Finite Group Databasebeta

← #7646727

Subgroups — #7646727

Order 512.

4318 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42983C214yesmaximal
2#42938C214yesmaximal, complemented
3#42164C214yesmaximal, complemented
4#42162C214yesmaximal, complemented
5#39515C212yesmaximal, complemented
6#39513C212yesmaximal, complemented
7#39203C212yesmaximal, complemented
8#39200C212yesmaximal, complemented
9#37859C214yesmaximal, complemented
10#37856C214yesmaximal, complemented
11#37582C214yesmaximal, complemented
12#37020C214yesmaximal, complemented
13#37014C214yesmaximal, complemented
14#35658C214yesmaximal, complemented
15#35322C211yesmaximal, characteristic, complemented
16#35240C211yesmaximal, characteristic
17#35188C214yesmaximal, complemented
18#35183C214yesmaximal, complemented
19#34946C211yesmaximal, characteristic
20#34912C211yesmaximal, characteristic, complemented
21#34231C211yesmaximal, characteristic, complemented
22#34154C211yesmaximal, characteristic, complemented
23#34058C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#2868C2211yescharacteristic, complemented
28#2866C2218yescomplemented
29#2865C2218yescomplemented
30#2862C2211yescharacteristic, complemented
31#2862C2211yescharacteristic, complemented
32#2862C2211yescharacteristic, complemented
33#2848C2212yes—
34#2848C2212yes—
35#2839C2218yescomplemented
36#2830C2218yes—
37#2798C2218yescomplemented
38#2798C2218yescomplemented
39#2793C2218yescomplemented
40#2793C2218yescomplemented
41#2773C2218yescomplemented
42#2759C2218yescomplemented
43#2754C2218yescomplemented
44#2754C2218yescomplemented
45#2745C2218yes—
46#2744C2218yes—
47#2739C2218yes—
48#2738C2218yes—
49#2736C2218yes—
50#2735C2218yes—
51#2735C2218yes—
52#2735C2218yes—
53#2666C2218yescomplemented
54#2655C2218yescomplemented
55#2654C2218yescomplemented
56#2651C2218yes—
57#2651C2218yes—
58#2650C2218yescomplemented
59#2633C2214yes—
60#2629C2214yescomplemented
61#2628C2214yescomplemented
62#2625C2214yescomplemented
63#2625C2214yescomplemented
64#2621C2214yes—
65#2608C2212yes—
66#2607C2212yes—
67#2606C2212yescomplemented
68#2605C2212yescomplemented
69#2596C2218yescomplemented
70#2594C2218yescomplemented
71#2593C2218yes—
72#2592C2214yes—
73#2592C2214yes—
74#2585C2218yescomplemented
75#2582C2214yescomplemented
76#2581C2214yescomplemented
77#2577C2218yescomplemented
78#2575C2218yescomplemented
79#2574C2218yescomplemented
80#2573C2218yescomplemented
81#2571C2214yescomplemented
82#2570C2214yescomplemented
83#2570C2212yescomplemented
84#2565C2214yescomplemented
85#2565C2212yescomplemented
86#2565C2212yescomplemented
87#2563C2212yes—
88#2562C2212yes—
89#2562C2212yes—
90#2561C2214yes—
91#2550C2212yescomplemented
92#2547C2212yes—
93#2547C2212yes—
94#2545C2214yes—
95#2545C2214yes—
96#2542C2212yes—
97#2536C2214yes—
98#2532C2218yescomplemented
99#2530C2218yescomplemented
100#2529C2218yescomplemented
101#2527C2218yescomplemented
102#2522C2218yescomplemented
103#2515C2218yescomplemented
104#2514C2214yescomplemented
105#2513C2214yes—
106#2513C2214yes—
107#2511C2214yescomplemented
108#2503C2212yes—
109#2502C2212yes—
110#2499C2212yes—
111#2499C2212yes—
112#2499C2214yes—
113#2497C2214yescomplemented
114#2497C2214yescomplemented
115#2495C2214yescomplemented
116#2494C2214yescomplemented
117#2492C2214yescomplemented
118#2489C2214yescomplemented
119#2482C2214yes—
120#2448C2214yes—
121#2448C2214yes—
122#2446C2214yescomplemented
123#2446C2214yescomplemented
124#2441C2212yes—
125#2439C2212yes—
126#2435C2212yes—
127#2435C2212yes—
128#2423C2214yescomplemented
129#2421C2214yescomplemented
130#2398C2214yes—
131#2396C2214yes—
132#2371C2214yescomplemented
133#2369C2212yescomplemented
134#2365C2212yescomplemented
135#2365C2212yescomplemented
136#2365C2212yescomplemented
137#2362C2214yes—
138#2362C2214yes—
139#2362C2214yes—
140#2356C2214yescomplemented
141#2347C2212yes—
142#2346C2212yes—
143#2332C2214yes—
144#2327C2214yescomplemented
145#2326C2214yes—
146#2323C2214yescomplemented
147#2323C2214yescomplemented
148#2320C2212yescomplemented
149#2319C2212yes—
150#2319C2212yes—
151#2319C2212yes—
152#2319C2212yes—
153#2316C2212yes—
154#2314C2214yescomplemented
155#2314C2214yescomplemented
156#2312C2212yes—
157#2312C2212yes—
158#2309C2212yes—
159C4×C4⋊Q8C2212yescomplemented
160C4×#125C2212yescomplemented
161C4×#125C2214yescomplemented
162C4×#124C2214yes—
163#2298C2214yes—
164#2295C2212yescomplemented
165#2295C2214yescomplemented
166#2295C2212yescomplemented
167#2293C2212yes—
168#2293C2212yes—
169#2293C2214yes—
170#2283C2211yescharacteristic
171#2280C2214yes—
172#2280C2214yes—
173#2276C2212yescomplemented
174C42×Q8C2212yescomplemented
175C42×Q8C2212yescomplemented
176C4×#117C2211yescharacteristic
177C4×#117C2211yescharacteristic
178C4×#117C2211yescharacteristic
179C23×D4C2311yescharacteristic
180C24×C4C2312yes—
181#533—28no—
182#533—28no—
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2314yes—
189C2×#125C2312yes—
190C2×#125C2312yes—
191C2×#125C2312yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×D4—28no—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2312yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C42C2311yescharacteristic
223#401C2318yes—
224#400C2314yes—
225#400C2314yes—
226#400C2318yes—
227#400C2314yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#399C2318yes—
237#399C2318yes—
238#399C2314yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2314yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2314yes—
267#396C2314yes—
268#395C2318yes—
269#395C2314yes—
270#394C2314yes—
271#394C2314yes—
272#394C2318yes—
273#393C2318yes—
274#393C2318yes—
275#393C2318yes—
276#393C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2312yes—
281#391C2312yes—
282#391C2312yes—
283#391C2312yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2318yes—
290#391C2314yes—
291#391C2318yes—
292#391C2314yes—
293#391C2314yes—
294#391C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2312yes—
298#390C2312yes—
299#390C2314yes—
300#390C2312yes—
301#390C2312yes—
302#390C2314yes—
303#389C2312yes—
304#389C2314yes—
305#389C2314yes—
306#389C2312yes—
307#389C2312yes—
308#389C2314yes—
309#389C2312yes—
310#389C2312yes—
311#389C2314yes—
312#389C2312yes—
313#389C2318yes—
314#389C2314yes—
315#389C2312yes—
316#389C2312yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2314yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2314yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2314yes—
376#387C2318yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2314yes—
386#385C2314yes—
387#384C2312yes—
388#384C2314yes—
389#384C2312yes—
390#384C2312yes—
391#384C2314yes—
392#383C2314yes—
393#383C2312yes—
394#383C2318yes—
395#382C2312yes—
396#382C2312yes—
397#382C2314yes—
398#382C2314yes—
399#382C2312yes—
400#382C2312yes—
401#382C2314yes—
402#382C2318yes—
403#382C2314yes—
404#381C2318yes—
405#381C2314yes—
406#381C2314yes—
407#381C2312yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#379C2318yes—
421#379C2314yes—
422#379C2314yes—
423#379C2314yes—
424#379C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2312yes—
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2312yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2312yes—
462#376C2312yes—
463#376C2312yes—
464#376C2312yes—
465#376C2314yes—
466#376C2312yes—
467#376C2314yes—
468C43C2311yescharacteristic
469C43C2312yes—
470C43C2311yescharacteristic
471C43C2314yes—
472C43C2312yes—
473C25C2412yes—
474C22×Q8C2412yes—
475C22×Q8C2412yes—
476C22×Q8C2412yes—
477C22×Q8C2412yes—
478C22×Q8C2414yes—
479C22×D4—24no—
480C22×D4—44no—
481C22×D4C2412yes—
482C22×D4C2412yes—
483C23×C4—28no—
484C23×C4—48no—
485C23×C4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2414yes—
490C23×C4C2411yescharacteristic
491C4⋊Q8—24no—
492C4⋊Q8—24no—
493C4⋊Q8—24no—
494C4⋊Q8—24no—
495C4⋊Q8—44no—
496C4⋊Q8—48no—
497#125—28no—
498#125—28no—
499#125—44no—
500#124—48no—
501#124—48no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8—28no—
505C22⋊Q8—28no—
506C22⋊Q8—48no—
507C22⋊Q8—48no—
508C4×Q8—28no—
509C4×Q8—28no—
510C4×Q8—28no—
511C4×Q8—28no—
512C4×Q8—48no—
513C4×Q8—48no—
514C4×Q8—48no—
515C4×Q8—48no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—28no—
519C4×D4—28no—
520#117—28no—
521#117—28no—
522#117—48no—
523#117—48no—
524#117—44no—
525#117—44no—
526#117—44no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C22⋊C4—28no—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C42#4118yes—
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2414yes—
603C2×C42C2412yes—
604C2×C42C2414yes—
605C2×C42C2412yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2418yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2418yes—
622C2×C42C2411yescharacteristic
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626#95C2412yes—
627#95C2412yes—
628#95C2412yes—
629#95C2412yes—
630#95C2412yes—
631#95C2412yes—
632#95C2412yes—
633#95C2412yes—
634#95C2414yes—
635#95C2414yes—
636#95C2412yes—
637#95C2412yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2418yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2414yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671C24—24no—
672C24—44no—
673C24—44no—
674C24—42no—
675C24—42no—
676C24C2514yes—
677C24C2511yescharacteristic
678C2×Q8—24no—
679C2×Q8—24no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—42no—
688C2×Q8—42no—
689C2×Q8—44no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—44no—
695C2×D4—416no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—816no—
709C22×C4C2×#4114yes—
710C22×C4C2×#4114yes—
711C22×C4C2×#4114yes—
712C22×C4C2514yes—
713C22×C4C2512yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2512yes—
721C22×C4C2512yes—
722C22×C4C2512yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C22×C4C2511yescharacteristic
730C22×C4C2511yescharacteristic
731C22×C4C2511yescharacteristic
732C22×C4C2511yescharacteristic
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—42no—
758C4⋊C4—42no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—48no—
783C22⋊C4—42no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—42no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—42no—
793C22⋊C4—42no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C42—28no—
803C42—28no—
804C42—28no—
805C42—24no—
806C42—24no—
807C42—24no—
808C42—24no—
809C42—28no—
810C42—28no—
811C42—42no—
812C42—42no—
813C42—42no—
814C42—42no—
815C42—41no—
816C42—41no—
817C42—41no—
818C42—41no—
819C42—48no—
820C42—44no—
821C42—44no—
822C42—48no—
823C42—48no—
824C42—48no—
825C42C2×#4114yes—
826C42C2×#4114yes—
827C42C2×#4114yes—
828C42C2×#4114yes—
829C23—22no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—88no—
844C23—88no—
845C23C22×#4112yes—
846C23C2611yescharacteristic
847Q8—48no—
848Q8—48no—
849Q8—48no—
850Q8—84no—
851Q8—88no—
852D4—48no—
853D4—48no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—44no—
905C2×C4—416no—
906C2×C4—88no—
907C2×C4—84no—
908C2×C4C22×#4112yes—
909C2×C4C22×#4112yes—
910C2×C4C22×#4112yes—
911C2×C4C22×#4112yes—
912C2×C4C22×#4112yes—
913C2×C4C22×#4112yes—
914C2×C4#58514yes—
915C2×C4#58514yes—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—816no—
929C22C23×#4111yescharacteristic
930C22C2×#58512yes—
931C22C2×#58512yes—
932C222−1+611yescharacteristic
933C222−1+611yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—44no—
939C4—44no—
940C4—44no—
941C4—44no—
942C4—42no—
943C4—44no—
944C4—44no—
945C4—42no—
946C4—44no—
947C4—42no—
948C4—42no—
949C4—44no—
950C4—44no—
951C4—44no—
952C4—44no—
953C4#345514yes—
954C4#351014yes—
955C2—42no—
956C2—84no—
957C2C2×#345511yescharacteristic
958C2C2×#351011yescharacteristic
959C2#6286011yescharacteristic
960C2#6293612yes—
961C2#6293912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42938C2semidirect
3. #42164C2semidirect
4. #42162C2semidirect
5. #39515C2semidirect
6. #39513C2semidirect
7. #39203C2semidirect
8. #39200C2semidirect
9. #37859C2semidirect
10. #37856C2semidirect
11. #37582C2semidirect
12. #37020C2semidirect
13. #37014C2semidirect
14. #35658C2semidirect
15. #35322C2semidirect
17. #35188C2semidirect
18. #35183C2semidirect
20. #34912C2semidirect
21. #34231C2semidirect
22. #34154C2semidirect
27. #2868C22semidirect
28. #2866C22semidirect
29. #2865C22semidirect
30. #2862C22semidirect
31. #2862C22semidirect
32. #2862C22semidirect
35. #2839C22semidirect
37. #2798C22semidirect
38. #2798C22semidirect
39. #2793C22semidirect
40. #2793C22semidirect
41. #2773C22semidirect
42. #2759C22semidirect
43. #2754C22semidirect
44. #2754C22semidirect
53. #2666C22semidirect
54. #2655C22semidirect
55. #2654C22semidirect
58. #2650C22semidirect
60. #2629C22semidirect
61. #2628C22semidirect
62. #2625C22semidirect
63. #2625C22semidirect
67. #2606C22semidirect
68. #2605C22semidirect
69. #2596C22semidirect
70. #2594C22semidirect
74. #2585C22semidirect
75. #2582C22semidirect
76. #2581C22semidirect
77. #2577C22semidirect
78. #2575C22semidirect
79. #2574C22semidirect
80. #2573C22semidirect
81. #2571C22semidirect
82. #2570C22semidirect
83. #2570C22semidirect
84. #2565C22semidirect
85. #2565C22semidirect
86. #2565C22semidirect
91. #2550C22semidirect
98. #2532C22semidirect
99. #2530C22semidirect
100. #2529C22semidirect
101. #2527C22semidirect
102. #2522C22semidirect
103. #2515C22semidirect
104. #2514C22semidirect
107. #2511C22semidirect
113. #2497C22semidirect
114. #2497C22semidirect
115. #2495C22semidirect
116. #2494C22semidirect
117. #2492C22semidirect
118. #2489C22semidirect
122. #2446C22semidirect
123. #2446C22semidirect
128. #2423C22semidirect
129. #2421C22semidirect
132. #2371C22semidirect
133. #2369C22semidirect
134. #2365C22semidirect
135. #2365C22semidirect
136. #2365C22semidirect
140. #2356C22semidirect
144. #2327C22semidirect
146. #2323C22semidirect
147. #2323C22semidirect
148. #2320C22semidirect
154. #2314C22semidirect
155. #2314C22semidirect
159. C4×C4⋊Q8C22semidirect
160. C4×#125C22semidirect
161. C4×#125C22semidirect
164. #2295C22semidirect
165. #2295C22semidirect
166. #2295C22semidirect
173. #2276C22semidirect
174. C42×Q8C22semidirect
175. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#429832
#429382
#421642
#421622
#395152
#395132
#392032
#392002
#378592
#378562
#375822
#370202
#370142
#356582
#353222
#352402
#351882
#351832
#349462
#349122
#342312
#341542
#340582