Finite Group Databasebeta

← #7656763

Subgroups — #7656763

Order 512.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1067 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42954C214yesmaximal, complemented
2#42931C214yesmaximal, complemented
3#41998C218yesmaximal, complemented
4#41997C218yesmaximal, complemented
5#39752C212yesmaximal, complemented
6#39624C212yesmaximal, complemented
7#37872C214yesmaximal, complemented
8#37684C214yesmaximal, complemented
9#37478C214yesmaximal, complemented
10#37477C212yesmaximal, complemented
11#36154C212yesmaximal, complemented
12D4×C22⋊Q8C212yesmaximal, complemented
13#35806C214yesmaximal, complemented
14#35739C214yesmaximal, complemented
15#35052C212yesmaximal, complemented
16#35002C211yesmaximal, characteristic, complemented
17#34578C211yesmaximal, characteristic, complemented
18C2×#2659C212yesmaximal, complemented
19#34175C212yesmaximal
20C2×#2339C211yesmaximal, characteristic
21C23×#41C2211yescharacteristic
22C2×#554C2212yescomplemented
23C2×D4×Q8C2212yescomplemented
24C2×#543C2212yes—
25C22×C22⋊Q8C2214yes—
26C2×#520C2212yes—
27C2×#520C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2848C2214yes—
33#2848C2214yes—
34#2841C2218yescomplemented
35#2841C2218yescomplemented
36#2841C2218yescomplemented
37#2811C2214yescomplemented
38#2809C2214yescomplemented
39#2806C2214yescomplemented
40#2806C2218yescomplemented
41#2806C2214yescomplemented
42#2799C2218yescomplemented
43#2784C2218yescomplemented
44#2780C2218yescomplemented
45#2748C2218yescomplemented
46#2732C2218yescomplemented
47#2692C2218yescomplemented
48#2692C2218yescomplemented
49#2692C2218yescomplemented
50#2683C2218yescomplemented
51#2667C2214yescomplemented
52#2667C2218yescomplemented
53#2665C2214yescomplemented
54#2665C2218yescomplemented
55#2659C2211yescharacteristic
56#2659C2214yes—
57#2659C2214yes—
58#2659C2212yes—
59#2659C2214yes—
60#2659C2211yescharacteristic
61#2659C2212yes—
62#2659C2218yescomplemented
63#2659C2218yescomplemented
64#2659C2214yescomplemented
65#2646C2212yes—
66#2646C2214yes—
67#2646C2214yescomplemented
68#2629C2214yescomplemented
69#2628C2214yescomplemented
70#2627C2218yescomplemented
71#2627C2218yescomplemented
72#2626C2212yes—
73#2626C2212yes—
74#2582C2214yescomplemented
75#2581C2214yescomplemented
76#2579C2218yescomplemented
77#2569C2218yes—
78#2569C2218yescomplemented
79#2567C2214yescomplemented
80#2565C2214yescomplemented
81#2564C2218yescomplemented
82#2563C2212yescomplemented
83#2549C2218yes—
84#2549C2218yescomplemented
85#2549C2218yescomplemented
86#2542C2212yescomplemented
87#2538C2212yescomplemented
88#2538C2212yescomplemented
89#2487C2214yescomplemented
90#2454C2214yescomplemented
91#2453C2214yescomplemented
92#2452C2214yescomplemented
93#2451C2214yescomplemented
94#2451C2214yescomplemented
95#2451C2214yescomplemented
96#2450C2218yescomplemented
97#2450C2218yescomplemented
98#2449C2218yescomplemented
99#2449C2218yescomplemented
100#2449C2218yescomplemented
101#2449C2218yescomplemented
102#2442C2214yes—
103#2442C2214yescomplemented
104#2440C2214yes—
105#2440C2214yescomplemented
106#2440C2214yescomplemented
107#2440C2214yescomplemented
108#2438C2218yescomplemented
109#2438C2218yescomplemented
110#2438C2218yescomplemented
111#2438C2218yescomplemented
112#2437C2218yes—
113#2437C2218yes—
114#2437C2218yes—
115#2417C2214yescomplemented
116#2417C2218yescomplemented
117#2417C2214yescomplemented
118#2409C2214yescomplemented
119#2409C2218yescomplemented
120#2396C2214yescomplemented
121#2396C2214yescomplemented
122C2×#398C2218yescomplemented
123C2×#395C2218yescomplemented
124#2349C2214yescomplemented
125D4×C4⋊C4C2212yescomplemented
126D4×C4⋊C4C2214yescomplemented
127D4×C4⋊C4C2212yescomplemented
128#2341C2214yes—
129Q8×C22⋊C4C2214yes—
130#2339C2218yes—
131#2339C2218yes—
132#2339C2214yes—
133#2339C2214yes—
134#2339C2214yes—
135D4×C22⋊C4C2218yes—
136D4×C22⋊C4C2214yes—
137#2329C2214yes—
138#2329C2214yes—
139#2315C2212yes—
140#2311C2214yes—
141#2311C2214yes—
142#2311C2212yes—
143#2311C2212yes—
144C4×C22⋊Q8C2212yes—
145C4×C22⋊Q8C2212yes—
146C2×#391C2211yescharacteristic
147C2×#391C2211yescharacteristic
148C2×#386C2212yes—
149C2×#386C2212yes—
150#2280C2212yes—
151#2280C2214yes—
152C2×#381C2212yes—
153C2×#380C2214yes—
154C2×#380C2214yes—
155C2×#380C2211yescharacteristic
156C2×#380C2212yes—
157C2×C4×C22⋊C4C2211yescharacteristic
158C22×#95C2212yes—
159C22×#41—44no—
160C22×#41—44no—
161C22×#41Q8116yescomplemented
162C22×#41C2312yes—
163C22×#41C2314yes—
164C22×#41C2312yes—
165C23×Q8C2314yes—
166C23×Q8C2311yescharacteristic
167C23×D4C2311yescharacteristic
168C23×D4C2312yes—
169C24×C4C2312yes—
170C24×C4C2312yes—
171C24×C4C2312yes—
172C24×C4C2311yescharacteristic
173#554—48no—
174D4×Q8—48no—
175#543—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×#125C2314yes—
180C2×C22⋊Q8—416no—
181C2×C22⋊Q8C2312yes—
182C2×C22⋊Q8C2314yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198#520—48no—
199#520—48no—
200C2×C4×Q8C2314yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×D4—44no—
205C2×C4×D4—44no—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2314yes—
225C22×C4⋊C4C2318yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2314yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2318yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2318yes—
245#400C2314yes—
246#399C2314yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#399C2314yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2314yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2314yes—
267#398C2318yes—
268#398C2314yes—
269#398C2318yes—
270#398C2318yes—
271#396C2314yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2314yes—
279#396C2314yes—
280#396C2314yes—
281#395C2318yes—
282#395C2318yes—
283#395C2318yes—
284#395C2318yes—
285#395C2318yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2314yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2314yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2314yes—
298#393C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#391C2318yes—
304#391C2314yes—
305#391C2318yes—
306#391C2318yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2312yes—
312#391C2318yes—
313#391C2312yes—
314#391C2318yes—
315#390C2314yes—
316#390C2318yes—
317#390C2318yes—
318#390C2314yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2318yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2312yes—
332#389C2312yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#384C2312yes—
370#384C2312yes—
371#384C2314yes—
372#382C2314yes—
373#381C2318yes—
374#381C2314yes—
375#381C2318yes—
376#381C2318yes—
377#380C2314yes—
378#380C2314yes—
379#380C2314yes—
380#380C2318yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2312yes—
385#380C2314yes—
386#380C2312yes—
387#380C2314yes—
388#380C2314yes—
389#380C2318yes—
390#380C2318yes—
391#380C2314yes—
392#380C2314yes—
393#380C2312yes—
394#380C2314yes—
395#380C2318yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2318yes—
401#380C2312yes—
402#380C2312yes—
403#380C2312yes—
404#380C2314yes—
405#380C2318yes—
406#380C2314yes—
407#380C2318yes—
408#379C2318yes—
409#379C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C2×#95C2318yes—
421C2×#95C2312yes—
422C2×#95C2318yes—
423C2×#95C2312yes—
424C2×#95C2312yes—
425C2×#95C2318yes—
426C2×#95C2318yes—
427C2×#95C2314yes—
428C2×#95C2312yes—
429C2×#95C2311yescharacteristic
430C2×#95C2311yescharacteristic
431C2×#95C2312yes—
432C25C2412yes—
433C25C2411yescharacteristic
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—48no—
437C2×#41—48no—
438C2×#41—44no—
439C2×#41—44no—
440C2×#41—464no—
441C2×#41C2×Q8116yes—
442C2×#41C2×Q8132yescomplemented
443C2×#41C2×Q8116yescomplemented
444C22×Q8—48no—
445C22×Q8—42no—
446C22×Q8—42no—
447C22×Q8—48no—
448C22×Q8—84no—
449C22×Q8C2×Q818yescomplemented
450C22×Q8C2412yes—
451C22×Q8C2412yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2414yes—
455C22×Q8C2418yes—
456C22×Q8C2412yes—
457C22×D4—24no—
458C22×D4—24no—
459C22×D4—44no—
460C22×D4—44no—
461C22×D4C2×Q818yes—
462C22×D4C2×Q8116yescomplemented
463C22×D4C2412yes—
464C22×D4C2414yes—
465C22×D4C2411yescharacteristic
466C22×D4C2414yes—
467C22×D4C2411yescharacteristic
468C23×C4—28no—
469C23×C4—28no—
470C23×C4—42no—
471C23×C4—42no—
472C23×C4—44no—
473C23×C4—44no—
474C23×C4—44no—
475C23×C4—44no—
476C23×C4—82no—
477C23×C4—82no—
478C23×C4C2×Q818yescomplemented
479C23×C4C2×Q8116yescomplemented
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2418yes—
490C23×C4C2418yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2411yescharacteristic
496C23×C4C2412yes—
497C23×C4C2414yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C4⋊Q8—44no—
502C4⋊Q8—48no—
503C4⋊Q8—44no—
504#125—48no—
505C22⋊Q8—28no—
506C22⋊Q8—216no—
507C22⋊Q8—28no—
508C22⋊Q8—416no—
509C22⋊Q8—48no—
510C22⋊Q8—416no—
511C22⋊Q8—48no—
512C22⋊Q8—416no—
513C22⋊Q8—48no—
514C22⋊Q8—416no—
515C22⋊Q8—416no—
516C22⋊Q8—416no—
517C22⋊Q8—48no—
518C22⋊Q8—48no—
519C22⋊Q8—88no—
520C22⋊Q8—84no—
521C22⋊Q8—84no—
522C4×Q8—44no—
523C4×Q8—44no—
524C4×Q8—48no—
525C4×Q8—48no—
526C4×D4—28no—
527C4×D4—28no—
528C4×D4—216no—
529C4×D4—216no—
530C4×D4—44no—
531C4×D4—44no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—416no—
535C4×D4—416no—
536#117—44no—
537#117—44no—
538#117—48no—
539#117—48no—
540C2×C4⋊C4—42no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4—48no—
545C2×C4⋊C4—416no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—48no—
548C2×C4⋊C4—48no—
549C2×C4⋊C4—84no—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—44no—
596C2×C22⋊C4—44no—
597C2×C22⋊C4—416no—
598C2×C22⋊C4—48no—
599C2×C22⋊C4—82no—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C42—42no—
622C2×C42—42no—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2418yes—
628C2×C42C2418yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—22no—
667C24—22no—
668C24—42no—
669C24—42no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24C22×Q818yes—
675C24C22×Q814yes—
676C24C2512yes—
677C24C2512yes—
678C24C2512yes—
679C24C2511yescharacteristic
680#41—264no—
681#41—464no—
682#41—432no—
683C2×Q8—24no—
684C2×Q8—24no—
685C2×Q8—24no—
686C2×Q8—28no—
687C2×Q8—24no—
688C2×Q8—42no—
689C2×Q8—42no—
690C2×Q8—42no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—48no—
694C2×Q8—44no—
695C2×Q8—48no—
696C2×Q8—42no—
697C2×Q8—44no—
698C2×Q8—48no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—416no—
703C2×Q8—832no—
704C2×Q8C22×Q818yes—
705C2×Q8C22×Q818yes—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—232no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—432no—
716C2×D4C22×Q818yes—
717C2×D4C22×Q814yes—
718C2×D4C22×Q8116yes—
719C2×D4C22×Q8116yes—
720C2×D4C22×Q814yes—
721C2×D4H(5,𝔽2)14yes—
722C2×D4H(5,𝔽2)14yes—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—22no—
732C22×C4—216no—
733C22×C4—216no—
734C22×C4—24no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—416no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—44no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—432no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—44no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—48no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—48no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—48no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—48no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—816no—
780C22×C4—816no—
781C22×C4C22×Q814yes—
782C22×C4C22×Q8116yes—
783C22×C4C22×Q818yes—
784C22×C4C22×Q814yes—
785C22×C4C22×Q818yes—
786C22×C4C22×Q818yes—
787C22×C4C22×Q8116yes—
788C22×C4H(5,𝔽2)14yes—
789C22×C42−1+414yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2518yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2518yes—
800C22×C4C2511yescharacteristic
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—216no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4—42no—
823C4⋊C4—48no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—42no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—42no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—216no—
854C22⋊C4—216no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C42—24no—
871C42—24no—
872C42—28no—
873C42—28no—
874C42—42no—
875C42—42no—
876C42—48no—
877C42—48no—
878C23—22no—
879C23—21no—
880C23—21no—
881C23—22no—
882C23—22no—
883C23—21no—
884C23—22no—
885C23—21no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—216no—
899C23—216no—
900C23—28no—
901C23—48no—
902C23—44no—
903C23—44no—
904C23—48no—
905C23—48no—
906C23—48no—
907C23—48no—
908C23—82no—
909C23—82no—
910C23—82no—
911C23—82no—
912C23C23×Q814yes—
913C23C23×Q814yes—
914C23C23×Q814yes—
915C23C23×Q812yes—
916C23C2×H(5,𝔽2)14yes—
917C23C2×H(5,𝔽2)14yes—
918C23C2×H(5,𝔽2)12yes—
919C23C2×2−1+412yes—
920C23C2611yescharacteristic
921Q8—216no—
922Q8—48no—
923Q8—48no—
924Q8—84no—
925Q8—88no—
926Q8—816no—
927Q8—164no—
928D4—216no—
929D4—232no—
930D4—28no—
931D4—416no—
932D4#543116yescomplemented
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—232no—
944C2×C4—28no—
945C2×C4—216no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—28no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—48no—
979C2×C4—416no—
980C2×C4—44no—
981C2×C4—44no—
982C2×C4—416no—
983C2×C4—416no—
984C2×C4—88no—
985C2×C4—88no—
986C2×C4—816no—
987C2×C4—82no—
988C2×C4—82no—
989C2×C4—84no—
990C2×C4—84no—
991C2×C4—816no—
992C2×C4—164no—
993C2×C4—164no—
994C2×C4C23×Q814yes—
995C2×C4C23×Q812yes—
996C2×C4C23×Q818yes—
997C2×C4C23×Q812yes—
998C2×C4C2×H(5,𝔽2)14yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×2−1+414yes—
1002C22—24no—
1003C22—22no—
1004C22—24no—
1005C22—24no—
1006C22—22no—
1007C22—24no—
1008C22—22no—
1009C22—24no—
1010C22—22no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—432no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—88no—
1030C22C2×#54318yes—
1031C22#350314yes—
1032C22C24×Q811yescharacteristic
1033C22C22×H(5,𝔽2)11yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×H(5,𝔽2)11yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22H(7,𝔽2)11yescharacteristic
1038C222−1+611yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—22no—
1043C4—28no—
1044C4—44no—
1045C4—44no—
1046C4—48no—
1047C4—44no—
1048C4—44no—
1049C4—44no—
1050C4—48no—
1051C4—42no—
1052C4—44no—
1053C4—42no—
1054C4C2×#54314yes—
1055C2—24no—
1056C2—28no—
1057C2—44no—
1058C2—44no—
1059C2C22×#54311yescharacteristic
1060C2C2×#350311yescharacteristic
1061C2#6285411yescharacteristic
1062C2#6289211yescharacteristic
1063C2#6289411yescharacteristic
1064C2#6291411yescharacteristic
1065C2#6291511yescharacteristic
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. #42931C2semidirect
3. #41998C2semidirect
4. #41997C2semidirect
5. #39752C2semidirect
6. #39624C2semidirect
7. #37872C2semidirect
8. #37684C2semidirect
9. #37478C2semidirect
10. #37477C2semidirect
11. #36154C2semidirect
12. D4×C22⋊Q8C2semidirect
13. #35806C2semidirect
14. #35739C2semidirect
15. #35052C2semidirect
16. #35002C2semidirect
17. #34578C2semidirect
18. C2×#2659C2semidirect
22. C2×#554C22semidirect
23. C2×D4×Q8C22semidirect
34. #2841C22semidirect
35. #2841C22semidirect
36. #2841C22semidirect
37. #2811C22semidirect
38. #2809C22semidirect
39. #2806C22semidirect
40. #2806C22semidirect
41. #2806C22semidirect
42. #2799C22semidirect
43. #2784C22semidirect
44. #2780C22semidirect
45. #2748C22semidirect
46. #2732C22semidirect
47. #2692C22semidirect
48. #2692C22semidirect
49. #2692C22semidirect
50. #2683C22semidirect
51. #2667C22semidirect
52. #2667C22semidirect
53. #2665C22semidirect
54. #2665C22semidirect
62. #2659C22semidirect
63. #2659C22semidirect
64. #2659C22semidirect
67. #2646C22semidirect
68. #2629C22semidirect
69. #2628C22semidirect
70. #2627C22semidirect
71. #2627C22semidirect
74. #2582C22semidirect
75. #2581C22semidirect
76. #2579C22semidirect
78. #2569C22semidirect
79. #2567C22semidirect
80. #2565C22semidirect
81. #2564C22semidirect
82. #2563C22semidirect
84. #2549C22semidirect
85. #2549C22semidirect
86. #2542C22semidirect
87. #2538C22semidirect
88. #2538C22semidirect
89. #2487C22semidirect
90. #2454C22semidirect
91. #2453C22semidirect
92. #2452C22semidirect
93. #2451C22semidirect
94. #2451C22semidirect
95. #2451C22semidirect
96. #2450C22semidirect
97. #2450C22semidirect
98. #2449C22semidirect
99. #2449C22semidirect
100. #2449C22semidirect
101. #2449C22semidirect
103. #2442C22semidirect
105. #2440C22semidirect
106. #2440C22semidirect
107. #2440C22semidirect
108. #2438C22semidirect
109. #2438C22semidirect
110. #2438C22semidirect
111. #2438C22semidirect
115. #2417C22semidirect
116. #2417C22semidirect
117. #2417C22semidirect
118. #2409C22semidirect
119. #2409C22semidirect
120. #2396C22semidirect
121. #2396C22semidirect
122. C2×#398C22semidirect
123. C2×#395C22semidirect
124. #2349C22semidirect
125. D4×C4⋊C4C22semidirect
126. D4×C4⋊C4C22semidirect
127. D4×C4⋊C4C22semidirect
161. C22×#41Q8semidirect
442. C2×#41C2×Q8semidirect
443. C2×#41C2×Q8semidirect
449. C22×Q8C2×Q8semidirect
462. C22×D4C2×Q8semidirect
478. C23×C4C2×Q8semidirect
479. C23×C4C2×Q8semidirect
932. D4#543semidirect

Maximal subgroups

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

subgroupindex
#429542
#429312
#419982
#419972
#397522
#396242
#378722
#376842
#374782
#374772
#361542
D4×C22⋊Q82
#358062
#357392
#350522
#350022
#345782
C2×#26592
#341752
C2×#23392