Finite Group Databasebeta

← #7731043

Subgroups — #7731043

Order 512.

5546 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#47885C214yesmaximal, complemented
2#47883C214yesmaximal, complemented
3#46999C212yesmaximal, complemented
4#46388C212yesmaximal, complemented
5#46386C212yesmaximal, complemented
6#46386C212yesmaximal, complemented
7#43091C218yesmaximal, complemented
8#39040C214yesmaximal, complemented
9#38060C214yesmaximal, complemented
10#37901C218yesmaximal, complemented
11#37750C214yesmaximal, complemented
12#37481C211yesmaximal, characteristic, complemented
13#37398C214yesmaximal, complemented
14#36143C214yesmaximal, complemented
15#35523C214yesmaximal, complemented
16#35305C211yesmaximal, characteristic, complemented
17#35084C211yesmaximal, characteristic, complemented
18#34736C211yesmaximal, characteristic
19#34370C211yesmaximal, characteristic, complemented
20#34172C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C2×#536C2212yescomplemented
24C2×#529C2214yescomplemented
25C2×#525C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C2×#518C2212yescomplemented
28C22×C4×D4C2211yescharacteristic
29#2857C2214yescomplemented
30#2855C2212yescomplemented
31#2855C2214yescomplemented
32#2848C2212yescomplemented
33#2848C2214yescomplemented
34#2842C2212yes—
35#2842C2212yes—
36#2805C2218yescomplemented
37#2788C2218yescomplemented
38#2774C2218yescomplemented
39#2771C2218yescomplemented
40#2765C2218yescomplemented
41#2750C2218yes—
42#2750C2218yescomplemented
43#2746C2218yescomplemented
44#2746C2218yescomplemented
45#2745C2218yescomplemented
46#2744C2218yescomplemented
47#2743C2218yes—
48#2743C2218yescomplemented
49#2743C2218yescomplemented
50#2743C2218yescomplemented
51#2695C2218yescomplemented
52#2693C2218yescomplemented
53#2693C2218yescomplemented
54#2689C2218yescomplemented
55#2687C2218yescomplemented
56#2667C2214yescomplemented
57#2667C2214yescomplemented
58#2645C2214yescomplemented
59#2642C2214yescomplemented
60#2638C2214yes—
61#2629C2214yescomplemented
62#2616C2214yes—
63#2608C2214yescomplemented
64#2600C2218yescomplemented
65#2583C2212yescomplemented
66#2576C2218yescomplemented
67#2575C2218yescomplemented
68#2573C2218yescomplemented
69#2569C2218yescomplemented
70#2561C2212yescomplemented
71#2553C2218yescomplemented
72#2534C2218yes—
73#2534C2218yescomplemented
74#2511C2214yescomplemented
75#2505C2218yescomplemented
76#2493C2218yescomplemented
77#2489C2214yescomplemented
78#2486C2212yescomplemented
79#2485C2218yescomplemented
80#2483C2212yes—
81#2482C2218yescomplemented
82#2480C2218yescomplemented
83#2470C2218yescomplemented
84#2470C2218yescomplemented
85#2466C2218yescomplemented
86#2466C2218yescomplemented
87#2457C2218yescomplemented
88#2457C2218yescomplemented
89#2455C2218yescomplemented
90#2454C2214yescomplemented
91#2450C2218yescomplemented
92#2447C2214yescomplemented
93#2446C2214yescomplemented
94#2441C2214yescomplemented
95#2441C2214yescomplemented
96#2438C2218yescomplemented
97#2435C2212yescomplemented
98#2434C2212yescomplemented
99#2432C2214yes—
100#2429C2214yescomplemented
101#2427C2214yescomplemented
102#2422C2214yescomplemented
103#2419C2218yescomplemented
104#2419C2218yescomplemented
105#2418C2218yes—
106#2418C2218yescomplemented
107#2415C2214yes—
108#2409C2212yes—
109#2409C2212yescomplemented
110#2408C2212yes—
111#2407C2214yes—
112#2406C2212yes—
113#2406C2214yescomplemented
114#2405C2212yes—
115#2405C2212yes—
116#2405C2212yes—
117#2405C2212yes—
118#2404C2212yes—
119#2403C2212yes—
120#2388C2214yes—
121#2378C2214yescomplemented
122#2362C2214yescomplemented
123#2359C2218yescomplemented
124#2349C2218yescomplemented
125#2345C2214yescomplemented
126#2345C2212yescomplemented
127Q8×C22⋊C4C2212yescomplemented
128#2339C2214yes—
129#2339C2214yes—
130#2339C2214yescomplemented
131#2339C2214yescomplemented
132#2332C2214yescomplemented
133#2326C2214yescomplemented
134#2323C2214yescomplemented
135#2322C2214yescomplemented
136#2319C2214yescomplemented
137#2318C2214yes—
138#2318C2214yescomplemented
139#2315C2212yescomplemented
140#2313C2212yescomplemented
141#2312C2211yescharacteristic
142#2312C2211yescharacteristic
143#2312C2212yes—
144#2312C2212yes—
145#2311C2212yescomplemented
146#2310C2212yescomplemented
147#2308C2211yescharacteristic
148#2308C2211yescharacteristic
149#2308C2212yes—
150#2308C2212yes—
151C4×#121C2214yescomplemented
152C4×#120C2214yes—
153#2297C2212yes—
154#2290C2214yes—
155#2290C2214yescomplemented
156#2283C2212yescomplemented
157#2280C2211yescharacteristic
158#2280C2211yescharacteristic
159#2280C2211yescharacteristic
160#2280C2211yescharacteristic
161C2×#381C2214yescomplemented
162C2×C4×C22⋊C4C2212yescomplemented
163C22×#41—28no—
164C22×#41—48no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C23×Q8C2311yescharacteristic
170C23×Q8C2311yescharacteristic
171C23×D4C2311yescharacteristic
172C23×D4C2312yes—
173C23×D4C2311yescharacteristic
174C24×C4C2312yes—
175C24×C4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177#536—48no—
178C2×C4⋊Q8C2314yes—
179#529—416no—
180C2×#126C2318yes—
181C2×#125C2314yes—
182C2×#124C2314yes—
183#525—48no—
184C2×#123C2314yes—
185C2×#123C2318yes—
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×C22⋊Q8—28no—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2314yes—
199C2×#120C2314yes—
200C2×#120C2314yes—
201#518—48no—
202C2×C4×Q8C2314yes—
203C2×C4×D4—28no—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2318yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2318yes—
218C2×#117C2312yes—
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2314yes—
228C22×C22⋊C4C2314yes—
229C22×C42C2311yescharacteristic
230C22×C42C2314yes—
231#401C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#399C2318yes—
244#399C2318yes—
245#399C2318yes—
246#398C2314yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#397C2314yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2314yes—
265#395C2318yes—
266#395C2314yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2314yes—
274#394C2318yes—
275#393C2314yes—
276#393C2314yes—
277#392C2314yes—
278#392C2318yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2318yes—
286#391C2314yes—
287#390C2314yes—
288#390C2314yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2318yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#388C2318yes—
301#388C2314yes—
302#388C2314yes—
303#388C2314yes—
304#388C2314yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#387C2314yes—
317#387C2314yes—
318#387C2314yes—
319#387C2314yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#386C2314yes—
333#386C2314yes—
334#386C2314yes—
335#386C2314yes—
336#386C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2314yes—
341#386C2314yes—
342#386C2314yes—
343#386C2318yes—
344#386C2318yes—
345#386C2314yes—
346#386C2314yes—
347#386C2314yes—
348#386C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2314yes—
352#385C2314yes—
353#385C2314yes—
354#385C2314yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2314yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#385C2314yes—
364#385C2314yes—
365#385C2314yes—
366#385C2318yes—
367#385C2314yes—
368#385C2318yes—
369#384C2314yes—
370#383C2314yes—
371#382C2314yes—
372#382C2318yes—
373#381C2314yes—
374#381C2314yes—
375#381C2314yes—
376#381C2312yes—
377#381C2312yes—
378#381C2318yes—
379#381C2312yes—
380#381C2312yes—
381#381C2318yes—
382#381C2314yes—
383#381C2318yes—
384#381C2318yes—
385#381C2312yes—
386#381C2312yes—
387#381C2318yes—
388#380C2318yes—
389#380C2312yes—
390#380C2312yes—
391#380C2314yes—
392#380C2314yes—
393#380C2312yes—
394#380C2312yes—
395#380C2318yes—
396#380C2318yes—
397#380C2312yes—
398#380C2312yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2318yes—
405#380C2318yes—
406#380C2318yes—
407#379C2314yes—
408#379C2311yescharacteristic
409#379C2311yescharacteristic
410#379C2312yes—
411#379C2311yescharacteristic
412#379C2311yescharacteristic
413#379C2312yes—
414#379C2314yes—
415#379C2314yes—
416#379C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436#376C2314yes—
437C2×#95C2318yes—
438C2×#95C2314yes—
439C2×#95C2318yes—
440C25C2411yescharacteristic
441C25C2412yes—
442C25C2411yescharacteristic
443C2×#41—28no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—48no—
450C2×#41—48no—
451C2×#41—44no—
452C2×#41—44no—
453C2×#41—464no—
454C22×Q8—24no—
455C22×Q8—24no—
456C22×Q8—44no—
457C22×Q8—44no—
458C22×Q8C2412yes—
459C22×Q8C2412yes—
460C22×Q8C2412yes—
461C22×Q8C2412yes—
462C22×D4—28no—
463C22×D4—24no—
464C22×D4—28no—
465C22×D4—24no—
466C22×D4—44no—
467C22×D4—48no—
468C22×D4C2412yes—
469C22×D4C2418yes—
470C22×D4C2412yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2412yes—
475C23×C4—28no—
476C23×C4—24no—
477C23×C4—44no—
478C23×C4—44no—
479C23×C4—48no—
480C23×C4#4118yes—
481C23×C4C2412yes—
482C23×C4C2414yes—
483C23×C4C2414yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2411yescharacteristic
490C23×C4C2412yes—
491C23×C4C2418yes—
492C23×C4C2414yes—
493C23×C4C2411yescharacteristic
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2418yes—
497C23×C4C2414yes—
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C4⋊Q8—48no—
502#126—416no—
503#125—48no—
504#124—216no—
505#123—416no—
506#123—48no—
507#123—48no—
508#123—416no—
509#123—48no—
510#123—48no—
511C22⋊Q8—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—28no—
515C22⋊Q8—416no—
516C22⋊Q8—48no—
517C22⋊Q8—48no—
518#121—216no—
519#120—48no—
520#120—48no—
521C4×Q8—48no—
522C4×D4—216no—
523C4×D4—28no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—28no—
527C4×D4—48no—
528C4×D4—416no—
529C4×D4—416no—
530C4×D4—416no—
531C4×D4—416no—
532#117—44no—
533#117—44no—
534#117—416no—
535#117—44no—
536#117—44no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—28no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—44no—
569C2×C22⋊C4—48no—
570C2×C22⋊C4—44no—
571C2×C22⋊C4—48no—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C42—24no—
611C2×C42—48no—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2418yes—
620C2×C42C2418yes—
621C2×C42C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2418yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—22no—
657C24—24no—
658C24—28no—
659C24—24no—
660C24—42no—
661C24—42no—
662C24—42no—
663C24—42no—
664C24—44no—
665C24—42no—
666C24—44no—
667C24C2×#4114yes—
668C24C2511yescharacteristic
669C24C2511yescharacteristic
670C24C2511yescharacteristic
671C24C2514yes—
672C24C2512yes—
673#41—432no—
674#41—432no—
675#41—432no—
676#41—432no—
677C2×Q8—24no—
678C2×Q8—24no—
679C2×Q8—24no—
680C2×Q8—24no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—416no—
687C2×Q8—88no—
688C2×D4—232no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—216no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—216no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—416no—
709C2×D4—432no—
710C2×D4H(5,𝔽2)18yes—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—216no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—416no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—42no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—42no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—432no—
753C22×C4—88no—
754C22×C4C2×#4114yes—
755C22×C4C2×#4114yes—
756C22×C4C2×#4114yes—
757C22×C4C2×#4114yes—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2512yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2518yes—
767C22×C4C2518yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—216no—
806C22⋊C4—216no—
807C22⋊C4—216no—
808C22⋊C4—216no—
809C22⋊C4—28no—
810C22⋊C4—216no—
811C22⋊C4—24no—
812C22⋊C4—24no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—44no—
816C22⋊C4—42no—
817C22⋊C4—44no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—44no—
824C22⋊C4—42no—
825C22⋊C4—42no—
826C22⋊C4—44no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—44no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—44no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—44no—
839C42—24no—
840C42—24no—
841C42—28no—
842C42—28no—
843C42—44no—
844C42—44no—
845C42—44no—
846C42—44no—
847C42—48no—
848C42—48no—
849C23—216no—
850C23—28no—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—24no—
858C23—22no—
859C23—28no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—28no—
867C23—24no—
868C23—44no—
869C23—44no—
870C23—44no—
871C23—82no—
872C23—84no—
873C23—82no—
874C23—84no—
875C23—88no—
876C23—816no—
877C23—88no—
878C23C22×#4112yes—
879C23C22×#4112yes—
880C23C22×#4112yes—
881C23C2×H(5,𝔽2)18yes—
882C23#58514yes—
883C23C2611yescharacteristic
884Q8—48no—
885Q8—48no—
886Q8—48no—
887Q8—84no—
888D4—216no—
889D4—216no—
890D4—432no—
891D4—48no—
892D4—48no—
893D4—416no—
894D4—416no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—28no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—48no—
939C2×C4—44no—
940C2×C4—48no—
941C2×C4—84no—
942C2×C4—84no—
943C2×C4—82no—
944C2×C4—88no—
945C2×C4—816no—
946C2×C4—82no—
947C2×C4—84no—
948C2×C4—88no—
949C2×C4—168no—
950C2×C4C22×#4112yes—
951C2×C4C22×#4112yes—
952C2×C4C22×#4112yes—
953C2×C4C22×#4112yes—
954C2×C4C2×H(5,𝔽2)14yes—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—28no—
959C22—22no—
960C22—22no—
961C22—24no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—28no—
967C22—216no—
968C22—42no—
969C22—44no—
970C22—42no—
971C22—44no—
972C22—44no—
973C22—48no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—88no—
978C22—816no—
979C22—88no—
980C22C23×#4111yescharacteristic
981C22C22×H(5,𝔽2)12yes—
982C22C2×#58512yes—
983C222−1+612yes—
984C4—22no—
985C4—22no—
986C4—22no—
987C4—44no—
988C4—42no—
989C4—44no—
990C4—42no—
991C4—44no—
992C4—42no—
993C4—44no—
994C4—44no—
995C4—44no—
996C4—48no—
997C4—44no—
998C4—48no—
999C4#349014yes—
1000C2—42no—
1001C2—48no—
1002C2—44no—
1003C2—42no—
1004C2—42no—
1005C2C2×#349011yescharacteristic
1006C2#6281411yescharacteristic
1007C2#6286011yescharacteristic
1008C2#6289814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34736C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #47885C2semidirect
2. #47883C2semidirect
3. #46999C2semidirect
4. #46388C2semidirect
5. #46386C2semidirect
6. #46386C2semidirect
7. #43091C2semidirect
8. #39040C2semidirect
9. #38060C2semidirect
10. #37901C2semidirect
11. #37750C2semidirect
12. #37481C2semidirect
13. #37398C2semidirect
14. #36143C2semidirect
15. #35523C2semidirect
16. #35305C2semidirect
17. #35084C2semidirect
19. #34370C2semidirect
20. #34172C2semidirect
21. #34057C2semidirect
23. C2×#536C22semidirect
24. C2×#529C22semidirect
27. C2×#518C22semidirect
29. #2857C22semidirect
30. #2855C22semidirect
31. #2855C22semidirect
32. #2848C22semidirect
33. #2848C22semidirect
36. #2805C22semidirect
37. #2788C22semidirect
38. #2774C22semidirect
39. #2771C22semidirect
40. #2765C22semidirect
42. #2750C22semidirect
43. #2746C22semidirect
44. #2746C22semidirect
45. #2745C22semidirect
46. #2744C22semidirect
48. #2743C22semidirect
49. #2743C22semidirect
50. #2743C22semidirect
51. #2695C22semidirect
52. #2693C22semidirect
53. #2693C22semidirect
54. #2689C22semidirect
55. #2687C22semidirect
56. #2667C22semidirect
57. #2667C22semidirect
58. #2645C22semidirect
59. #2642C22semidirect
61. #2629C22semidirect
63. #2608C22semidirect
64. #2600C22semidirect
65. #2583C22semidirect
66. #2576C22semidirect
67. #2575C22semidirect
68. #2573C22semidirect
69. #2569C22semidirect
70. #2561C22semidirect
71. #2553C22semidirect
73. #2534C22semidirect
74. #2511C22semidirect
75. #2505C22semidirect
76. #2493C22semidirect
77. #2489C22semidirect
78. #2486C22semidirect
79. #2485C22semidirect
81. #2482C22semidirect
82. #2480C22semidirect
83. #2470C22semidirect
84. #2470C22semidirect
85. #2466C22semidirect
86. #2466C22semidirect
87. #2457C22semidirect
88. #2457C22semidirect
89. #2455C22semidirect
90. #2454C22semidirect
91. #2450C22semidirect
92. #2447C22semidirect
93. #2446C22semidirect
94. #2441C22semidirect
95. #2441C22semidirect
96. #2438C22semidirect
97. #2435C22semidirect
98. #2434C22semidirect
100. #2429C22semidirect
101. #2427C22semidirect
102. #2422C22semidirect
103. #2419C22semidirect
104. #2419C22semidirect
106. #2418C22semidirect
109. #2409C22semidirect
113. #2406C22semidirect
121. #2378C22semidirect
122. #2362C22semidirect
123. #2359C22semidirect
124. #2349C22semidirect
125. #2345C22semidirect
126. #2345C22semidirect
127. Q8×C22⋊C4C22semidirect
130. #2339C22semidirect
131. #2339C22semidirect
132. #2332C22semidirect
133. #2326C22semidirect
134. #2323C22semidirect
135. #2322C22semidirect
136. #2319C22semidirect
138. #2318C22semidirect
139. #2315C22semidirect
140. #2313C22semidirect
145. #2311C22semidirect
146. #2310C22semidirect
151. C4×#121C22semidirect
155. #2290C22semidirect
156. #2283C22semidirect
161. C2×#381C22semidirect
162. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#478852
#478832
#469992
#463882
#463862
#430912
#390402
#380602
#379012
#377502
#374812
#373982
#361432
#355232
#353052
#350842
#347362
#343702
#341722
#340572