Finite Group Databasebeta

← #7674541

Subgroups — #7674541

Order 512.

5778 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44786C214yesmaximal, complemented
2#43931C218yesmaximal, complemented
3#43047C214yesmaximal, complemented
4#39567C214yesmaximal, complemented
5#39565C214yesmaximal, complemented
6#39562C214yesmaximal, complemented
7#39560C214yesmaximal, complemented
8#37975C214yesmaximal, complemented
9#37972C214yesmaximal, complemented
10#37970C214yesmaximal, complemented
11#37969C214yesmaximal, complemented
12#35584C211yesmaximal, characteristic, complemented
13#35544C212yesmaximal, complemented
14#35540C211yesmaximal, characteristic, complemented
15#35262C212yesmaximal, complemented
16#35253C212yesmaximal, complemented
17C2×#2615C211yesmaximal, characteristic
18#34204C212yesmaximal, complemented
19#34180C212yesmaximal, complemented
20#34044C212yesmaximal, complemented
21C23×#41C2211yescharacteristic
22C2×#544C2211yescharacteristic
23C22×#121C2212yes—
24C22×#121C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C22×#117C2212yes—
27C22×#117C2212yes—
28#2857C2214yescomplemented
29#2854C2214yescomplemented
30#2854C2214yescomplemented
31#2851C2214yescomplemented
32#2798C2218yescomplemented
33#2797C2218yescomplemented
34#2778C2218yescomplemented
35#2764C2214yescomplemented
36#2763C2214yescomplemented
37#2760C2214yescomplemented
38#2759C2218yescomplemented
39#2756C2218yescomplemented
40#2754C2218yescomplemented
41#2753C2218yescomplemented
42#2752C2218yescomplemented
43#2749C2218yescomplemented
44#2749C2218yescomplemented
45#2730C2218yescomplemented
46#2706C2218yescomplemented
47#2705C2218yescomplemented
48#2696C2218yescomplemented
49#2693C2214yescomplemented
50#2629C2214yescomplemented
51#2628C2214yescomplemented
52#2624C2214yescomplemented
53#2624C2214yescomplemented
54#2615C2214yes—
55#2615C2214yes—
56#2615C2214yes—
57#2615C2214yes—
58#2610C2218yescomplemented
59#2607C2214yescomplemented
60#2603C2218yescomplemented
61#2602C2218yescomplemented
62#2600C2214yescomplemented
63#2598C2218yescomplemented
64#2589C2218yescomplemented
65#2561C2214yes—
66#2557C2218yescomplemented
67#2554C2218yescomplemented
68#2532C2218yescomplemented
69#2527C2218yescomplemented
70#2523C2214yescomplemented
71#2504C2214yescomplemented
72#2501C2214yescomplemented
73#2500C2214yescomplemented
74#2500C2214yescomplemented
75#2497C2214yescomplemented
76#2497C2214yescomplemented
77#2496C2214yescomplemented
78#2496C2214yescomplemented
79#2495C2214yescomplemented
80#2495C2214yescomplemented
81#2494C2214yescomplemented
82#2494C2214yescomplemented
83#2493C2218yes—
84#2491C2214yescomplemented
85#2491C2214yescomplemented
86#2490C2214yescomplemented
87#2490C2214yescomplemented
88#2483C2214yes—
89#2482C2218yes—
90#2480C2218yes—
91#2471C2218yescomplemented
92#2471C2218yescomplemented
93#2467C2218yescomplemented
94#2463C2214yescomplemented
95#2461C2218yescomplemented
96#2457C2218yescomplemented
97#2442C2214yescomplemented
98#2441C2214yescomplemented
99#2440C2214yescomplemented
100#2439C2214yescomplemented
101#2438C2218yes—
102#2437C2218yes—
103#2435C2214yes—
104#2422C2214yescomplemented
105#2422C2214yescomplemented
106#2420C2214yescomplemented
107#2420C2214yescomplemented
108#2405C2218yes—
109#2405C2214yes—
110C2×#393C2212yes—
111C2×#392C2212yes—
112C2×#392C2214yes—
113#2363C2214yescomplemented
114#2363C2214yescomplemented
115#2361C2214yescomplemented
116#2361C2214yescomplemented
117#2347C2214yescomplemented
118#2346C2214yescomplemented
119#2345C2214yescomplemented
120#2344C2214yescomplemented
121#2343C2218yes—
122#2342C2218yes—
123#2342C2218yes—
124D4×C22⋊C4C2218yes—
125#2324C2214yescomplemented
126#2324C2214yescomplemented
127#2317C2212yes—
128#2317C2212yes—
129#2317C2212yes—
130#2316C2212yes—
131#2314C2214yescomplemented
132#2314C2214yescomplemented
133#2311C2212yescomplemented
134#2311C2212yescomplemented
135#2311C2212yescomplemented
136#2311C2212yescomplemented
137#2311C2212yescomplemented
138#2311C2212yescomplemented
139#2311C2212yescomplemented
140#2311C2212yescomplemented
141#2310C2214yes—
142#2309C2212yes—
143#2309C2214yes—
144#2309C2211yescharacteristic
145#2308C2214yes—
146#2308C2214yes—
147C4×#121C2214yescomplemented
148C4×#121C2214yescomplemented
149#2297C2214yescomplemented
150#2297C2214yescomplemented
151#2297C2214yescomplemented
152#2297C2214yescomplemented
153#2285C2214yescomplemented
154#2283C2214yescomplemented
155#2280C2212yes—
156#2280C2212yes—
157#2280C2212yes—
158#2280C2212yes—
159C2×#380C2212yes—
160C2×#380C2211yescharacteristic
161#2274C2211yescharacteristic
162#2274C2212yes—
163C22×#41—216no—
164C22×#41—44no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C23×Q8C2311yescharacteristic
170C23×D4C2311yescharacteristic
171C23×D4C2311yescharacteristic
172C23×D4C2312yes—
173C23×D4C2314yes—
174C23×D4C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177#544—44no—
178C2×C4⋊Q8C2314yes—
179C2×#126C2318yes—
180C2×#125C2314yes—
181C2×#124C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2318yes—
187C2×#121—216no—
188C2×#121—44no—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195#518—44no—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C2318yes—
200C2×#117—216no—
201C2×#117—48no—
202C2×#117C2314yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2318yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C22⋊C4C2314yes—
222C22×C22⋊C4C2314yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2312yes—
228C22×C42C2314yes—
229C22×C42C2314yes—
230#401C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#399C2318yes—
236#399C2318yes—
237#399C2318yes—
238#398C2318yes—
239#398C2318yes—
240#397C2314yes—
241#397C2314yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#395C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#393C2314yes—
262#393C2314yes—
263#393C2318yes—
264#393C2314yes—
265#393C2318yes—
266#393C2314yes—
267#392C2318yes—
268#392C2314yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2314yes—
273#392C2318yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2314yes—
282#391C2318yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2318yes—
298#390C2318yes—
299#390C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#386C2314yes—
338#386C2314yes—
339#386C2314yes—
340#386C2314yes—
341#386C2314yes—
342#386C2314yes—
343#386C2314yes—
344#386C2314yes—
345#386C2314yes—
346#386C2314yes—
347#386C2314yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#386C2314yes—
352#386C2314yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#384C2314yes—
370#384C2314yes—
371#384C2314yes—
372#383C2318yes—
373#383C2318yes—
374#382C2314yes—
375#382C2314yes—
376#382C2314yes—
377#382C2318yes—
378#381C2314yes—
379#381C2314yes—
380#381C2314yes—
381#381C2314yes—
382#381C2318yes—
383#381C2314yes—
384#381C2314yes—
385#380C2312yes—
386#380C2312yes—
387#380C2312yes—
388#380C2312yes—
389#380C2312yes—
390#380C2312yes—
391#380C2312yes—
392#380C2312yes—
393#380C2312yes—
394#380C2312yes—
395#380C2312yes—
396#380C2312yes—
397#380C2312yes—
398#380C2312yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2318yes—
403#380C2318yes—
404#380C2314yes—
405#380C2318yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#379C2318yes—
411#379C2314yes—
412#379C2314yes—
413#379C2314yes—
414#379C2314yes—
415#379C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436#376C2318yes—
437C2×#95C2314yes—
438C2×#95C2312yes—
439C25C2412yes—
440C25C2411yescharacteristic
441C25C2412yes—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—44no—
451C2×#41—44no—
452C2×#41—44no—
453C2×#41—44no—
454C2×#41—464no—
455C22×Q8—28no—
456C22×Q8—42no—
457C22×Q8C2412yes—
458C22×Q8C2411yescharacteristic
459C22×Q8C2411yescharacteristic
460C22×Q8C2414yes—
461C22×D4—28no—
462C22×D4—28no—
463C22×D4—216no—
464C22×D4—28no—
465C22×D4—28no—
466C22×D4—24no—
467C22×D4—44no—
468C22×D4—42no—
469C22×D4—44no—
470C22×D4—84no—
471C22×D4—84no—
472C22×D4—84no—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C22×D4C2411yescharacteristic
476C22×D4C2411yescharacteristic
477C22×D4C2412yes—
478C22×D4C2412yes—
479C22×D4C2412yes—
480C22×D4C2412yes—
481C22×D4C2418yes—
482C22×D4C2418yes—
483C22×D4C2418yes—
484C23×C4—28no—
485C23×C4—28no—
486C23×C4—28no—
487C23×C4—24no—
488C23×C4#41116yes—
489C23×C4C2411yescharacteristic
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2411yescharacteristic
506C4⋊Q8—48no—
507#126—88no—
508#125—48no—
509#124—88no—
510#123—88no—
511#123—88no—
512#123—88no—
513C22⋊Q8—48no—
514C22⋊Q8—88no—
515#121—216no—
516#121—216no—
517#121—216no—
518#121—216no—
519#121—48no—
520#121—48no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—88no—
524C4×D4—88no—
525#117—216no—
526#117—28no—
527#117—28no—
528#117—216no—
529#117—28no—
530#117—28no—
531#117—28no—
532#117—28no—
533#117—48no—
534#117—48no—
535#117—44no—
536#117—44no—
537#117—88no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4—28no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C22⋊C4—216no—
570C2×C22⋊C4—216no—
571C2×C22⋊C4—48no—
572C2×C22⋊C4—48no—
573C2×C22⋊C4—44no—
574C2×C22⋊C4—84no—
575C2×C22⋊C4—82no—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C42—216no—
616C2×C42—48no—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2418yes—
626C2×C42C2418yes—
627C2×C42C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660C24—24no—
661C24—24no—
662C24—22no—
663C24—28no—
664C24—24no—
665C24—24no—
666C24—42no—
667C24—41no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—41no—
673C24—42no—
674C24—44no—
675C24—42no—
676C24C2×#4118yes—
677C24C2514yes—
678C24C2512yes—
679C24C2512yes—
680C24C2512yes—
681C24C2511yescharacteristic
682#41—432no—
683#41—432no—
684#41—432no—
685#41—432no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—24no—
689C2×Q8—24no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—41no—
693C2×Q8—44no—
694C2×Q8—48no—
695C2×Q8—416no—
696C2×D4—216no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—216no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—28no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—41no—
722C2×D4—432no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—416no—
729C2×D4—416no—
730C2×D4—832no—
731C2×D4—816no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—264no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—44no—
773C22×C4—416no—
774C22×C4C2×#4118yes—
775C22×C4C2×#4118yes—
776C22×C4C2×#4118yes—
777C22×C4C2×#4118yes—
778C22×C4C2×#4118yes—
779C22×C4C2×#4118yes—
780C22×C4H(5,𝔽2)14yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2518yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2512yes—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—48no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—216no—
828C22⋊C4—216no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C42—28no—
861C42—28no—
862C42—28no—
863C42—28no—
864C42—28no—
865C42—28no—
866C42—44no—
867C42—44no—
868C42—48no—
869C42—48no—
870C42—48no—
871C23—21no—
872C23—22no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—216no—
887C23—28no—
888C23—22no—
889C23—22no—
890C23—24no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—24no—
896C23—28no—
897C23—22no—
898C23—24no—
899C23—48no—
900C23—48no—
901C23—44no—
902C23—44no—
903C23—44no—
904C23—48no—
905C23—84no—
906C23—84no—
907C23—84no—
908C23—84no—
909C23—84no—
910C23—84no—
911C23—88no—
912C23—84no—
913C23—88no—
914C23—84no—
915C23C22×#4114yes—
916C23C22×#4114yes—
917C23C22×#4114yes—
918C23C2×H(5,𝔽2)12yes—
919C23C2611yescharacteristic
920Q8—44no—
921Q8—48no—
922Q8—44no—
923Q8—164no—
924D4—48no—
925D4—48no—
926D4—48no—
927D4—48no—
928D4—44no—
929D4—48no—
930D4—44no—
931D4—432no—
932D4—416no—
933D4—816no—
934D4—816no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—216no—
940C2×C4—216no—
941C2×C4—216no—
942C2×C4—216no—
943C2×C4—216no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—28no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—416no—
978C2×C4—44no—
979C2×C4—48no—
980C2×C4—48no—
981C2×C4—88no—
982C2×C4—88no—
983C2×C4—84no—
984C2×C4—88no—
985C2×C4—88no—
986C2×C4—164no—
987C2×C4—164no—
988C2×C4#551116yes—
989C2×C4C22×#4114yes—
990C2×C4C22×#4114yes—
991C2×C4C22×#4114yes—
992C2×C4C22×#4114yes—
993C2×C4C2×H(5,𝔽2)14yes—
994C22—24no—
995C22—24no—
996C22—22no—
997C22—22no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—48no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—48no—
1018C22—44no—
1019C22—42no—
1020C22—44no—
1021C22—42no—
1022C22—42no—
1023C22—44no—
1024C22—816no—
1025C22—88no—
1026C22—168no—
1027C22C2×#55114yes—
1028C22C23×#4112yes—
1029C22C22×H(5,𝔽2)11yescharacteristic
1030C22H(7,𝔽2)11yescharacteristic
1031C22H(7,𝔽2)12yes—
1032C222−1+611yescharacteristic
1033C4—24no—
1034C4—24no—
1035C4—44no—
1036C4—44no—
1037C4—48no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—44no—
1045C4—41no—
1046C4—41no—
1047C4C2×#55118yes—
1048C2—24no—
1049C2—44no—
1050C2—44no—
1051C2—82no—
1052C2—84no—
1053C2C22×#55111yescharacteristic
1054C2#6285512yes—
1055C2#6285612yes—
1056C2#6287411yescharacteristic
1057C2#6287511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#2615C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44786C2semidirect
2. #43931C2semidirect
3. #43047C2semidirect
4. #39567C2semidirect
5. #39565C2semidirect
6. #39562C2semidirect
7. #39560C2semidirect
8. #37975C2semidirect
9. #37972C2semidirect
10. #37970C2semidirect
11. #37969C2semidirect
12. #35584C2semidirect
13. #35544C2semidirect
14. #35540C2semidirect
15. #35262C2semidirect
16. #35253C2semidirect
18. #34204C2semidirect
19. #34180C2semidirect
20. #34044C2semidirect
28. #2857C22semidirect
29. #2854C22semidirect
30. #2854C22semidirect
31. #2851C22semidirect
32. #2798C22semidirect
33. #2797C22semidirect
34. #2778C22semidirect
35. #2764C22semidirect
36. #2763C22semidirect
37. #2760C22semidirect
38. #2759C22semidirect
39. #2756C22semidirect
40. #2754C22semidirect
41. #2753C22semidirect
42. #2752C22semidirect
43. #2749C22semidirect
44. #2749C22semidirect
45. #2730C22semidirect
46. #2706C22semidirect
47. #2705C22semidirect
48. #2696C22semidirect
49. #2693C22semidirect
50. #2629C22semidirect
51. #2628C22semidirect
52. #2624C22semidirect
53. #2624C22semidirect
58. #2610C22semidirect
59. #2607C22semidirect
60. #2603C22semidirect
61. #2602C22semidirect
62. #2600C22semidirect
63. #2598C22semidirect
64. #2589C22semidirect
66. #2557C22semidirect
67. #2554C22semidirect
68. #2532C22semidirect
69. #2527C22semidirect
70. #2523C22semidirect
71. #2504C22semidirect
72. #2501C22semidirect
73. #2500C22semidirect
74. #2500C22semidirect
75. #2497C22semidirect
76. #2497C22semidirect
77. #2496C22semidirect
78. #2496C22semidirect
79. #2495C22semidirect
80. #2495C22semidirect
81. #2494C22semidirect
82. #2494C22semidirect
84. #2491C22semidirect
85. #2491C22semidirect
86. #2490C22semidirect
87. #2490C22semidirect
91. #2471C22semidirect
92. #2471C22semidirect
93. #2467C22semidirect
94. #2463C22semidirect
95. #2461C22semidirect
96. #2457C22semidirect
97. #2442C22semidirect
98. #2441C22semidirect
99. #2440C22semidirect
100. #2439C22semidirect
104. #2422C22semidirect
105. #2422C22semidirect
106. #2420C22semidirect
107. #2420C22semidirect
113. #2363C22semidirect
114. #2363C22semidirect
115. #2361C22semidirect
116. #2361C22semidirect
117. #2347C22semidirect
118. #2346C22semidirect
119. #2345C22semidirect
120. #2344C22semidirect
125. #2324C22semidirect
126. #2324C22semidirect
131. #2314C22semidirect
132. #2314C22semidirect
133. #2311C22semidirect
134. #2311C22semidirect
135. #2311C22semidirect
136. #2311C22semidirect
137. #2311C22semidirect
138. #2311C22semidirect
139. #2311C22semidirect
140. #2311C22semidirect
147. C4×#121C22semidirect
148. C4×#121C22semidirect
149. #2297C22semidirect
150. #2297C22semidirect
151. #2297C22semidirect
152. #2297C22semidirect
153. #2285C22semidirect
154. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#447862
#439312
#430472
#395672
#395652
#395622
#395602
#379752
#379722
#379702
#379692
#355842
#355442
#355402
#352622
#352532
C2×#26152
#342042
#341802
#340442