Finite Group Databasebeta

← #7678287

Subgroups — #7678287

Order 512.

4678 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59718C214yesmaximal, complemented
2#59715C214yesmaximal, complemented
3#59712C214yesmaximal, complemented
4#59574C214yesmaximal, complemented
5#45341C214yesmaximal, complemented
6#45295C214yesmaximal, complemented
7#45174C214yesmaximal, complemented
8#45014C214yesmaximal, complemented
9#39512C214yesmaximal, complemented
10#37959C214yesmaximal, complemented
11#37956C214yesmaximal
12#36204C214yesmaximal
13#35644C212yesmaximal
14#35630C212yesmaximal, complemented
15#35224C211yesmaximal, characteristic
16#35167C211yesmaximal, characteristic, complemented
17#35154C211yesmaximal, characteristic, complemented
18#34814C212yesmaximal
19#34272C212yesmaximal, complemented
20#34271C211yesmaximal, characteristic, complemented
21#34178C211yesmaximal, characteristic
22C2×#2360C211yesmaximal, characteristic
23#34059C211yesmaximal, characteristic, complemented
24C2×#544C2212yes—
25C2×#544C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2857C2214yes—
30#2855C2214yes—
31#2848C2214yes—
32#2810C2218yescomplemented
33#2805C2218yescomplemented
34#2789C2218yescomplemented
35#2788C2218yes—
36#2787C2218yes—
37#2776C2218yescomplemented
38#2776C2218yescomplemented
39#2767C2218yescomplemented
40#2762C2218yescomplemented
41#2758C2218yescomplemented
42#2745C2218yes—
43#2689C2218yes—
44#2659C2214yes—
45#2627C2214yes—
46#2627C2214yes—
47#2605C2218yescomplemented
48#2599C2218yes—
49#2588C2218yescomplemented
50#2581C2218yescomplemented
51#2577C2218yes—
52#2573C2218yes—
53#2570C2218yescomplemented
54#2561C2218yes—
55#2552C2214yescomplemented
56#2551C2214yescomplemented
57#2550C2214yescomplemented
58#2550C2214yescomplemented
59#2528C2218yescomplemented
60#2527C2218yes—
61#2524C2218yescomplemented
62#2523C2218yes—
63#2514C2214yescomplemented
64#2514C2214yescomplemented
65#2514C2214yescomplemented
66#2514C2214yescomplemented
67#2514C2218yescomplemented
68#2511C2214yescomplemented
69#2511C2214yescomplemented
70#2511C2214yescomplemented
71#2511C2214yescomplemented
72#2503C2218yes—
73#2499C2214yes—
74#2497C2212yes—
75#2497C2212yes—
76#2496C2214yes—
77#2496C2212yes—
78#2496C2212yes—
79#2495C2212yes—
80#2495C2212yes—
81#2494C2212yes—
82#2494C2214yes—
83#2494C2212yes—
84#2493C2218yes—
85#2493C2218yes—
86#2493C2214yes—
87#2493C2214yes—
88#2492C2214yes—
89#2492C2214yes—
90#2492C2214yes—
91#2492C2214yes—
92#2492C2214yes—
93#2489C2214yes—
94#2489C2214yes—
95#2489C2214yes—
96#2489C2214yes—
97#2480C2214yes—
98#2480C2214yes—
99#2478C2218yes—
100#2465C2218yes—
101#2453C2214yescomplemented
102#2453C2214yescomplemented
103#2451C2214yescomplemented
104#2451C2214yescomplemented
105#2446C2218yescomplemented
106#2442C2214yes—
107#2442C2214yes—
108#2440C2214yes—
109#2440C2214yes—
110#2439C2214yes—
111#2421C2214yes—
112#2401C2214yes—
113#2401C2214yes—
114#2373C2218yes—
115#2370C2214yescomplemented
116#2370C2214yescomplemented
117#2370C2214yescomplemented
118#2370C2214yescomplemented
119#2369C2214yescomplemented
120#2369C2214yescomplemented
121#2368C2218yes—
122#2365C2214yescomplemented
123#2365C2214yescomplemented
124#2362C2214yes—
125#2360C2214yes—
126#2360C2214yes—
127#2360C2214yes—
128#2360C2218yes—
129#2360C2214yes—
130#2347C2214yes—
131#2345C2214yes—
132#2345C2214yes—
133#2344C2214yes—
134#2344C2214yes—
135#2331C2214yescomplemented
136#2330C2214yescomplemented
137#2329C2214yes—
138#2320C2214yescomplemented
139#2320C2214yescomplemented
140#2317C2212yes—
141#2316C2211yescharacteristic
142#2316C2211yescharacteristic
143#2316C2211yescharacteristic
144#2313C2214yes—
145#2313C2214yes—
146#2310C2212yes—
147#2310C2212yes—
148C4×C4⋊Q8C2214yescomplemented
149C4×#125C2214yescomplemented
150C4×#126C2214yes—
151C4×#126C2214yes—
152C4×C22⋊Q8C2214yes—
153#2296C2212yes—
154#2296C2212yes—
155#2295C2214yescomplemented
156#2295C2214yescomplemented
157C2×#391C2211yescharacteristic
158C2×#389C2212yes—
159C2×#389C2211yescharacteristic
160C2×#387C2212yes—
161C2×#385C2212yes—
162#2285C2212yes—
163#2283C2214yes—
164#2280C2212yes—
165#2280C2212yes—
166#2280C2214yes—
167#2274C2212yes—
168#2274C2212yes—
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×C4×C22⋊C4C2211yescharacteristic
173C23×Q8C2311yescharacteristic
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177#544—216no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×#126C2314yes—
183C2×#126C2314yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×C22⋊Q8—28no—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C4×Q8—28no—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2318yes—
198C2×C4×Q8C2314yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2314yes—
204C2×#117C2314yes—
205C22×C4⋊C4—28no—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2314yes—
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222#401C2314yes—
223#401C2314yes—
224#401C2318yes—
225#401C2318yes—
226#400C2314yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2314yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2314yes—
253#397C2314yes—
254#397C2314yes—
255#397C2314yes—
256#397C2314yes—
257#397C2314yes—
258#396C2314yes—
259#396C2314yes—
260#395C2318yes—
261#395C2318yes—
262#395C2318yes—
263#395C2318yes—
264#393C2318yes—
265#393C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2318yes—
276#391C2318yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#389C2312yes—
287#389C2314yes—
288#389C2312yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2312yes—
304#389C2314yes—
305#389C2318yes—
306#389C2312yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2312yes—
313#389C2314yes—
314#389C2312yes—
315#389C2312yes—
316#388C2314yes—
317#388C2314yes—
318#388C2314yes—
319#388C2314yes—
320#388C2314yes—
321#388C2314yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#384C2314yes—
369#384C2314yes—
370#384C2312yes—
371#384C2312yes—
372#383C2314yes—
373#383C2314yes—
374#383C2318yes—
375#383C2318yes—
376#383C2318yes—
377#382C2314yes—
378#382C2318yes—
379#382C2318yes—
380#382C2314yes—
381#382C2314yes—
382#382C2312yes—
383#382C2312yes—
384#381C2318yes—
385#381C2318yes—
386#381C2314yes—
387#381C2318yes—
388#381C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2312yes—
395#380C2312yes—
396#380C2314yes—
397#380C2312yes—
398#380C2312yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#379C2314yes—
407#379C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2318yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452#376C2314yes—
453#376C2318yes—
454C2×#95C2312yes—
455C2×#95C2312yes—
456C2×#95C2311yescharacteristic
457C2×#95C2311yescharacteristic
458C2×#95C2312yes—
459C2×#95C2312yes—
460C43C2314yes—
461C25C2411yescharacteristic
462C22×Q8—24no—
463C22×Q8—24no—
464C22×Q8—24no—
465C22×Q8C2414yes—
466C22×Q8C2414yes—
467C22×Q8C2418yes—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—24no—
471C23×C4—28no—
472C23×C4—44no—
473C23×C4—82no—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2412yes—
484C23×C4C2414yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C4⋊Q8—216no—
489C4⋊Q8—216no—
490C4⋊Q8—216no—
491C4⋊Q8—84no—
492#126—216no—
493#126—48no—
494#125—216no—
495#125—216no—
496#125—216no—
497C22⋊Q8—216no—
498C22⋊Q8—232no—
499C22⋊Q8—216no—
500C22⋊Q8—216no—
501C22⋊Q8—48no—
502C22⋊Q8—84no—
503C4×Q8—216no—
504C4×Q8—216no—
505C4×Q8—84no—
506C4×Q8—88no—
507#117—28no—
508#117—28no—
509#117—28no—
510#117—28no—
511#117—48no—
512#117—84no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—28no—
517C2×C4⋊C4—216no—
518C2×C4⋊C4—216no—
519C2×C4⋊C4—82no—
520C2×C4⋊C4#4118yes—
521C2×C4⋊C4#4118yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C22⋊C4—28no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2411yescharacteristic
569C2×C22⋊C4C2411yescharacteristic
570C2×C22⋊C4C2411yescharacteristic
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2411yescharacteristic
585C2×C42—28no—
586C2×C42—24no—
587C2×C42—24no—
588C2×C42—82no—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2418yes—
601C2×C42C2418yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2418yes—
609#95C2414yes—
610#95C2412yes—
611#95C2412yes—
612#95C2414yes—
613#95C2414yes—
614#95C2412yes—
615#95C2414yes—
616#95C2412yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—41no—
666C24—41no—
667C24C2511yescharacteristic
668C24C2511yescharacteristic
669C24C2511yescharacteristic
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—28no—
673C2×Q8—216no—
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—48no—
677C2×Q8—44no—
678C2×Q8—48no—
679C2×Q8—416no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—24no—
688C22×C4—28no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—22no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—41no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—44no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—42no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—42no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—42no—
716C22×C4—41no—
717C22×C4—416no—
718C22×C4—816no—
719C22×C4C2×#4118yes—
720C22×C4C2×#4118yes—
721C22×C4C2×#4114yes—
722C22×C4C2×#4114yes—
723C22×C42−1+414yes—
724C22×C4C2514yes—
725C22×C4C2512yes—
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2512yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2511yescharacteristic
742C22×C4C2511yescharacteristic
743C22×C4C2512yes—
744C4⋊C4—216no—
745C4⋊C4—28no—
746C4⋊C4—216no—
747C4⋊C4—216no—
748C4⋊C4—24no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—28no—
755C4⋊C4—216no—
756C4⋊C4—216no—
757C4⋊C4—216no—
758C4⋊C4—216no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—48no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4C2×#41116yes—
783C4⋊C4C2×#41116yes—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—22no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—24no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—42no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C42−1+414yes—
804C42—24no—
805C42—28no—
806C42—24no—
807C42—28no—
808C42—28no—
809C42—28no—
810C42—28no—
811C42—24no—
812C42—24no—
813C42—28no—
814C42—28no—
815C42—44no—
816C42—44no—
817C42—44no—
818C42—48no—
819C42—48no—
820C42—48no—
821C42—48no—
822C42—44no—
823C42—44no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—28no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23C22×#4112yes—
848C23C22×#4112yes—
849C23C2×2−1+412yes—
850C23C2×2−1+412yes—
851C23#58512yes—
852C23C2611yescharacteristic
853Q8—416no—
854Q8—88no—
855Q8—816no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—24no—
859C2×C4—21no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—21no—
863C2×C4—24no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—21no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—48no—
910C2×C4—48no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—416no—
914C2×C4—44no—
915C2×C4—48no—
916C2×C4—48no—
917C2×C4—48no—
918C2×C4—88no—
919C2×C4—82no—
920C2×C4—82no—
921C2×C4—84no—
922C2×C4#556116yes—
923C2×C4C22×#4118yes—
924C2×C4C22×#4118yes—
925C2×C4C22×#4114yes—
926C2×C4C22×#4114yes—
927C2×C4C2×2−1+412yes—
928C2×C4C2×2−1+412yes—
929C2×C4C2×2−1+414yes—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—416no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22C2×#55614yes—
952C22C23×#4111yescharacteristic
953C22C23×#4111yescharacteristic
954C22C22×2−1+411yescharacteristic
955C22C22×2−1+411yescharacteristic
956C22C2×#58511yescharacteristic
957C22H(7,𝔽2)11yescharacteristic
958C222−1+611yescharacteristic
959C4—28no—
960C4—22no—
961C4—28no—
962C4—22no—
963C4—44no—
964C4—42no—
965C4—44no—
966C4—44no—
967C4—41no—
968C4—44no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—42no—
974C4—44no—
975C4—41no—
976C4—42no—
977C4—44no—
978C4C2×#55618yes—
979C2—24no—
980C2—42no—
981C2—42no—
982C2C22×#55611yescharacteristic
983C2#6278811yescharacteristic
984C2#6284711yescharacteristic
985C2#6292811yescharacteristic
986C2#6294511yescharacteristic
987C2#6299011yescharacteristic
988C2#6299811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59718C2semidirect
2. #59715C2semidirect
3. #59712C2semidirect
4. #59574C2semidirect
5. #45341C2semidirect
6. #45295C2semidirect
7. #45174C2semidirect
8. #45014C2semidirect
9. #39512C2semidirect
10. #37959C2semidirect
14. #35630C2semidirect
16. #35167C2semidirect
17. #35154C2semidirect
19. #34272C2semidirect
20. #34271C2semidirect
23. #34059C2semidirect
32. #2810C22semidirect
33. #2805C22semidirect
34. #2789C22semidirect
37. #2776C22semidirect
38. #2776C22semidirect
39. #2767C22semidirect
40. #2762C22semidirect
41. #2758C22semidirect
47. #2605C22semidirect
49. #2588C22semidirect
50. #2581C22semidirect
53. #2570C22semidirect
55. #2552C22semidirect
56. #2551C22semidirect
57. #2550C22semidirect
58. #2550C22semidirect
59. #2528C22semidirect
61. #2524C22semidirect
63. #2514C22semidirect
64. #2514C22semidirect
65. #2514C22semidirect
66. #2514C22semidirect
67. #2514C22semidirect
68. #2511C22semidirect
69. #2511C22semidirect
70. #2511C22semidirect
71. #2511C22semidirect
101. #2453C22semidirect
102. #2453C22semidirect
103. #2451C22semidirect
104. #2451C22semidirect
105. #2446C22semidirect
115. #2370C22semidirect
116. #2370C22semidirect
117. #2370C22semidirect
118. #2370C22semidirect
119. #2369C22semidirect
120. #2369C22semidirect
122. #2365C22semidirect
123. #2365C22semidirect
135. #2331C22semidirect
136. #2330C22semidirect
138. #2320C22semidirect
139. #2320C22semidirect
148. C4×C4⋊Q8C22semidirect
149. C4×#125C22semidirect
155. #2295C22semidirect
156. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#597182
#597152
#597122
#595742
#453412
#452952
#451742
#450142
#395122
#379592
#379562
#362042
#356442
#356302
#352242
#351672
#351542
#348142
#342722
#342712
#341782
C2×#23602
#340592