Finite Group Databasebeta

← #7647165

Subgroups — #7647165

Order 512.

5486 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42954C214yesmaximal, complemented
2#42953C214yesmaximal, complemented
3#42931C214yesmaximal, complemented
4#42930C214yesmaximal, complemented
5#39985C214yesmaximal, complemented
6#39984C214yesmaximal, complemented
7#39981C214yesmaximal, complemented
8#39980C214yesmaximal, complemented
9#37478C214yesmaximal, complemented
10#37134C218yesmaximal, complemented
11#35529C212yesmaximal, complemented
12#35515C212yesmaximal, complemented
13#35253C212yesmaximal, complemented
14#35179C212yesmaximal, complemented
15#35154C212yesmaximal, complemented
16#35065C214yesmaximal, complemented
17#34739C212yesmaximal, complemented
18#34172C211yesmaximal, characteristic
19C2×#2341C211yesmaximal, characteristic
20#34044C211yesmaximal, characteristic
21C23×#41C2211yescharacteristic
22C2×#544C2212yes—
23C2×#533C2212yes—
24C2×#518C2212yes—
25C22×C4×Q8C2212yes—
26C22×#117C2212yes—
27#2857C2214yescomplemented
28#2855C2218yes—
29#2855C2218yes—
30#2851C2214yescomplemented
31#2841C2218yescomplemented
32#2841C2218yescomplemented
33#2804C2218yescomplemented
34#2784C2218yescomplemented
35#2784C2218yescomplemented
36#2780C2218yescomplemented
37#2780C2218yescomplemented
38#2780C2218yescomplemented
39#2780C2218yescomplemented
40#2748C2218yescomplemented
41#2748C2218yescomplemented
42#2732C2218yescomplemented
43#2732C2218yescomplemented
44#2692C2218yescomplemented
45#2692C2218yescomplemented
46#2692C2218yescomplemented
47#2692C2218yescomplemented
48#2683C2218yescomplemented
49#2667C2218yescomplemented
50#2667C2214yescomplemented
51#2667C2214yescomplemented
52#2665C2218yescomplemented
53#2665C2214yescomplemented
54#2665C2214yescomplemented
55#2659C2218yescomplemented
56#2646C2218yescomplemented
57#2629C2214yescomplemented
58#2628C2214yescomplemented
59#2627C2218yes—
60#2627C2218yes—
61#2608C2218yescomplemented
62#2607C2218yescomplemented
63#2582C2214yescomplemented
64#2582C2214yescomplemented
65#2581C2214yescomplemented
66#2581C2214yescomplemented
67#2580C2214yescomplemented
68#2580C2214yescomplemented
69#2569C2214yescomplemented
70#2569C2214yescomplemented
71#2569C2218yescomplemented
72#2568C2214yescomplemented
73#2567C2214yescomplemented
74#2566C2214yescomplemented
75#2566C2214yescomplemented
76#2565C2214yescomplemented
77#2565C2214yescomplemented
78#2563C2214yescomplemented
79#2549C2214yescomplemented
80#2549C2214yescomplemented
81#2549C2218yescomplemented
82#2542C2214yescomplemented
83#2538C2214yescomplemented
84#2538C2214yescomplemented
85#2454C2214yescomplemented
86#2454C2214yescomplemented
87#2454C2214yescomplemented
88#2454C2214yescomplemented
89#2453C2214yescomplemented
90#2453C2214yescomplemented
91#2453C2214yescomplemented
92#2453C2214yescomplemented
93#2452C2214yescomplemented
94#2452C2214yescomplemented
95#2452C2214yescomplemented
96#2452C2214yescomplemented
97#2451C2214yescomplemented
98#2451C2214yescomplemented
99#2451C2214yescomplemented
100#2451C2214yescomplemented
101#2442C2214yescomplemented
102#2442C2212yescomplemented
103#2442C2212yescomplemented
104#2441C2212yescomplemented
105#2441C2214yescomplemented
106#2441C2212yescomplemented
107#2440C2212yescomplemented
108#2440C2212yescomplemented
109#2440C2214yescomplemented
110#2439C2214yescomplemented
111#2439C2212yescomplemented
112#2439C2212yescomplemented
113#2438C2214yes—
114#2438C2218yes—
115#2438C2214yes—
116#2437C2214yes—
117#2437C2214yes—
118#2437C2218yes—
119#2437C2218yes—
120#2437C2218yes—
121#2437C2218yes—
122#2437C2218yes—
123#2396C2214yescomplemented
124#2396C2214yescomplemented
125#2341C2214yes—
126#2341C2214yes—
127#2341C2214yes—
128#2341C2214yes—
129#2339C2214yes—
130#2339C2214yes—
131#2339C2214yes—
132#2339C2214yes—
133#2329C2218yescomplemented
134#2329C2218yescomplemented
135#2317C2212yes—
136#2317C2212yes—
137#2316C2212yes—
138#2311C2214yes—
139#2311C2214yes—
140#2310C2211yescharacteristic
141#2310C2212yes—
142#2310C2211yescharacteristic
143#2309C2211yescharacteristic
144#2309C2211yescharacteristic
145#2308C2214yes—
146#2308C2214yes—
147C4×C22⋊Q8C2214yescomplemented
148C4×C22⋊Q8C2214yescomplemented
149#2297C2214yes—
150#2297C2214yes—
151#2296C2212yes—
152#2296C2212yes—
153C2×#390C2214yes—
154C2×#390C2212yes—
155#2285C2212yes—
156#2280C2214yes—
157#2280C2212yes—
158C2×#381C2214yes—
159C2×#380C2212yes—
160C2×#380C2211yescharacteristic
161C2×C4×C22⋊C4C2211yescharacteristic
162C2×C4×C22⋊C4C2212yes—
163C22×#41—48no—
164C22×#41Q8116yescomplemented
165C22×#41C2314yes—
166C22×#41C2314yes—
167C23×Q8C2311yescharacteristic
168C23×D4C2311yescharacteristic
169C23×D4C2312yes—
170C24×C4C2311yescharacteristic
171C24×C4C2312yes—
172#544—48no—
173#533—48no—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×#125C2312yes—
179C2×#125C2312yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2318yes—
192#518—48no—
193C2×C4×Q8—48no—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×#117—48no—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2314yes—
217C22×C22⋊C4C2314yes—
218C22×C22⋊C4C2318yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2314yes—
221C22×C22⋊C4C2314yes—
222C22×C22⋊C4C2312yes—
223C22×C42C2312yes—
224C22×C42C2314yes—
225C22×C42C2314yes—
226#400C2318yes—
227#400C2318yes—
228#400C2314yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2318yes—
233#399C2318yes—
234#399C2318yes—
235#399C2318yes—
236#399C2318yes—
237#399C2318yes—
238#399C2314yes—
239#399C2314yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2314yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2314yes—
265#396C2314yes—
266#396C2314yes—
267#396C2314yes—
268#395C2318yes—
269#395C2318yes—
270#395C2314yes—
271#395C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2314yes—
275#393C2318yes—
276#393C2318yes—
277#393C2318yes—
278#393C2318yes—
279#393C2318yes—
280#393C2314yes—
281#393C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2318yes—
291#391C2318yes—
292#391C2314yes—
293#391C2318yes—
294#391C2318yes—
295#391C2318yes—
296#391C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2318yes—
304#390C2318yes—
305#390C2318yes—
306#390C2318yes—
307#390C2314yes—
308#390C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2312yes—
320#389C2312yes—
321#389C2314yes—
322#389C2318yes—
323#389C2318yes—
324#389C2318yes—
325#389C2314yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2314yes—
337#387C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2314yes—
343#387C2314yes—
344#387C2318yes—
345#387C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#385C2314yes—
374#384C2314yes—
375#384C2314yes—
376#384C2312yes—
377#384C2312yes—
378#382C2312yes—
379#382C2314yes—
380#382C2314yes—
381#382C2312yes—
382#381C2314yes—
383#381C2314yes—
384#381C2318yes—
385#381C2314yes—
386#381C2314yes—
387#381C2318yes—
388#381C2314yes—
389#380C2318yes—
390#380C2318yes—
391#380C2318yes—
392#380C2314yes—
393#380C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2318yes—
399#380C2318yes—
400#380C2312yes—
401#380C2312yes—
402#380C2312yes—
403#380C2312yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2318yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#379C2314yes—
412#379C2314yes—
413#379C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432C2×#95C2314yes—
433C2×#95C2318yes—
434C2×#95C2314yes—
435C2×#95C2311yescharacteristic
436C2×#95C2311yescharacteristic
437C2×#95C2312yes—
438C25C2411yescharacteristic
439C25C2412yes—
440C2×#41—464no—
441C2×#41—48no—
442C2×#41—48no—
443C2×#41—48no—
444C2×#41—48no—
445C2×#41C2×Q8132yes—
446C2×#41C2×Q8132yes—
447C22×Q8—28no—
448C22×Q8C2×Q818yes—
449C22×Q8C2414yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×Q8C2418yes—
453C22×D4—28no—
454C22×D4—48no—
455C22×D4C2×Q818yes—
456C22×D4C2×Q8116yes—
457C22×D4C2414yes—
458C22×D4C2418yes—
459C23×C4—28no—
460C23×C4—48no—
461C23×C4C2×Q818yes—
462C23×C4C2×Q8116yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2418yes—
473C23×C4C2418yes—
474C23×C4C2414yes—
475C23×C4C2414yes—
476C23×C4C2411yescharacteristic
477C4⋊Q8—44no—
478C4⋊Q8—44no—
479C4⋊Q8—48no—
480C4⋊Q8—48no—
481#125—44no—
482#125—44no—
483#125—48no—
484#125—48no—
485C22⋊Q8—48no—
486C22⋊Q8—48no—
487C22⋊Q8—416no—
488C22⋊Q8—48no—
489C22⋊Q8—416no—
490C22⋊Q8—48no—
491C22⋊Q8—416no—
492C22⋊Q8—88no—
493C22⋊Q8—88no—
494C22⋊Q8—88no—
495C4×Q8—48no—
496C4×Q8—48no—
497C4×Q8—48no—
498C4×Q8—48no—
499C4×Q8—48no—
500C4×Q8—48no—
501C4×D4—48no—
502C4×D4—48no—
503C4×D4—48no—
504C4×D4—48no—
505#117—28no—
506#117—28no—
507#117—28no—
508#117—28no—
509#117—48no—
510#117—48no—
511#117—44no—
512#117—44no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—44no—
516C2×C4⋊C4—48no—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C22⋊C4—44no—
559C2×C22⋊C4—48no—
560C2×C22⋊C4—48no—
561C2×C22⋊C4—416no—
562C2×C22⋊C4—84no—
563C2×C22⋊C4—82no—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C42—28no—
592C2×C42—48no—
593C2×C42—48no—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2418yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2412yes—
611#95C2411yescharacteristic
612#95C2411yescharacteristic
613#95C2411yescharacteristic
614#95C2414yes—
615#95C2411yescharacteristic
616#95C2412yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646C24—24no—
647C24—28no—
648C24—42no—
649C24—44no—
650C24—41no—
651C24—42no—
652C24—41no—
653C24—42no—
654C24C22×Q814yes—
655C24C22×Q818yes—
656C24C2512yes—
657C24C2514yes—
658C24C2511yescharacteristic
659#41—464no—
660#41—464no—
661C2×Q8—232no—
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C2×Q8—48no—
671C2×Q8—48no—
672C2×Q8—48no—
673C2×Q8C22×Q8116yes—
674C2×D4—232no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—432no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4C22×Q8116yes—
681C2×D4C22×Q8132yes—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—232no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—432no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—42no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4C22×Q814yes—
714C22×C4C22×Q818yes—
715C22×C4C22×Q818yes—
716C22×C4C22×Q818yes—
717C22×C4C22×Q8116yes—
718C22×C4C22×Q8116yes—
719C22×C4C22×Q814yes—
720C22×C4H(5,𝔽2)18yes—
721C22×C4C2514yes—
722C22×C4C2514yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2512yes—
726C22×C4C2514yes—
727C22×C4C2512yes—
728C22×C4C2514yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2518yes—
732C22×C4C2512yes—
733C22×C4C2511yescharacteristic
734C22×C4C2514yes—
735C22×C4C2511yescharacteristic
736C22×C4C2512yes—
737C22×C4C2512yes—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—44no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—44no—
770C4⋊C4—48no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—44no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—24no—
784C22⋊C4—216no—
785C22⋊C4—24no—
786C22⋊C4—42no—
787C22⋊C4—48no—
788C22⋊C4—42no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C42—24no—
807C42—24no—
808C42—24no—
809C42—24no—
810C42—28no—
811C42—28no—
812C42—28no—
813C42—28no—
814C42—44no—
815C42—44no—
816C42—48no—
817C42—48no—
818C23—22no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—28no—
823C23—22no—
824C23—22no—
825C23—28no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—22no—
830C23—24no—
831C23—28no—
832C23—216no—
833C23—44no—
834C23—48no—
835C23—44no—
836C23—48no—
837C23—84no—
838C23—88no—
839C23—84no—
840C23—88no—
841C23C23×Q814yes—
842C23C23×Q818yes—
843C23C23×Q812yes—
844C23C2×H(5,𝔽2)14yes—
845C23C2611yescharacteristic
846Q8—232no—
847Q8—88no—
848Q8—88no—
849Q8—168no—
850D4—232no—
851D4—432no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—28no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—28no—
858C2×C4—216no—
859C2×C4—216no—
860C2×C4—216no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—28no—
887C2×C4—22no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—416no—
898C2×C4—416no—
899C2×C4—48no—
900C2×C4—84no—
901C2×C4—88no—
902C2×C4—88no—
903C2×C4—88no—
904C2×C4—168no—
905C2×C4—168no—
906C2×C4#543116yes—
907C2×C4C23×Q812yes—
908C2×C4C23×Q812yes—
909C2×C4C23×Q818yes—
910C2×C4C23×Q814yes—
911C2×C4C2×H(5,𝔽2)14yes—
912C2×C4C2×H(5,𝔽2)14yes—
913C2×C4#58514yes—
914C22—22no—
915C22—22no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—28no—
920C22—24no—
921C22—28no—
922C22—24no—
923C22—28no—
924C22—42no—
925C22—48no—
926C22—42no—
927C22—42no—
928C22—48no—
929C22—42no—
930C22—88no—
931C22—816no—
932C22C2×#54314yes—
933C22C24×Q811yescharacteristic
934C22C22×H(5,𝔽2)12yes—
935C22C2×#58512yes—
936C22H(7,𝔽2)11yescharacteristic
937C222−1+611yescharacteristic
938C4—22no—
939C4—22no—
940C4—28no—
941C4—24no—
942C4—42no—
943C4—44no—
944C4—44no—
945C4—44no—
946C4—44no—
947C4—42no—
948C4—44no—
949C4—42no—
950C4—48no—
951C4—44no—
952C4—44no—
953C4—44no—
954C4C2×#54318yes—
955C2—24no—
956C2—44no—
957C2—48no—
958C2C22×#54311yescharacteristic
959C2#6281311yescharacteristic
960C2#6285411yescharacteristic
961C2#6295412yes—
962C2#6295512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42954C2semidirect
2. #42953C2semidirect
3. #42931C2semidirect
4. #42930C2semidirect
5. #39985C2semidirect
6. #39984C2semidirect
7. #39981C2semidirect
8. #39980C2semidirect
9. #37478C2semidirect
10. #37134C2semidirect
11. #35529C2semidirect
12. #35515C2semidirect
13. #35253C2semidirect
14. #35179C2semidirect
15. #35154C2semidirect
16. #35065C2semidirect
17. #34739C2semidirect
27. #2857C22semidirect
30. #2851C22semidirect
31. #2841C22semidirect
32. #2841C22semidirect
33. #2804C22semidirect
34. #2784C22semidirect
35. #2784C22semidirect
36. #2780C22semidirect
37. #2780C22semidirect
38. #2780C22semidirect
39. #2780C22semidirect
40. #2748C22semidirect
41. #2748C22semidirect
42. #2732C22semidirect
43. #2732C22semidirect
44. #2692C22semidirect
45. #2692C22semidirect
46. #2692C22semidirect
47. #2692C22semidirect
48. #2683C22semidirect
49. #2667C22semidirect
50. #2667C22semidirect
51. #2667C22semidirect
52. #2665C22semidirect
53. #2665C22semidirect
54. #2665C22semidirect
55. #2659C22semidirect
56. #2646C22semidirect
57. #2629C22semidirect
58. #2628C22semidirect
61. #2608C22semidirect
62. #2607C22semidirect
63. #2582C22semidirect
64. #2582C22semidirect
65. #2581C22semidirect
66. #2581C22semidirect
67. #2580C22semidirect
68. #2580C22semidirect
69. #2569C22semidirect
70. #2569C22semidirect
71. #2569C22semidirect
72. #2568C22semidirect
73. #2567C22semidirect
74. #2566C22semidirect
75. #2566C22semidirect
76. #2565C22semidirect
77. #2565C22semidirect
78. #2563C22semidirect
79. #2549C22semidirect
80. #2549C22semidirect
81. #2549C22semidirect
82. #2542C22semidirect
83. #2538C22semidirect
84. #2538C22semidirect
85. #2454C22semidirect
86. #2454C22semidirect
87. #2454C22semidirect
88. #2454C22semidirect
89. #2453C22semidirect
90. #2453C22semidirect
91. #2453C22semidirect
92. #2453C22semidirect
93. #2452C22semidirect
94. #2452C22semidirect
95. #2452C22semidirect
96. #2452C22semidirect
97. #2451C22semidirect
98. #2451C22semidirect
99. #2451C22semidirect
100. #2451C22semidirect
101. #2442C22semidirect
102. #2442C22semidirect
103. #2442C22semidirect
104. #2441C22semidirect
105. #2441C22semidirect
106. #2441C22semidirect
107. #2440C22semidirect
108. #2440C22semidirect
109. #2440C22semidirect
110. #2439C22semidirect
111. #2439C22semidirect
112. #2439C22semidirect
123. #2396C22semidirect
124. #2396C22semidirect
133. #2329C22semidirect
134. #2329C22semidirect
147. C4×C22⋊Q8C22semidirect
148. C4×C22⋊Q8C22semidirect
164. C22×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#429542
#429532
#429312
#429302
#399852
#399842
#399812
#399802
#374782
#371342
#355292
#355152
#352532
#351792
#351542
#350652
#347392
#341722
C2×#23412
#340442