Finite Group Databasebeta

← #7683804

Subgroups — #7683804

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1061 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59849C218yesmaximal, complemented
2#59695C214yesmaximal, complemented
3#59694C214yesmaximal, complemented
4#59682C214yesmaximal, complemented
5#59681C214yesmaximal, complemented
6#45344C214yesmaximal, complemented
7#45342C214yesmaximal, complemented
8#45184C214yesmaximal, complemented
9#45156C214yesmaximal, complemented
10#44495C218yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic
13#35667C211yesmaximal, characteristic
14#35667C211yesmaximal, characteristic
15#35630C211yesmaximal, characteristic, complemented
16#35619C211yesmaximal, characteristic
17C2×#2546C211yesmaximal, characteristic, complemented
18#34816C211yesmaximal, characteristic
19#34815C211yesmaximal, characteristic, complemented
20#34276C211yesmaximal, characteristic
21#34266C211yesmaximal, characteristic
22#34254C211yesmaximal, characteristic, complemented
23#34249C211yesmaximal, characteristic, complemented
24#34209C211yesmaximal, characteristic, complemented
25#34209C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2802C2218yes—
39#2802C2218yes—
40#2793C2218yes—
41#2790C2218yes—
42#2783C2218yes—
43#2776C2218yes—
44#2776C2218yes—
45#2772C2218yes—
46#2766C2218yes—
47#2766C2218yes—
48#2765C2218yes—
49#2725C2218yes—
50#2608C2218yes—
51#2606C2218yes—
52#2606C2218yes—
53#2594C2218yes—
54#2590C2218yes—
55#2590C2218yes—
56#2587C2218yes—
57#2587C2218yes—
58#2585C2218yes—
59#2585C2218yes—
60#2573C2218yes—
61#2570C2218yes—
62#2546C2214yes—
63#2546C2212yes—
64#2546C2214yes—
65#2546C2214yes—
66#2546C2214yes—
67#2546C2212yes—
68#2546C2214yes—
69#2546C2214yes—
70#2545C2212yes—
71#2545C2214yes—
72#2545C2214yes—
73#2545C2212yes—
74#2529C2218yes—
75#2525C2218yes—
76#2525C2218yes—
77#2515C2218yes—
78#2514C2212yes—
79#2514C2214yes—
80#2514C2214yes—
81#2513C2212yes—
82#2512C2212yes—
83#2511C2212yes—
84#2511C2214yes—
85#2511C2214yes—
86#2510C2214yes—
87#2509C2218yes—
88#2509C2212yes—
89#2508C2212yes—
90#2507C2218yes—
91#2507C2212yes—
92#2506C2212yes—
93#2505C2214yes—
94#2503C2212yes—
95#2502C2212yes—
96#2499C2212yes—
97#2499C2212yes—
98#2493C2218yes—
99#2484C2214yes—
100#2484C2214yes—
101#2481C2214yes—
102#2473C2214yes—
103#2447C2214yes—
104#2446C2214yes—
105#2446C2214yes—
106#2446C2214yes—
107#2446C2214yes—
108#2446C2214yes—
109#2429C2214yes—
110#2429C2214yes—
111#2429C2214yes—
112#2429C2214yes—
113#2429C2214yes—
114#2429C2214yes—
115#2419C2218yes—
116#2413C2214yes—
117#2413C2218yes—
118#2413C2218yes—
119#2413C2214yes—
120#2402C2214yes—
121#2401C2214yes—
122C2×#398C2214yes—
123#2373C2218yes—
124#2370C2218yes—
125#2367C2214yes—
126#2365C2214yes—
127#2365C2214yes—
128#2365C2214yes—
129#2365C2214yes—
130#2365C2214yes—
131#2362C2214yes—
132#2362C2214yes—
133#2360C2214yes—
134#2360C2214yes—
135#2359C2218yes—
136#2356C2214yes—
137#2355C2214yes—
138#2351C2214yes—
139#2351C2214yes—
140Q8×C4⋊C4C2214yes—
141Q8×C4⋊C4C2214yes—
142#2344C2218yes—
143#2344C2218yes—
144#2343C2218yes—
145#2327C2212yes—
146#2327C2212yes—
147#2327C2214yes—
148#2327C2212yes—
149#2326C2212yes—
150#2322C2214yes—
151#2320C2214yes—
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2214yes—
155#2310C2211yescharacteristic
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160C4×C4⋊Q8C2212yes—
161C4×C4⋊Q8C2214yes—
162C4×C4⋊Q8C2212yes—
163C4×C4⋊Q8C2212yes—
164C4×#125C2214yes—
165C4×#126C2214yes—
166C4×#124C2212yes—
167C4×#123C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2214yes—
177#2295C2214yes—
178C2×#391C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#389C2214yes—
181#2285C2211yescharacteristic
182#2285C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191#536—28no—
192#536—28no—
193#536—44no—
194C2×C4⋊Q8—28no—
195C2×C4⋊Q8—28no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×#126C2314yes—
209C2×#125C2314yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220#520—44no—
221#519—28no—
222#519—28no—
223#519—44no—
224#519—44no—
225C2×C4×Q8—44no—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2312yes—
267#401C2318yes—
268#401C2314yes—
269#400C2314yes—
270#400C2318yes—
271#400C2314yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#397C2314yes—
300#397C2318yes—
301#397C2314yes—
302#397C2314yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#396C2318yes—
310#396C2318yes—
311#391C2311yescharacteristic
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2311yescharacteristic
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#390C2311yescharacteristic
336#390C2312yes—
337#390C2312yes—
338#390C2311yescharacteristic
339#389C2314yes—
340#389C2314yes—
341#389C2318yes—
342#389C2318yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2312yes—
362#389C2312yes—
363#389C2318yes—
364#389C2318yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2318yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
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#386C2312yes—
419#386C2314yes—
420#386C2314yes—
421#386C2312yes—
422#385C2314yes—
423#385C2312yes—
424#385C2314yes—
425#385C2312yes—
426#385C2318yes—
427#385C2312yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2312yes—
432#385C2314yes—
433#385C2312yes—
434#385C2312yes—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2312yes—
438#384C2312yes—
439#384C2318yes—
440#384C2312yes—
441#383C2314yes—
442#383C2318yes—
443#383C2318yes—
444#382C2314yes—
445#382C2318yes—
446#382C2312yes—
447#382C2312yes—
448#382C2318yes—
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#382C2312yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2318yes—
458#380C2314yes—
459#380C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497#376C2312yes—
498#376C2318yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#95C2312yes—
502C43C2312yes—
503C43C2312yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8—24no—
515C22×Q8#4118yes—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2412yes—
522C22×Q8C2412yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2412yes—
534C23×C4C2414yes—
535C23×C4C2411yescharacteristic
536C4⋊Q8—28no—
537C4⋊Q8—28no—
538C4⋊Q8—216no—
539C4⋊Q8—28no—
540C4⋊Q8—28no—
541C4⋊Q8—216no—
542C4⋊Q8—28no—
543C4⋊Q8—28no—
544C4⋊Q8—48no—
545C4⋊Q8—48no—
546C4⋊Q8—44no—
547#126—216no—
548#125—216no—
549#124—28no—
550#124—28no—
551#124—44no—
552#123—216no—
553#123—216no—
554#123—48no—
555C22⋊Q8—216no—
556C22⋊Q8—216no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—216no—
563C4×Q8—48no—
564C4×Q8—48no—
565C4×Q8—44no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×Q8—44no—
569C4×Q8—44no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—44no—
574C4×D4—44no—
575C4×D4—48no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—24no—
582#117—216no—
583#117—216no—
584#117—48no—
585#117—48no—
586#117—44no—
587#117#4118yes—
588C2×C4⋊C4—216no—
589C2×C4⋊C4—216no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—28no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—44no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
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⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—24no—
667C2×C42—44no—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2418yes—
673C2×C42C2412yes—
674C2×C42C2418yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2418yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2412yes—
696#95C2418yes—
697#95C2418yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2412yes—
702#95C2418yes—
703#95C2418yes—
704#95C2414yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741C24C2512yes—
742C24C2511yescharacteristic
743#41—416no—
744C2×Q8—232no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—416no—
765C2×Q8—416no—
766C2×Q8C2×#4118yes—
767C2×Q8C2×#4118yes—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4C2×#4118yes—
800C22×C4C2×#4114yes—
801C22×C4C2×#4114yes—
802C22×C4H(5,𝔽2)14yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C4⋊C4—216no—
827C4⋊C4—216no—
828C4⋊C4—216no—
829C4⋊C4—216no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—216no—
834C4⋊C4—24no—
835C4⋊C4—216no—
836C4⋊C4—216no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4C2×#4118yes—
875C4⋊C42−1+418yes—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4C2×#4118yes—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—24no—
898C42—22no—
899C42—22no—
900C42—216no—
901C42—24no—
902C42—24no—
903C42—216no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—28no—
911C42—28no—
912C42—48no—
913C42—44no—
914C42—44no—
915C42—48no—
916C42—44no—
917C42—44no—
918C42—44no—
919C42—44no—
920C42—44no—
921C42C2×#4118yes—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23C22×#4112yes—
930C23C22×#4112yes—
931C23C2×H(5,𝔽2)12yes—
932C23C2611yescharacteristic
933Q8—216no—
934Q8—216no—
935Q8—48no—
936Q8—48no—
937Q8—48no—
938Q8—48no—
939Q8—44no—
940D4—48no—
941D4—44no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—216no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—48no—
996C2×C4—48no—
997C2×C4—44no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—84no—
1002C2×C4—164no—
1003C2×C4#553116yes—
1004C2×C4C22×#4118yes—
1005C2×C4C22×#4118yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×2−1+414yes—
1013C2×C4C2×2−1+414yes—
1014C2×C4C2×2−1+414yes—
1015C22—24no—
1016C22—24no—
1017C22—22no—
1018C22—22no—
1019C22—44no—
1020C22—44no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22C2×#55314yes—
1025C22C23×#4111yescharacteristic
1026C22C23×#4111yescharacteristic
1027C22C22×H(5,𝔽2)11yescharacteristic
1028C22C22×2−1+412yes—
1029C222−1+612yes—
1030C4—24no—
1031C4—24no—
1032C4—28no—
1033C4—24no—
1034C4—28no—
1035C4—44no—
1036C4—42no—
1037C4—42no—
1038C4—44no—
1039C4—44no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4C2×#55314yes—
1052C4C2×#55314yes—
1053C2—24no—
1054C2—82no—
1055C2C22×#55311yescharacteristic
1056C2#6283311yescharacteristic
1057C2#6288711yescharacteristic
1058C2#6299812yes—
1059C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59849C2semidirect
2. #59695C2semidirect
3. #59694C2semidirect
4. #59682C2semidirect
5. #59681C2semidirect
6. #45344C2semidirect
7. #45342C2semidirect
8. #45184C2semidirect
9. #45156C2semidirect
10. #44495C2semidirect
11. #35674C2semidirect
15. #35630C2semidirect
17. C2×#2546C2semidirect
19. #34815C2semidirect
22. #34254C2semidirect
23. #34249C2semidirect
24. #34209C2semidirect
25. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#598492
#596952
#596942
#596822
#596812
#453442
#453422
#451842
#451562
#444952
#356742
#356672
#356302
#356192
C2×#25462
#348162
#348152
#342762
#342662
#342542
#342492
#342092