Finite Group Databasebeta

← #7987166

Subgroups — #7987166

Order 512.

4283 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59673C212yesmaximal, complemented
3#59655C212yesmaximal
4#59248C212yesmaximal, complemented
5#51723C218yesmaximal, complemented
6#45690C214yesmaximal, complemented
7#45383C214yesmaximal
8#45341C214yesmaximal, complemented
9#42747C214yesmaximal, complemented
10#42744C214yesmaximal, complemented
11#39762C212yesmaximal, complemented
12#39149C214yesmaximal, complemented
13#38986C212yesmaximal, complemented
14#38977C212yesmaximal
15#38943C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36563C211yesmaximal, characteristic, complemented
18#36194C211yesmaximal, characteristic
19#36177C212yesmaximal, complemented
20#36175C212yesmaximal
21#35239C212yesmaximal, complemented
22#35177C212yesmaximal
23#34951C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic
25#34491C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic
27C2×Q82C2212yes—
28C2×#554C2211yescharacteristic
29#2868C2211yescharacteristic
30#2862C2212yes—
31#2859C2212yes—
32#2857C2212yes—
33#2857C2214yes—
34#2855C2214yes—
35#2851C2214yes—
36#2839C2218yes—
37#2799C2218yes—
38#2789C2218yes—
39#2789C2218yes—
40#2787C2218yes—
41#2776C2218yes—
42#2776C2218yes—
43#2776C2218yes—
44#2769C2218yes—
45#2765C2218yes—
46#2764C2218yes—
47#2762C2218yes—
48#2758C2218yes—
49#2744C2218yes—
50#2739C2218yes—
51#2739C2218yes—
52#2734C2214yes—
53#2729C2218yes—
54#2666C2218yes—
55#2665C2218yes—
56#2645C2214yes—
57#2645C2218yes—
58#2642C2214yes—
59#2599C2218yes—
60#2585C2214yes—
61#2582C2212yes—
62#2582C2212yes—
63#2582C2211yescharacteristic
64#2582C2212yes—
65#2581C2218yes—
66#2573C2214yes—
67#2571C2211yescharacteristic
68#2571C2214yes—
69#2571C2212yes—
70#2571C2212yes—
71#2570C2214yes—
72#2570C2214yes—
73#2568C2211yescharacteristic
74#2568C2211yescharacteristic
75#2568C2212yes—
76#2567C2212yes—
77#2563C2212yes—
78#2552C2212yes—
79#2552C2211yescharacteristic
80#2551C2212yes—
81#2551C2212yes—
82#2550C2214yes—
83#2550C2214yes—
84#2550C2214yes—
85#2547C2211yescharacteristic
86#2546C2211yescharacteristic
87#2546C2214yes—
88#2538C2212yes—
89#2538C2211yescharacteristic
90#2533C2218yes—
91#2527C2218yes—
92#2523C2218yes—
93#2514C2214yes—
94#2514C2214yes—
95#2514C2214yes—
96#2514C2214yes—
97#2514C2214yes—
98#2514C2214yes—
99#2514C2212yes—
100#2511C2212yes—
101#2511C2214yes—
102#2509C2214yes—
103#2509C2214yes—
104#2509C2214yes—
105#2509C2212yes—
106#2508C2214yes—
107#2508C2214yes—
108#2507C2214yes—
109#2503C2214yes—
110#2497C2214yes—
111#2497C2214yes—
112#2495C2214yes—
113#2494C2214yes—
114#2494C2214yes—
115#2494C2212yes—
116#2493C2218yes—
117#2492C2214yes—
118#2492C2214yes—
119#2492C2214yes—
120#2489C2214yes—
121#2465C2218yes—
122#2453C2214yes—
123#2453C2212yes—
124#2452C2214yes—
125#2451C2214yes—
126#2451C2214yes—
127#2451C2214yes—
128#2447C2214yes—
129#2447C2212yes—
130#2446C2214yes—
131#2446C2212yes—
132#2442C2214yes—
133#2440C2214yes—
134#2439C2214yes—
135#2438C2218yes—
136#2429C2218yes—
137#2429C2214yes—
138#2421C2218yes—
139#2421C2212yes—
140#2402C2214yes—
141#2401C2214yes—
142#2381C2218yes—
143#2370C2212yes—
144#2369C2212yes—
145#2369C2212yes—
146#2369C2211yescharacteristic
147#2368C2214yes—
148#2367C2214yes—
149#2365C2214yes—
150#2365C2214yes—
151#2365C2212yes—
152#2365C2214yes—
153#2365C2212yes—
154#2365C2212yes—
155#2360C2214yes—
156#2360C2212yes—
157#2356C2214yes—
158#2356C2214yes—
159#2355C2212yes—
160#2355C2212yes—
161#2355C2212yes—
162#2355C2211yescharacteristic
163#2355C2212yes—
164#2354C2212yes—
165Q8×C4⋊C4C2212yes—
166#2349C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2345C2212yes—
169#2331C2214yes—
170#2331C2214yes—
171#2330C2214yes—
172#2327C2218yes—
173#2320C2214yes—
174#2320C2214yes—
175#2319C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#125C2212yes—
183C4×#125C2212yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2214yes—
188#2295C2212yes—
189#2295C2212yes—
190#2295C2212yes—
191#2285C2212yes—
192#2283C2212yes—
193#2283C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199Q82—216no—
200#554—28no—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2318yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#124C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2318yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2318yes—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×#117C2314yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C42C2312yes—
244C22×C42C2314yes—
245#401C2314yes—
246#401C2318yes—
247#401C2318yes—
248#401C2318yes—
249#400C2318yes—
250#400C2314yes—
251#400C2314yes—
252#400C2318yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#397C2314yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2318yes—
287#396C2314yes—
288#396C2318yes—
289#396C2318yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#393C2318yes—
295#393C2318yes—
296#391C2312yes—
297#391C2314yes—
298#391C2314yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2314yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2318yes—
315#391C2318yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2318yes—
328#391C2318yes—
329#390C2314yes—
330#390C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2314yes—
336#389C2312yes—
337#389C2314yes—
338#389C2312yes—
339#389C2314yes—
340#389C2314yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2318yes—
358#389C2314yes—
359#389C2312yes—
360#389C2318yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2314yes—
367#389C2318yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#383C2314yes—
433#383C2318yes—
434#383C2318yes—
435#383C2318yes—
436#383C2318yes—
437#382C2312yes—
438#382C2312yes—
439#382C2314yes—
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2318yes—
445#382C2314yes—
446#382C2312yes—
447#382C2312yes—
448#382C2318yes—
449#382C2314yes—
450#381C2314yes—
451#381C2318yes—
452#381C2318yes—
453#380C2314yes—
454#380C2314yes—
455#380C2318yes—
456#380C2312yes—
457#380C2312yes—
458#380C2314yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2312yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2314yes—
516#376C2318yes—
517C2×#95C2314yes—
518C43C2312yes—
519C43C2311yescharacteristic
520C43C2312yes—
521C22×Q8C2412yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2412yes—
525C22×Q8C2418yes—
526C22×Q8C2414yes—
527C22×Q8C2412yes—
528C22×D4C2411yescharacteristic
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2414yes—
533C23×C4C2414yes—
534C4⋊Q8—232no—
535C4⋊Q8—216no—
536C4⋊Q8—216no—
537C4⋊Q8—24no—
538C4⋊Q8—24no—
539C4⋊Q8—28no—
540C4⋊Q8—48no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—82no—
544C4⋊Q8#4118yes—
545#125—28no—
546#125—44no—
547#125—48no—
548#124—28no—
549C22⋊Q8—216no—
550C22⋊Q8—28no—
551C22⋊Q8—48no—
552C22⋊Q8—44no—
553C22⋊Q8—88no—
554C4×Q8—216no—
555C4×Q8—216no—
556C4×Q8—24no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—24no—
560C4×Q8—24no—
561C4×Q8—24no—
562C4×Q8—44no—
563C4×Q8—42no—
564C4×Q8—42no—
565C4×Q8—88no—
566C4×Q8—84no—
567C4×Q8—84no—
568C4×D4—24no—
569C4×D4—28no—
570C4×D4—28no—
571C4×D4—24no—
572C4×D4—24no—
573#117—84no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C42—28no—
647C2×C42—48no—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2414yes—
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2418yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2418yes—
670C2×C42C2418yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2411yescharacteristic
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679#95C2412yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2412yes—
698#95C2414yes—
699#95C2412yes—
700#95C2412yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2418yes—
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737C24C2512yes—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—22no—
741C2×Q8—216no—
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8—22no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—28no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—42no—
753C2×Q8—42no—
754C2×Q8—48no—
755C2×Q8—44no—
756C2×Q8—44no—
757C2×Q8—48no—
758C2×Q8C2×#4118yes—
759C2×D4—22no—
760C2×D4—22no—
761C2×D42−1+414yes—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—42no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2512yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2512yes—
782C22×C4C2512yes—
783C22×C4C2512yes—
784C22×C4C2514yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2511yescharacteristic
789C22×C4C2512yes—
790C22×C4C2518yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C4⋊C4—22no—
803C4⋊C4—28no—
804C4⋊C4—22no—
805C4⋊C4—24no—
806C4⋊C4—216no—
807C4⋊C4—216no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—22no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—22no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—44no—
835C4⋊C4—42no—
836C4⋊C4—44no—
837C4⋊C4—42no—
838C4⋊C4—44no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4C2×#4118yes—
860C4⋊C4C2×#4118yes—
861C22⋊C4—24no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C42—24no—
873C42—216no—
874C42—28no—
875C42—28no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—22no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—22no—
888C42—22no—
889C42—24no—
890C42—44no—
891C42—44no—
892C42—48no—
893C42—42no—
894C42—42no—
895C42—42no—
896C42—42no—
897C42—48no—
898C42—48no—
899C42—41no—
900C42C2×#4114yes—
901C422−1+414yes—
902C422−1+414yes—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23C2×2−1+414yes—
910C23C2611yescharacteristic
911Q8—48no—
912Q8—48no—
913Q8—44no—
914Q8—48no—
915Q8—44no—
916Q8—816no—
917Q8—88no—
918D4—28no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—24no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—24no—
926C2×C4—21no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—28no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—88no—
985C2×C4—88no—
986C2×C4C22×#4118yes—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4112yes—
990C2×C4C2×2−1+412yes—
991C2×C4C2×2−1+412yes—
992C2×C4C2×2−1+412yes—
993C2×C4C2×2−1+412yes—
994C2×C4C2×2−1+412yes—
995C2×C4C2×2−1+412yes—
996C2×C4C2×2−1+412yes—
997C2×C4#58512yes—
998C2×C4#58512yes—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22C23×#4111yescharacteristic
1007C22C22×2−1+411yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C22×2−1+411yescharacteristic
1010C22C2×#58511yescharacteristic
1011C22C2×#58511yescharacteristic
1012C22H(7,𝔽2)11yescharacteristic
1013C4—28no—
1014C4—22no—
1015C4—22no—
1016C4—22no—
1017C4—42no—
1018C4—44no—
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—41no—
1023C4—42no—
1024C4—44no—
1025C4—42no—
1026C4—44no—
1027C4—42no—
1028C4—44no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—48no—
1035C4#351814yes—
1036C4#352314yes—
1037C4#355514yes—
1038C2—44no—
1039C2C2×#355511yescharacteristic
1040C2C2×#352311yescharacteristic
1041C2C2×#351811yescharacteristic
1042C2#6294511yescharacteristic
1043C2#6296211yescharacteristic
1044C2#6299211yescharacteristic
1045C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59673C2semidirect
4. #59248C2semidirect
5. #51723C2semidirect
6. #45690C2semidirect
8. #45341C2semidirect
9. #42747C2semidirect
10. #42744C2semidirect
11. #39762C2semidirect
12. #39149C2semidirect
13. #38986C2semidirect
15. #38943C2semidirect
16. #36598C2semidirect
17. #36563C2semidirect
19. #36177C2semidirect
21. #35239C2semidirect
23. #34951C2semidirect
25. #34491C2semidirect

Maximal subgroups

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

subgroupindex
#598322
#596732
#596552
#592482
#517232
#456902
#453832
#453412
#427472
#427442
#397622
#391492
#389862
#389772
#389432
#365982
#365632
#361942
#361772
#361752
#352392
#351772
#349512
#349452
#344912
C4×#5542