Finite Group Databasebeta

← #7658030

Subgroups — #7658030

Order 512.

4926 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42606C214yesmaximal, complemented
2#42601C214yesmaximal, complemented
3#40911C218yesmaximal, complemented
4#40897C218yesmaximal, complemented
5#39608C212yesmaximal, complemented
6#39514C211yesmaximal, characteristic, complemented
7#39378C211yesmaximal, characteristic, complemented
8#37888C212yesmaximal, complemented
9#37858C214yesmaximal, complemented
10#37710C212yesmaximal, complemented
11#37636C212yesmaximal, complemented
12#37511C214yesmaximal, complemented
13#36187C211yesmaximal, characteristic, complemented
14#36160C212yesmaximal, complemented
15#36132C211yesmaximal, characteristic, complemented
16#36000C214yesmaximal, complemented
17#35828C214yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#35261C212yesmaximal, complemented
20#34634C212yesmaximal, complemented
21#34621C211yesmaximal, characteristic, complemented
22#34321C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C2×#555C2212yes—
25C2×#540C2212yescomplemented
26C2×#533C2212yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×#117C2212yes—
29#2868C2211yescharacteristic, complemented
30#2859C2211yescharacteristic, complemented
31#2857C2212yes—
32#2856C2212yescomplemented
33#2851C2212yescomplemented
34#2847C2214yes—
35#2832C2218yescomplemented
36#2827C2218yescomplemented
37#2824C2218yes—
38#2781C2218yes—
39#2770C2218yescomplemented
40#2763C2218yescomplemented
41#2743C2218yescomplemented
42#2737C2218yescomplemented
43#2716C2218yescomplemented
44#2701C2218yescomplemented
45#2692C2218yes—
46#2685C2218yes—
47#2684C2218yes—
48#2681C2218yescomplemented
49#2676C2218yes—
50#2651C2214yescomplemented
51#2651C2218yescomplemented
52#2650C2218yescomplemented
53#2648C2214yes—
54#2647C2211yescharacteristic, complemented
55#2647C2212yescomplemented
56#2644C2212yescomplemented
57#2641C2211yescharacteristic, complemented
58#2638C2218yescomplemented
59#2636C2218yes—
60#2632C2218yescomplemented
61#2629C2211yescharacteristic
62#2629C2212yes—
63#2629C2212yescomplemented
64#2629C2212yescomplemented
65#2628C2214yes—
66#2628C2214yescomplemented
67#2628C2214yescomplemented
68#2627C2218yescomplemented
69#2626C2218yes—
70#2624C2214yes—
71#2624C2212yes—
72#2624C2214yescomplemented
73#2619C2211yescharacteristic
74#2578C2218yescomplemented
75#2575C2218yescomplemented
76#2572C2218yes—
77#2570C2214yescomplemented
78#2563C2212yes—
79#2563C2214yes—
80#2563C2212yescomplemented
81#2560C2218yescomplemented
82#2551C2212yescomplemented
83#2537C2212yes—
84#2537C2214yes—
85#2525C2218yescomplemented
86#2524C2218yescomplemented
87#2521C2218yescomplemented
88#2516C2218yes—
89#2512C2214yes—
90#2508C2214yescomplemented
91#2507C2214yescomplemented
92#2500C2214yescomplemented
93#2497C2214yes—
94#2497C2214yescomplemented
95#2496C2214yescomplemented
96#2495C2214yescomplemented
97#2495C2214yescomplemented
98#2491C2214yes—
99#2491C2214yescomplemented
100#2491C2218yescomplemented
101#2487C2214yes—
102#2486C2214yescomplemented
103#2485C2214yes—
104#2476C2218yescomplemented
105#2472C2218yes—
106#2471C2218yes—
107#2465C2218yescomplemented
108#2459C2218yes—
109#2458C2218yescomplemented
110#2452C2214yes—
111#2452C2214yescomplemented
112#2446C2214yescomplemented
113#2443C2218yescomplemented
114#2440C2214yescomplemented
115#2439C2214yescomplemented
116#2429C2214yes—
117#2426C2218yescomplemented
118#2424C2218yes—
119#2420C2214yes—
120#2420C2214yescomplemented
121#2416C2214yes—
122#2414C2214yes—
123#2408C2214yes—
124#2396C2218yes—
125#2396C2218yescomplemented
126#2395C2214yescomplemented
127#2392C2214yes—
128#2369C2212yescomplemented
129#2367C2218yescomplemented
130#2365C2214yescomplemented
131#2363C2214yes—
132#2363C2214yescomplemented
133#2361C2214yes—
134#2354C2212yes—
135#2354C2212yes—
136#2354C2214yescomplemented
137#2352C2214yes—
138#2352C2214yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2212yescomplemented
141#2347C2214yescomplemented
142#2347C2214yescomplemented
143#2344C2212yes—
144#2342C2214yes—
145D4×C22⋊C4C2212yes—
146#2337C2218yescomplemented
147#2330C2212yescomplemented
148#2324C2214yes—
149#2324C2214yes—
150#2314C2212yes—
151#2314C2212yescomplemented
152C4×C4⋊Q8C2212yescomplemented
153C4×#127C2211yescharacteristic, complemented
154C4×#125C2211yescharacteristic, complemented
155C4×#121C2212yes—
156C4×#121C2214yescomplemented
157#2296C2214yescomplemented
158#2293C2211yescharacteristic
159#2293C2211yescharacteristic
160#2293C2212yescomplemented
161#2290C2212yes—
162#2290C2212yes—
163#2285C2211yescharacteristic
164#2285C2212yescomplemented
165#2280C2214yes—
166#2280C2212yes—
167#2274C2214yescomplemented
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#555—216no—
174#540—48no—
175#533—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×#127C2311yescharacteristic
181C2×#126C2318yes—
182C2×#125C2311yescharacteristic
183C2×#125C2312yes—
184C2×#124C2318yes—
185C2×#124C2318yes—
186C2×#123C2318yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×#121C2312yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2318yes—
196C2×#121C2318yes—
197C2×#120C2318yes—
198C2×C4×Q8C2318yes—
199C2×C4×Q8C2314yes—
200C2×C4×D4—28no—
201C2×C4×D4C2312yes—
202C2×C4×D4C2311yescharacteristic
203C2×C4×D4C2311yescharacteristic
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2311yescharacteristic
214C2×#117—48no—
215C2×#117C2311yescharacteristic
216C2×#117C2312yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2311yescharacteristic
220C2×#117C2312yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2314yes—
224C2×#117C2314yes—
225C2×#117C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2314yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2314yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2314yes—
241#399C2318yes—
242#399C2318yes—
243#399C2314yes—
244#399C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#398C2314yes—
252#397C2314yes—
253#397C2314yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2314yes—
260#397C2314yes—
261#396C2318yes—
262#396C2318yes—
263#396C2314yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2314yes—
268#395C2318yes—
269#395C2318yes—
270#395C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2314yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2314yes—
282#394C2314yes—
283#394C2314yes—
284#394C2314yes—
285#393C2318yes—
286#393C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2318yes—
292#392C2318yes—
293#392C2314yes—
294#391C2318yes—
295#391C2314yes—
296#391C2318yes—
297#391C2314yes—
298#390C2318yes—
299#390C2312yes—
300#390C2314yes—
301#390C2318yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2318yes—
306#390C2312yes—
307#390C2312yes—
308#390C2318yes—
309#390C2312yes—
310#390C2312yes—
311#390C2312yes—
312#389C2312yes—
313#389C2314yes—
314#389C2314yes—
315#389C2312yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2318yes—
320#389C2312yes—
321#389C2314yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2312yes—
329#389C2312yes—
330#388C2314yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2314yes—
338#388C2314yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2314yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2318yes—
350#388C2314yes—
351#387C2318yes—
352#387C2314yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2314yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#386C2318yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2314yes—
371#386C2314yes—
372#385C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2314yes—
380#384C2311yescharacteristic
381#384C2312yes—
382#384C2312yes—
383#384C2312yes—
384#384C2314yes—
385#384C2312yes—
386#383C2318yes—
387#383C2318yes—
388#382C2311yescharacteristic
389#382C2314yes—
390#382C2318yes—
391#382C2314yes—
392#382C2312yes—
393#382C2312yes—
394#381C2314yes—
395#381C2318yes—
396#381C2318yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2314yes—
409#380C2314yes—
410#380C2312yes—
411#380C2318yes—
412#380C2314yes—
413#379C2314yes—
414#379C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2312yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436C4×C22⋊C4C2318yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2312yes—
447#376C2311yescharacteristic
448#376C2311yescharacteristic
449C43C2311yescharacteristic
450C43C2311yescharacteristic
451C25C2412yes—
452C22×Q8C2414yes—
453C22×Q8C2418yes—
454C22×D4—24no—
455C22×D4—44no—
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C22×D4C2411yescharacteristic
459C22×D4C2412yes—
460C22×D4C2414yes—
461C22×D4C2418yes—
462C22×D4C2414yes—
463C22×D4C2418yes—
464C23×C4—28no—
465C23×C4—28no—
466C23×C4—44no—
467C23×C4C2414yes—
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2418yes—
479C4⋊Q8—28no—
480C4⋊Q8—48no—
481C4⋊Q8—48no—
482C4⋊Q8—84no—
483#127—24no—
484#126—88no—
485#125—24no—
486#125—28no—
487#124—232no—
488#124—88no—
489#123—416no—
490C22⋊Q8—416no—
491C22⋊Q8—84no—
492C22⋊Q8—88no—
493#121—216no—
494#121—216no—
495#121—28no—
496#121—416no—
497#121—48no—
498#121—48no—
499#121—88no—
500#120—88no—
501C4×Q8—416no—
502C4×Q8—84no—
503C4×D4—24no—
504C4×D4—28no—
505C4×D4—24no—
506C4×D4—28no—
507C4×D4—24no—
508C4×D4—28no—
509C4×D4—44no—
510C4×D4—44no—
511C4×D4—48no—
512C4×D4—48no—
513C4×D4—48no—
514C4×D4—88no—
515C4×D4#4118yes—
516#117—216no—
517#117—24no—
518#117—216no—
519#117—24no—
520#117—28no—
521#117—44no—
522#117—44no—
523#117—48no—
524#117—48no—
525#117—48no—
526#117—48no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4—48no—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2411yescharacteristic
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C22⋊C4—28no—
565C2×C22⋊C4—48no—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2412yes—
602C2×C42—24no—
603C2×C42—28no—
604C2×C42—44no—
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2418yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2414yes—
619C2×C42C2418yes—
620C2×C42C2418yes—
621C2×C42C2412yes—
622C2×C42C2418yes—
623C2×C42C2412yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626#95C2412yes—
627#95C2412yes—
628#95C2412yes—
629#95C2412yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2412yes—
634#95C2412yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—24no—
660C24—24no—
661C24—42no—
662C24—44no—
663C24—44no—
664C24C2512yes—
665C24C2514yes—
666C24C2512yes—
667C24C2511yescharacteristic
668C2×Q8—28no—
669C2×Q8—48no—
670C2×Q8—44no—
671C2×Q8—48no—
672C2×Q8—44no—
673C2×Q8—48no—
674C2×D4—24no—
675C2×D4—216no—
676C2×D4—28no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4—44no—
689C2×D4—48no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—416no—
695C2×D4C2×#4114yes—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—22no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—28no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—432no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—42no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4C2×#4118yes—
730C22×C42−1+414yes—
731C22×C4C2511yescharacteristic
732C22×C4C2512yes—
733C22×C4C2514yes—
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2518yes—
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2511yescharacteristic
744C22×C4C2512yes—
745C22×C4C2511yescharacteristic
746C22×C4C2512yes—
747C22×C4C2511yescharacteristic
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C4⋊C4—24no—
751C4⋊C4—22no—
752C4⋊C4—24no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—24no—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—216no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—28no—
765C4⋊C4—24no—
766C4⋊C4—48no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—44no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—44no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4C2×#4114yes—
784C22⋊C4—24no—
785C22⋊C4—216no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—216no—
790C22⋊C4—28no—
791C22⋊C4—24no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—48no—
806C22⋊C4—44no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4C2×#4118yes—
820C42—22no—
821C42—22no—
822C42—22no—
823C42—216no—
824C42—28no—
825C42—24no—
826C42—22no—
827C42—24no—
828C42—22no—
829C42—22no—
830C42—24no—
831C42—28no—
832C42—24no—
833C42—44no—
834C42—48no—
835C42—48no—
836C42—42no—
837C42—48no—
838C42—42no—
839C42C2×#4114yes—
840C42H(5,𝔽2)14yes—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—24no—
847C23—22no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—22no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—48no—
862C23—48no—
863C23—84no—
864C23—88no—
865C23—88no—
866C23C22×#4114yes—
867C23C2×2−1+412yes—
868C23C2611yescharacteristic
869Q8—88no—
870Q8—816no—
871D4—28no—
872D4—48no—
873D4—44no—
874D4—48no—
875D4—88no—
876D4—816no—
877D4—88no—
878D4—168no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—28no—
887C2×C4—216no—
888C2×C4—21no—
889C2×C4—24no—
890C2×C4—21no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—24no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—48no—
926C2×C4—48no—
927C2×C4—48no—
928C2×C4—416no—
929C2×C4—44no—
930C2×C4—48no—
931C2×C4—82no—
932C2×C4—88no—
933C2×C4—88no—
934C2×C4—168no—
935C2×C4C22×#4114yes—
936C2×C4C22×#4112yes—
937C2×C4C22×#4112yes—
938C2×C4C22×#4112yes—
939C2×C4C2×H(5,𝔽2)14yes—
940C2×C4C2×H(5,𝔽2)12yes—
941C2×C4C2×2−1+412yes—
942C2×C4C2×2−1+412yes—
943C2×C4#58514yes—
944C22—22no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—41no—
950C22—44no—
951C22—44no—
952C22—42no—
953C22—41no—
954C22—42no—
955C22—44no—
956C22—44no—
957C22—42no—
958C22—44no—
959C22—44no—
960C22—44no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—44no—
965C22—42no—
966C22—816no—
967C22C23×#4111yescharacteristic
968C22C22×H(5,𝔽2)11yescharacteristic
969C22C22×2−1+411yescharacteristic
970C22C2×#58512yes—
971C22H(7,𝔽2)12yes—
972C4—22no—
973C4—24no—
974C4—22no—
975C4—24no—
976C4—42no—
977C4—41no—
978C4—48no—
979C4—42no—
980C4—42no—
981C4—44no—
982C4—42no—
983C4—44no—
984C4—44no—
985C4—48no—
986C4—44no—
987C4—44no—
988C4—41no—
989C4#345514yes—
990C4#352014yes—
991C2—44no—
992C2—42no—
993C2—84no—
994C2—82no—
995C2C2×#345511yescharacteristic
996C2C2×#352011yescharacteristic
997C2#6285811yescharacteristic
998C2#6292912yes—
999C2#6293012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42606C2semidirect
2. #42601C2semidirect
3. #40911C2semidirect
4. #40897C2semidirect
5. #39608C2semidirect
6. #39514C2semidirect
7. #39378C2semidirect
8. #37888C2semidirect
9. #37858C2semidirect
10. #37710C2semidirect
11. #37636C2semidirect
12. #37511C2semidirect
13. #36187C2semidirect
14. #36160C2semidirect
15. #36132C2semidirect
16. #36000C2semidirect
17. #35828C2semidirect
18. #35284C2semidirect
19. #35261C2semidirect
20. #34634C2semidirect
21. #34621C2semidirect
22. #34321C2semidirect
23. D4×#117C2semidirect
25. C2×#540C22semidirect
26. C2×#533C22semidirect
29. #2868C22semidirect
30. #2859C22semidirect
32. #2856C22semidirect
33. #2851C22semidirect
35. #2832C22semidirect
36. #2827C22semidirect
39. #2770C22semidirect
40. #2763C22semidirect
41. #2743C22semidirect
42. #2737C22semidirect
43. #2716C22semidirect
44. #2701C22semidirect
48. #2681C22semidirect
50. #2651C22semidirect
51. #2651C22semidirect
52. #2650C22semidirect
54. #2647C22semidirect
55. #2647C22semidirect
56. #2644C22semidirect
57. #2641C22semidirect
58. #2638C22semidirect
60. #2632C22semidirect
63. #2629C22semidirect
64. #2629C22semidirect
66. #2628C22semidirect
67. #2628C22semidirect
68. #2627C22semidirect
72. #2624C22semidirect
74. #2578C22semidirect
75. #2575C22semidirect
77. #2570C22semidirect
80. #2563C22semidirect
81. #2560C22semidirect
82. #2551C22semidirect
85. #2525C22semidirect
86. #2524C22semidirect
87. #2521C22semidirect
90. #2508C22semidirect
91. #2507C22semidirect
92. #2500C22semidirect
94. #2497C22semidirect
95. #2496C22semidirect
96. #2495C22semidirect
97. #2495C22semidirect
99. #2491C22semidirect
100. #2491C22semidirect
102. #2486C22semidirect
104. #2476C22semidirect
107. #2465C22semidirect
109. #2458C22semidirect
111. #2452C22semidirect
112. #2446C22semidirect
113. #2443C22semidirect
114. #2440C22semidirect
115. #2439C22semidirect
117. #2426C22semidirect
120. #2420C22semidirect
125. #2396C22semidirect
126. #2395C22semidirect
128. #2369C22semidirect
129. #2367C22semidirect
130. #2365C22semidirect
132. #2363C22semidirect
136. #2354C22semidirect
140. D4×C4⋊C4C22semidirect
141. #2347C22semidirect
142. #2347C22semidirect
146. #2337C22semidirect
147. #2330C22semidirect
151. #2314C22semidirect
152. C4×C4⋊Q8C22semidirect
153. C4×#127C22semidirect
154. C4×#125C22semidirect
156. C4×#121C22semidirect
157. #2296C22semidirect
160. #2293C22semidirect
164. #2285C22semidirect
167. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#426062
#426012
#409112
#408972
#396082
#395142
#393782
#378882
#378582
#377102
#376362
#375112
#361872
#361602
#361322
#360002
#358282
#352842
#352612
#346342
#346212
#343212
D4×#1172