Finite Group Databasebeta

← #7715140

Subgroups — #7715140

Order 512.

5130 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51869C218yesmaximal, complemented
2#51865C218yesmaximal, complemented
3#47621C214yesmaximal, complemented
4#47096C214yesmaximal, complemented
5#46807C214yesmaximal, complemented
6#46548C214yesmaximal, complemented
7#38214C214yesmaximal, complemented
8#38206C214yesmaximal, complemented
9#37893C212yesmaximal, complemented
10#37889C212yesmaximal, complemented
11#37710C212yesmaximal, complemented
12#37694C212yesmaximal, complemented
13#37523C212yesmaximal, complemented
14#37284C212yesmaximal, complemented
15#37269C212yesmaximal, complemented
16#35334C211yesmaximal, characteristic, complemented
17#35295C212yesmaximal, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35261C212yesmaximal, complemented
20#34415C212yesmaximal, complemented
21#34065C211yesmaximal, characteristic, complemented
22C2×#540C2212yes—
23C2×#535C2212yes—
24C2×#533C2211yescharacteristic, complemented
25C22×#127C2211yescharacteristic, complemented
26C2×#525C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C22×#117C2211yescharacteristic, complemented
29#2860C2214yescomplemented
30#2856C2212yes—
31#2856C2212yescomplemented
32#2851C2212yescomplemented
33#2851C2212yescomplemented
34#2847C2214yescomplemented
35#2826C2214yescomplemented
36#2824C2214yescomplemented
37#2803C2218yescomplemented
38#2801C2218yescomplemented
39#2787C2218yescomplemented
40#2779C2218yes—
41#2778C2218yescomplemented
42#2778C2218yescomplemented
43#2761C2218yescomplemented
44#2760C2214yescomplemented
45#2753C2218yescomplemented
46#2753C2218yescomplemented
47#2752C2214yescomplemented
48#2736C2218yescomplemented
49#2730C2218yescomplemented
50#2723C2218yescomplemented
51#2709C2218yescomplemented
52#2709C2214yescomplemented
53#2703C2218yescomplemented
54#2697C2214yes—
55#2686C2218yescomplemented
56#2685C2218yes—
57#2681C2218yescomplemented
58#2679C2214yes—
59#2676C2218yescomplemented
60#2673C2218yes—
61#2670C2214yescomplemented
62#2669C2214yescomplemented
63#2668C2218yes—
64#2668C2214yescomplemented
65#2663C2218yescomplemented
66#2649C2218yescomplemented
67#2647C2212yescomplemented
68#2641C2212yescomplemented
69#2629C2212yescomplemented
70#2628C2212yescomplemented
71#2628C2212yescomplemented
72#2624C2214yescomplemented
73#2624C2214yescomplemented
74#2619C2212yes—
75#2619C2212yes—
76#2619C2212yescomplemented
77#2610C2218yescomplemented
78#2597C2218yescomplemented
79#2581C2214yescomplemented
80#2580C2214yes—
81#2564C2214yescomplemented
82#2564C2214yescomplemented
83#2559C2218yescomplemented
84#2559C2218yescomplemented
85#2548C2214yescomplemented
86#2543C2218yescomplemented
87#2541C2214yes—
88#2529C2218yescomplemented
89#2528C2218yescomplemented
90#2526C2218yescomplemented
91#2513C2214yescomplemented
92#2509C2214yescomplemented
93#2494C2214yescomplemented
94#2491C2214yescomplemented
95#2485C2214yes—
96#2482C2218yescomplemented
97#2479C2218yescomplemented
98#2476C2218yescomplemented
99#2476C2218yescomplemented
100#2472C2218yes—
101#2471C2218yescomplemented
102#2470C2218yescomplemented
103#2467C2218yescomplemented
104#2463C2214yescomplemented
105#2458C2218yescomplemented
106#2455C2214yescomplemented
107#2452C2214yescomplemented
108#2445C2214yescomplemented
109#2444C2218yescomplemented
110#2443C2218yescomplemented
111#2428C2214yes—
112#2426C2218yescomplemented
113#2424C2218yescomplemented
114#2420C2214yescomplemented
115#2416C2214yescomplemented
116#2414C2218yescomplemented
117#2414C2214yescomplemented
118#2410C2218yes—
119#2408C2214yes—
120#2408C2214yes—
121#2408C2214yescomplemented
122#2405C2218yescomplemented
123#2379C2214yescomplemented
124#2375C2214yescomplemented
125#2372C2214yescomplemented
126#2363C2214yescomplemented
127#2361C2214yescomplemented
128#2358C2214yescomplemented
129#2346C2214yescomplemented
130D4×C22⋊C4C2214yescomplemented
131#2330C2212yescomplemented
132#2328C2212yescomplemented
133#2328C2218yescomplemented
134#2324C2214yes—
135#2324C2214yescomplemented
136#2324C2214yescomplemented
137#2323C2214yescomplemented
138#2322C2212yes—
139#2322C2212yescomplemented
140#2321C2212yes—
141#2321C2218yes—
142#2321C2212yescomplemented
143#2316C2212yescomplemented
144#2314C2212yescomplemented
145#2311C2212yes—
146#2309C2212yescomplemented
147C4×#121C2214yescomplemented
148#2297C2211yescharacteristic
149#2296C2211yescharacteristic, complemented
150#2293C2212yes—
151#2293C2212yescomplemented
152#2293C2214yescomplemented
153#2290C2212yes—
154#2290C2212yescomplemented
155#2285C2211yescharacteristic, complemented
156C2×#382C2211yescharacteristic, complemented
157#2280C2211yescharacteristic, complemented
158C4×#117C2211yescharacteristic, complemented
159C22×#41C2311yescharacteristic
160C23×D4C2312yes—
161C23×D4C2314yes—
162C24×C4C2311yescharacteristic
163#540—48no—
164#535—216no—
165#533—44no—
166C2×C4⋊Q8C2312yes—
167C2×#127—44no—
168C2×#127C2314yes—
169C2×#127C2312yes—
170C2×#127C2312yes—
171C2×#127C2314yes—
172C2×#126C2318yes—
173C2×#125C2312yes—
174C2×#124C2314yes—
175C2×#124C2318yes—
176#525—28no—
177C2×#123C2311yescharacteristic
178C2×#123C2311yescharacteristic
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×C22⋊Q8C2312yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2318yes—
184C2×#121C2312yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2314yes—
188C2×#121C2314yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C2318yes—
193C2×#121C2318yes—
194C2×#120C2314yes—
195C2×#120C2311yescharacteristic
196C2×#120C2311yescharacteristic
197C2×#120C2314yes—
198C2×#120C2318yes—
199C2×#120C2318yes—
200C4×#41—44no—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2318yes—
212C2×#117—44no—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2312yes—
218C2×#117C2311yescharacteristic
219C2×#117C2314yes—
220C2×#117C2311yescharacteristic
221C2×#117C2312yes—
222C2×#117C2311yescharacteristic
223C2×#117C2318yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2318yes—
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232#401C2318yes—
233#400C2314yes—
234#400C2314yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#399C2314yes—
239#399C2314yes—
240#399C2318yes—
241#399C2318yes—
242#398C2318yes—
243#398C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#395C2314yes—
255#395C2314yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2314yes—
263#394C2318yes—
264#394C2314yes—
265#394C2314yes—
266#394C2314yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#393C2314yes—
277#393C2314yes—
278#393C2318yes—
279#393C2318yes—
280#392C2314yes—
281#392C2314yes—
282#392C2318yes—
283#392C2318yes—
284#392C2314yes—
285#392C2314yes—
286#392C2318yes—
287#392C2318yes—
288#391C2314yes—
289#391C2312yes—
290#390C2314yes—
291#390C2314yes—
292#390C2318yes—
293#390C2314yes—
294#390C2314yes—
295#390C2318yes—
296#390C2314yes—
297#390C2312yes—
298#390C2314yes—
299#390C2318yes—
300#390C2314yes—
301#390C2318yes—
302#390C2314yes—
303#390C2318yes—
304#390C2318yes—
305#390C2314yes—
306#390C2318yes—
307#389C2314yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2318yes—
316#389C2314yes—
317#389C2314yes—
318#389C2318yes—
319#388C2318yes—
320#388C2314yes—
321#388C2314yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#386C2314yes—
354#386C2314yes—
355#386C2318yes—
356#386C2312yes—
357#386C2314yes—
358#386C2318yes—
359#386C2312yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2312yes—
378#385C2312yes—
379#385C2318yes—
380#385C2314yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#384C2312yes—
386#382C2312yes—
387#382C2314yes—
388#382C2318yes—
389#382C2312yes—
390#382C2312yes—
391#381C2312yes—
392#381C2318yes—
393#380C2318yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#379C2318yes—
401#379C2312yes—
402#379C2318yes—
403#379C2318yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2312yes—
419#376C2312yes—
420#376C2318yes—
421C2×#95C2314yes—
422C43C2312yes—
423C25C2411yescharacteristic
424C25C2414yes—
425C2×#41—42no—
426C2×#41—42no—
427C2×#41#4118yes—
428C22×Q8C2414yes—
429C22×Q8C2411yescharacteristic
430C22×D4—28no—
431C22×D4—44no—
432C22×D4—48no—
433C22×D4—44no—
434C22×D4—88no—
435C22×D4C2414yes—
436C22×D4C2412yes—
437C22×D4C2418yes—
438C22×D4C2412yes—
439C22×D4C2418yes—
440C22×D4C2418yes—
441C22×D4C2414yes—
442C22×D4C2418yes—
443C22×D4C2418yes—
444C22×D4C2414yes—
445C22×D4C2414yes—
446C22×D4C2411yescharacteristic
447C22×D4C2411yescharacteristic
448C22×D4C2411yescharacteristic
449C23×C4—24no—
450C23×C4—42no—
451C23×C4—42no—
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2418yes—
463C23×C4C2418yes—
464C23×C4C2414yes—
465C4⋊Q8—44no—
466#127—216no—
467#127—28no—
468#127—44no—
469#127—48no—
470#126—88no—
471#125—28no—
472#124—216no—
473#124—88no—
474#123—24no—
475#123—24no—
476#123—416no—
477#123—88no—
478C22⋊Q8—28no—
479C22⋊Q8—48no—
480C22⋊Q8—88no—
481#121—28no—
482#121—216no—
483#121—216no—
484#121—416no—
485#121—48no—
486#121—48no—
487#121—88no—
488#121—88no—
489#121—88no—
490#121—88no—
491#120—24no—
492#120—24no—
493#120—216no—
494#120—216no—
495#120—88no—
496#120—88no—
497C4×Q8—44no—
498C4×Q8—48no—
499C4×D4—28no—
500C4×D4—28no—
501C4×D4—48no—
502C4×D4—48no—
503C4×D4—44no—
504C4×D4—44no—
505C4×D4—44no—
506C4×D4—88no—
507C4×D4—88no—
508#117—24no—
509#117—28no—
510#117—28no—
511#117—44no—
512#117—42no—
513#117—42no—
514#117—42no—
515#117—42no—
516#117—48no—
517#117—44no—
518#117—88no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4—44no—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2414yes—
545C2×C22⋊C4—44no—
546C2×C22⋊C4—88no—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2411yescharacteristic
550C2×C22⋊C4C2411yescharacteristic
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C42—24no—
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—42no—
591C2×C42C2411yescharacteristic
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2418yes—
606C2×C42C2414yes—
607C2×C42C2411yescharacteristic
608#95C2414yes—
609#95C2418yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633C24—22no—
634C24—28no—
635C24—41no—
636C24—41no—
637C24—44no—
638C24—44no—
639C24—48no—
640C24—48no—
641C24—44no—
642C24C2512yes—
643C24C2518yes—
644C24C2511yescharacteristic
645C24C2511yescharacteristic
646C24C2511yescharacteristic
647#41—416no—
648C2×Q8—41no—
649C2×Q8—41no—
650C2×Q8—44no—
651C2×Q8—48no—
652C2×Q8C2×#4114yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—216no—
656C2×D4—216no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—216no—
661C2×D4—28no—
662C2×D4—41no—
663C2×D4—41no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—44no—
671C2×D4—48no—
672C2×D4—44no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—816no—
689C2×D4—832no—
690C2×D4C2×#4114yes—
691C2×D4C2×#4114yes—
692C2×D4C2×#4114yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—41no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—41no—
711C22×C4—44no—
712C22×C4—42no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—44no—
716C22×C4—48no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—48no—
720C22×C4—44no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—416no—
725C22×C4C2×#4114yes—
726C22×C4C2×#4114yes—
727C22×C4C2×#4114yes—
728C22×C4C2512yes—
729C22×C4C2518yes—
730C22×C4C2512yes—
731C22×C4C2514yes—
732C22×C4C2518yes—
733C22×C4C2514yes—
734C22×C4C2512yes—
735C22×C4C2512yes—
736C22×C4C2512yes—
737C22×C4C2518yes—
738C22×C4C2512yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2511yescharacteristic
742C22×C4C2512yes—
743C22×C4C2511yescharacteristic
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—216no—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—42no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—42no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—44no—
768C22⋊C4—28no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—28no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—44no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—44no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C42—24no—
809C42—28no—
810C42—22no—
811C42—24no—
812C42—22no—
813C42—22no—
814C42—24no—
815C42—24no—
816C42—24no—
817C42—24no—
818C42—42no—
819C42—44no—
820C42—44no—
821C42—48no—
822C42—48no—
823C42—44no—
824C42H(5,𝔽2)14yes—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—22no—
835C23—28no—
836C23—22no—
837C23—28no—
838C23—28no—
839C23—22no—
840C23—24no—
841C23—28no—
842C23—28no—
843C23—28no—
844C23—28no—
845C23—24no—
846C23—44no—
847C23—84no—
848C23—88no—
849C23—816no—
850C23—84no—
851C23—84no—
852C23—816no—
853C23—164no—
854C23—164no—
855C23C22×#4112yes—
856C23C22×#4112yes—
857C23C22×#4112yes—
858C23C2611yescharacteristic
859Q8—44no—
860Q8—88no—
861D4—44no—
862D4—44no—
863D4—44no—
864D4—416no—
865D4—88no—
866D4—816no—
867D4—84no—
868D4—84no—
869D4—816no—
870D4—816no—
871D4—88no—
872D4—88no—
873D4—168no—
874D4—168no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—24no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—28no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—24no—
910C2×C4—28no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—44no—
916C2×C4—48no—
917C2×C4—84no—
918C2×C4—84no—
919C2×C4—84no—
920C2×C4—816no—
921C2×C4—168no—
922C2×C4—164no—
923C2×C4C22×#4112yes—
924C2×C4C22×#4112yes—
925C2×C4C22×#4112yes—
926C2×C4C22×#4112yes—
927C2×C4C2×H(5,𝔽2)14yes—
928C2×C4C2×H(5,𝔽2)12yes—
929C2×C4#58512yes—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—48no—
944C22—42no—
945C22—48no—
946C22—48no—
947C22—42no—
948C22—48no—
949C22—48no—
950C22—44no—
951C22—48no—
952C22—44no—
953C22—48no—
954C22—88no—
955C22—1616no—
956C22C23×#4111yescharacteristic
957C22C22×H(5,𝔽2)11yescharacteristic
958C22C2×#58511yescharacteristic
959C22H(7,𝔽2)14yes—
960C4—22no—
961C4—22no—
962C4—22no—
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—48no—
968C4—42no—
969C4—42no—
970C4—44no—
971C4—42no—
972C4—48no—
973C4—44no—
974C4—48no—
975C4#350514yes—
976C2—42no—
977C2—42no—
978C2—42no—
979C2—82no—
980C2—88no—
981C2C2×#350511yescharacteristic
982C2#6285812yes—
983C2#6287412yes—
984C2#6288512yes—
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. #51869C2semidirect
2. #51865C2semidirect
3. #47621C2semidirect
4. #47096C2semidirect
5. #46807C2semidirect
6. #46548C2semidirect
7. #38214C2semidirect
8. #38206C2semidirect
9. #37893C2semidirect
10. #37889C2semidirect
11. #37710C2semidirect
12. #37694C2semidirect
13. #37523C2semidirect
14. #37284C2semidirect
15. #37269C2semidirect
16. #35334C2semidirect
17. #35295C2semidirect
18. #35272C2semidirect
19. #35261C2semidirect
20. #34415C2semidirect
21. #34065C2semidirect
24. C2×#533C22semidirect
25. C22×#127C22semidirect
28. C22×#117C22semidirect
29. #2860C22semidirect
31. #2856C22semidirect
32. #2851C22semidirect
33. #2851C22semidirect
34. #2847C22semidirect
35. #2826C22semidirect
36. #2824C22semidirect
37. #2803C22semidirect
38. #2801C22semidirect
39. #2787C22semidirect
41. #2778C22semidirect
42. #2778C22semidirect
43. #2761C22semidirect
44. #2760C22semidirect
45. #2753C22semidirect
46. #2753C22semidirect
47. #2752C22semidirect
48. #2736C22semidirect
49. #2730C22semidirect
50. #2723C22semidirect
51. #2709C22semidirect
52. #2709C22semidirect
53. #2703C22semidirect
55. #2686C22semidirect
57. #2681C22semidirect
59. #2676C22semidirect
61. #2670C22semidirect
62. #2669C22semidirect
64. #2668C22semidirect
65. #2663C22semidirect
66. #2649C22semidirect
67. #2647C22semidirect
68. #2641C22semidirect
69. #2629C22semidirect
70. #2628C22semidirect
71. #2628C22semidirect
72. #2624C22semidirect
73. #2624C22semidirect
76. #2619C22semidirect
77. #2610C22semidirect
78. #2597C22semidirect
79. #2581C22semidirect
81. #2564C22semidirect
82. #2564C22semidirect
83. #2559C22semidirect
84. #2559C22semidirect
85. #2548C22semidirect
86. #2543C22semidirect
88. #2529C22semidirect
89. #2528C22semidirect
90. #2526C22semidirect
91. #2513C22semidirect
92. #2509C22semidirect
93. #2494C22semidirect
94. #2491C22semidirect
96. #2482C22semidirect
97. #2479C22semidirect
98. #2476C22semidirect
99. #2476C22semidirect
101. #2471C22semidirect
102. #2470C22semidirect
103. #2467C22semidirect
104. #2463C22semidirect
105. #2458C22semidirect
106. #2455C22semidirect
107. #2452C22semidirect
108. #2445C22semidirect
109. #2444C22semidirect
110. #2443C22semidirect
112. #2426C22semidirect
113. #2424C22semidirect
114. #2420C22semidirect
115. #2416C22semidirect
116. #2414C22semidirect
117. #2414C22semidirect
121. #2408C22semidirect
122. #2405C22semidirect
123. #2379C22semidirect
124. #2375C22semidirect
125. #2372C22semidirect
126. #2363C22semidirect
127. #2361C22semidirect
128. #2358C22semidirect
129. #2346C22semidirect
130. D4×C22⋊C4C22semidirect
131. #2330C22semidirect
132. #2328C22semidirect
133. #2328C22semidirect
135. #2324C22semidirect
136. #2324C22semidirect
137. #2323C22semidirect
139. #2322C22semidirect
142. #2321C22semidirect
143. #2316C22semidirect
144. #2314C22semidirect
146. #2309C22semidirect
147. C4×#121C22semidirect
149. #2296C22semidirect
151. #2293C22semidirect
152. #2293C22semidirect
154. #2290C22semidirect
155. #2285C22semidirect
156. C2×#382C22semidirect
157. #2280C22semidirect
158. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#518692
#518652
#476212
#470962
#468072
#465482
#382142
#382062
#378932
#378892
#377102
#376942
#375232
#372842
#372692
#353342
#352952
#352722
#352612
#344152
#340652