Finite Group Databasebeta

← #7655843

Subgroups — #7655843

Order 512.

5690 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42699C214yesmaximal, complemented
2#42529C214yesmaximal, complemented
3#41750C218yesmaximal, complemented
4#41094C218yesmaximal, complemented
5#39768C212yesmaximal, complemented
6#39415C214yesmaximal, complemented
7#39383C212yesmaximal, complemented
8#37745C214yesmaximal, complemented
9#37536C212yesmaximal, complemented
10#37459C214yesmaximal, complemented
11#36580C212yesmaximal, complemented
12#36101C212yesmaximal, complemented
13#35930C214yesmaximal, complemented
14#35860C214yesmaximal, complemented
15#35166C211yesmaximal, characteristic, complemented
16#35003C212yesmaximal, complemented
17#34595C211yesmaximal, characteristic, complemented
18#34575C212yesmaximal, complemented
19#34236C212yesmaximal, complemented
20C2×#2367C211yesmaximal, characteristic, complemented
21C2×#559C2212yescomplemented
22C2×#550C2212yes—
23C2×#538C2214yes—
24C2×#537C2212yes—
25C2×#537C2212yes—
26C2×#532C2212yes—
27C22×#124C2211yescharacteristic
28C2×#525C2214yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31#2856C2212yes—
32#2856C2212yes—
33#2850C2214yes—
34#2847C2214yes—
35#2837C2218yescomplemented
36#2828C2218yescomplemented
37#2819C2214yes—
38#2819C2214yes—
39#2808C2214yescomplemented
40#2804C2214yescomplemented
41#2751C2218yescomplemented
42#2733C2214yes—
43#2714C2218yes—
44#2703C2218yescomplemented
45#2702C2218yescomplemented
46#2700C2218yescomplemented
47#2699C2218yescomplemented
48#2692C2218yescomplemented
49#2688C2218yescomplemented
50#2687C2218yescomplemented
51#2682C2214yes—
52#2671C2218yescomplemented
53#2666C2214yescomplemented
54#2666C2214yescomplemented
55#2663C2218yescomplemented
56#2661C2218yescomplemented
57#2661C2218yescomplemented
58#2659C2211yescharacteristic
59#2659C2211yescharacteristic
60#2657C2214yes—
61#2656C2212yes—
62#2656C2212yes—
63#2651C2218yescomplemented
64#2649C2218yescomplemented
65#2646C2212yes—
66#2640C2214yes—
67#2639C2214yes—
68#2635C2218yescomplemented
69#2631C2218yes—
70#2627C2212yes—
71#2627C2212yes—
72#2617C2214yes—
73#2617C2214yes—
74#2617C2214yes—
75#2592C2214yescomplemented
76#2592C2214yescomplemented
77#2582C2212yescomplemented
78#2580C2214yescomplemented
79#2560C2218yescomplemented
80#2555C2218yescomplemented
81#2555C2218yescomplemented
82#2553C2218yescomplemented
83#2548C2214yes—
84#2548C2212yescomplemented
85#2544C2214yes—
86#2544C2214yes—
87#2544C2214yescomplemented
88#2543C2218yescomplemented
89#2542C2214yescomplemented
90#2541C2212yes—
91#2541C2214yes—
92#2541C2214yescomplemented
93#2540C2218yescomplemented
94#2538C2212yes—
95#2521C2218yescomplemented
96#2516C2218yescomplemented
97#2512C2214yes—
98#2511C2214yescomplemented
99#2488C2218yescomplemented
100#2477C2218yescomplemented
101#2464C2218yescomplemented
102#2464C2218yescomplemented
103#2464C2218yescomplemented
104#2458C2218yescomplemented
105#2456C2218yes—
106#2450C2218yescomplemented
107#2448C2214yescomplemented
108#2447C2214yescomplemented
109#2445C2214yes—
110#2445C2214yes—
111#2444C2218yes—
112#2443C2218yes—
113#2436C2214yes—
114#2433C2214yes—
115#2430C2218yescomplemented
116#2424C2218yes—
117#2424C2218yes—
118#2414C2214yes—
119#2407C2214yes—
120#2404C2218yes—
121#2402C2214yescomplemented
122#2399C2214yescomplemented
123#2395C2218yescomplemented
124#2388C2218yescomplemented
125#2369C2212yescomplemented
126#2369C2212yescomplemented
127#2367C2214yes—
128#2367C2218yes—
129#2367C2214yes—
130#2367C2214yescomplemented
131#2366C2214yes—
132#2366C2212yescomplemented
133#2366C2212yescomplemented
134#2361C2214yes—
135#2361C2214yes—
136#2357C2214yescomplemented
137#2355C2212yescomplemented
138#2354C2212yes—
139#2349C2214yescomplemented
140#2339C2218yes—
141#2337C2218yescomplemented
142#2325C2214yes—
143#2319C2214yescomplemented
144C4×C22⋊Q8C2212yes—
145C4×C22⋊Q8C2212yes—
146C4×#121C2214yes—
147C4×#121C2214yes—
148C4×#121C2214yes—
149C2×#391C2211yescharacteristic
150C2×#390C2211yescharacteristic
151C2×#388C2212yes—
152C2×#388C2212yes—
153C2×#385C2212yes—
154#2283C2212yes—
155#2275C2214yescomplemented
156C2×C4×C4⋊C4C2211yescharacteristic
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2212yes—
159C22×#41C2314yes—
160C22×#41C2314yes—
161C23×Q8C2311yescharacteristic
162C23×D4C2311yescharacteristic
163C24×C4C2312yes—
164#559—48no—
165#550—48no—
166#538—416no—
167#537—48no—
168#537—48no—
169#532—216no—
170C2×C4⋊Q8C2312yes—
171C2×#127C2312yes—
172C2×#127C2312yes—
173C2×#127C2312yes—
174C2×#127C2314yes—
175C2×#127C2314yes—
176C2×#126C2318yes—
177C2×#124—28no—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2314yes—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2318yes—
185#525—416no—
186C2×#123C2318yes—
187C2×#123C2318yes—
188C2×#123C2318yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2318yes—
203C2×#121C2318yes—
204C2×#121C2318yes—
205C2×#121C2318yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#120C2318yes—
209C2×#120C2318yes—
210C2×C4×Q8—44no—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2314yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×D4—44no—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2318yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×#117C2314yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246#400C2314yes—
247#400C2318yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2318yes—
252#399C2318yes—
253#399C2318yes—
254#399C2318yes—
255#398C2314yes—
256#398C2314yes—
257#398C2318yes—
258#398C2314yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#398C2314yes—
263#398C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#396C2318yes—
272#396C2318yes—
273#395C2314yes—
274#395C2314yes—
275#395C2314yes—
276#395C2314yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#392C2318yes—
296#392C2318yes—
297#392C2318yes—
298#392C2318yes—
299#392C2318yes—
300#392C2318yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#391C2318yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2314yes—
314#391C2312yes—
315#390C2318yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2318yes—
333#389C2314yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
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#388C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2314yes—
360#387C2314yes—
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#386C2318yes—
376#386C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2314yes—
385#384C2312yes—
386#384C2312yes—
387#383C2314yes—
388#382C2312yes—
389#382C2312yes—
390#382C2314yes—
391#381C2318yes—
392#381C2314yes—
393#381C2318yes—
394#380C2318yes—
395#380C2312yes—
396#380C2314yes—
397#380C2314yes—
398#380C2312yes—
399#380C2312yes—
400#380C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424#376C2314yes—
425C2×#95C2312yes—
426C2×#95C2312yes—
427C2×#95C2318yes—
428C2×#95C2311yescharacteristic
429C2×#95C2311yescharacteristic
430C2×#95C2312yes—
431C25C2412yes—
432C2×#41—216no—
433C2×#41—48no—
434C2×#41—48no—
435C2×#41—48no—
436C2×#41—48no—
437C2×#41—84no—
438C22×Q8—24no—
439C22×Q8—42no—
440C22×Q8—42no—
441C22×Q8C2412yes—
442C22×Q8C2412yes—
443C22×Q8C2412yes—
444C22×Q8C2412yes—
445C22×Q8C2414yes—
446C22×D4—24no—
447C22×D4—42no—
448C22×D4—42no—
449C22×D4C2414yes—
450C22×D4C2418yes—
451C22×D4C2412yes—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2418yes—
458C22×D4C2418yes—
459C22×D4C2418yes—
460C22×D4C2418yes—
461C22×D4C2414yes—
462C22×D4C2414yes—
463C23×C4—28no—
464C23×C4—44no—
465C23×C4—82no—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2418yes—
475C23×C4C2418yes—
476C23×C4C2414yes—
477C23×C4C2418yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C4⋊Q8—28no—
482#127—28no—
483#127—48no—
484#127—44no—
485#127—48no—
486#127—44no—
487#126—416no—
488#124—216no—
489#124—216no—
490#124—216no—
491#124—48no—
492#124—48no—
493#124—48no—
494#124—416no—
495#123—416no—
496#123—416no—
497#123—416no—
498C22⋊Q8—28no—
499C22⋊Q8—28no—
500C22⋊Q8—416no—
501C22⋊Q8—416no—
502C22⋊Q8—48no—
503#121—216no—
504#121—216no—
505#121—216no—
506#121—216no—
507#121—416no—
508#121—48no—
509#121—416no—
510#121—416no—
511#121—416no—
512#121—48no—
513#121—48no—
514#121—48no—
515#121—88no—
516#121—84no—
517#120—416no—
518#120—416no—
519C4×Q8—28no—
520C4×Q8—44no—
521C4×Q8—44no—
522C4×Q8—48no—
523C4×Q8—44no—
524C4×D4—28no—
525C4×D4—216no—
526C4×D4—216no—
527C4×D4—216no—
528C4×D4—44no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—416no—
533C4×D4—416no—
534C4×D4—416no—
535C4×D4—84no—
536C4×D4—84no—
537#117—48no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2411yescharacteristic
576C2×C22⋊C4—28no—
577C2×C22⋊C4—28no—
578C2×C22⋊C4—28no—
579C2×C22⋊C4—44no—
580C2×C22⋊C4—82no—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C42—42no—
610C2×C42—44no—
611C2×C42—42no—
612C2×C42—82no—
613C2×C42#4118yescomplemented
614C2×C42C2412yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2412yes—
619C2×C42C2418yes—
620C2×C42C2412yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—24no—
657C24—24no—
658C24—24no—
659C24—42no—
660C24—42no—
661C24—42no—
662C24—42no—
663C24C2514yes—
664C24C2518yes—
665C24C2511yescharacteristic
666#41—832no—
667#41—832no—
668C2×Q8—24no—
669C2×Q8—24no—
670C2×Q8—28no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8—42no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—42no—
683C2×Q8—416no—
684C2×D4—216no—
685C2×D4—216no—
686C2×D4—216no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—24no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—416no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—48no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—216no—
740C22×C4—216no—
741C22×C4—28no—
742C22×C4—41no—
743C22×C4—42no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—41no—
748C22×C4—44no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—42no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—42no—
755C22×C4—41no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—48no—
762C22×C4—44no—
763C22×C4—41no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—816no—
768C22×C4C2×#4114yes—
769C22×C4C2×#4114yes—
770C22×C4C2×#4114yes—
771C22×C4H(5,𝔽2)14yes—
772C22×C4H(5,𝔽2)14yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2518yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—24no—
793C4⋊C4—22no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—42no—
805C4⋊C4—44no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—42no—
809C4⋊C4—44no—
810C4⋊C4—42no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—42no—
821C4⋊C4—44no—
822C4⋊C4H(5,𝔽2)14yes—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—216no—
827C22⋊C4—216no—
828C22⋊C4—216no—
829C22⋊C4—216no—
830C22⋊C4—28no—
831C22⋊C4—216no—
832C22⋊C4—216no—
833C22⋊C4—216no—
834C22⋊C4—44no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C42—24no—
852C42—28no—
853C42—24no—
854C42—28no—
855C42—28no—
856C42—42no—
857C42—42no—
858C42—44no—
859C42—44no—
860C42—44no—
861C42—48no—
862C42—48no—
863C42C2×#4118yes—
864C42C2×#4118yes—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—24no—
870C23—28no—
871C23—24no—
872C23—28no—
873C23—28no—
874C23—28no—
875C23—24no—
876C23—24no—
877C23—28no—
878C23—24no—
879C23—28no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—48no—
884C23—48no—
885C23—48no—
886C23—84no—
887C23—84no—
888C23—84no—
889C23—84no—
890C23C22×#4112yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2×H(5,𝔽2)12yes—
893C23C2611yescharacteristic
894Q8—48no—
895Q8—48no—
896Q8—48no—
897Q8—84no—
898Q8—88no—
899D4—416no—
900D4—48no—
901D4—432no—
902D4—416no—
903D4—48no—
904D4—88no—
905D4—88no—
906D4—88no—
907D4—816no—
908D4—816no—
909D4—164no—
910D4—164no—
911D4—168no—
912D4—168no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—28no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—44no—
960C2×C4—416no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—88no—
964C2×C4—816no—
965C2×C4—816no—
966C2×C4—82no—
967C2×C4—82no—
968C2×C4—84no—
969C2×C4—168no—
970C2×C4C22×#4114yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4114yes—
973C2×C4C22×#4112yes—
974C2×C4C2×H(5,𝔽2)14yes—
975C2×C4C2×H(5,𝔽2)14yes—
976C2×C4C2×H(5,𝔽2)14yes—
977C2×C4C2×H(5,𝔽2)12yes—
978C2×C4#58512yes—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—48no—
986C22—44no—
987C22—48no—
988C22—44no—
989C22—44no—
990C22—48no—
991C22—48no—
992C22—44no—
993C22—44no—
994C22—48no—
995C22—44no—
996C22—48no—
997C22—48no—
998C22—44no—
999C22—816no—
1000C22#350814yes—
1001C22C23×#4111yescharacteristic
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C22×H(5,𝔽2)11yescharacteristic
1004C22C22×H(5,𝔽2)11yescharacteristic
1005C22C2×#58511yescharacteristic
1006C22H(7,𝔽2)11yescharacteristic
1007C222−1+611yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—24no—
1013C4—22no—
1014C4—48no—
1015C4—42no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—44no—
1024C4#346014yes—
1025C2—24no—
1026C2—88no—
1027C2—84no—
1028C2C2×#346011yescharacteristic
1029C2C2×#350811yescharacteristic
1030C2#6284511yescharacteristic
1031C2#6289211yescharacteristic
1032C2#6289511yescharacteristic
1033C2#6296011yescharacteristic
1034C2#6296111yescharacteristic
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. #42699C2semidirect
2. #42529C2semidirect
3. #41750C2semidirect
4. #41094C2semidirect
5. #39768C2semidirect
6. #39415C2semidirect
7. #39383C2semidirect
8. #37745C2semidirect
9. #37536C2semidirect
10. #37459C2semidirect
11. #36580C2semidirect
12. #36101C2semidirect
13. #35930C2semidirect
14. #35860C2semidirect
15. #35166C2semidirect
16. #35003C2semidirect
17. #34595C2semidirect
18. #34575C2semidirect
19. #34236C2semidirect
20. C2×#2367C2semidirect
21. C2×#559C22semidirect
35. #2837C22semidirect
36. #2828C22semidirect
39. #2808C22semidirect
40. #2804C22semidirect
41. #2751C22semidirect
44. #2703C22semidirect
45. #2702C22semidirect
46. #2700C22semidirect
47. #2699C22semidirect
48. #2692C22semidirect
49. #2688C22semidirect
50. #2687C22semidirect
52. #2671C22semidirect
53. #2666C22semidirect
54. #2666C22semidirect
55. #2663C22semidirect
56. #2661C22semidirect
57. #2661C22semidirect
63. #2651C22semidirect
64. #2649C22semidirect
68. #2635C22semidirect
75. #2592C22semidirect
76. #2592C22semidirect
77. #2582C22semidirect
78. #2580C22semidirect
79. #2560C22semidirect
80. #2555C22semidirect
81. #2555C22semidirect
82. #2553C22semidirect
84. #2548C22semidirect
87. #2544C22semidirect
88. #2543C22semidirect
89. #2542C22semidirect
92. #2541C22semidirect
93. #2540C22semidirect
95. #2521C22semidirect
96. #2516C22semidirect
98. #2511C22semidirect
99. #2488C22semidirect
100. #2477C22semidirect
101. #2464C22semidirect
102. #2464C22semidirect
103. #2464C22semidirect
104. #2458C22semidirect
106. #2450C22semidirect
107. #2448C22semidirect
108. #2447C22semidirect
115. #2430C22semidirect
121. #2402C22semidirect
122. #2399C22semidirect
123. #2395C22semidirect
124. #2388C22semidirect
125. #2369C22semidirect
126. #2369C22semidirect
130. #2367C22semidirect
132. #2366C22semidirect
133. #2366C22semidirect
136. #2357C22semidirect
137. #2355C22semidirect
139. #2349C22semidirect
141. #2337C22semidirect
143. #2319C22semidirect
155. #2275C22semidirect
613. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#426992
#425292
#417502
#410942
#397682
#394152
#393832
#377452
#375362
#374592
#365802
#361012
#359302
#358602
#351662
#350032
#345952
#345752
#342362
C2×#23672