Finite Group Databasebeta

← #7646160

Subgroups — #7646160

Order 512.

4396 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42753C214yesmaximal, complemented
2#42728C214yesmaximal, complemented
3#42610C214yesmaximal, complemented
4#42546C214yesmaximal, complemented
5#40202C214yesmaximal, complemented
6#40096C214yesmaximal, complemented
7#39661C214yesmaximal, complemented
8#39250C214yesmaximal, complemented
9#37466C214yesmaximal, complemented
10#36762C214yesmaximal, complemented
11#36728C214yesmaximal
12#35544C212yesmaximal
13#35543C212yesmaximal, complemented
14#35265C212yesmaximal, complemented
15#35224C211yesmaximal, characteristic
16#35224C211yesmaximal, characteristic
17#35167C211yesmaximal, characteristic, complemented
18#35159C211yesmaximal, characteristic, complemented
19#35086C214yesmaximal
20#34814C212yesmaximal
21#34271C211yesmaximal, characteristic, complemented
22C2×#2345C211yesmaximal, characteristic
23C4×#544C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2864C2214yescomplemented
28#2859C2214yescomplemented
29#2857C2214yes—
30#2851C2214yes—
31#2848C2214yes—
32#2848C2214yes—
33#2839C2218yescomplemented
34#2833C2218yescomplemented
35#2802C2218yescomplemented
36#2794C2218yescomplemented
37#2789C2218yescomplemented
38#2776C2218yescomplemented
39#2766C2218yescomplemented
40#2758C2218yescomplemented
41#2747C2218yes—
42#2747C2218yes—
43#2722C2218yes—
44#2722C2218yes—
45#2719C2218yescomplemented
46#2713C2218yescomplemented
47#2704C2218yes—
48#2704C2218yes—
49#2690C2218yes—
50#2690C2218yes—
51#2666C2218yescomplemented
52#2659C2214yes—
53#2655C2218yescomplemented
54#2655C2218yescomplemented
55#2652C2218yes—
56#2652C2218yes—
57#2647C2214yescomplemented
58#2647C2214yescomplemented
59#2646C2214yes—
60#2634C2218yescomplemented
61#2627C2214yes—
62#2627C2214yes—
63#2571C2214yescomplemented
64#2570C2214yescomplemented
65#2570C2214yescomplemented
66#2552C2214yescomplemented
67#2552C2214yescomplemented
68#2551C2214yescomplemented
69#2550C2214yescomplemented
70#2550C2214yescomplemented
71#2524C2218yescomplemented
72#2509C2214yescomplemented
73#2509C2214yescomplemented
74#2509C2214yescomplemented
75#2508C2214yescomplemented
76#2508C2214yescomplemented
77#2508C2214yescomplemented
78#2507C2214yescomplemented
79#2507C2214yescomplemented
80#2507C2214yescomplemented
81#2506C2214yescomplemented
82#2506C2214yescomplemented
83#2506C2214yescomplemented
84#2505C2218yes—
85#2505C2218yes—
86#2497C2214yes—
87#2497C2214yes—
88#2497C2212yes—
89#2497C2212yes—
90#2496C2214yes—
91#2496C2214yes—
92#2496C2214yes—
93#2496C2212yes—
94#2496C2214yes—
95#2496C2212yes—
96#2495C2212yes—
97#2495C2214yes—
98#2495C2214yes—
99#2495C2212yes—
100#2494C2212yes—
101#2494C2214yes—
102#2494C2212yes—
103#2494C2214yes—
104#2493C2214yes—
105#2493C2218yes—
106#2493C2214yes—
107#2489C2214yes—
108#2489C2214yes—
109#2480C2214yes—
110#2480C2218yes—
111#2480C2214yes—
112#2473C2218yes—
113#2473C2218yes—
114#2462C2218yescomplemented
115#2442C2214yes—
116#2442C2214yes—
117#2442C2214yes—
118#2442C2214yes—
119#2440C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2440C2214yes—
123#2429C2214yes—
124#2429C2214yes—
125#2421C2214yes—
126#2421C2214yes—
127#2401C2214yes—
128#2401C2214yes—
129#2370C2214yescomplemented
130#2370C2214yescomplemented
131#2369C2214yescomplemented
132#2365C2214yescomplemented
133#2345C2214yes—
134#2345C2214yes—
135#2345C2214yes—
136#2345C2214yes—
137#2334C2218yes—
138#2334C2218yes—
139#2331C2214yescomplemented
140#2330C2214yescomplemented
141#2329C2214yes—
142#2329C2214yes—
143#2317C2212yes—
144#2317C2212yes—
145#2317C2212yes—
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2316C2212yes—
150C4×C4⋊Q8C2214yescomplemented
151C4×#125C2214yescomplemented
152C4×#126C2214yes—
153C4×#126C2214yes—
154C4×C22⋊Q8C2214yes—
155C4×C22⋊Q8C2214yes—
156#2296C2212yes—
157#2296C2212yes—
158C2×#389C2211yescharacteristic
159C2×#389C2211yescharacteristic
160C2×#387C2212yes—
161C2×#387C2212yes—
162#2285C2212yes—
163#2280C2212yes—
164#2280C2212yes—
165C2×#380C2212yes—
166C2×#380C2211yescharacteristic
167#2274C2212yes—
168C4×#117C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C22⋊C4C2212yes—
172C2×C4×C22⋊C4C2211yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2312yes—
175#544—28no—
176#544—28no—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×#126C2314yes—
181C2×#126C2314yes—
182C2×#126C2318yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×#125C2318yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C22×C4⋊C4—28no—
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2314yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2312yes—
216C22×C42C2312yes—
217#401C2314yes—
218#401C2318yes—
219#401C2314yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2314yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2314yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2314yes—
239#400C2314yes—
240#400C2314yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#397C2314yes—
258#397C2314yes—
259#397C2314yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2314yes—
265#397C2314yes—
266#396C2314yes—
267#396C2318yes—
268#396C2314yes—
269#395C2318yes—
270#395C2318yes—
271#395C2318yes—
272#395C2318yes—
273#391C2318yes—
274#391C2314yes—
275#391C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2318yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2314yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#388C2314yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#388C2314yes—
324#388C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2314yes—
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#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2314yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#384C2314yes—
370#384C2312yes—
371#384C2314yes—
372#384C2314yes—
373#384C2314yes—
374#384C2314yes—
375#384C2312yes—
376#383C2314yes—
377#383C2314yes—
378#383C2318yes—
379#382C2314yes—
380#382C2314yes—
381#382C2312yes—
382#382C2314yes—
383#382C2312yes—
384#382C2318yes—
385#382C2314yes—
386#382C2318yes—
387#382C2314yes—
388#381C2314yes—
389#381C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2318yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2318yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2312yes—
411#379C2314yes—
412#379C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2314yes—
450#376C2314yes—
451C2×#95C2312yes—
452C2×#95C2312yes—
453C2×#95C2311yescharacteristic
454C2×#95C2311yescharacteristic
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C43C2314yes—
459C25C2411yescharacteristic
460C22×Q8C2414yes—
461C22×Q8C2414yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—28no—
466C23×C4—82no—
467C23×C4—82no—
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C4⋊Q8—216no—
483C4⋊Q8—216no—
484C4⋊Q8—84no—
485#126—216no—
486#126—48no—
487#126—416no—
488#125—216no—
489#125—216no—
490#125—84no—
491#125—88no—
492#125—88no—
493C22⋊Q8—216no—
494C22⋊Q8—216no—
495C22⋊Q8—84no—
496C22⋊Q8—84no—
497C22⋊Q8—84no—
498C22⋊Q8—84no—
499C4×Q8—84no—
500C4×Q8—84no—
501#117—28no—
502#117—28no—
503#117—28no—
504#117—28no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—216no—
510C2×C4⋊C4—216no—
511C2×C4⋊C4—82no—
512C2×C4⋊C4—82no—
513C2×C4⋊C4#4118yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—44no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2411yescharacteristic
565C2×C22⋊C4C2411yescharacteristic
566C2×C22⋊C4C2411yescharacteristic
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2411yescharacteristic
582C2×C42—24no—
583C2×C42—24no—
584C2×C42—82no—
585C2×C42—82no—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2418yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2418yes—
603C2×C42C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2412yes—
607#95C2412yes—
608#95C2412yes—
609#95C2414yes—
610#95C2412yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2418yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—41no—
659C24—41no—
660C24C2511yescharacteristic
661C24C2511yescharacteristic
662C24C2511yescharacteristic
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C22×C4—24no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—41no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—42no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—416no—
708C22×C4—816no—
709C22×C4C2×#4118yes—
710C22×C4C2×#4114yes—
711C22×C42−1+414yes—
712C22×C42−1+414yes—
713C22×C4C2512yes—
714C22×C4C2511yescharacteristic
715C22×C4C2511yescharacteristic
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2512yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2514yes—
729C22×C4C2514yes—
730C22×C4C2511yescharacteristic
731C22×C4C2511yescharacteristic
732C22×C4C2512yes—
733C4⋊C4—216no—
734C4⋊C4—28no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—216no—
742C4⋊C4—216no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—44no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—44no—
777C4⋊C4C2×#41116yes—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—22no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—24no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—42no—
792C22⋊C4—44no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C42−1+414yes—
798C42—28no—
799C42—28no—
800C42—24no—
801C42—24no—
802C42—24no—
803C42—24no—
804C42—28no—
805C42—28no—
806C42—28no—
807C42—44no—
808C42—44no—
809C42—44no—
810C42—44no—
811C42—44no—
812C42—48no—
813C42—44no—
814C42—48no—
815C42—44no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—28no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23C22×#4112yes—
840C23C2×2−1+412yes—
841C23C2×2−1+412yes—
842C23C2×2−1+412yes—
843C23#58512yes—
844C23C2611yescharacteristic
845Q8—88no—
846Q8—88no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—48no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—48no—
905C2×C4—44no—
906C2×C4—48no—
907C2×C4—48no—
908C2×C4—88no—
909C2×C4—88no—
910C2×C4—82no—
911C2×C4—82no—
912C2×C4—84no—
913C2×C4—84no—
914C2×C4#541116yes—
915C2×C4C22×#4118yes—
916C2×C4C22×#4114yes—
917C2×C4C2×2−1+412yes—
918C2×C4C2×2−1+412yes—
919C2×C4C2×2−1+414yes—
920C2×C4C2×2−1+414yes—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—416no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22C2×#54114yes—
943C22C23×#4111yescharacteristic
944C22C22×2−1+411yescharacteristic
945C22C22×2−1+411yescharacteristic
946C22C22×2−1+411yescharacteristic
947C22C2×#58511yescharacteristic
948C22H(7,𝔽2)11yescharacteristic
949C22H(7,𝔽2)11yescharacteristic
950C4—28no—
951C4—22no—
952C4—22no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4—44no—
958C4—42no—
959C4—44no—
960C4—44no—
961C4—41no—
962C4—41no—
963C4—44no—
964C4—44no—
965C4—42no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4C2×#54118yes—
970C2—24no—
971C2—42no—
972C2—42no—
973C2C22×#54111yescharacteristic
974C2#6278811yescharacteristic
975C2#6284611yescharacteristic
976C2#6294511yescharacteristic
977C2#6294511yescharacteristic
978C2#6295811yescharacteristic
979C2#6295811yescharacteristic
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. #42753C2semidirect
2. #42728C2semidirect
3. #42610C2semidirect
4. #42546C2semidirect
5. #40202C2semidirect
6. #40096C2semidirect
7. #39661C2semidirect
8. #39250C2semidirect
9. #37466C2semidirect
10. #36762C2semidirect
13. #35543C2semidirect
14. #35265C2semidirect
17. #35167C2semidirect
18. #35159C2semidirect
21. #34271C2semidirect
23. C4×#544C2semidirect
27. #2864C22semidirect
28. #2859C22semidirect
33. #2839C22semidirect
34. #2833C22semidirect
35. #2802C22semidirect
36. #2794C22semidirect
37. #2789C22semidirect
38. #2776C22semidirect
39. #2766C22semidirect
40. #2758C22semidirect
45. #2719C22semidirect
46. #2713C22semidirect
51. #2666C22semidirect
53. #2655C22semidirect
54. #2655C22semidirect
57. #2647C22semidirect
58. #2647C22semidirect
60. #2634C22semidirect
63. #2571C22semidirect
64. #2570C22semidirect
65. #2570C22semidirect
66. #2552C22semidirect
67. #2552C22semidirect
68. #2551C22semidirect
69. #2550C22semidirect
70. #2550C22semidirect
71. #2524C22semidirect
72. #2509C22semidirect
73. #2509C22semidirect
74. #2509C22semidirect
75. #2508C22semidirect
76. #2508C22semidirect
77. #2508C22semidirect
78. #2507C22semidirect
79. #2507C22semidirect
80. #2507C22semidirect
81. #2506C22semidirect
82. #2506C22semidirect
83. #2506C22semidirect
114. #2462C22semidirect
129. #2370C22semidirect
130. #2370C22semidirect
131. #2369C22semidirect
132. #2365C22semidirect
139. #2331C22semidirect
140. #2330C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#427532
#427282
#426102
#425462
#402022
#400962
#396612
#392502
#374662
#367622
#367282
#355442
#355432
#352652
#352242
#351672
#351592
#350862
#348142
#342712
C2×#23452
C4×#5442