Finite Group Databasebeta

← #7646830

Subgroups — #7646830

Order 512.

4576 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42636C214yesmaximal, complemented
2#42623C214yesmaximal, complemented
3#42587C214yesmaximal, complemented
4#42573C214yesmaximal, complemented
5#40178C214yesmaximal, complemented
6#40051C214yesmaximal, complemented
7#39407C214yesmaximal, complemented
8#39032C214yesmaximal, complemented
9#37466C214yesmaximal, complemented
10#36762C214yesmaximal, complemented
11#36732C214yesmaximal
12#35544C212yesmaximal
13#35543C212yesmaximal, complemented
14#35310C214yesmaximal
15#35265C212yesmaximal, complemented
16#35224C211yesmaximal, characteristic
17#35224C211yesmaximal, characteristic
18#35167C211yesmaximal, characteristic, complemented
19#35159C211yesmaximal, characteristic, complemented
20#34814C212yesmaximal
21#34271C211yesmaximal, characteristic, complemented
22C2×#2344C211yesmaximal, characteristic
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#541C2214yes—
27C22×#117C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29#2864C2214yescomplemented
30#2859C2214yescomplemented
31#2857C2214yes—
32#2851C2214yes—
33#2848C2214yes—
34#2848C2214yes—
35#2839C2218yescomplemented
36#2833C2218yescomplemented
37#2802C2218yescomplemented
38#2794C2218yescomplemented
39#2789C2218yescomplemented
40#2776C2218yescomplemented
41#2766C2218yescomplemented
42#2758C2218yescomplemented
43#2744C2218yes—
44#2744C2218yes—
45#2739C2218yes—
46#2739C2218yes—
47#2719C2218yescomplemented
48#2713C2218yescomplemented
49#2698C2218yes—
50#2698C2218yes—
51#2689C2218yes—
52#2689C2218yes—
53#2666C2218yescomplemented
54#2659C2214yes—
55#2655C2218yescomplemented
56#2655C2218yescomplemented
57#2647C2214yescomplemented
58#2647C2214yescomplemented
59#2646C2214yes—
60#2634C2218yescomplemented
61#2629C2214yes—
62#2627C2214yes—
63#2627C2214yes—
64#2625C2214yes—
65#2625C2214yes—
66#2621C2214yes—
67#2571C2214yescomplemented
68#2570C2214yescomplemented
69#2570C2214yescomplemented
70#2552C2214yescomplemented
71#2552C2214yescomplemented
72#2551C2214yescomplemented
73#2550C2214yescomplemented
74#2550C2214yescomplemented
75#2524C2218yescomplemented
76#2509C2214yescomplemented
77#2509C2214yescomplemented
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2508C2214yescomplemented
81#2508C2214yescomplemented
82#2507C2214yescomplemented
83#2507C2214yescomplemented
84#2507C2214yescomplemented
85#2506C2214yescomplemented
86#2506C2214yescomplemented
87#2506C2214yescomplemented
88#2505C2218yes—
89#2505C2218yes—
90#2497C2214yes—
91#2497C2212yes—
92#2497C2212yes—
93#2497C2214yes—
94#2496C2214yes—
95#2496C2212yes—
96#2496C2214yes—
97#2496C2212yes—
98#2495C2212yes—
99#2495C2214yes—
100#2495C2214yes—
101#2495C2212yes—
102#2494C2214yes—
103#2494C2212yes—
104#2494C2214yes—
105#2494C2212yes—
106#2493C2214yes—
107#2493C2218yes—
108#2493C2214yes—
109#2480C2214yes—
110#2480C2218yes—
111#2480C2214yes—
112#2478C2218yes—
113#2478C2218yes—
114#2475C2218yes—
115#2475C2218yes—
116#2473C2218yes—
117#2473C2218yes—
118#2462C2218yescomplemented
119#2442C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2442C2214yes—
123#2440C2214yes—
124#2440C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2401C2214yes—
128#2401C2214yes—
129#2370C2214yescomplemented
130#2370C2214yescomplemented
131#2369C2214yescomplemented
132#2365C2214yescomplemented
133#2344C2214yes—
134#2344C2214yes—
135#2344C2214yes—
136#2344C2214yes—
137#2331C2214yescomplemented
138#2330C2214yescomplemented
139#2329C2214yes—
140#2329C2214yes—
141#2323C2214yes—
142#2323C2214yes—
143#2317C2212yes—
144#2317C2212yes—
145#2317C2212yes—
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2316C2212yes—
150#2314C2214yes—
151C4×C4⋊Q8C2214yescomplemented
152C4×#125C2214yescomplemented
153C4×#126C2214yes—
154C4×#126C2214yes—
155C4×C22⋊Q8C2214yes—
156C4×C22⋊Q8C2214yes—
157#2296C2212yes—
158#2296C2212yes—
159C2×#389C2211yescharacteristic
160C2×#389C2211yescharacteristic
161C2×#387C2212yes—
162C2×#387C2212yes—
163#2285C2212yes—
164#2280C2212yes—
165#2280C2212yes—
166C2×#381C2212yes—
167C2×#380C2211yescharacteristic
168#2274C2212yes—
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2312yes—
175#544—28no—
176#544—28no—
177#541—416no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×#126C2314yes—
182C2×#126C2314yes—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×#125C2318yes—
188C2×#125C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×#117—48no—
198C2×#117C2314yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2314yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C22×C4⋊C4—28no—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2314yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223#401C2314yes—
224#401C2318yes—
225#401C2314yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2314yes—
235#400C2314yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2314yes—
266#397C2314yes—
267#397C2318yes—
268#397C2318yes—
269#397C2314yes—
270#397C2314yes—
271#397C2314yes—
272#396C2314yes—
273#396C2318yes—
274#396C2314yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#395C2318yes—
279#391C2318yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2318yes—
284#391C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2314yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2312yes—
316#389C2318yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2318yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#387C2314yes—
335#387C2314yes—
336#387C2314yes—
337#387C2314yes—
338#387C2314yes—
339#387C2314yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2314yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2314yes—
373#385C2314yes—
374#385C2314yes—
375#384C2314yes—
376#384C2314yes—
377#384C2312yes—
378#384C2314yes—
379#384C2314yes—
380#384C2314yes—
381#384C2312yes—
382#383C2314yes—
383#383C2314yes—
384#383C2318yes—
385#382C2314yes—
386#382C2314yes—
387#382C2314yes—
388#382C2312yes—
389#382C2314yes—
390#382C2312yes—
391#382C2318yes—
392#382C2314yes—
393#382C2318yes—
394#381C2318yes—
395#381C2318yes—
396#381C2314yes—
397#381C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2318yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2312yes—
410#380C2312yes—
411#380C2312yes—
412#380C2312yes—
413#380C2312yes—
414#380C2312yes—
415#380C2312yes—
416#380C2312yes—
417#379C2314yes—
418#379C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2318yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2312yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2314yes—
452#376C2314yes—
453C2×#95C2312yes—
454C2×#95C2312yes—
455C2×#95C2311yescharacteristic
456C2×#95C2311yescharacteristic
457C2×#95C2312yes—
458C2×#95C2312yes—
459C2×#95C2312yes—
460C43C2314yes—
461C25C2411yescharacteristic
462C22×Q8C2414yes—
463C22×Q8C2414yes—
464C23×C4—28no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—44no—
469C23×C4—44no—
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2412yes—
483C23×C4C2411yescharacteristic
484C4⋊Q8—216no—
485C4⋊Q8—216no—
486C4⋊Q8—48no—
487#126—216no—
488#126—48no—
489#126—416no—
490#125—216no—
491#125—216no—
492#125—48no—
493#125—416no—
494#125—416no—
495C22⋊Q8—216no—
496C22⋊Q8—216no—
497C22⋊Q8—48no—
498C22⋊Q8—48no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501C4×Q8—48no—
502C4×Q8—48no—
503#117—28no—
504#117—28no—
505#117—28no—
506#117—28no—
507#117—216no—
508#117—48no—
509#117—48no—
510#117—48no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—216no—
516C2×C4⋊C4—216no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4—44no—
519C2×C4⋊C4#4118yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—44no—
570C2×C22⋊C4C2411yescharacteristic
571C2×C22⋊C4C2411yescharacteristic
572C2×C22⋊C4C2411yescharacteristic
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2411yescharacteristic
590C2×C42—24no—
591C2×C42—24no—
592C2×C42—44no—
593C2×C42—44no—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2418yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2418yes—
612#95C2412yes—
613#95C2412yes—
614#95C2412yes—
615#95C2412yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—41no—
665C24—41no—
666C24C2511yescharacteristic
667C24C2511yescharacteristic
668C24C2511yescharacteristic
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8—44no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C22×C4—24no—
676C22×C4—22no—
677C22×C4—28no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—28no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—44no—
700C22×C4—42no—
701C22×C4—44no—
702C22×C4—42no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—42no—
710C22×C4—41no—
711C22×C4—42no—
712C22×C4—41no—
713C22×C4—432no—
714C22×C4—416no—
715C22×C4C2×#4118yes—
716C22×C4C2×#4114yes—
717C22×C42−1+414yes—
718C22×C42−1+414yes—
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2512yes—
722C22×C4C2514yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2511yescharacteristic
726C22×C4C2511yescharacteristic
727C22×C4C2514yes—
728C22×C4C2514yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2511yescharacteristic
737C22×C4C2511yescharacteristic
738C22×C4C2512yes—
739C4⋊C4—216no—
740C4⋊C4—28no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—216no—
748C4⋊C4—216no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4C2×#41116yes—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—22no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—24no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—42no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4H(5,𝔽2)14yes—
806C42—28no—
807C42—28no—
808C42—28no—
809C42—28no—
810C42—28no—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—28no—
816C42—28no—
817C42—44no—
818C42—44no—
819C42—44no—
820C42—48no—
821C42—44no—
822C42—48no—
823C42—44no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—28no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23C22×#4112yes—
848C23C2×H(5,𝔽2)12yes—
849C23C2×2−1+412yes—
850C23C2×2−1+412yes—
851C23#58512yes—
852C23C2611yescharacteristic
853Q8—88no—
854Q8—88no—
855C2×C4—24no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—24no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—48no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—416no—
913C2×C4—416no—
914C2×C4—48no—
915C2×C4—44no—
916C2×C4—48no—
917C2×C4—48no—
918C2×C4—84no—
919C2×C4—84no—
920C2×C4—82no—
921C2×C4—82no—
922C2×C4#541116yescomplemented
923C2×C4C22×#4118yes—
924C2×C4C22×#4114yes—
925C2×C4C2×H(5,𝔽2)12yes—
926C2×C4C2×H(5,𝔽2)12yes—
927C2×C4C2×2−1+414yes—
928C2×C4C2×2−1+414yes—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—416no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22C2×#54114yes—
951C22C23×#4111yescharacteristic
952C22C22×H(5,𝔽2)11yescharacteristic
953C22C22×2−1+411yescharacteristic
954C22C22×2−1+411yescharacteristic
955C22C2×#58511yescharacteristic
956C222−1+611yescharacteristic
957C222−1+611yescharacteristic
958C4—28no—
959C4—22no—
960C4—22no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—41no—
969C4—41no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4C2×#54118yes—
978C2—24no—
979C2—42no—
980C2—42no—
981C2C22×#54111yescharacteristic
982C2#6277311yescharacteristic
983C2#6285011yescharacteristic
984C2#6291511yescharacteristic
985C2#6291511yescharacteristic
986C2#6292811yescharacteristic
987C2#6292811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42636C2semidirect
2. #42623C2semidirect
3. #42587C2semidirect
4. #42573C2semidirect
5. #40178C2semidirect
6. #40051C2semidirect
7. #39407C2semidirect
8. #39032C2semidirect
9. #37466C2semidirect
10. #36762C2semidirect
13. #35543C2semidirect
15. #35265C2semidirect
18. #35167C2semidirect
19. #35159C2semidirect
21. #34271C2semidirect
23. C4×#544C2semidirect
29. #2864C22semidirect
30. #2859C22semidirect
35. #2839C22semidirect
36. #2833C22semidirect
37. #2802C22semidirect
38. #2794C22semidirect
39. #2789C22semidirect
40. #2776C22semidirect
41. #2766C22semidirect
42. #2758C22semidirect
47. #2719C22semidirect
48. #2713C22semidirect
53. #2666C22semidirect
55. #2655C22semidirect
56. #2655C22semidirect
57. #2647C22semidirect
58. #2647C22semidirect
60. #2634C22semidirect
67. #2571C22semidirect
68. #2570C22semidirect
69. #2570C22semidirect
70. #2552C22semidirect
71. #2552C22semidirect
72. #2551C22semidirect
73. #2550C22semidirect
74. #2550C22semidirect
75. #2524C22semidirect
76. #2509C22semidirect
77. #2509C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2508C22semidirect
81. #2508C22semidirect
82. #2507C22semidirect
83. #2507C22semidirect
84. #2507C22semidirect
85. #2506C22semidirect
86. #2506C22semidirect
87. #2506C22semidirect
118. #2462C22semidirect
129. #2370C22semidirect
130. #2370C22semidirect
131. #2369C22semidirect
132. #2365C22semidirect
137. #2331C22semidirect
138. #2330C22semidirect
151. C4×C4⋊Q8C22semidirect
152. C4×#125C22semidirect
922. C2×C4#541semidirect

Maximal subgroups

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

subgroupindex
#426362
#426232
#425872
#425732
#401782
#400512
#394072
#390322
#374662
#367622
#367322
#355442
#355432
#353102
#352652
#352242
#351672
#351592
#348142
#342712
C2×#23442
C4×#5442