Finite Group Databasebeta

← #7683743

Subgroups — #7683743

Order 512.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59585C214yesmaximal, complemented
2#59582C214yesmaximal, complemented
3#59575C214yesmaximal, complemented
4#59437C214yesmaximal, complemented
5#59328C218yesmaximal, complemented
6#45221C214yesmaximal, complemented
7#45220C214yesmaximal, complemented
8#45173C214yesmaximal, complemented
9#45155C214yesmaximal, complemented
10#43597C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35630C211yesmaximal, characteristic, complemented
14#35619C211yesmaximal, characteristic, complemented
15#35617C211yesmaximal, characteristic
16#35617C211yesmaximal, characteristic
17C2×#2547C211yesmaximal, characteristic, complemented
18#34816C211yesmaximal, characteristic, complemented
19#34815C211yesmaximal, characteristic, complemented
20#34276C211yesmaximal, characteristic, complemented
21#34265C211yesmaximal, characteristic
22#34254C211yesmaximal, characteristic, complemented
23#34248C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25#34211C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×#518C2211yescharacteristic
36C2×#518C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2787C2218yescomplemented
39#2787C2218yescomplemented
40#2786C2218yescomplemented
41#2782C2218yescomplemented
42#2781C2218yescomplemented
43#2779C2218yescomplemented
44#2770C2218yescomplemented
45#2770C2218yescomplemented
46#2757C2218yescomplemented
47#2750C2218yescomplemented
48#2747C2218yescomplemented
49#2747C2218yescomplemented
50#2595C2218yescomplemented
51#2579C2218yescomplemented
52#2578C2218yescomplemented
53#2577C2218yescomplemented
54#2577C2218yescomplemented
55#2576C2218yescomplemented
56#2569C2218yescomplemented
57#2569C2218yescomplemented
58#2547C2212yes—
59#2547C2214yes—
60#2547C2212yes—
61#2547C2214yes—
62#2547C2214yes—
63#2547C2214yes—
64#2547C2214yes—
65#2546C2214yescomplemented
66#2545C2214yescomplemented
67#2544C2212yes—
68#2544C2214yes—
69#2544C2212yes—
70#2531C2218yescomplemented
71#2530C2218yescomplemented
72#2530C2218yescomplemented
73#2514C2212yescomplemented
74#2514C2214yescomplemented
75#2514C2214yescomplemented
76#2513C2212yescomplemented
77#2512C2212yescomplemented
78#2511C2212yescomplemented
79#2511C2214yescomplemented
80#2511C2214yescomplemented
81#2510C2214yes—
82#2510C2218yescomplemented
83#2509C2212yescomplemented
84#2508C2212yescomplemented
85#2507C2212yescomplemented
86#2506C2212yescomplemented
87#2505C2214yes—
88#2503C2212yescomplemented
89#2502C2212yescomplemented
90#2499C2212yescomplemented
91#2499C2212yescomplemented
92#2495C2218yescomplemented
93#2494C2218yescomplemented
94#2493C2218yes—
95#2484C2214yes—
96#2484C2214yes—
97#2481C2214yes—
98#2481C2218yescomplemented
99#2473C2214yes—
100#2468C2218yescomplemented
101#2460C2218yescomplemented
102#2447C2214yescomplemented
103#2446C2214yescomplemented
104#2446C2214yescomplemented
105#2446C2214yescomplemented
106#2446C2214yescomplemented
107#2446C2214yescomplemented
108#2442C2218yescomplemented
109#2429C2214yescomplemented
110#2429C2214yescomplemented
111#2427C2214yes—
112#2427C2214yes—
113#2427C2214yes—
114#2427C2214yes—
115#2419C2218yes—
116#2413C2214yes—
117#2413C2214yes—
118#2412C2218yes—
119#2412C2218yes—
120#2402C2214yescomplemented
121#2401C2214yescomplemented
122C2×#397C2214yes—
123#2367C2214yes—
124#2367C2214yes—
125#2367C2214yes—
126#2367C2214yes—
127#2367C2214yes—
128#2366C2214yes—
129#2363C2214yes—
130#2362C2214yescomplemented
131#2361C2214yes—
132#2360C2214yescomplemented
133#2359C2218yes—
134#2356C2214yescomplemented
135#2355C2214yescomplemented
136#2353C2218yescomplemented
137#2349C2214yes—
138#2349C2214yes—
139D4×C4⋊C4C2214yes—
140D4×C4⋊C4C2214yes—
141#2345C2218yescomplemented
142#2343C2218yes—
143#2342C2218yes—
144#2342C2218yes—
145#2327C2212yescomplemented
146#2326C2214yes—
147#2326C2212yes—
148#2326C2212yes—
149#2326C2212yescomplemented
150#2321C2214yes—
151#2320C2214yescomplemented
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2315C2214yes—
155#2310C2211yescharacteristic
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2309C2211yescharacteristic
160C4×C4⋊Q8C2212yescomplemented
161C4×#125C2214yescomplemented
162C4×#126C2214yescomplemented
163C4×#124C2214yes—
164C4×#124C2212yes—
165C4×#124C2212yes—
166C4×#124C2212yescomplemented
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2295C2214yescomplemented
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#385C2214yes—
180#2285C2211yescharacteristic
181#2285C2211yescharacteristic
182C2×#380C2214yes—
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×D4C2311yescharacteristic
191C24×C4C2312yes—
192#536—28no—
193#536—44no—
194#535—28no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2312yes—
201C2×#126C2314yes—
202C2×#125C2314yes—
203C2×#124—28no—
204C2×#124—28no—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×#121C2314yes—
220C2×#120C2314yes—
221#520—44no—
222#519—28no—
223#519—44no—
224#518—28no—
225#518—44no—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×D4—44no—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2318yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C22⋊C4C2314yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269#401C2318yes—
270#401C2314yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#391C2311yescharacteristic
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2311yescharacteristic
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2318yes—
338#390C2311yescharacteristic
339#390C2312yes—
340#390C2312yes—
341#390C2311yescharacteristic
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2318yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2318yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2312yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2314yes—
407#386C2312yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2312yes—
413#385C2312yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2312yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2318yes—
425#385C2314yes—
426#385C2312yes—
427#385C2312yes—
428#385C2312yes—
429#384C2312yes—
430#384C2312yes—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2312yes—
434#383C2314yes—
435#383C2318yes—
436#383C2318yes—
437#382C2314yes—
438#382C2312yes—
439#382C2312yes—
440#382C2318yes—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2312yes—
444#381C2314yes—
445#381C2314yes—
446#381C2314yes—
447#381C2314yes—
448#381C2318yes—
449#380C2318yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2318yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2318yes—
461#379C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2318yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2318yes—
498C2×#95C2318yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#95C2312yes—
502C43C2312yes—
503C43C2312yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2411yescharacteristic
519C22×D4—24no—
520C22×D4—24no—
521C22×D4#4118yes—
522C22×D4C2412yes—
523C22×D4C2411yescharacteristic
524C22×D4C2412yes—
525C22×D4C2412yes—
526C22×D4C2418yes—
527C23×C4—48no—
528C23×C4—44no—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2418yes—
538C23×C4C2418yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2411yescharacteristic
543C4⋊Q8—28no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547#127—28no—
548#126—48no—
549#125—48no—
550#124—28no—
551#124—216no—
552#124—28no—
553#124—28no—
554#124—216no—
555#124—28no—
556#124—28no—
557#124—28no—
558#124—44no—
559#123—216no—
560#123—48no—
561C22⋊Q8—216no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564#121—216no—
565#120—216no—
566C4×Q8—216no—
567C4×Q8—216no—
568C4×Q8—44no—
569C4×Q8—44no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×D4—216no—
574C4×D4—216no—
575C4×D4—48no—
576C4×D4—48no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—416no—
583C4×D4—48no—
584#117—24no—
585#117—24no—
586#117—24no—
587#117—24no—
588#117—24no—
589#117—24no—
590#117—216no—
591#117—48no—
592#117—44no—
593#117#4118yes—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—416no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—44no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C22⋊C4—216no—
642C2×C22⋊C4—216no—
643C2×C22⋊C4—216no—
644C2×C22⋊C4—48no—
645C2×C22⋊C4—44no—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C42—24no—
675C2×C42—24no—
676C2×C42—24no—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744C24—24no—
745C24—24no—
746C24—44no—
747C24—44no—
748C24C2×#4118yes—
749C24C2512yes—
750C24C2514yes—
751C24C2511yescharacteristic
752#41—416no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—24no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—24no—
762C2×Q8—22no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—416no—
769C2×Q8—416no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—24no—
773C2×D4—216no—
774C2×D4—232no—
775C2×D4—24no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—22no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4C2×#4118yes—
785C2×D4C2×#4118yes—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—216no—
802C22×C4—216no—
803C22×C4—42no—
804C22×C4—48no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—48no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—816no—
820C22×C4C2×#4114yes—
821C22×C4C2×#4114yes—
822C22×C4H(5,𝔽2)14yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—216no—
848C4⋊C4—24no—
849C4⋊C4—216no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—48no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4C2×#4118yes—
886C22⋊C4—24no—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—216no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—216no—
898C22⋊C4—216no—
899C22⋊C4—28no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4C2×#4118yes—
914C42—22no—
915C42—22no—
916C42—24no—
917C42—22no—
918C42—22no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—216no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—44no—
930C42—44no—
931C42—44no—
932C42—44no—
933C42—44no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42C2×#4118yes—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—28no—
943C23—28no—
944C23—216no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—416no—
951C23—84no—
952C23—88no—
953C23—84no—
954C23C22×#4118yes—
955C23C22×#4112yes—
956C23C22×#4112yes—
957C23C2×H(5,𝔽2)12yes—
958C23C2611yescharacteristic
959Q8—48no—
960Q8—48no—
961Q8—48no—
962Q8—48no—
963Q8—44no—
964D4—216no—
965D4—216no—
966D4—48no—
967D4—44no—
968D4—816no—
969C2×C4—28no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—44no—
1022C2×C4—48no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—816no—
1026C2×C4—816no—
1027C2×C4—84no—
1028C2×C4—84no—
1029C2×C4—84no—
1030C2×C4—164no—
1031C2×C4—164no—
1032C2×C4—164no—
1033C2×C4#553116yes—
1034C2×C4C22×#4118yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C2×H(5,𝔽2)12yes—
1040C2×C4C2×H(5,𝔽2)12yes—
1041C2×C4#58514yes—
1042C22—24no—
1043C22—24no—
1044C22—22no—
1045C22—22no—
1046C22—216no—
1047C22—28no—
1048C22—48no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—816no—
1057C22C2×#55314yes—
1058C22C23×#4111yescharacteristic
1059C22C23×#4111yescharacteristic
1060C22C22×H(5,𝔽2)11yescharacteristic
1061C22C2×#58512yes—
1062C222−1+612yes—
1063C4—28no—
1064C4—24no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—42no—
1069C4—44no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—42no—
1074C4—42no—
1075C4—42no—
1076C4—42no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C4—42no—
1081C4—44no—
1082C4—44no—
1083C4C2×#55314yes—
1084C4C2×#55314yes—
1085C2—24no—
1086C2—48no—
1087C2—82no—
1088C2C22×#55311yescharacteristic
1089C2#6282411yescharacteristic
1090C2#6288711yescharacteristic
1091C2#6299112yes—
1092C2#6299512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59585C2semidirect
2. #59582C2semidirect
3. #59575C2semidirect
4. #59437C2semidirect
5. #59328C2semidirect
6. #45221C2semidirect
7. #45220C2semidirect
8. #45173C2semidirect
9. #45155C2semidirect
10. #43597C2semidirect
11. #35674C2semidirect
12. #35667C2semidirect
13. #35630C2semidirect
14. #35619C2semidirect
17. C2×#2547C2semidirect
18. #34816C2semidirect
19. #34815C2semidirect
20. #34276C2semidirect
22. #34254C2semidirect
23. #34248C2semidirect
24. #34211C2semidirect
25. #34211C2semidirect
38. #2787C22semidirect
39. #2787C22semidirect
40. #2786C22semidirect
41. #2782C22semidirect
42. #2781C22semidirect
43. #2779C22semidirect
44. #2770C22semidirect
45. #2770C22semidirect
46. #2757C22semidirect
47. #2750C22semidirect
48. #2747C22semidirect
49. #2747C22semidirect
50. #2595C22semidirect
51. #2579C22semidirect
52. #2578C22semidirect
53. #2577C22semidirect
54. #2577C22semidirect
55. #2576C22semidirect
56. #2569C22semidirect
57. #2569C22semidirect
65. #2546C22semidirect
66. #2545C22semidirect
70. #2531C22semidirect
71. #2530C22semidirect
72. #2530C22semidirect
73. #2514C22semidirect
74. #2514C22semidirect
75. #2514C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2511C22semidirect
79. #2511C22semidirect
80. #2511C22semidirect
82. #2510C22semidirect
83. #2509C22semidirect
84. #2508C22semidirect
85. #2507C22semidirect
86. #2506C22semidirect
88. #2503C22semidirect
89. #2502C22semidirect
90. #2499C22semidirect
91. #2499C22semidirect
92. #2495C22semidirect
93. #2494C22semidirect
98. #2481C22semidirect
100. #2468C22semidirect
101. #2460C22semidirect
102. #2447C22semidirect
103. #2446C22semidirect
104. #2446C22semidirect
105. #2446C22semidirect
106. #2446C22semidirect
107. #2446C22semidirect
108. #2442C22semidirect
109. #2429C22semidirect
110. #2429C22semidirect
120. #2402C22semidirect
121. #2401C22semidirect
130. #2362C22semidirect
132. #2360C22semidirect
134. #2356C22semidirect
135. #2355C22semidirect
136. #2353C22semidirect
141. #2345C22semidirect
145. #2327C22semidirect
149. #2326C22semidirect
151. #2320C22semidirect
160. C4×C4⋊Q8C22semidirect
161. C4×#125C22semidirect
162. C4×#126C22semidirect
166. C4×#124C22semidirect
176. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#595852
#595822
#595752
#594372
#593282
#452212
#452202
#451732
#451552
#435972
#356742
#356672
#356302
#356192
#356172
C2×#25472
#348162
#348152
#342762
#342652
#342542
#342482
#342112