Finite Group Databasebeta

← #7672356

Subgroups — #7672356

Order 512.

5652 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59874C214yesmaximal, complemented
2#59867C214yesmaximal, complemented
3#59638C214yesmaximal, complemented
4#59425C214yesmaximal, complemented
5#39559C218yesmaximal, complemented
6#38113C214yesmaximal, complemented
7#38111C214yesmaximal, complemented
8#36625C211yesmaximal, characteristic, complemented
9#36304C214yesmaximal, complemented
10#36277C214yesmaximal, complemented
11#36206C218yesmaximal, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35630C211yesmaximal, characteristic, complemented
15#35628C211yesmaximal, characteristic, complemented
16#35313C211yesmaximal, characteristic, complemented
17#35307C211yesmaximal, characteristic, complemented
18#35242C211yesmaximal, characteristic
19#35227C211yesmaximal, characteristic
20#34268C211yesmaximal, characteristic, complemented
21#34254C211yesmaximal, characteristic, complemented
22#34178C211yesmaximal, characteristic, complemented
23#34173C211yesmaximal, characteristic, complemented
24C4×#525C211yesmaximal, characteristic
25C22×#391C211yesmaximal, characteristic, complemented
26C24×Q8C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2863C2214yescomplemented
37#2857C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2855C2214yescomplemented
41#2851C2212yes—
42#2851C2212yes—
43#2849C2214yes—
44#2849C2214yes—
45#2848C2214yes—
46#2799C2218yescomplemented
47#2798C2218yescomplemented
48#2798C2218yescomplemented
49#2789C2218yescomplemented
50#2759C2218yescomplemented
51#2758C2218yescomplemented
52#2755C2218yescomplemented
53#2754C2218yescomplemented
54#2645C2214yescomplemented
55#2625C2214yescomplemented
56#2623C2214yes—
57#2614C2214yes—
58#2607C2218yescomplemented
59#2605C2218yescomplemented
60#2592C2214yescomplemented
61#2589C2218yescomplemented
62#2588C2218yescomplemented
63#2588C2218yescomplemented
64#2582C2214yescomplemented
65#2581C2214yescomplemented
66#2569C2218yes—
67#2568C2214yescomplemented
68#2564C2218yes—
69#2527C2218yescomplemented
70#2523C2218yescomplemented
71#2520C2218yescomplemented
72#2514C2214yescomplemented
73#2514C2214yescomplemented
74#2514C2214yescomplemented
75#2511C2214yescomplemented
76#2511C2214yescomplemented
77#2511C2214yescomplemented
78#2510C2218yes—
79#2510C2218yes—
80#2505C2218yes—
81#2505C2218yes—
82#2504C2212yes—
83#2503C2212yes—
84#2502C2212yes—
85#2501C2212yes—
86#2498C2218yes—
87#2498C2218yes—
88#2493C2218yes—
89#2493C2218yes—
90#2493C2218yes—
91#2493C2218yes—
92#2492C2214yescomplemented
93#2489C2214yescomplemented
94#2488C2218yes—
95#2488C2218yes—
96#2487C2214yes—
97#2486C2214yes—
98#2453C2214yescomplemented
99#2451C2214yescomplemented
100#2448C2214yescomplemented
101#2447C2214yescomplemented
102#2446C2214yescomplemented
103#2446C2214yescomplemented
104#2438C2218yes—
105#2438C2218yes—
106#2436C2212yes—
107#2436C2212yes—
108#2434C2212yes—
109#2434C2212yes—
110#2423C2214yescomplemented
111#2421C2214yescomplemented
112#2419C2218yes—
113#2419C2218yes—
114#2409C2214yes—
115#2409C2214yes—
116#2368C2218yes—
117#2367C2214yescomplemented
118#2365C2214yescomplemented
119#2359C2218yes—
120#2359C2218yes—
121#2356C2214yescomplemented
122#2355C2214yescomplemented
123#2353C2218yes—
124#2345C2214yes—
125#2345C2214yes—
126#2344C2214yes—
127#2344C2214yes—
128#2343C2218yes—
129#2343C2218yes—
130Q8×C22⋊C4C2214yes—
131Q8×C22⋊C4C2214yes—
132Q8×C22⋊C4C2214yes—
133Q8×C22⋊C4C2214yes—
134#2323C2214yescomplemented
135#2320C2214yescomplemented
136#2317C2211yescharacteristic
137#2317C2211yescharacteristic
138#2316C2211yescharacteristic
139#2316C2211yescharacteristic
140#2313C2214yes—
141#2311C2211yescharacteristic
142#2311C2211yescharacteristic
143#2310C2211yescharacteristic
144#2310C2211yescharacteristic
145#2310C2211yescharacteristic
146#2310C2211yescharacteristic
147#2310C2214yes—
148C4×C22⋊Q8C2214yes—
149C4×C22⋊Q8C2214yes—
150C4×C22⋊Q8C2212yes—
151C4×C22⋊Q8C2212yes—
152C4×C22⋊Q8C2214yescomplemented
153C4×#123C2214yes—
154C4×#121C2212yes—
155C4×#121C2212yes—
156C4×#120C2214yes—
157#2297C2211yescharacteristic
158#2296C2211yescharacteristic
159#2296C2211yescharacteristic
160#2296C2211yescharacteristic
161#2295C2214yescomplemented
162C2×#391C2214yes—
163C2×#391C2211yescharacteristic
164C2×#391C2211yescharacteristic
165C2×#391C2214yes—
166C2×#391C2212yes—
167C2×#391C2211yescharacteristic
168C2×#391C2212yes—
169C2×#391C2214yes—
170C2×#391C2212yes—
171C2×#391C2212yes—
172C2×#391C2211yescharacteristic
173#2290C2212yes—
174#2290C2212yes—
175#2285C2211yescharacteristic
176#2280C2211yescharacteristic
177#2280C2211yescharacteristic
178#2280C2214yes—
179#2280C2214yes—
180#2280C2211yescharacteristic
181#2274C2211yescharacteristic
182#2274C2211yescharacteristic
183C42×D4C2212yes—
184C42×D4C2212yes—
185C4×#117C2211yescharacteristic
186C22×#95C2214yes—
187C22×#41C2311yescharacteristic
188C23×Q8—28no—
189C23×Q8—28no—
190C23×Q8—44no—
191C23×Q8C2311yescharacteristic
192C23×Q8C2312yes—
193C23×Q8C2312yes—
194C23×Q8C2312yes—
195C23×Q8C2312yes—
196C23×Q8C2312yes—
197C23×Q8C2311yescharacteristic
198C24×C4C2312yes—
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201C24×C4C2312yes—
202#536—28no—
203#536—44no—
204#533—44no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×#125C2312yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211#525—28no—
212C2×#123C2314yes—
213C2×#123C2312yes—
214C2×#123C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120C2312yes—
226#519—28no—
227#519—44no—
228C4×#41—44no—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2314yes—
249C2×#117C2314yes—
250C2×#117C2312yes—
251C2×#117C2318yes—
252C22×C4⋊C4—28no—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C42—44no—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2312yes—
270C22×C42C2312yes—
271#401C2318yes—
272#401C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#393C2318yes—
301#393C2318yes—
302#393C2318yes—
303#391C2314yes—
304#391C2314yes—
305#391C2312yes—
306#391C2312yes—
307#391C2318yes—
308#391C2318yes—
309#391C2318yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2318yes—
322#391C2312yes—
323#391C2314yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2318yes—
338#391C2318yes—
339#391C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2318yes—
352#389C2312yes—
353#389C2312yes—
354#389C2318yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2314yes—
395#386C2318yes—
396#386C2318yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2318yes—
416#385C2314yes—
417#385C2314yes—
418#385C2314yes—
419#384C2312yes—
420#384C2312yes—
421#384C2312yes—
422#383C2318yes—
423#383C2318yes—
424#383C2318yes—
425#382C2318yes—
426#382C2312yes—
427#382C2312yes—
428#382C2318yes—
429#382C2312yes—
430#381C2312yes—
431#381C2312yes—
432#381C2314yes—
433#381C2314yes—
434#381C2314yes—
435#381C2314yes—
436#381C2312yes—
437#381C2318yes—
438#381C2318yes—
439#381C2318yes—
440#380C2318yes—
441#380C2318yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2312yes—
455#380C2318yes—
456#379C2312yes—
457#379C2312yes—
458#379C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493#376C2312yes—
494#376C2318yes—
495C2×#95C2318yes—
496C2×#95C2314yes—
497C2×#95C2318yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C2×#95C2318yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C22×Q8—28no—
509C22×Q8—28no—
510C22×Q8—28no—
511C22×Q8—28no—
512C22×Q8—24no—
513C22×Q8—28no—
514C22×Q8—28no—
515C22×Q8—28no—
516C22×Q8—28no—
517C22×Q8—28no—
518C22×Q8—28no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8—24no—
523C22×Q8—44no—
524C22×Q8—44no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8—464no—
529C22×Q8#4118yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—28no—
545C23×C4—28no—
546C23×C4—28no—
547C23×C4—28no—
548C23×C4—44no—
549C23×C4—44no—
550C23×C4—44no—
551C23×C4—48no—
552C23×C4#4118yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2414yes—
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2414yes—
570C23×C4C2412yes—
571C23×C4C2414yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C4⋊Q8—28no—
576C4⋊Q8—44no—
577C4⋊Q8—44no—
578#125—44no—
579#124—28no—
580#124—44no—
581#123—28no—
582#123—216no—
583#123—416no—
584#123—48no—
585C22⋊Q8—216no—
586C22⋊Q8—24no—
587C22⋊Q8—24no—
588C22⋊Q8—216no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591C22⋊Q8—48no—
592#121—24no—
593#121—24no—
594#120—28no—
595C4×Q8—216no—
596C4×Q8—216no—
597C4×Q8—48no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×D4—28no—
602C4×D4—28no—
603C4×D4—216no—
604C4×D4—44no—
605C4×D4—48no—
606C4×D4—48no—
607#117—216no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—24no—
612#117—24no—
613#117—24no—
614#117—24no—
615#117—44no—
616#117—416no—
617#117—48no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—28no—
622C2×C4⋊C4—28no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C42—24no—
686C2×C42—24no—
687C2×C42—44no—
688C2×C42—42no—
689C2×C42—42no—
690C2×C42—42no—
691C2×C42—42no—
692C2×C42—44no—
693C2×C42—44no—
694C2×C42—44no—
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2418yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2418yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761C24—22no—
762C24—22no—
763C24—24no—
764C24—24no—
765C24C2×#4114yes—
766C24C2512yes—
767C24C2511yescharacteristic
768C24C2511yescharacteristic
769C24C2511yescharacteristic
770#41—416no—
771C2×Q8—232no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—28no—
777C2×Q8—28no—
778C2×Q8—28no—
779C2×Q8—28no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—28no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—432no—
795C2×Q8—432no—
796C2×Q8—432no—
797C2×Q8—432no—
798C2×Q8—432no—
799C2×Q8—416no—
800C2×Q8C2×#4118yes—
801C2×Q8C2×#4118yes—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—22no—
812C22×C4—22no—
813C22×C4—24no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—232no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—216no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—28no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—28no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—28no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—816no—
868C22×C4C2×#4114yes—
869C22×C4C2×#4114yes—
870C22×C4C2×#4114yes—
871C22×C4C2×#4114yes—
872C22×C4C2×#4114yes—
873C22×C4C2×#4118yes—
874C22×C4C2×#4114yes—
875C22×C4C2×#4114yes—
876C22×C4H(5,𝔽2)14yes—
877C22×C42−1+418yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2514yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—216no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—216no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—216no—
953C22⋊C4—28no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C42—24no—
960C42—216no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—22no—
966C42—24no—
967C42—24no—
968C42—22no—
969C42—22no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—42no—
975C42—42no—
976C42—42no—
977C42—42no—
978C42—44no—
979C42—48no—
980C42—48no—
981C42—48no—
982C42—44no—
983C23—216no—
984C23—216no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—28no—
994C23—28no—
995C23—28no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23C22×#4112yes—
1002C23C22×#4112yes—
1003C23C22×#4112yes—
1004C23C22×#4112yes—
1005C23C2×H(5,𝔽2)12yes—
1006C23C2×2−1+414yes—
1007C23#58514yes—
1008C23C2611yescharacteristic
1009Q8—216no—
1010Q8—216no—
1011Q8—416no—
1012Q8—416no—
1013Q8—48no—
1014Q8—48no—
1015Q8—44no—
1016Q8—88no—
1017D4—48no—
1018D4—48no—
1019D4—48no—
1020D4—44no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—28no—
1032C2×C4—216no—
1033C2×C4—28no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—28no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—28no—
1074C2×C4—22no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—416no—
1081C2×C4—416no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—416no—
1085C2×C4—48no—
1086C2×C4—88no—
1087C2×C4—84no—
1088C2×C4—88no—
1089C2×C4—84no—
1090C2×C4#551116yes—
1091C2×C4C22×#4118yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4112yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×2−1+414yes—
1101C2×C4C2×2−1+414yes—
1102C22—232no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—22no—
1114C22—22no—
1115C22—44no—
1116C22—42no—
1117C22—42no—
1118C22—44no—
1119C22—42no—
1120C22C2×#55114yes—
1121C22#350914yes—
1122C22#351014yes—
1123C22C23×#4111yescharacteristic
1124C22C23×#4111yescharacteristic
1125C22C22×H(5,𝔽2)11yescharacteristic
1126C22C22×2−1+412yes—
1127C22C2×#58512yes—
1128C4—24no—
1129C4—24no—
1130C4—22no—
1131C4—22no—
1132C4—28no—
1133C4—44no—
1134C4—44no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4—42no—
1147C4C2×#55114yes—
1148C4C2×#55114yes—
1149C2—24no—
1150C2—24no—
1151C2—24no—
1152C2—82no—
1153C2C22×#55111yescharacteristic
1154C2#6278812yes—
1155C2C2×#350911yescharacteristic
1156C2C2×#351011yescharacteristic
1157C2#6281912yes—
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. #59874C2semidirect
2. #59867C2semidirect
3. #59638C2semidirect
4. #59425C2semidirect
5. #39559C2semidirect
6. #38113C2semidirect
7. #38111C2semidirect
8. #36625C2semidirect
9. #36304C2semidirect
10. #36277C2semidirect
11. #36206C2semidirect
12. #35673C2semidirect
13. #35662C2semidirect
14. #35630C2semidirect
15. #35628C2semidirect
16. #35313C2semidirect
17. #35307C2semidirect
20. #34268C2semidirect
21. #34254C2semidirect
22. #34178C2semidirect
23. #34173C2semidirect
25. C22×#391C2semidirect
36. #2863C22semidirect
40. #2855C22semidirect
46. #2799C22semidirect
47. #2798C22semidirect
48. #2798C22semidirect
49. #2789C22semidirect
50. #2759C22semidirect
51. #2758C22semidirect
52. #2755C22semidirect
53. #2754C22semidirect
54. #2645C22semidirect
55. #2625C22semidirect
58. #2607C22semidirect
59. #2605C22semidirect
60. #2592C22semidirect
61. #2589C22semidirect
62. #2588C22semidirect
63. #2588C22semidirect
64. #2582C22semidirect
65. #2581C22semidirect
67. #2568C22semidirect
69. #2527C22semidirect
70. #2523C22semidirect
71. #2520C22semidirect
72. #2514C22semidirect
73. #2514C22semidirect
74. #2514C22semidirect
75. #2511C22semidirect
76. #2511C22semidirect
77. #2511C22semidirect
92. #2492C22semidirect
93. #2489C22semidirect
98. #2453C22semidirect
99. #2451C22semidirect
100. #2448C22semidirect
101. #2447C22semidirect
102. #2446C22semidirect
103. #2446C22semidirect
110. #2423C22semidirect
111. #2421C22semidirect
117. #2367C22semidirect
118. #2365C22semidirect
121. #2356C22semidirect
122. #2355C22semidirect
134. #2323C22semidirect
135. #2320C22semidirect
152. C4×C22⋊Q8C22semidirect
161. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#598742
#598672
#596382
#594252
#395592
#381132
#381112
#366252
#363042
#362772
#362062
#356732
#356622
#356302
#356282
#353132
#353072
#352422
#352272
#342682
#342542
#341782
#341732
C4×#5252
C22×#3912