Finite Group Databasebeta

← #7665000

Subgroups — #7665000

Order 512.

5132 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39492C214yesmaximal, complemented
2#38961C214yesmaximal, complemented
3#38960C214yesmaximal, complemented
4#38107C214yesmaximal, complemented
5#38105C214yesmaximal, complemented
6#38100C214yesmaximal, complemented
7#38098C214yesmaximal, complemented
8#37877C214yesmaximal, complemented
9#37872C214yesmaximal
10#36387C214yesmaximal, complemented
11#36363C214yesmaximal, complemented
12#36190C214yesmaximal, complemented
13#35339C212yesmaximal, complemented
14#35253C212yesmaximal, complemented
15#35253C212yesmaximal, complemented
16#35224C211yesmaximal, characteristic, complemented
17#35167C211yesmaximal, characteristic, complemented
18#35151C211yesmaximal, characteristic, complemented
19D4×#117C212yesmaximal
20C2×#2352C211yesmaximal, characteristic
21C4×#544C211yesmaximal, characteristic, complemented
22#34052C211yesmaximal, characteristic, complemented
23C2×#2316C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2212yes—
29C22×#117C2212yes—
30C23×C4⋊C4C2211yescharacteristic
31#2864C2214yescomplemented
32#2864C2214yescomplemented
33#2857C2214yes—
34#2857C2214yescomplemented
35#2857C2214yescomplemented
36#2855C2214yes—
37#2851C2214yescomplemented
38#2851C2214yescomplemented
39#2848C2214yes—
40#2807C2218yescomplemented
41#2792C2218yescomplemented
42#2791C2218yescomplemented
43#2790C2218yescomplemented
44#2788C2218yescomplemented
45#2784C2218yes—
46#2780C2218yes—
47#2774C2218yescomplemented
48#2755C2218yescomplemented
49#2748C2218yes—
50#2729C2218yescomplemented
51#2692C2218yes—
52#2659C2214yes—
53#2647C2214yescomplemented
54#2647C2214yescomplemented
55#2629C2214yescomplemented
56#2629C2214yescomplemented
57#2628C2214yescomplemented
58#2628C2214yescomplemented
59#2627C2214yes—
60#2626C2214yes—
61#2590C2218yescomplemented
62#2589C2218yescomplemented
63#2588C2218yescomplemented
64#2587C2218yescomplemented
65#2586C2218yescomplemented
66#2585C2218yescomplemented
67#2579C2218yes—
68#2574C2218yescomplemented
69#2570C2214yescomplemented
70#2570C2214yescomplemented
71#2570C2214yescomplemented
72#2570C2214yescomplemented
73#2569C2218yes—
74#2569C2218yes—
75#2564C2218yes—
76#2552C2214yescomplemented
77#2551C2214yescomplemented
78#2550C2214yescomplemented
79#2550C2214yescomplemented
80#2522C2218yescomplemented
81#2522C2218yescomplemented
82#2505C2218yescomplemented
83#2502C2214yescomplemented
84#2497C2214yescomplemented
85#2497C2214yescomplemented
86#2492C2214yescomplemented
87#2465C2218yescomplemented
88#2450C2218yes—
89#2449C2218yes—
90#2442C2214yescomplemented
91#2442C2214yescomplemented
92#2442C2214yescomplemented
93#2442C2214yescomplemented
94#2441C2214yescomplemented
95#2441C2214yescomplemented
96#2441C2214yescomplemented
97#2441C2214yescomplemented
98#2440C2214yescomplemented
99#2440C2214yescomplemented
100#2440C2214yescomplemented
101#2440C2214yescomplemented
102#2440C2214yescomplemented
103#2439C2214yescomplemented
104#2439C2214yescomplemented
105#2439C2214yescomplemented
106#2439C2214yescomplemented
107#2438C2218yes—
108#2438C2218yes—
109#2437C2218yes—
110#2437C2218yes—
111#2423C2214yescomplemented
112#2368C2218yescomplemented
113#2360C2214yescomplemented
114#2354C2212yes—
115#2354C2212yes—
116#2352C2212yes—
117#2352C2214yes—
118#2352C2212yes—
119#2352C2212yes—
120#2352C2214yes—
121#2352C2212yes—
122#2352C2214yes—
123#2352C2214yes—
124D4×C4⋊C4C2212yes—
125D4×C4⋊C4C2212yes—
126#2345C2214yescomplemented
127#2344C2214yes—
128#2342C2214yes—
129#2342C2214yes—
130D4×C22⋊C4C2214yes—
131#2331C2214yescomplemented
132#2330C2214yescomplemented
133#2329C2214yes—
134#2317C2212yes—
135#2317C2212yes—
136#2317C2212yes—
137#2317C2214yescomplemented
138#2317C2214yescomplemented
139#2316C2211yescharacteristic
140#2316C2212yes—
141#2316C2214yes—
142#2316C2211yescharacteristic
143#2316C2212yes—
144#2316C2211yescharacteristic
145#2316C2214yescomplemented
146#2316C2214yescomplemented
147#2315C2214yes—
148C4×C4⋊Q8C2214yescomplemented
149C4×#125C2214yescomplemented
150C4×C22⋊Q8C2214yes—
151#2296C2214yescomplemented
152#2296C2214yescomplemented
153#2293C2214yes—
154C2×#389C2214yescomplemented
155C2×#389C2214yescomplemented
156#2290C2214yes—
157#2290C2214yes—
158C2×#388C2212yes—
159C2×#387C2212yes—
160C2×#386C2212yes—
161#2285C2214yes—
162#2285C2212yes—
163C2×#382C2211yescharacteristic
164#2280C2212yes—
165#2280C2212yes—
166C2×#380C2214yes—
167C2×#380C2211yescharacteristic
168C2×#380C2211yescharacteristic
169C42×D4C2214yes—
170C4×#117C2212yes—
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2212yes—
173C23×D4C2311yescharacteristic
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177#544—28no—
178#544—48no—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2318yes—
192C2×C4×Q8C2314yes—
193C2×C4×D4Q8116yescomplemented
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2312yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2312yes—
200C2×#117—28no—
201C2×#117—48no—
202C2×#117—48no—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2314yes—
208C2×#117C2314yes—
209C2×#117C2314yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C22×C4⋊C4—28no—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2314yes—
241C22×C42C2314yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#399C2318yes—
252#399C2318yes—
253#399C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#395C2318yes—
273#395C2318yes—
274#395C2318yes—
275#395C2318yes—
276#395C2318yes—
277#393C2318yes—
278#393C2318yes—
279#393C2318yes—
280#391C2318yes—
281#391C2318yes—
282#391C2314yes—
283#391C2318yes—
284#391C2314yes—
285#391C2318yes—
286#391C2314yes—
287#390C2314yes—
288#390C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2318yes—
299#389C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2318yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#388C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2314yes—
353#387C2318yes—
354#387C2314yes—
355#387C2314yes—
356#387C2318yes—
357#386C2314yes—
358#386C2318yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#384C2314yes—
381#384C2314yes—
382#384C2314yes—
383#384C2314yes—
384#384C2314yes—
385#384C2314yes—
386#384C2312yes—
387#384C2312yes—
388#382C2314yes—
389#382C2314yes—
390#382C2314yes—
391#382C2314yes—
392#382C2314yes—
393#382C2318yes—
394#382C2312yes—
395#382C2312yes—
396#381C2314yes—
397#381C2314yes—
398#380C2314yes—
399#380C2318yes—
400#380C2318yes—
401#380C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2318yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2312yes—
412#380C2312yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2312yes—
417#380C2318yes—
418#380C2312yes—
419#380C2312yes—
420#380C2314yes—
421#380C2314yes—
422#380C2312yes—
423#380C2312yes—
424#379C2314yes—
425#379C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C22⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455#376C2314yes—
456C2×#95C2318yes—
457C2×#95C2312yes—
458C2×#95C2312yes—
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2312yes—
462C43C2314yes—
463C25C2411yescharacteristic
464C25C2411yescharacteristic
465C22×Q8C2414yes—
466C22×Q8C2418yes—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4C2×Q818yes—
470C22×D4C2412yes—
471C22×D4C2412yes—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—28no—
477C23×C4—44no—
478C23×C4—82no—
479C23×C4C2×Q818yes—
480C23×C4C2×Q818yes—
481C23×C4C2414yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C4⋊Q8—216no—
501C4⋊Q8—48no—
502C4⋊Q8—48no—
503C4⋊Q8—84no—
504#125—216no—
505#125—48no—
506#125—48no—
507C22⋊Q8—216no—
508C22⋊Q8—416no—
509C22⋊Q8—48no—
510C22⋊Q8—416no—
511C22⋊Q8—88no—
512C22⋊Q8—84no—
513C4×Q8—84no—
514C4×D4—48no—
515C4×D4—48no—
516C4×D4C2×Q8116yes—
517C4×D4C2×Q8116yes—
518C4×D4C2×Q8116yes—
519C4×D4C2×Q8116yes—
520#117—28no—
521#117—28no—
522#117—28no—
523#117—28no—
524#117—216no—
525#117—216no—
526#117—48no—
527#117—48no—
528#117—48no—
529#117—48no—
530#117—44no—
531#117—44no—
532#117—44no—
533#117—44no—
534C2×C4⋊C4—28no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—216no—
539C2×C4⋊C4—216no—
540C2×C4⋊C4—44no—
541C2×C4⋊C4—44no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4—48no—
545C2×C4⋊C4—84no—
546C2×C4⋊C4C2×Q818yes—
547C2×C4⋊C4#4118yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C22⋊C4—28no—
593C2×C22⋊C4—44no—
594C2×C22⋊C4—48no—
595C2×C22⋊C4—48no—
596C2×C22⋊C4—82no—
597C2×C22⋊C4C2×Q818yes—
598C2×C22⋊C4C2×Q818yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2411yescharacteristic
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2411yescharacteristic
624C2×C22⋊C4C2412yes—
625C2×C42—28no—
626C2×C42—48no—
627C2×C42—48no—
628C2×C42—82no—
629C2×C42C2×Q818yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2414yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2414yes—
679#95C2414yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—41no—
691C24—41no—
692C24—41no—
693C24—41no—
694C24—41no—
695C24—41no—
696C24C22×Q814yes—
697C24C22×Q814yes—
698C24C2512yes—
699C24C2511yescharacteristic
700C24C2511yescharacteristic
701C24C2511yescharacteristic
702C2×Q8—28no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—48no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—416no—
713C2×D4C22×Q818yes—
714C2×D4C22×Q818yes—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—232no—
720C22×C4—232no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—41no—
738C22×C4—42no—
739C22×C4—44no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—42no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—42no—
762C22×C4—816no—
763C22×C4C22×Q814yes—
764C22×C4C22×Q814yes—
765C22×C4C22×Q818yes—
766C22×C4C22×Q818yes—
767C22×C4C22×Q818yes—
768C22×C4C22×Q818yes—
769C22×C4C22×Q814yes—
770C22×C4C22×Q814yes—
771C22×C4C22×Q814yes—
772C22×C4C2×#4118yes—
773C22×C4C2×#4114yes—
774C22×C4H(5,𝔽2)14yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C4⋊C4—216no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—216no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—48no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4—48no—
832C4⋊C4—48no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4C22×Q818yes—
836C4⋊C4C22×Q818yes—
837C4⋊C4C2×#41116yes—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4C22×Q818yes—
859C22⋊C4C22×Q814yes—
860C22⋊C4C22×Q814yes—
861C22⋊C4C22×Q818yes—
862C22⋊C4C22×Q814yes—
863C22⋊C4C22×Q814yes—
864C42—28no—
865C42—28no—
866C42—28no—
867C42—28no—
868C42—28no—
869C42—28no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—44no—
874C42—44no—
875C42—44no—
876C42—44no—
877C42—44no—
878C42—44no—
879C42—44no—
880C42C22×Q818yes—
881C42C22×Q818yes—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—22no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—21no—
895C23—22no—
896C23—22no—
897C23—21no—
898C23—22no—
899C23—21no—
900C23—21no—
901C23—22no—
902C23—28no—
903C23—28no—
904C23—28no—
905C23—44no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—82no—
913C23—82no—
914C23—82no—
915C23—82no—
916C23C23×Q814yes—
917C23C23×Q812yes—
918C23C23×Q812yes—
919C23C23×Q812yes—
920C23C22×#4112yes—
921C23C2×H(5,𝔽2)12yes—
922C23#58512yes—
923C23#58512yes—
924C23C2611yescharacteristic
925Q8—88no—
926Q8—168no—
927D4—216no—
928D4—48no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—21no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—24no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—216no—
946C2×C4—216no—
947C2×C4—216no—
948C2×C4—216no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
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—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—48no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—416no—
986C2×C4—88no—
987C2×C4—84no—
988C2×C4—88no—
989C2×C4—88no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4—88no—
993C2×C4—88no—
994C2×C4#554116yes—
995C2×C4C23×Q812yes—
996C2×C4C23×Q812yes—
997C2×C4C23×Q814yes—
998C2×C4C23×Q812yes—
999C2×C4C23×Q812yes—
1000C2×C4C23×Q814yes—
1001C2×C4C23×Q814yes—
1002C2×C4C22×#4118yes—
1003C2×C4C22×#4114yes—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—24no—
1019C22—24no—
1020C22—22no—
1021C22—22no—
1022C22—24no—
1023C22—416no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—42no—
1028C22—42no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—88no—
1033C22#345814yes—
1034C22C2×#55414yes—
1035C22C24×Q811yescharacteristic
1036C22C23×#4111yescharacteristic
1037C22C22×H(5,𝔽2)11yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58511yescharacteristic
1040C22H(7,𝔽2)11yescharacteristic
1041C222−1+611yescharacteristic
1042C4—28no—
1043C4—22no—
1044C4—22no—
1045C4—24no—
1046C4—22no—
1047C4—22no—
1048C4—24no—
1049C4—44no—
1050C4—44no—
1051C4—44no—
1052C4—44no—
1053C4—44no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—44no—
1060C4C2×#55418yes—
1061C2—24no—
1062C2—24no—
1063C2—42no—
1064C2—44no—
1065C2C2×#345811yescharacteristic
1066C2C22×#55411yescharacteristic
1067C2#6285411yescharacteristic
1068C2#6292711yescharacteristic
1069C2#6295711yescharacteristic
1070C2#6299011yescharacteristic
1071C2#6300511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39492C2semidirect
2. #38961C2semidirect
3. #38960C2semidirect
4. #38107C2semidirect
5. #38105C2semidirect
6. #38100C2semidirect
7. #38098C2semidirect
8. #37877C2semidirect
10. #36387C2semidirect
11. #36363C2semidirect
12. #36190C2semidirect
13. #35339C2semidirect
14. #35253C2semidirect
15. #35253C2semidirect
16. #35224C2semidirect
17. #35167C2semidirect
18. #35151C2semidirect
21. C4×#544C2semidirect
22. #34052C2semidirect
23. C2×#2316C2semidirect
31. #2864C22semidirect
32. #2864C22semidirect
34. #2857C22semidirect
35. #2857C22semidirect
37. #2851C22semidirect
38. #2851C22semidirect
40. #2807C22semidirect
41. #2792C22semidirect
42. #2791C22semidirect
43. #2790C22semidirect
44. #2788C22semidirect
47. #2774C22semidirect
48. #2755C22semidirect
50. #2729C22semidirect
53. #2647C22semidirect
54. #2647C22semidirect
55. #2629C22semidirect
56. #2629C22semidirect
57. #2628C22semidirect
58. #2628C22semidirect
61. #2590C22semidirect
62. #2589C22semidirect
63. #2588C22semidirect
64. #2587C22semidirect
65. #2586C22semidirect
66. #2585C22semidirect
68. #2574C22semidirect
69. #2570C22semidirect
70. #2570C22semidirect
71. #2570C22semidirect
72. #2570C22semidirect
76. #2552C22semidirect
77. #2551C22semidirect
78. #2550C22semidirect
79. #2550C22semidirect
80. #2522C22semidirect
81. #2522C22semidirect
82. #2505C22semidirect
83. #2502C22semidirect
84. #2497C22semidirect
85. #2497C22semidirect
86. #2492C22semidirect
87. #2465C22semidirect
90. #2442C22semidirect
91. #2442C22semidirect
92. #2442C22semidirect
93. #2442C22semidirect
94. #2441C22semidirect
95. #2441C22semidirect
96. #2441C22semidirect
97. #2441C22semidirect
98. #2440C22semidirect
99. #2440C22semidirect
100. #2440C22semidirect
101. #2440C22semidirect
102. #2440C22semidirect
103. #2439C22semidirect
104. #2439C22semidirect
105. #2439C22semidirect
106. #2439C22semidirect
111. #2423C22semidirect
112. #2368C22semidirect
113. #2360C22semidirect
126. #2345C22semidirect
131. #2331C22semidirect
132. #2330C22semidirect
137. #2317C22semidirect
138. #2317C22semidirect
145. #2316C22semidirect
146. #2316C22semidirect
148. C4×C4⋊Q8C22semidirect
149. C4×#125C22semidirect
151. #2296C22semidirect
152. #2296C22semidirect
154. C2×#389C22semidirect
155. C2×#389C22semidirect
193. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#394922
#389612
#389602
#381072
#381052
#381002
#380982
#378772
#378722
#363872
#363632
#361902
#353392
#352532
#352242
#351672
#351512
D4×#1172
C2×#23522
C4×#5442
#340522
C2×#23162