Finite Group Databasebeta

← #7683726

Subgroups — #7683726

Order 512.

8032 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3487C211yesmaximal, characteristic
3#59415C214yesmaximal, complemented
4#59411C214yesmaximal, complemented
5#59101C214yesmaximal, complemented
6#59061C214yesmaximal, complemented
7#59010C218yesmaximal, complemented
8#45307C214yesmaximal, complemented
9#45141C214yesmaximal, complemented
10#45095C214yesmaximal, complemented
11#44891C214yesmaximal, complemented
12#43905C218yesmaximal, complemented
13#35666C211yesmaximal, characteristic, complemented
14#35662C211yesmaximal, characteristic, complemented
15#35661C211yesmaximal, characteristic, complemented
16#35633C211yesmaximal, characteristic, complemented
17#35617C211yesmaximal, characteristic, complemented
18#35541C211yesmaximal, characteristic, complemented
19#34813C211yesmaximal, characteristic, complemented
20#34742C211yesmaximal, characteristic, complemented
21C2×#2432C211yesmaximal, characteristic, complemented
22#34275C211yesmaximal, characteristic, complemented
23#34259C211yesmaximal, characteristic, complemented
24#34209C211yesmaximal, characteristic, complemented
25#34172C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C23×#41C2211yescharacteristic
28#3510—216no—
29#3487—216no—
30C2×#559C2214yescomplemented
31C2×#556C2214yescomplemented
32C2×#551C2218yes—
33C2×#550C2214yes—
34C2×#550C2214yes—
35C2×#548C2214yes—
36C2×#548C2214yes—
37C2×#542C2214yescomplemented
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#535C2211yescharacteristic
41C2×#535C2214yes—
42C2×#535C2211yescharacteristic
43C2×#533C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic
45C2×#529C2214yescomplemented
46C22×#124C2211yescharacteristic
47C2×#525C2211yescharacteristic
48C2×#525C2211yescharacteristic
49C2×#525C2214yes—
50C22×C22⋊Q8C2211yescharacteristic
51C2×#520C2211yescharacteristic
52C2×#519C2211yescharacteristic
53C2×#519C2211yescharacteristic
54C2×#518C2211yescharacteristic
55C2×#518C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57#2715C2218yescomplemented
58#2709C2218yescomplemented
59#2709C2218yescomplemented
60#2701C2218yescomplemented
61#2701C2218yescomplemented
62#2700C2218yescomplemented
63#2698C2218yescomplemented
64#2691C2218yescomplemented
65#2689C2218yescomplemented
66#2686C2218yescomplemented
67#2686C2218yescomplemented
68#2672C2218yescomplemented
69#2582C2214yescomplemented
70#2581C2214yescomplemented
71#2559C2218yescomplemented
72#2549C2218yescomplemented
73#2547C2212yescomplemented
74#2547C2212yescomplemented
75#2544C2218yescomplemented
76#2544C2212yescomplemented
77#2544C2212yescomplemented
78#2538C2214yescomplemented
79#2536C2214yescomplemented
80#2534C2214yes—
81#2521C2218yescomplemented
82#2492C2212yescomplemented
83#2491C2212yescomplemented
84#2490C2212yescomplemented
85#2489C2212yescomplemented
86#2488C2214yes—
87#2486C2214yes—
88#2476C2218yescomplemented
89#2474C2218yescomplemented
90#2472C2214yes—
91#2468C2218yescomplemented
92#2466C2218yescomplemented
93#2453C2214yescomplemented
94#2451C2214yescomplemented
95#2450C2218yescomplemented
96#2447C2218yescomplemented
97#2447C2214yescomplemented
98#2445C2218yescomplemented
99#2445C2214yescomplemented
100#2444C2218yescomplemented
101#2444C2218yescomplemented
102#2438C2218yes—
103#2438C2218yescomplemented
104#2434C2212yescomplemented
105#2434C2214yescomplemented
106#2434C2212yescomplemented
107#2432C2214yes—
108#2432C2214yes—
109#2432C2214yes—
110#2432C2214yes—
111#2432C2212yescomplemented
112#2432C2212yescomplemented
113#2432C2214yescomplemented
114#2429C2214yescomplemented
115#2429C2214yescomplemented
116#2427C2214yescomplemented
117#2427C2214yescomplemented
118#2427C2214yescomplemented
119#2426C2214yescomplemented
120#2425C2218yescomplemented
121#2425C2218yescomplemented
122#2423C2212yescomplemented
123#2422C2212yescomplemented
124#2422C2214yescomplemented
125#2421C2212yescomplemented
126#2420C2212yescomplemented
127#2420C2214yescomplemented
128#2419C2214yes—
129#2419C2218yescomplemented
130#2419C2218yescomplemented
131#2418C2214yes—
132#2417C2214yescomplemented
133#2415C2214yescomplemented
134#2413C2214yes—
135#2412C2218yes—
136#2412C2218yes—
137#2411C2214yes—
138#2406C2218yes—
139#2398C2214yescomplemented
140#2395C2214yescomplemented
141C2×#394C2214yes—
142#2365C2214yescomplemented
143#2365C2214yescomplemented
144#2363C2214yescomplemented
145#2361C2214yescomplemented
146#2359C2218yescomplemented
147#2358C2218yes—
148#2349C2218yescomplemented
149#2344C2218yes—
150Q8×C22⋊C4C2214yescomplemented
151#2339C2214yes—
152#2339C2214yes—
153#2339C2214yes—
154#2339C2214yes—
155#2339C2218yes—
156#2339C2214yescomplemented
157#2328C2212yescomplemented
158#2327C2214yescomplemented
159#2326C2212yescomplemented
160#2317C2211yescharacteristic
161#2316C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2212yescomplemented
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2211yescharacteristic
167#2310C2212yescomplemented
168#2308C2214yes—
169C4×C4⋊Q8C2214yescomplemented
170C4×#127C2212yescomplemented
171C4×#124C2214yescomplemented
172C4×#124C2212yescomplemented
173C4×#123C2214yescomplemented
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2297C2212yescomplemented
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#391C2212yescomplemented
181C2×#390C2211yescharacteristic
182C2×#385C2214yes—
183#2285C2211yescharacteristic
184#2280C2211yescharacteristic
185#2280C2211yescharacteristic
186C2×#381C2214yes—
187C4×#117C2211yescharacteristic
188C2×C4×C22⋊C4C2211yescharacteristic
189C2×2−1+4—28no—
190C2×2−1+4—28no—
191C2×2−1+4—44no—
192C22×#41—28no—
193C22×#41—28no—
194C22×#41—44no—
195C22×#41C2311yescharacteristic
196C22×#41C2314yes—
197C22×#41C2314yes—
198C22×#41C2312yes—
199C22×#41C2314yes—
200C22×#41C2312yes—
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2312yes—
204C23×Q8C2312yes—
205C23×Q8C2311yescharacteristic
206C23×D4C2312yes—
207C23×D4C2311yescharacteristic
208C24×C4C2311yescharacteristic
209C24×C4C2312yes—
210#559—232no—
211#556—232no—
212#551—264no—
213#550—232no—
214#550—232no—
215#548—232no—
216#548—232no—
217#542—232no—
218#536—28no—
219#536—44no—
220#535—28no—
221#535—232no—
222#535D4116yes—
223#533—28no—
224C2×C4⋊Q8—28no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×#127C2312yes—
232C2×#127C2318yes—
233C2×#127C2312yes—
234#529—232no—
235C2×#126C2318yes—
236C2×#126C2318yes—
237C2×#125C2312yes—
238C2×#124—28no—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2318yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2318yes—
246C2×#124C2314yes—
247C2×#124C2312yes—
248C2×#124C2312yes—
249#525—28no—
250#525—232no—
251#525—28no—
252C2×#123C2314yes—
253C2×#123C2312yes—
254C2×#123C2312yes—
255C2×#123C2318yes—
256C2×#123C2318yes—
257C2×#123C2318yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×C22⋊Q8—44no—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2318yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2318yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×#121C2312yes—
272C2×#121C2318yes—
273C2×#121C2312yes—
274C2×#121C2318yes—
275C2×#121C2314yes—
276C2×#121C2318yes—
277C2×#121C2314yes—
278C2×#120C2312yes—
279C2×#120C2314yes—
280C2×#120C2312yes—
281C2×#120C2314yes—
282#520—44no—
283#519—28no—
284#519—28no—
285#518—28no—
286#518—44no—
287C4×#41—28no—
288C2×C4×Q8C2314yes—
289C2×C4×Q8C2314yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2318yes—
300C2×C4×D4C2318yes—
301C2×C4×D4C2318yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2318yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×#117C2311yescharacteristic
312C2×#117C2311yescharacteristic
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2314yes—
319C2×#117C2318yes—
320C2×#117C2312yes—
321C2×#117C2311yescharacteristic
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2314yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2312yes—
326C22×C22⋊C4C2314yes—
327C22×C22⋊C4C2314yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2314yes—
330C22×C22⋊C4C2312yes—
331C22×C22⋊C4C2312yes—
332C22×C42C2311yescharacteristic
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335#400C2318yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#399C2314yes—
340#398C2318yes—
341#398C2318yes—
342#398C2314yes—
343#398C2318yes—
344#398C2318yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2318yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2318yes—
358#395C2318yes—
359#395C2318yes—
360#395C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2318yes—
370#394C2318yes—
371#394C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#393C2314yes—
378#393C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2314yes—
386#391C2312yes—
387#391C2312yes—
388#391C2311yescharacteristic
389#391C2312yes—
390#391C2312yes—
391#391C2318yes—
392#391C2314yes—
393#391C2311yescharacteristic
394#391C2318yes—
395#391C2318yes—
396#391C2311yescharacteristic
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2318yes—
403#390C2312yes—
404#390C2312yes—
405#390C2311yescharacteristic
406#390C2312yes—
407#390C2311yescharacteristic
408#390C2314yes—
409#390C2318yes—
410#390C2312yes—
411#390C2314yes—
412#390C2311yescharacteristic
413#389C2318yes—
414#389C2318yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2318yes—
421#389C2318yes—
422#389C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2314yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2314yes—
441#387C2314yes—
442#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2314yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2314yes—
451#386C2318yes—
452#386C2314yes—
453#386C2318yes—
454#386C2314yes—
455#386C2318yes—
456#386C2318yes—
457#386C2318yes—
458#386C2314yes—
459#385C2314yes—
460#385C2318yes—
461#385C2314yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#385C2318yes—
467#385C2318yes—
468#385C2314yes—
469#385C2318yes—
470#385C2318yes—
471#385C2318yes—
472#384C2312yes—
473#384C2312yes—
474#382C2312yes—
475#382C2312yes—
476#382C2314yes—
477#381C2314yes—
478#381C2314yes—
479#381C2314yes—
480#381C2318yes—
481#381C2318yes—
482#381C2318yes—
483#381C2318yes—
484#381C2312yes—
485#381C2314yes—
486#381C2312yes—
487#380C2314yes—
488#380C2318yes—
489#380C2314yes—
490#380C2312yes—
491#380C2312yes—
492#380C2312yes—
493#380C2312yes—
494#380C2314yes—
495#380C2318yes—
496#380C2318yes—
497#380C2318yes—
498#379C2312yes—
499#379C2312yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2318yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520#376C2312yes—
521C2×#95C2318yes—
522C2×#95C2318yes—
523C2×#95C2314yes—
524C2×#95C2318yes—
525C2×#95C2312yes—
526C43C2312yes—
527C25C2411yescharacteristic
528C25C2412yes—
5292−1+4—464no—
530C2×#41—216no—
531C2×#41—216no—
532C2×#41—28no—
533C2×#41—28no—
534C2×#41—216no—
535C2×#41—216no—
536C2×#41—216no—
537C2×#41—28no—
538C2×#41—24no—
539C2×#41—28no—
540C2×#41—24no—
541C2×#41—216no—
542C2×#41—24no—
543C2×#41—24no—
544C2×#41—24no—
545C2×#41—48no—
546C2×#41—48no—
547C2×#41—48no—
548C2×#41—44no—
549C2×#41—44no—
550C2×#41—464no—
551C2×#41C2×D418yes—
552C22×Q8—28no—
553C22×Q8—28no—
554C22×Q8—28no—
555C22×Q8—24no—
556C22×Q8—24no—
557C22×Q8—28no—
558C22×Q8—24no—
559C22×Q8—24no—
560C22×Q8—24no—
561C22×Q8—44no—
562C22×Q8—44no—
563C22×Q8#4118yes—
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2414yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2414yes—
572C22×D4—28no—
573C22×D4—24no—
574C22×D4—28no—
575C22×D4—24no—
576C22×D4—44no—
577C22×D4C2×D418yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2418yes—
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C22×D4C2414yes—
587C22×D4C2418yes—
588C22×D4C2414yes—
589C22×D4C2418yes—
590C23×C4—28no—
591C23×C4—24no—
592C23×C4—28no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—44no—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2418yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2418yes—
610C23×C4C2414yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2411yescharacteristic
615C4⋊Q8—28no—
616C4⋊Q8—28no—
617C4⋊Q8—28no—
618C4⋊Q8—216no—
619C4⋊Q8—28no—
620C4⋊Q8—44no—
621#127—232no—
622#127—28no—
623#127C2×D4116yes—
624#126—232no—
625#126—232no—
626#125—28no—
627#124—28no—
628#124—28no—
629#124—216no—
630#124—28no—
631#124—28no—
632#124—232no—
633#124—232no—
634#124—48no—
635#124—44no—
636#124C2×D4116yes—
637#123—28no—
638#123—232no—
639#123—216no—
640#123—232no—
641#123—28no—
642#123—416no—
643#123—48no—
644#123—48no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—28no—
648C22⋊Q8—232no—
649C22⋊Q8—216no—
650C22⋊Q8—232no—
651C22⋊Q8—48no—
652C22⋊Q8—48no—
653C22⋊Q8—44no—
654C22⋊Q8—44no—
655#121—28no—
656#121—232no—
657#121—216no—
658#121—232no—
659#121—28no—
660#121—232no—
661#121C2×D4132yes—
662#120—216no—
663#120—28no—
664#120—28no—
665#120C2×D4132yes—
666C4×Q8—28no—
667C4×Q8—216no—
668C4×Q8—216no—
669C4×Q8—216no—
670C4×Q8—216no—
671C4×Q8—216no—
672C4×Q8—44no—
673C4×D4—216no—
674C4×D4—28no—
675C4×D4—216no—
676C4×D4—216no—
677C4×D4—232no—
678C4×D4—232no—
679C4×D4—216no—
680C4×D4—232no—
681C4×D4—216no—
682C4×D4—416no—
683C4×D4—44no—
684C4×D4—44no—
685C4×D4—44no—
686C4×D4—44no—
687C4×D4—44no—
688C4×D4—48no—
689#117—24no—
690#117—28no—
691#117—24no—
692#117—24no—
693#117—24no—
694#117—24no—
695#117—216no—
696#117—216no—
697#117—232no—
698#117—44no—
699#117C2×D418yes—
700C2×C4⋊C4—216no—
701C2×C4⋊C4—24no—
702C2×C4⋊C4—44no—
703C2×C4⋊C4—44no—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2418yes—
718C2×C4⋊C4C2418yes—
719C2×C4⋊C4C2418yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2418yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C22⋊C4—216no—
736C2×C22⋊C4—216no—
737C2×C22⋊C4—48no—
738C2×C22⋊C4—44no—
739C2×C22⋊C4—48no—
740C2×C22⋊C4—44no—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C2418yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2418yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2418yes—
781C2×C42—24no—
782C2×C42—28no—
783C2×C42—24no—
784C2×C42C2412yes—
785C2×C42C2418yes—
786C2×C42C2414yes—
787C2×C42C2411yescharacteristic
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2418yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2414yes—
794C2×C42C2412yes—
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2412yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2418yes—
808#95C2418yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2412yes—
813#95C2418yes—
814#95C2418yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2418yes—
825#95C2414yes—
826#95C2418yes—
827#95C2414yes—
828#95C2414yes—
829#95C2418yes—
830#95C2414yes—
831#95C2414yes—
832#95C2418yes—
833C24—24no—
834C24—24no—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—44no—
839C24—42no—
840C24—44no—
841C24—42no—
842C24C22×D418yes—
843C24C2512yes—
844C24C2512yes—
845C24C2514yes—
846C24C2512yes—
847C24C2511yescharacteristic
848#41—232no—
849#41—464no—
850#41—432no—
851#41—464no—
852#41—464no—
853#41—432no—
854#41—416no—
855C2×Q8—232no—
856C2×Q8—24no—
857C2×Q8—24no—
858C2×Q8—24no—
859C2×Q8—24no—
860C2×Q8—28no—
861C2×Q8—22no—
862C2×Q8—28no—
863C2×Q8—22no—
864C2×Q8—24no—
865C2×Q8—24no—
866C2×Q8—28no—
867C2×Q8—22no—
868C2×Q8—22no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—22no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—44no—
877C2×Q8—432no—
878C2×Q8—432no—
879C2×Q8—416no—
880C2×Q8C22×D414yes—
881C2×Q8C2×#4118yes—
882C2×Q8C2×#4118yes—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—216no—
887C2×D4—28no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—28no—
891C2×D4—216no—
892C2×D4—232no—
893C2×D4—22no—
894C2×D4—28no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—22no—
898C2×D4—216no—
899C2×D4—28no—
900C2×D4—22no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—48no—
906C2×D4—48no—
907C2×D4—48no—
908C2×D4—44no—
909C2×D4—432no—
910C2×D4—48no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—48no—
916C2×D4C22×D418yes—
917C2×D4C22×D418yes—
918C2×D4C22×D414yes—
919C2×D4C22×D418yes—
920C2×D4C22×D4132yes—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—216no—
928C22×C4—22no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—22no—
932C22×C4—24no—
933C22×C4—22no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—216no—
937C22×C4—24no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—216no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—28no—
946C22×C4—28no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—48no—
953C22×C4—42no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—42no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—48no—
960C22×C4—44no—
961C22×C4—42no—
962C22×C4—48no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—48no—
967C22×C4—48no—
968C22×C4—48no—
969C22×C4—432no—
970C22×C4—416no—
971C22×C4C22×D418yes—
972C22×C4C22×D414yes—
973C22×C4C2×#4118yes—
974C22×C4C2×#4114yes—
975C22×C4H(5,𝔽2)14yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—216no—
1001C4⋊C4—24no—
1002C4⋊C4—216no—
1003C4⋊C4—216no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—216no—
1009C4⋊C4—216no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—28no—
1017C4⋊C4—44no—
1018C4⋊C4—48no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—48no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—48no—
1025C4⋊C4—44no—
1026C4⋊C4C22×D418yes—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—216no—
1030C22⋊C4—216no—
1031C22⋊C4—216no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—216no—
1036C22⋊C4—216no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—216no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—42no—
1048C22⋊C4—48no—
1049C22⋊C4—42no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—48no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4C22×D418yes—
1066C22⋊C4C22×D4132yes—
1067C42—22no—
1068C42—24no—
1069C42—28no—
1070C42—22no—
1071C42—24no—
1072C42—216no—
1073C42—216no—
1074C42—24no—
1075C42—24no—
1076C42—22no—
1077C42—24no—
1078C42—22no—
1079C42—24no—
1080C42—24no—
1081C42—28no—
1082C42—44no—
1083C42—44no—
1084C42C22×D418yes—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—24no—
1089C23—22no—
1090C23—24no—
1091C23—28no—
1092C23—24no—
1093C23—24no—
1094C23—28no—
1095C23—216no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—24no—
1103C23—22no—
1104C23—22no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23—416no—
1109C23—44no—
1110C23—44no—
1111C23—44no—
1112C23—84no—
1113C23—88no—
1114C23—84no—
1115C23—84no—
1116C23—84no—
1117C23C23×D418yes—
1118C23C23×D414yes—
1119C23C23×D412yes—
1120C23C22×#4112yes—
1121C23C2×H(5,𝔽2)12yes—
1122C23C2611yescharacteristic
1123Q8—216no—
1124Q8—216no—
1125Q8—28no—
1126Q8—416no—
1127Q8—48no—
1128Q8—48no—
1129Q8—44no—
1130Q8—88no—
1131D4—216no—
1132D4—216no—
1133D4—216no—
1134D4—28no—
1135D4—432no—
1136D4—432no—
1137D4—416no—
1138D4—48no—
1139D4—44no—
1140D4—88no—
1141D4—88no—
1142D4—816no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—216no—
1152C2×C4—216no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—28no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—416no—
1191C2×C4—48no—
1192C2×C4—432no—
1193C2×C4—416no—
1194C2×C4—44no—
1195C2×C4—48no—
1196C2×C4—48no—
1197C2×C4—48no—
1198C2×C4—48no—
1199C2×C4—88no—
1200C2×C4—816no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—164no—
1204C2×C4—164no—
1205C2×C4—164no—
1206C2×C4#546116yes—
1207C2×C4C23×D418yes—
1208C2×C4C23×D414yes—
1209C2×C4C23×D412yes—
1210C2×C4C23×D412yes—
1211C2×C4C22×#4118yes—
1212C2×C4C22×#4112yes—
1213C2×C4C22×#4112yes—
1214C2×C4C2×H(5,𝔽2)12yes—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4#58514yes—
1217C22—24no—
1218C22—24no—
1219C22—22no—
1220C22—22no—
1221C22—28no—
1222C22—216no—
1223C22—24no—
1224C22—28no—
1225C22—44no—
1226C22—48no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—42no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—816no—
1244C22—88no—
1245C22C2×#54614yes—
1246C22C24×D411yescharacteristic
1247C22C23×#4111yescharacteristic
1248C22C22×H(5,𝔽2)11yescharacteristic
1249C22C2×#58512yes—
1250C222−1+612yes—
1251C4—28no—
1252C4—24no—
1253C4—28no—
1254C4—24no—
1255C4—42no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—44no—
1260C4—42no—
1261C4—44no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—44no—
1269C4C2×#54614yes—
1270C4C2×#54614yes—
1271C2—24no—
1272C2—44no—
1273C2—48no—
1274C2—82no—
1275C2—82no—
1276C2C22×#54611yescharacteristic
1277C2#6283611yescharacteristic
1278C2#6288711yescharacteristic
1279C2#6298812yes—
1280C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3487C2
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×#3510C2semidirect
3. #59415C2semidirect
4. #59411C2semidirect
5. #59101C2semidirect
6. #59061C2semidirect
7. #59010C2semidirect
8. #45307C2semidirect
9. #45141C2semidirect
10. #45095C2semidirect
11. #44891C2semidirect
12. #43905C2semidirect
13. #35666C2semidirect
14. #35662C2semidirect
15. #35661C2semidirect
16. #35633C2semidirect
17. #35617C2semidirect
18. #35541C2semidirect
19. #34813C2semidirect
20. #34742C2semidirect
21. C2×#2432C2semidirect
22. #34275C2semidirect
23. #34259C2semidirect
24. #34209C2semidirect
25. #34172C2semidirect
30. C2×#559C22semidirect
31. C2×#556C22semidirect
37. C2×#542C22semidirect
45. C2×#529C22semidirect
57. #2715C22semidirect
58. #2709C22semidirect
59. #2709C22semidirect
60. #2701C22semidirect
61. #2701C22semidirect
62. #2700C22semidirect
63. #2698C22semidirect
64. #2691C22semidirect
65. #2689C22semidirect
66. #2686C22semidirect
67. #2686C22semidirect
68. #2672C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
71. #2559C22semidirect
72. #2549C22semidirect
73. #2547C22semidirect
74. #2547C22semidirect
75. #2544C22semidirect
76. #2544C22semidirect
77. #2544C22semidirect
78. #2538C22semidirect
79. #2536C22semidirect
81. #2521C22semidirect
82. #2492C22semidirect
83. #2491C22semidirect
84. #2490C22semidirect
85. #2489C22semidirect
88. #2476C22semidirect
89. #2474C22semidirect
91. #2468C22semidirect
92. #2466C22semidirect
93. #2453C22semidirect
94. #2451C22semidirect
95. #2450C22semidirect
96. #2447C22semidirect
97. #2447C22semidirect
98. #2445C22semidirect
99. #2445C22semidirect
100. #2444C22semidirect
101. #2444C22semidirect
103. #2438C22semidirect
104. #2434C22semidirect
105. #2434C22semidirect
106. #2434C22semidirect
111. #2432C22semidirect
112. #2432C22semidirect
113. #2432C22semidirect
114. #2429C22semidirect
115. #2429C22semidirect
116. #2427C22semidirect
117. #2427C22semidirect
118. #2427C22semidirect
119. #2426C22semidirect
120. #2425C22semidirect
121. #2425C22semidirect
122. #2423C22semidirect
123. #2422C22semidirect
124. #2422C22semidirect
125. #2421C22semidirect
126. #2420C22semidirect
127. #2420C22semidirect
129. #2419C22semidirect
130. #2419C22semidirect
132. #2417C22semidirect
133. #2415C22semidirect
139. #2398C22semidirect
140. #2395C22semidirect
142. #2365C22semidirect
143. #2365C22semidirect
144. #2363C22semidirect
145. #2361C22semidirect
146. #2359C22semidirect
148. #2349C22semidirect
150. Q8×C22⋊C4C22semidirect
156. #2339C22semidirect
157. #2328C22semidirect
158. #2327C22semidirect
159. #2326C22semidirect
163. #2311C22semidirect
167. #2310C22semidirect
169. C4×C4⋊Q8C22semidirect
170. C4×#127C22semidirect
171. C4×#124C22semidirect
172. C4×#124C22semidirect
173. C4×#123C22semidirect
177. #2297C22semidirect
180. C2×#391C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#34872
#594152
#594112
#591012
#590612
#590102
#453072
#451412
#450952
#448912
#439052
#356662
#356622
#356612
#356332
#356172
#355412
#348132
#347422
C2×#24322
#342752
#342592
#342092
#341722