Finite Group Databasebeta

← #7715455

Subgroups — #7715455

Order 512.

4490 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51720C218yesmaximal, complemented
2#51714C218yesmaximal, complemented
3#47452C214yesmaximal, complemented
4#47193C214yesmaximal, complemented
5#47183C214yesmaximal, complemented
6#46912C214yesmaximal, complemented
7#38215C214yesmaximal, complemented
8#38207C214yesmaximal, complemented
9#37894C212yesmaximal, complemented
10#37888C212yesmaximal, complemented
11#37709C212yesmaximal, complemented
12#37695C212yesmaximal, complemented
13#37526C212yesmaximal, complemented
14#37381C212yesmaximal, complemented
15#37374C212yesmaximal
16#35334C211yesmaximal, characteristic, complemented
17#35323C212yesmaximal, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35310C212yesmaximal, complemented
20#34413C212yesmaximal, complemented
21#34065C211yesmaximal, characteristic
22C2×#541C2212yes—
23C2×#536C2212yes—
24C2×#533C2211yescharacteristic, complemented
25C22×C4⋊Q8C2211yescharacteristic, complemented
26C2×#525C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2863C2214yescomplemented
30#2857C2212yes—
31#2857C2212yescomplemented
32#2851C2212yes—
33#2851C2212yescomplemented
34#2848C2214yes—
35#2835C2214yes—
36#2834C2214yes—
37#2802C2218yescomplemented
38#2788C2218yes—
39#2786C2218yes—
40#2781C2218yes—
41#2772C2218yes—
42#2772C2218yes—
43#2771C2214yes—
44#2770C2218yes—
45#2770C2218yescomplemented
46#2766C2218yescomplemented
47#2764C2214yes—
48#2759C2218yes—
49#2758C2218yescomplemented
50#2747C2218yescomplemented
51#2738C2218yescomplemented
52#2737C2218yes—
53#2736C2214yes—
54#2735C2214yes—
55#2729C2218yes—
56#2724C2214yes—
57#2717C2214yes—
58#2716C2218yes—
59#2713C2218yescomplemented
60#2708C2218yes—
61#2702C2218yes—
62#2697C2214yes—
63#2690C2218yescomplemented
64#2684C2214yes—
65#2666C2218yescomplemented
66#2655C2218yescomplemented
67#2647C2212yescomplemented
68#2642C2212yescomplemented
69#2629C2212yes—
70#2628C2212yes—
71#2628C2212yescomplemented
72#2625C2214yes—
73#2625C2214yes—
74#2621C2212yes—
75#2621C2212yes—
76#2621C2212yescomplemented
77#2606C2218yescomplemented
78#2590C2218yescomplemented
79#2586C2218yescomplemented
80#2581C2214yescomplemented
81#2580C2214yes—
82#2577C2218yes—
83#2569C2218yescomplemented
84#2564C2214yes—
85#2564C2214yescomplemented
86#2547C2214yes—
87#2546C2214yescomplemented
88#2533C2218yescomplemented
89#2532C2218yes—
90#2531C2218yes—
91#2530C2218yes—
92#2527C2218yescomplemented
93#2525C2218yes—
94#2525C2218yes—
95#2524C2218yescomplemented
96#2523C2214yes—
97#2517C2214yes—
98#2516C2218yes—
99#2514C2214yescomplemented
100#2510C2218yes—
101#2508C2214yescomplemented
102#2495C2214yes—
103#2495C2218yescomplemented
104#2492C2214yes—
105#2486C2214yes—
106#2486C2214yescomplemented
107#2485C2214yes—
108#2481C2218yes—
109#2480C2218yes—
110#2478C2218yes—
111#2475C2218yes—
112#2473C2218yes—
113#2473C2218yescomplemented
114#2469C2218yes—
115#2453C2218yescomplemented
116#2451C2214yescomplemented
117#2446C2214yescomplemented
118#2429C2214yes—
119#2421C2214yes—
120#2417C2214yes—
121#2415C2214yes—
122#2409C2214yes—
123#2381C2214yescomplemented
124#2376C2214yescomplemented
125#2374C2214yescomplemented
126#2369C2214yescomplemented
127#2362C2214yescomplemented
128#2360C2214yescomplemented
129#2347C2214yescomplemented
130Q8×C22⋊C4C2214yescomplemented
131#2337C2218yes—
132#2335C2218yes—
133#2330C2212yescomplemented
134#2327C2212yescomplemented
135#2324C2214yes—
136#2323C2214yes—
137#2323C2214yes—
138#2323C2214yes—
139#2322C2212yes—
140#2322C2212yes—
141#2321C2212yes—
142#2321C2212yes—
143#2316C2212yescomplemented
144#2314C2212yes—
145#2311C2212yes—
146#2310C2212yescomplemented
147C4×C22⋊Q8C2214yes—
148#2297C2211yescharacteristic
149#2296C2211yescharacteristic
150#2295C2214yescomplemented
151#2293C2212yes—
152#2293C2212yes—
153#2290C2212yes—
154#2290C2212yes—
155#2285C2211yescharacteristic, complemented
156C2×#382C2211yescharacteristic, complemented
157#2280C2211yescharacteristic
158C4×#117C2211yescharacteristic
159C22×#41C2311yescharacteristic
160C23×Q8C2312yes—
161C24×C4C2311yescharacteristic
162#541—48no—
163#536—216no—
164#533—44no—
165C2×C4⋊Q8—44no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×#126C2318yes—
172C2×#125C2312yes—
173C2×#125C2318yes—
174C2×#124C2314yes—
175#525—28no—
176C2×#123C2311yescharacteristic
177C2×#123C2311yescharacteristic
178C2×#123C2314yes—
179C2×#123C2314yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×#121C2312yes—
187C2×#120C2311yescharacteristic
188C2×#120C2311yescharacteristic
189C4×#41—44no—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2314yes—
194C2×C4×D4C2312yes—
195C2×C4×D4C2312yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×#117—44no—
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2312yes—
205C2×#117C2311yescharacteristic
206C2×#117C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2311yescharacteristic
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2314yes—
213C22×C22⋊C4C2312yes—
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218#401C2318yes—
219#400C2314yes—
220#400C2314yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#399C2314yes—
233#399C2314yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2314yes—
242#398C2318yes—
243#398C2314yes—
244#398C2314yes—
245#398C2314yes—
246#398C2318yes—
247#398C2318yes—
248#397C2318yes—
249#397C2314yes—
250#397C2318yes—
251#397C2314yes—
252#397C2318yes—
253#397C2314yes—
254#397C2314yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2314yes—
265#395C2314yes—
266#395C2318yes—
267#395C2318yes—
268#394C2318yes—
269#394C2318yes—
270#393C2314yes—
271#393C2314yes—
272#393C2318yes—
273#393C2318yes—
274#391C2314yes—
275#391C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2312yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2318yes—
283#391C2318yes—
284#391C2314yes—
285#391C2314yes—
286#391C2318yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2312yes—
291#389C2314yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#388C2318yes—
310#388C2314yes—
311#388C2314yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2314yes—
317#388C2314yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2314yes—
340#387C2314yes—
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#386C2314yes—
356#386C2314yes—
357#386C2312yes—
358#386C2312yes—
359#386C2314yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2312yes—
368#385C2312yes—
369#385C2314yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#384C2312yes—
376#383C2318yes—
377#383C2318yes—
378#383C2318yes—
379#383C2318yes—
380#382C2312yes—
381#382C2314yes—
382#382C2312yes—
383#382C2312yes—
384#382C2318yes—
385#381C2318yes—
386#381C2312yes—
387#380C2318yes—
388#380C2314yes—
389#380C2314yes—
390#380C2318yes—
391#380C2318yes—
392#380C2314yes—
393#380C2318yes—
394#380C2314yes—
395#380C2314yes—
396#380C2318yes—
397#380C2314yes—
398#379C2312yes—
399#379C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C22⋊C4C2318yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2312yes—
419#376C2312yes—
420#376C2318yes—
421C2×#95C2314yes—
422C43C2312yes—
423C25C2411yescharacteristic
424C2×#41—42no—
425C2×#41—42no—
426C2×#41#4118yes—
427C22×Q8—28no—
428C22×Q8—44no—
429C22×Q8—44no—
430C22×Q8C2414yes—
431C22×Q8C2414yes—
432C22×Q8C2414yes—
433C22×Q8C2411yescharacteristic
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2411yescharacteristic
437C22×D4C2411yescharacteristic
438C22×D4C2411yescharacteristic
439C23×C4—24no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2414yes—
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2414yes—
454C4⋊Q8—216no—
455C4⋊Q8—28no—
456C4⋊Q8—48no—
457C4⋊Q8—44no—
458C4⋊Q8—44no—
459#126—416no—
460#125—28no—
461#125—416no—
462#124—216no—
463#123—24no—
464#123—24no—
465#123—216no—
466#123—216no—
467C22⋊Q8—28no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—48no—
471C22⋊Q8—48no—
472C22⋊Q8—48no—
473#121—28no—
474#120—24no—
475#120—24no—
476C4×Q8—44no—
477C4×Q8—48no—
478C4×Q8—48no—
479C4×Q8—48no—
480C4×D4—28no—
481C4×D4—28no—
482C4×D4—44no—
483C4×D4—44no—
484C4×D4—44no—
485#117—24no—
486#117—28no—
487#117—28no—
488#117—44no—
489#117—42no—
490#117—42no—
491#117—42no—
492#117—42no—
493#117—48no—
494#117—44no—
495C2×C4⋊C4—44no—
496C2×C4⋊C4—44no—
497C2×C4⋊C4—48no—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C22⋊C4—44no—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2411yescharacteristic
534C2×C22⋊C4C2411yescharacteristic
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C42—24no—
559C2×C42—24no—
560C2×C42—24no—
561C2×C42—42no—
562C2×C42C2411yescharacteristic
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2411yescharacteristic
566C2×C42C2411yescharacteristic
567C2×C42C2412yes—
568C2×C42C2412yes—
569C2×C42C2414yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2414yes—
574C2×C42C2418yes—
575C2×C42C2418yes—
576C2×C42C2414yes—
577C2×C42C2414yes—
578C2×C42C2418yes—
579C2×C42C2418yes—
580C2×C42C2411yescharacteristic
581#95C2414yes—
582#95C2418yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2414yes—
601#95C2414yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618C24—22no—
619C24—41no—
620C24—41no—
621C24—44no—
622C24C2512yes—
623C24C2511yescharacteristic
624C24C2511yescharacteristic
625C24C2511yescharacteristic
626#41—416no—
627C2×Q8—28no—
628C2×Q8—28no—
629C2×Q8—28no—
630C2×Q8—28no—
631C2×Q8—41no—
632C2×Q8—41no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—48no—
637C2×Q8—816no—
638C2×Q8C2×#4114yes—
639C2×D4—24no—
640C2×D4—24no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—41no—
644C2×D4—41no—
645C2×D4—41no—
646C2×D4—41no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4C2×#4114yes—
650C2×D4C2×#4114yes—
651C2×D4C2×#4114yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—41no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—41no—
671C22×C4—44no—
672C22×C4—42no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—48no—
680C22×C4—416no—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2512yes—
685C22×C4C2512yes—
686C22×C4C2518yes—
687C22×C4C2512yes—
688C22×C4C2514yes—
689C22×C4C2518yes—
690C22×C4C2512yes—
691C22×C4C2514yes—
692C22×C4C2518yes—
693C22×C4C2512yes—
694C22×C4C2518yes—
695C22×C4C2512yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2511yescharacteristic
699C22×C4C2512yes—
700C22×C4C2511yescharacteristic
701C4⋊C4—24no—
702C4⋊C4—28no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—216no—
706C4⋊C4—216no—
707C4⋊C4—28no—
708C4⋊C4—216no—
709C4⋊C4—28no—
710C4⋊C4—216no—
711C4⋊C4—28no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—48no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—42no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—42no—
729C4⋊C4—48no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—28no—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—216no—
740C22⋊C4—216no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—48no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—42no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—44no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C42—24no—
761C42—28no—
762C42—22no—
763C42—24no—
764C42—22no—
765C42—22no—
766C42—24no—
767C42—24no—
768C42—24no—
769C42—24no—
770C42—42no—
771C42—48no—
772C42—44no—
773C42—48no—
774C42—44no—
775C42—44no—
776C42—48no—
777C42—48no—
778C42H(5,𝔽2)14yes—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—24no—
793C23—44no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23C22×#4112yes—
798C23C22×#4112yes—
799C23C22×#4112yes—
800C23C2611yescharacteristic
801Q8—44no—
802Q8—416no—
803Q8—88no—
804Q8—88no—
805D4—44no—
806D4—44no—
807D4—44no—
808D4—84no—
809D4—84no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—24no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—28no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—28no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—28no—
849C2×C4—28no—
850C2×C4—24no—
851C2×C4—48no—
852C2×C4—48no—
853C2×C4—44no—
854C2×C4—48no—
855C2×C4—84no—
856C2×C4—84no—
857C2×C4—88no—
858C2×C4—84no—
859C2×C4—164no—
860C2×C4C22×#4112yes—
861C2×C4C22×#4112yes—
862C2×C4C22×#4112yes—
863C2×C4C22×#4112yes—
864C2×C4C2×H(5,𝔽2)14yes—
865C2×C4C2×H(5,𝔽2)12yes—
866C2×C4#58512yes—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—44no—
883C22—44no—
884C22—88no—
885C22C23×#4111yescharacteristic
886C22C22×H(5,𝔽2)11yescharacteristic
887C22C2×#58511yescharacteristic
888C222−1+614yes—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—24no—
893C4—42no—
894C4—48no—
895C4—48no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—44no—
901C4—42no—
902C4—48no—
903C4—44no—
904C4—48no—
905C4#350514yes—
906C2—42no—
907C2—42no—
908C2—42no—
909C2—82no—
910C2C2×#350511yescharacteristic
911C2#6286112yes—
912C2#6288612yes—
913C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51720C2semidirect
2. #51714C2semidirect
3. #47452C2semidirect
4. #47193C2semidirect
5. #47183C2semidirect
6. #46912C2semidirect
7. #38215C2semidirect
8. #38207C2semidirect
9. #37894C2semidirect
10. #37888C2semidirect
11. #37709C2semidirect
12. #37695C2semidirect
13. #37526C2semidirect
14. #37381C2semidirect
16. #35334C2semidirect
17. #35323C2semidirect
18. #35316C2semidirect
19. #35310C2semidirect
20. #34413C2semidirect
24. C2×#533C22semidirect
25. C22×C4⋊Q8C22semidirect
29. #2863C22semidirect
31. #2857C22semidirect
33. #2851C22semidirect
37. #2802C22semidirect
45. #2770C22semidirect
46. #2766C22semidirect
49. #2758C22semidirect
50. #2747C22semidirect
51. #2738C22semidirect
59. #2713C22semidirect
63. #2690C22semidirect
65. #2666C22semidirect
66. #2655C22semidirect
67. #2647C22semidirect
68. #2642C22semidirect
71. #2628C22semidirect
76. #2621C22semidirect
77. #2606C22semidirect
78. #2590C22semidirect
79. #2586C22semidirect
80. #2581C22semidirect
83. #2569C22semidirect
85. #2564C22semidirect
87. #2546C22semidirect
88. #2533C22semidirect
92. #2527C22semidirect
95. #2524C22semidirect
99. #2514C22semidirect
101. #2508C22semidirect
103. #2495C22semidirect
106. #2486C22semidirect
113. #2473C22semidirect
115. #2453C22semidirect
116. #2451C22semidirect
117. #2446C22semidirect
123. #2381C22semidirect
124. #2376C22semidirect
125. #2374C22semidirect
126. #2369C22semidirect
127. #2362C22semidirect
128. #2360C22semidirect
129. #2347C22semidirect
130. Q8×C22⋊C4C22semidirect
133. #2330C22semidirect
134. #2327C22semidirect
143. #2316C22semidirect
146. #2310C22semidirect
150. #2295C22semidirect
155. #2285C22semidirect
156. C2×#382C22semidirect

Maximal subgroups

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

subgroupindex
#517202
#517142
#474522
#471932
#471832
#469122
#382152
#382072
#378942
#378882
#377092
#376952
#375262
#373812
#373742
#353342
#353232
#353162
#353102
#344132
#340652