412yes—
1181C2×C4C22×#4112yes—
1182C2×C4C22×#4112yes—
1183C2×C4C22×#4112yes—
1184C2×C4C22×#4112yes—
1185C2×C4C22×#4112yes—
1186C2×C4C22×#4112yes—
1187C2×C4#58514yes—
1188C22—24no—
1189C22—24no—
1190C22—22no—
1191C22—22no—
1192C22—216no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—22no—
1197C22—28no—
1198C22—22no—
1199C22—22no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—48no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—816no—
1213C22—88no—
1214C22C2×#52514yes—
1215C22C24×D411yescharacteristic
1216C22C23×#4111yescharacteristic
1217C22C23×#4111yescharacteristic
1218C22C2×#58512yes—
1219C222−1+612yes—
1220C4—24no—
1221C4—28no—
1222C4—28no—
1223C4—22no—
1224C4—22no—
1225C4—28no—
1226C4—42no—
1227C4—42no—
1228C4—44no—
1229C4—42no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4—44no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4C2×#52514yes—
1239C4C2×#52514yes—
1240C2—24no—
1241C2—48no—
1242C2—42no—
1243C2—42no—
1244C2—82no—
1245C2C22×#52511yescharacteristic
1246C2#6281511yescharacteristic
1247C2#6286011yescharacteristic
1248C2#6299112yes—
1249C2#6300212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35149C2
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×#3509C2semidirect
2. C2×#3428C2semidirect
3. #36505C2semidirect
4. #36229C2semidirect
5. #36223C2semidirect
6. #35787C2semidirect
7. #35753C2semidirect
8. #35712C2semidirect
9. #35674C2semidirect
10. #35673C2semidirect
11. #35625C2semidirect
12. #35617C2semidirect
13. #35526C2semidirect
14. #35515C2semidirect
15. #35306C2semidirect
16. #35205C2semidirect
18. #34739C2semidirect
19. #34720C2semidirect
20. C2×#2432C2semidirect
21. #34269C2semidirect
22. #34254C2semidirect
23. #34211C2semidirect
24. #34203C2semidirect
25. #34136C2semidirect
28. C2×#557C22semidirect
29. C2×#556C22semidirect
31. C2×#541C22semidirect
36. C2×#533C22semidirect
56. #2857C22semidirect
57. #2852C22semidirect
58. #2851C22semidirect
59. #2850C22semidirect
61. #2636C22semidirect
62. #2633C22semidirect
63. #2621C22semidirect
64. #2620C22semidirect
66. #2611C22semidirect
67. #2609C22semidirect
68. #2603C22semidirect
69. #2601C22semidirect
70. #2599C22semidirect
71. #2598C22semidirect
72. #2580C22semidirect
73. #2562C22semidirect
74. #2547C22semidirect
75. #2544C22semidirect
76. #2538C22semidirect
77. #2536C22semidirect
80. #2481C22semidirect
81. #2479C22semidirect
82. #2477C22semidirect
83. #2475C22semidirect
84. #2475C22semidirect
85. #2473C22semidirect
86. #2473C22semidirect
87. #2467C22semidirect
88. #2467C22semidirect
89. #2463C22semidirect
90. #2463C22semidirect
91. #2460C22semidirect
92. #2460C22semidirect
93. #2460C22semidirect
94. #2460C22semidirect
95. #2454C22semidirect
96. #2452C22semidirect
97. #2449C22semidirect
98. #2448C22semidirect
99. #2446C22semidirect
100. #2446C22semidirect
101. #2446C22semidirect
102. #2446C22semidirect
103. #2446C22semidirect
104. #2442C22semidirect
105. #2441C22semidirect
106. #2440C22semidirect
107. #2439C22semidirect
121. #2427C22semidirect
122. #2427C22semidirect
123. #2423C22semidirect
124. #2421C22semidirect
125. #2417C22semidirect
126. #2415C22semidirect
132. #2398C22semidirect
133. #2396C22semidirect
134. #2392C22semidirect
136. #2367C22semidirect
137. #2367C22semidirect
138. #2367C22semidirect
139. #2366C22semidirect
140. #2363C22semidirect
141. #2362C22semidirect
142. #2362C22semidirect
143. #2361C22semidirect
144. #2360C22semidirect
145. #2360C22semidirect
149. #2356C22semidirect
150. #2355C22semidirect
155. #2326C22semidirect
156. #2324C22semidirect
157. #2323C22semidirect
158. #2320C22semidirect
166. C4×#124C22semidirect
167. C4×C22⋊Q8C22semidirect
168. C4×C22⋊Q8C22semidirect
169. C4×C22⋊Q8C22semidirect
170. C4×#121C22semidirect
175. #2295C22semidirect
177. #2293C22semidirect
179. #2290C22semidirect
180. #2290C22semidirect
181. #2290C22semidirect
186. C42×D4C22semidirect
259. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34282
#365052
#362292
#362232
#357872
#357532
#357122
#356742
#356732
#356252
#356172
#355262
#355152
#353062
#352052
#351492
#347392
#347202
C2×#24322
#342692
#342542
#342112
#342032
#341362