Finite Group Databasebeta

← #7652079

Subgroups — #7652079

Order 512.

4860 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42921C214yesmaximal, complemented
2#42848C214yesmaximal, complemented
3#42559C214yesmaximal, complemented
4#42451C214yesmaximal, complemented
5#40895C218yesmaximal, complemented
6#40048C214yesmaximal, complemented
7#39914C214yesmaximal, complemented
8#39662C214yesmaximal, complemented
9#39604C214yesmaximal, complemented
10#38541C218yesmaximal, complemented
11#35672C211yesmaximal, characteristic, complemented
12#35668C211yesmaximal, characteristic, complemented
13#35633C211yesmaximal, characteristic
14#35630C211yesmaximal, characteristic, complemented
15#35555C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35307C211yesmaximal, characteristic, complemented
18#35286C211yesmaximal, characteristic, complemented
19#35224C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21C2×#2502C211yesmaximal, characteristic, complemented
22#34742C211yesmaximal, characteristic
23#34276C211yesmaximal, characteristic, complemented
24#34200C211yesmaximal, characteristic
25#34183C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#525C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35#2859C2214yescomplemented
36#2855C2214yescomplemented
37#2848C2214yes—
38#2839C2218yescomplemented
39#2834C2218yescomplemented
40#2807C2218yes—
41#2792C2218yescomplemented
42#2791C2218yescomplemented
43#2790C2218yes—
44#2787C2218yes—
45#2782C2218yes—
46#2776C2218yescomplemented
47#2770C2218yescomplemented
48#2746C2218yes—
49#2744C2218yescomplemented
50#2738C2218yescomplemented
51#2728C2218yes—
52#2726C2218yescomplemented
53#2720C2218yes—
54#2695C2218yes—
55#2690C2218yescomplemented
56#2666C2218yescomplemented
57#2655C2218yescomplemented
58#2652C2218yes—
59#2652C2218yescomplemented
60#2647C2214yescomplemented
61#2633C2218yes—
62#2627C2214yes—
63#2627C2218yescomplemented
64#2625C2214yescomplemented
65#2590C2218yescomplemented
66#2577C2218yes—
67#2571C2214yescomplemented
68#2570C2214yescomplemented
69#2568C2212yescomplemented
70#2567C2212yescomplemented
71#2567C2212yescomplemented
72#2566C2212yescomplemented
73#2565C2212yescomplemented
74#2565C2212yescomplemented
75#2565C2212yescomplemented
76#2556C2218yes—
77#2552C2214yescomplemented
78#2552C2214yescomplemented
79#2542C2212yescomplemented
80#2534C2214yes—
81#2514C2214yescomplemented
82#2514C2214yescomplemented
83#2511C2214yescomplemented
84#2511C2214yescomplemented
85#2507C2214yescomplemented
86#2506C2214yescomplemented
87#2502C2214yes—
88#2502C2214yes—
89#2502C2214yes—
90#2502C2214yes—
91#2497C2212yes—
92#2496C2212yes—
93#2495C2212yes—
94#2494C2212yes—
95#2493C2218yes—
96#2493C2214yes—
97#2486C2214yes—
98#2484C2214yes—
99#2482C2214yes—
100#2480C2214yes—
101#2473C2218yes—
102#2473C2218yescomplemented
103#2460C2218yes—
104#2453C2214yescomplemented
105#2451C2214yescomplemented
106#2449C2218yes—
107#2449C2218yes—
108#2447C2214yescomplemented
109#2446C2214yescomplemented
110#2442C2214yes—
111#2442C2218yes—
112#2442C2214yes—
113#2441C2214yescomplemented
114#2440C2214yes—
115#2440C2214yes—
116#2440C2214yescomplemented
117#2438C2218yes—
118#2429C2214yes—
119#2427C2214yes—
120#2423C2214yes—
121#2423C2214yes—
122#2423C2212yes—
123#2422C2212yes—
124#2421C2214yes—
125#2421C2214yes—
126#2421C2212yes—
127#2420C2212yes—
128#2419C2218yes—
129#2419C2214yes—
130#2418C2214yes—
131#2417C2214yes—
132#2415C2214yes—
133#2401C2214yes—
134#2395C2214yes—
135C2×#398C2214yes—
136#2362C2214yescomplemented
137#2361C2214yes—
138#2360C2214yes—
139#2360C2214yescomplemented
140#2359C2218yes—
141#2352C2214yes—
142Q8×C4⋊C4C2214yescomplemented
143D4×C4⋊C4C2218yes—
144D4×C4⋊C4C2214yes—
145D4×C4⋊C4C2214yescomplemented
146#2334C2218yes—
147#2327C2212yescomplemented
148#2326C2212yescomplemented
149#2322C2218yes—
150#2322C2214yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2212yescomplemented
157#2317C2212yescomplemented
158#2316C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163C4×C4⋊Q8C2212yescomplemented
164C4×#126C2214yes—
165C4×#124C2212yescomplemented
166C4×#123C2214yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172C2×#391C2211yescharacteristic
173C2×#391C2211yescharacteristic
174C2×#385C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2285C2212yescomplemented
178C2×#384C2211yescharacteristic
179C2×#384C2211yescharacteristic
180C2×#384C2212yescomplemented
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2312yes—
191#544—44no—
192#536—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×#126C2314yes—
197C2×#125C2312yes—
198C2×#125C2312yes—
199C2×#125C2318yes—
200C2×#125C2318yes—
201C2×#124C2312yes—
202#525—28no—
203C2×#123C2312yes—
204C2×#123C2314yes—
205C2×#123C2314yes—
206C2×C22⋊Q8—44no—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×#121C2312yes—
215C2×#120C2312yes—
216#520—44no—
217#520—44no—
218#519—44no—
219C4×#41—28no—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2314yes—
246C22×C4⋊C4—44no—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2318yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C42C2312yes—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#401C2314yes—
265#401C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2314yes—
271#400C2314yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#397C2314yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#395C2318yes—
315#395C2318yes—
316#395C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2314yes—
320#391C2311yescharacteristic
321#391C2312yes—
322#391C2312yes—
323#391C2311yescharacteristic
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2318yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#390C2311yescharacteristic
336#390C2312yes—
337#390C2311yescharacteristic
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#388C2314yes—
364#388C2314yes—
365#388C2314yes—
366#388C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#386C2314yes—
395#386C2318yes—
396#386C2318yes—
397#386C2314yes—
398#386C2314yes—
399#385C2318yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2314yes—
417#385C2314yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#384C2312yes—
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2314yes—
429#384C2314yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#384C2312yes—
434#384C2318yes—
435#384C2312yes—
436#383C2314yes—
437#383C2318yes—
438#382C2311yescharacteristic
439#382C2312yes—
440#382C2312yes—
441#382C2311yescharacteristic
442#382C2312yes—
443#382C2312yes—
444#382C2318yes—
445#382C2312yes—
446#382C2312yes—
447#381C2314yes—
448#381C2314yes—
449#381C2312yes—
450#381C2318yes—
451#381C2312yes—
452#381C2312yes—
453#381C2314yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2318yes—
458#380C2312yes—
459#380C2314yes—
460#380C2318yes—
461#380C2312yes—
462#380C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468#379C2312yes—
469#379C2312yes—
470#379C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C2×#95C2314yes—
500C43C2312yes—
501C25C2411yescharacteristic
502C2×#41—24no—
503C2×#41—24no—
504C2×#41#4118yes—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×D4C2414yes—
513C22×D4C2412yes—
514C22×D4C2411yescharacteristic
515C23×C4—24no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—44no—
519C23×C4—84no—
520C23×C4C2412yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2414yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2418yes—
534C23×C4C2411yescharacteristic
535C4⋊Q8—28no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538#126—216no—
539#125—44no—
540#125—44no—
541#125—88no—
542#125—88no—
543#124—28no—
544#123—28no—
545#123—216no—
546#123—216no—
547C22⋊Q8—28no—
548C22⋊Q8—216no—
549C22⋊Q8—48no—
550C22⋊Q8—48no—
551C22⋊Q8—48no—
552C22⋊Q8—88no—
553C22⋊Q8—88no—
554#121—28no—
555#120—28no—
556C4×Q8—28no—
557C4×Q8—44no—
558C4×Q8—44no—
559C4×Q8—44no—
560C4×Q8—44no—
561C4×Q8—44no—
562C4×Q8—44no—
563C4×D4—216no—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—48no—
569C4×D4—48no—
570C4×D4—88no—
571#117—28no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—48no—
580#117—44no—
581#117—44no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—48no—
586C2×C4⋊C4—48no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—88no—
592C2×C4⋊C4—84no—
593C2×C4⋊C4—84no—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C22⋊C4—28no—
644C2×C22⋊C4—44no—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C42—28no—
673C2×C42—24no—
674C2×C42—24no—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696#95C2412yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2418yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737C24—22no—
738C24—24no—
739C24—22no—
740C24—22no—
741C24—42no—
742C24C2512yes—
743C24C2512yes—
744C24C2511yescharacteristic
745#41—232no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—22no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—44no—
755C2×Q8—48no—
756C2×Q8—416no—
757C2×Q8C2×#4114yes—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—44no—
765C2×D4C2×#4118yes—
766C2×D4C2×#4114yes—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—48no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—48no—
802C22×C4—48no—
803C22×C4—416no—
804C22×C4—816no—
805C22×C4C2×#4118yes—
806C22×C4C2×#4114yes—
807C22×C4H(5,𝔽2)14yes—
808C22×C42−1+414yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C22×C4C2511yescharacteristic
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—216no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—28no—
885C22⋊C4—216no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C42−1+418yes—
907C42—22no—
908C42—24no—
909C42—22no—
910C42—28no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—22no—
918C42—24no—
919C42—22no—
920C42—24no—
921C42—28no—
922C42—44no—
923C42—44no—
924C42—44no—
925C42—44no—
926C42—48no—
927C42—44no—
928C23—22no—
929C23—22no—
930C23—28no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—24no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—22no—
941C23—48no—
942C23—48no—
943C23—44no—
944C23—44no—
945C23C22×#4114yes—
946C23C22×#4112yes—
947C23C2×H(5,𝔽2)12yes—
948C23C2×2−1+414yes—
949C23C2×2−1+412yes—
950C23C2611yescharacteristic
951Q8—28no—
952Q8—48no—
953Q8—48no—
954Q8—164no—
955D4—216no—
956D4—28no—
957D4—416no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—216no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—28no—
1007C2×C4—48no—
1008C2×C4—416no—
1009C2×C4—48no—
1010C2×C4—44no—
1011C2×C4—48no—
1012C2×C4—48no—
1013C2×C4—48no—
1014C2×C4—84no—
1015C2×C4—84no—
1016C2×C4—84no—
1017C2×C4—816no—
1018C2×C4—164no—
1019C2×C4—164no—
1020C2×C4#539116yes—
1021C2×C4C22×#4114yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C2×H(5,𝔽2)12yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C2×C4C2×2−1+414yes—
1027C2×C4C2×2−1+414yes—
1028C2×C4C2×2−1+412yes—
1029C2×C4C2×2−1+412yes—
1030C22—24no—
1031C22—22no—
1032C22—22no—
1033C22—24no—
1034C22—28no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—416no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—44no—
1046C22—42no—
1047C22C2×#53914yes—
1048C22C23×#4111yescharacteristic
1049C22C22×H(5,𝔽2)11yescharacteristic
1050C22C22×2−1+412yes—
1051C22C22×2−1+411yescharacteristic
1052C22H(7,𝔽2)12yes—
1053C4—24no—
1054C4—24no—
1055C4—24no—
1056C4—44no—
1057C4—42no—
1058C4—44no—
1059C4—44no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—44no—
1064C4—44no—
1065C4—44no—
1066C4—42no—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—44no—
1071C4—44no—
1072C4—42no—
1073C4C2×#53914yes—
1074C4C2×#53914yes—
1075C2—24no—
1076C2—44no—
1077C2—44no—
1078C2C22×#53911yescharacteristic
1079C2#6283311yescharacteristic
1080C2#6287611yescharacteristic
1081C2#6294512yes—
1082C2#6300012yes—
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. #42921C2semidirect
2. #42848C2semidirect
3. #42559C2semidirect
4. #42451C2semidirect
5. #40895C2semidirect
6. #40048C2semidirect
7. #39914C2semidirect
8. #39662C2semidirect
9. #39604C2semidirect
10. #38541C2semidirect
11. #35672C2semidirect
12. #35668C2semidirect
14. #35630C2semidirect
15. #35555C2semidirect
16. #35532C2semidirect
17. #35307C2semidirect
18. #35286C2semidirect
19. #35224C2semidirect
20. #34814C2semidirect
21. C2×#2502C2semidirect
23. #34276C2semidirect
25. #34183C2semidirect
35. #2859C22semidirect
36. #2855C22semidirect
38. #2839C22semidirect
39. #2834C22semidirect
41. #2792C22semidirect
42. #2791C22semidirect
46. #2776C22semidirect
47. #2770C22semidirect
49. #2744C22semidirect
50. #2738C22semidirect
52. #2726C22semidirect
55. #2690C22semidirect
56. #2666C22semidirect
57. #2655C22semidirect
59. #2652C22semidirect
60. #2647C22semidirect
63. #2627C22semidirect
64. #2625C22semidirect
65. #2590C22semidirect
67. #2571C22semidirect
68. #2570C22semidirect
69. #2568C22semidirect
70. #2567C22semidirect
71. #2567C22semidirect
72. #2566C22semidirect
73. #2565C22semidirect
74. #2565C22semidirect
75. #2565C22semidirect
77. #2552C22semidirect
78. #2552C22semidirect
79. #2542C22semidirect
81. #2514C22semidirect
82. #2514C22semidirect
83. #2511C22semidirect
84. #2511C22semidirect
85. #2507C22semidirect
86. #2506C22semidirect
102. #2473C22semidirect
104. #2453C22semidirect
105. #2451C22semidirect
108. #2447C22semidirect
109. #2446C22semidirect
113. #2441C22semidirect
116. #2440C22semidirect
136. #2362C22semidirect
139. #2360C22semidirect
142. Q8×C4⋊C4C22semidirect
145. D4×C4⋊C4C22semidirect
147. #2327C22semidirect
148. #2326C22semidirect
156. #2317C22semidirect
157. #2317C22semidirect
163. C4×C4⋊Q8C22semidirect
165. C4×#124C22semidirect
177. #2285C22semidirect
180. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#429212
#428482
#425592
#424512
#408952
#400482
#399142
#396622
#396042
#385412
#356722
#356682
#356332
#356302
#355552
#355322
#353072
#352862
#352242
#348142
C2×#25022
#347422
#342762
#342002
#341832