Finite Group Databasebeta

← #7652075

Subgroups — #7652075

Order 512.

5338 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42853C214yesmaximal, complemented
2#42851C214yesmaximal, complemented
3#42844C214yesmaximal, complemented
4#42834C214yesmaximal, complemented
5#42319C218yesmaximal, complemented
6#40190C214yesmaximal, complemented
7#40098C214yesmaximal, complemented
8#39663C214yesmaximal, complemented
9#39654C214yesmaximal, complemented
10#38397C218yesmaximal, complemented
11#35672C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35662C211yesmaximal, characteristic, complemented
15#35633C211yesmaximal, characteristic
16#35619C211yesmaximal, characteristic, complemented
17#35320C211yesmaximal, characteristic, complemented
18#35313C211yesmaximal, characteristic, complemented
19#35242C211yesmaximal, characteristic
20#34814C211yesmaximal, characteristic, complemented
21#34813C211yesmaximal, characteristic
22C2×#2434C211yesmaximal, characteristic, complemented
23#34276C211yesmaximal, characteristic, complemented
24#34209C211yesmaximal, characteristic, complemented
25#34173C211yesmaximal, characteristic, complemented
26C24×Q8C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39#2863C2214yescomplemented
40#2862C2214yescomplemented
41#2849C2214yes—
42#2833C2218yescomplemented
43#2831C2218yescomplemented
44#2806C2218yescomplemented
45#2805C2218yescomplemented
46#2788C2218yes—
47#2788C2218yescomplemented
48#2787C2218yes—
49#2781C2218yes—
50#2780C2218yes—
51#2775C2218yescomplemented
52#2774C2218yescomplemented
53#2774C2218yescomplemented
54#2770C2218yes—
55#2768C2218yes—
56#2759C2218yescomplemented
57#2750C2218yes—
58#2745C2218yescomplemented
59#2715C2218yes—
60#2666C2218yescomplemented
61#2666C2218yescomplemented
62#2665C2218yescomplemented
63#2652C2218yes—
64#2650C2218yescomplemented
65#2649C2218yes—
66#2645C2214yescomplemented
67#2642C2214yescomplemented
68#2614C2214yes—
69#2597C2218yes—
70#2589C2218yes—
71#2587C2218yes—
72#2586C2218yescomplemented
73#2582C2214yescomplemented
74#2581C2214yescomplemented
75#2576C2218yes—
76#2574C2218yescomplemented
77#2568C2214yescomplemented
78#2568C2214yescomplemented
79#2546C2212yescomplemented
80#2546C2214yescomplemented
81#2546C2212yescomplemented
82#2545C2212yescomplemented
83#2545C2214yescomplemented
84#2545C2212yescomplemented
85#2534C2214yes—
86#2514C2214yescomplemented
87#2511C2214yescomplemented
88#2503C2218yes—
89#2503C2212yescomplemented
90#2502C2212yescomplemented
91#2499C2212yescomplemented
92#2499C2212yescomplemented
93#2497C2212yes—
94#2496C2212yes—
95#2495C2212yes—
96#2494C2212yes—
97#2493C2214yes—
98#2493C2218yes—
99#2492C2212yes—
100#2491C2212yes—
101#2490C2212yes—
102#2489C2212yes—
103#2488C2214yes—
104#2486C2214yes—
105#2484C2214yes—
106#2482C2214yes—
107#2480C2214yes—
108#2472C2214yes—
109#2453C2214yescomplemented
110#2451C2214yescomplemented
111#2447C2214yescomplemented
112#2446C2214yescomplemented
113#2438C2218yes—
114#2436C2214yes—
115#2434C2214yes—
116#2434C2214yes—
117#2434C2214yes—
118#2434C2214yes—
119#2434C2214yes—
120#2429C2214yes—
121#2429C2214yescomplemented
122#2429C2214yescomplemented
123#2429C2214yescomplemented
124#2429C2214yescomplemented
125#2427C2214yes—
126#2423C2214yes—
127#2423C2214yes—
128#2421C2214yes—
129#2421C2214yes—
130#2419C2218yes—
131#2417C2214yes—
132#2415C2214yes—
133#2413C2218yes—
134#2413C2218yes—
135#2409C2214yes—
136#2409C2214yes—
137#2401C2214yes—
138#2398C2214yes—
139C2×#395C2214yes—
140#2365C2214yescomplemented
141#2365C2214yescomplemented
142#2362C2214yescomplemented
143#2360C2214yescomplemented
144#2359C2218yes—
145#2344C2218yes—
146Q8×C22⋊C4C2214yes—
147Q8×C22⋊C4C2214yes—
148Q8×C22⋊C4C2214yes—
149Q8×C22⋊C4C2214yes—
150#2337C2218yes—
151#2334C2218yes—
152#2327C2212yescomplemented
153#2327C2212yescomplemented
154#2327C2212yescomplemented
155#2326C2212yescomplemented
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2316C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2214yes—
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166C4×C4⋊Q8C2212yescomplemented
167C4×C4⋊Q8C2212yescomplemented
168C4×C4⋊Q8C2212yescomplemented
169C4×#126C2214yes—
170C4×#124C2214yes—
171C4×#124C2212yescomplemented
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#385C2214yes—
179#2285C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2214yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8—28no—
189C23×Q8—44no—
190C23×Q8—44no—
191C23×Q8C2311yescharacteristic
192C23×Q8C2311yescharacteristic
193C23×Q8C2311yescharacteristic
194C23×Q8C2312yes—
195C23×Q8C2314yes—
196C23×Q8C2314yes—
197C24×C4C2311yescharacteristic
198C24×C4C2312yes—
199#536—28no—
200#536—44no—
201#536—44no—
202#533—44no—
203C2×C4⋊Q8—28no—
204C2×C4⋊Q8—44no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×#126C2314yes—
216C2×#125C2312yes—
217C2×#124C2312yes—
218C2×#124C2314yes—
219C2×#124C2312yes—
220C2×#124C2312yes—
221#525—44no—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2312yes—
225C2×#123C2314yes—
226C2×C22⋊Q8—44no—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×#121C2312yes—
236C2×#120C2312yes—
237#520—44no—
238#519—44no—
239#519—44no—
240#519—44no—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2312yes—
274C22×C42C2311yescharacteristic
275C22×C42C2311yescharacteristic
276#401C2318yes—
277#401C2314yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2314yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2314yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#394C2314yes—
326#394C2318yes—
327#394C2314yes—
328#393C2318yes—
329#393C2314yes—
330#393C2318yes—
331#393C2314yes—
332#391C2311yescharacteristic
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2314yes—
342#391C2318yes—
343#391C2318yes—
344#391C2314yes—
345#391C2314yes—
346#391C2318yes—
347#391C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2318yes—
355#391C2318yes—
356#391C2314yes—
357#391C2312yes—
358#391C2318yes—
359#391C2311yescharacteristic
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2314yes—
364#391C2312yes—
365#390C2311yescharacteristic
366#390C2314yes—
367#390C2312yes—
368#390C2311yescharacteristic
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2312yes—
385#389C2312yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#386C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2312yes—
441#383C2314yes—
442#383C2318yes—
443#382C2318yes—
444#382C2318yes—
445#382C2312yes—
446#382C2312yes—
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2314yes—
450#381C2314yes—
451#381C2314yes—
452#381C2312yes—
453#381C2312yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2314yes—
458#381C2318yes—
459#381C2312yes—
460#380C2314yes—
461#380C2318yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2318yes—
467#380C2318yes—
468#380C2314yes—
469#380C2312yes—
470#380C2312yes—
471#379C2312yes—
472#379C2312yes—
473#379C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500#376C2312yes—
501#376C2312yes—
502C2×#95C2314yes—
503C2×#95C2312yes—
504C2×#95C2314yes—
505C43C2312yes—
506C43C2312yes—
507C25C2411yescharacteristic
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C22×Q8—216no—
512C22×Q8—216no—
513C22×Q8—24no—
514C22×Q8—28no—
515C22×Q8—24no—
516C22×Q8—24no—
517C22×Q8—24no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8—44no—
523C22×Q8—44no—
524C22×Q8—48no—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8—464no—
529C22×Q8#4118yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×Q8C2418yes—
539C22×D4C2412yes—
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C23×C4—28no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4—44no—
547C23×C4—44no—
548C23×C4C2412yes—
549C23×C4C2411yescharacteristic
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2418yes—
559C23×C4C2414yes—
560C23×C4C2411yescharacteristic
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—216no—
564C4⋊Q8—28no—
565C4⋊Q8—44no—
566C4⋊Q8—48no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569C4⋊Q8—44no—
570C4⋊Q8—44no—
571#126—216no—
572#125—44no—
573#124—28no—
574#124—216no—
575#124—44no—
576#124—44no—
577#123—216no—
578#123—44no—
579#123—48no—
580#123—48no—
581C22⋊Q8—216no—
582C22⋊Q8—48no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—48no—
589#121—44no—
590#120—44no—
591C4×Q8—48no—
592C4×Q8—44no—
593C4×Q8—44no—
594C4×Q8—44no—
595C4×Q8—44no—
596C4×Q8—48no—
597C4×Q8—44no—
598C4×Q8—44no—
599C4×Q8—44no—
600C4×Q8—44no—
601C4×Q8—48no—
602C4×Q8—44no—
603C4×D4—44no—
604C4×D4—48no—
605C4×D4—48no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—24no—
613#117—48no—
614#117—48no—
615#117—48no—
616#117—44no—
617C2×C4⋊C4—216no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—44no—
620C2×C4⋊C4—44no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C22⋊C4—28no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2414yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24—22no—
762C24—24no—
763C24—22no—
764C24—22no—
765C24—42no—
766C24C2512yes—
767C24C2512yes—
768C24C2511yescharacteristic
769#41—416no—
770C2×Q8—232no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—216no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—28no—
792C2×Q8—48no—
793C2×Q8—48no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8—432no—
797C2×Q8—464no—
798C2×Q8—464no—
799C2×Q8—416no—
800C2×Q8—416no—
801C2×Q8C2×#4118yes—
802C2×Q8C2×#4118yes—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—28no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—44no—
811C2×D4—44no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—22no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—22no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—216no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—48no—
845C22×C4—432no—
846C22×C4—416no—
847C22×C4C2×#4118yes—
848C22×C4C2×#4114yes—
849C22×C4H(5,𝔽2)14yes—
850C22×C4H(5,𝔽2)14yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C4⋊C4—216no—
874C4⋊C4—216no—
875C4⋊C4—24no—
876C4⋊C4—216no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—216no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C42−1+418yes—
942C42—22no—
943C42—24no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—22no—
948C42—22no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—28no—
956C42—28no—
957C42—44no—
958C42—44no—
959C42—44no—
960C42—44no—
961C42—44no—
962C42—48no—
963C42—44no—
964C42—44no—
965C23—22no—
966C23—22no—
967C23—28no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—48no—
980C23—48no—
981C23—44no—
982C23—44no—
983C23C22×#4112yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2×H(5,𝔽2)12yes—
986C23C2×2−1+414yes—
987C23C2611yescharacteristic
988Q8—216no—
989Q8—216no—
990Q8—432no—
991Q8—48no—
992Q8—48no—
993Q8—48no—
994Q8—48no—
995Q8—44no—
996Q8—88no—
997D4—48no—
998D4—44no—
999D4—88no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—216no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—432no—
1054C2×C4—44no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—84no—
1061C2×C4—164no—
1062C2×C4#538116yes—
1063C2×C4C22×#4118yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4C2×H(5,𝔽2)12yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×2−1+414yes—
1071C2×C4C2×2−1+414yes—
1072C22—24no—
1073C22—22no—
1074C22—22no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—416no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—44no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—44no—
1089C22C2×#53814yes—
1090C22C23×#4111yescharacteristic
1091C22C22×H(5,𝔽2)11yescharacteristic
1092C22C22×H(5,𝔽2)11yescharacteristic
1093C22C22×2−1+412yes—
1094C222−1+612yes—
1095C4—24no—
1096C4—28no—
1097C4—24no—
1098C4—44no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—44no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4—42no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4C2×#53814yes—
1116C4C2×#53814yes—
1117C2—24no—
1118C2—44no—
1119C2—82no—
1120C2C22×#53811yescharacteristic
1121C2#6283311yescharacteristic
1122C2#6288711yescharacteristic
1123C2#6294212yes—
1124C2#6299812yes—
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. #42853C2semidirect
2. #42851C2semidirect
3. #42844C2semidirect
4. #42834C2semidirect
5. #42319C2semidirect
6. #40190C2semidirect
7. #40098C2semidirect
8. #39663C2semidirect
9. #39654C2semidirect
10. #38397C2semidirect
11. #35672C2semidirect
12. #35667C2semidirect
13. #35667C2semidirect
14. #35662C2semidirect
16. #35619C2semidirect
17. #35320C2semidirect
18. #35313C2semidirect
20. #34814C2semidirect
22. C2×#2434C2semidirect
23. #34276C2semidirect
24. #34209C2semidirect
25. #34173C2semidirect
39. #2863C22semidirect
40. #2862C22semidirect
42. #2833C22semidirect
43. #2831C22semidirect
44. #2806C22semidirect
45. #2805C22semidirect
47. #2788C22semidirect
51. #2775C22semidirect
52. #2774C22semidirect
53. #2774C22semidirect
56. #2759C22semidirect
58. #2745C22semidirect
60. #2666C22semidirect
61. #2666C22semidirect
62. #2665C22semidirect
64. #2650C22semidirect
66. #2645C22semidirect
67. #2642C22semidirect
72. #2586C22semidirect
73. #2582C22semidirect
74. #2581C22semidirect
76. #2574C22semidirect
77. #2568C22semidirect
78. #2568C22semidirect
79. #2546C22semidirect
80. #2546C22semidirect
81. #2546C22semidirect
82. #2545C22semidirect
83. #2545C22semidirect
84. #2545C22semidirect
86. #2514C22semidirect
87. #2511C22semidirect
89. #2503C22semidirect
90. #2502C22semidirect
91. #2499C22semidirect
92. #2499C22semidirect
109. #2453C22semidirect
110. #2451C22semidirect
111. #2447C22semidirect
112. #2446C22semidirect
121. #2429C22semidirect
122. #2429C22semidirect
123. #2429C22semidirect
124. #2429C22semidirect
140. #2365C22semidirect
141. #2365C22semidirect
142. #2362C22semidirect
143. #2360C22semidirect
152. #2327C22semidirect
153. #2327C22semidirect
154. #2327C22semidirect
155. #2326C22semidirect
166. C4×C4⋊Q8C22semidirect
167. C4×C4⋊Q8C22semidirect
168. C4×C4⋊Q8C22semidirect
171. C4×#124C22semidirect

Maximal subgroups

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

subgroupindex
#428532
#428512
#428442
#428342
#423192
#401902
#400982
#396632
#396542
#383972
#356722
#356672
#356622
#356332
#356192
#353202
#353132
#352422
#348142
#348132
C2×#24342
#342762
#342092
#341732