Finite Group Databasebeta

← #7654877

Subgroups — #7654877

Order 512.

6994 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic
3#42918C214yesmaximal, complemented
4#41939C218yesmaximal, complemented
5#39744C212yesmaximal, complemented
6#39597C214yesmaximal, complemented
7#39170C212yesmaximal, complemented
8#38081C214yesmaximal, complemented
9#38040C218yesmaximal, complemented
10#37675C214yesmaximal, complemented
11#37641C211yesmaximal, characteristic, complemented
12#37617C212yesmaximal, complemented
13#36303C212yesmaximal, complemented
14#36275C214yesmaximal, complemented
15D4×C4⋊Q8C212yesmaximal, complemented
16#35998C214yesmaximal, complemented
17#35316C211yesmaximal, characteristic, complemented
18#35281C211yesmaximal, characteristic, complemented
19#35248C212yesmaximal, complemented
20#35241C212yesmaximal, complemented
21#34979C211yesmaximal, characteristic, complemented
22C2×#2546C212yesmaximal, complemented
23#34127C211yesmaximal, characteristic, complemented
24#3503—216no—
25#3482—216no—
26C2×Q82C2212yes—
27C2×#557C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×#556C2212yes—
31C2×#554C2214yes—
32C2×#554C2212yes—
33C2×#552C2212yes—
34C2×#552C2214yes—
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2214yes—
38C2×#548C2212yes—
39C2×#547C2212yes—
40C2×#547C2211yescharacteristic
41C2×#544C2212yes—
42C2×#544C2214yes—
43C2×#536C2212yes—
44C2×#533C2211yescharacteristic
45C2×#533C2211yescharacteristic
46C2×#533C2212yes—
47C2×#533C2212yes—
48C22×C4⋊Q8C2212yes—
49C22×C4⋊Q8C2211yescharacteristic
50C22×C4⋊Q8C2214yes—
51C2×#529C2214yes—
52C2×#529C2212yes—
53C2×#520C2212yes—
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2212yes—
56C2×C4×#41C2211yescharacteristic
57C22×C4×Q8C2212yes—
58#2868C2212yes—
59#2862C2212yes—
60#2857C2214yes—
61#2857C2214yes—
62#2855C2218yes—
63#2850C2214yes—
64#2822C2214yes—
65#2821C2218yes—
66#2721C22116yes—
67#2719C22116yes—
68#2713C22116yes—
69#2689C22116yes—
70#2677C22116yes—
71#2674C22116yes—
72#2664C2218yes—
73#2660C2214yes—
74#2658C2214yes—
75#2642C2214yes—
76#2634C2218yes—
77#2628C2218yes—
78#2625C2214yes—
79#2625C2214yes—
80#2623C2218yes—
81#2621C2214yes—
82#2621C2214yes—
83#2611C2214yes—
84#2582C2214yes—
85#2581C2218yes—
86#2568C2212yes—
87#2568C2212yes—
88#2568C2211yescharacteristic
89#2567C2214yes—
90#2565C2214yes—
91#2551C2218yes—
92#2547C2212yes—
93#2547C2211yescharacteristic
94#2547C2212yes—
95#2546C2212yes—
96#2546C2214yes—
97#2546C2212yes—
98#2546C2212yes—
99#2546C2214yes—
100#2546C2211yescharacteristic
101#2546C2218yes—
102#2546C2218yes—
103#2546C2212yes—
104#2546C2212yes—
105#2546C2212yes—
106#2545C2214yes—
107#2542C2211yescharacteristic
108#2503C2214yes—
109#2502C2214yes—
110#2499C2212yes—
111#2498C2218yes—
112#2492C2218yes—
113#2488C22116yes—
114#2487C2218yes—
115#2486C2214yes—
116#2486C2214yes—
117#2484C2218yes—
118#2453C2218yes—
119#2449C22116yes—
120#2446C2218yes—
121#2443C22116yes—
122#2441C2218yes—
123#2440C22116yes—
124#2438C22116yes—
125#2436C2214yes—
126#2434C2214yes—
127#2434C2214yes—
128#2434C2214yes—
129#2432C2212yes—
130#2423C2218yes—
131#2419C22116yes—
132#2417C2218yes—
133#2415C2214yes—
134#2395C2214yes—
135C2×#398C2218yes—
136#2355C2212yes—
137#2352C2214yes—
138D4×C4⋊C4C2218yes—
139D4×C4⋊C4C2212yes—
140#2347C2212yes—
141#2343C2214yes—
142#2339C2212yes—
143#2339C2218yes—
144#2327C2214yes—
145#2327C2214yes—
146#2323C2218yes—
147#2317C2214yes—
148#2310C2212yes—
149C4×C4⋊Q8C2212yes—
150C4×#124C2212yes—
151C4×C22⋊Q8C2214yes—
152#2295C2212yes—
153C2×#391C2214yes—
154C2×#389C2218yes—
155#2290C2214yes—
156#2285C2211yescharacteristic
157#2283C2212yes—
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×C4×C4⋊C4C2212yes—
161C22×#41C2312yes—
162C22×#41C2311yescharacteristic
163C22×#41C2311yescharacteristic
164C23×Q8C2312yes—
165C23×Q8C2312yes—
166C23×Q8C2314yes—
167Q82—216no—
168#557—28no—
169#557—216no—
170#556—28no—
171#556—216no—
172#554—216no—
173#554—232no—
174#552—216no—
175#552—232no—
176D4×Q8—28no—
177D4×Q8—216no—
178D4×Q8—232no—
179#548—216no—
180#547—216no—
181#547—28no—
182#544—232no—
183#544—216no—
184#536—48no—
185#533—216no—
186#533—28no—
187#533—216no—
188#533—28no—
189C2×C4⋊Q8—216no—
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8—416no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2318yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C23116yes—
213#529—232no—
214#529—216no—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#126C2314yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×C22⋊Q8C2318yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252#520—216no—
253C4×#41—216no—
254C4×#41—28no—
255C4×#41D4116yes—
256C2×C4×Q8—216no—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2314yes—
282C2×C4×D4C2318yes—
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2314yes—
296C2×#117C2312yes—
297C2×#117C2312yes—
298C2×#117C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2312yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C23116yes—
307C22×C42C2314yes—
308C22×C42C2312yes—
309C22×C42C2314yes—
310C22×C42C2312yes—
311C22×C42C2311yescharacteristic
312#400C23116yes—
313#400C2318yes—
314#400C2318yes—
315#400C2314yes—
316#400C23116yes—
317#400C23116yes—
318#399C23116yes—
319#399C2314yes—
320#399C23116yes—
321#398C23116yes—
322#398C2318yes—
323#398C2318yes—
324#398C23116yes—
325#398C2318yes—
326#398C2314yes—
327#398C2318yes—
328#398C2318yes—
329#398C2318yes—
330#398C23116yes—
331#398C23116yes—
332#397C2314yes—
333#397C2318yes—
334#397C23116yes—
335#397C2318yes—
336#397C2318yes—
337#396C23116yes—
338#395C23116yes—
339#395C23116yes—
340#395C23116yes—
341#394C2318yes—
342#393C23116yes—
343#391C2312yes—
344#391C2312yes—
345#391C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2318yes—
349#391C2318yes—
350#391C2318yes—
351#391C2314yes—
352#391C2318yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C23116yes—
358#391C2312yes—
359#390C2312yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C23116yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2314yes—
369#389C2314yes—
370#389C23116yes—
371#389C23116yes—
372#388C23116yes—
373#388C23116yes—
374#388C2318yes—
375#388C2318yes—
376#387C23116yes—
377#387C23116yes—
378#387C23116yes—
379#387C23116yes—
380#387C23116yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#386C23116yes—
385#386C2318yes—
386#386C23116yes—
387#385C23116yes—
388#385C2318yes—
389#385C23116yes—
390#385C23116yes—
391#385C2318yes—
392#384C2312yes—
393#384C2318yes—
394#384C2318yes—
395#384C2312yes—
396#383C2314yes—
397#382C2314yes—
398#382C2312yes—
399#382C2312yes—
400#382C2318yes—
401#382C2314yes—
402#381C2318yes—
403#381C2314yes—
404#381C23116yes—
405#380C2318yes—
406#380C2318yes—
407#380C2312yes—
408#380C2314yes—
409#380C23116yes—
410#380C2312yes—
411#380C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2314yes—
427#376C2314yes—
428#376C2312yes—
429C2×#95C2314yes—
430C2×#95C23116yes—
431C43C2312yes—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—216no—
436C2×#41—24no—
437C2×#41—42no—
438C2×#41C2×D418yes—
439C22×Q8—28no—
440C22×Q8—28no—
441C22×Q8—216no—
442C22×Q8—28no—
443C22×Q8—44no—
444C22×Q8—48no—
445C22×Q8—44no—
446C22×Q8—48no—
447C22×Q8—44no—
448C22×Q8C2412yes—
449C22×Q8C2412yes—
450C22×Q8C2412yes—
451C22×Q8C2414yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2411yescharacteristic
456C22×Q8C2414yes—
457C22×Q8C2418yes—
458C22×D4C2414yes—
459C22×D4C2411yescharacteristic
460C22×D4C2412yes—
461C22×D4C2412yes—
462C22×D4C2411yescharacteristic
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2418yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2418yes—
476C23×C4C2414yes—
477C4⋊Q8—28no—
478C4⋊Q8—28no—
479C4⋊Q8—216no—
480C4⋊Q8—28no—
481C4⋊Q8—232no—
482C4⋊Q8—216no—
483C4⋊Q8—24no—
484C4⋊Q8—28no—
485C4⋊Q8—28no—
486C4⋊Q8—216no—
487C4⋊Q8—28no—
488C4⋊Q8—216no—
489C4⋊Q8—28no—
490C4⋊Q8—216no—
491C4⋊Q8—24no—
492C4⋊Q8—24no—
493C4⋊Q8—24no—
494C4⋊Q8—48no—
495C4⋊Q8—48no—
496C4⋊Q8—48no—
497C4⋊Q8—432no—
498#126—216no—
499#126—216no—
500#126—216no—
501#125—216no—
502#125—216no—
503#125—216no—
504#125—232no—
505#125—28no—
506#125—28no—
507#125—216no—
508#125—28no—
509#124—216no—
510#124—28no—
511#124—44no—
512#124—48no—
513#123—216no—
514#123—216no—
515#123—216no—
516#123—416no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8—216no—
522C22⋊Q8—28no—
523C22⋊Q8—216no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—232no—
530C22⋊Q8—232no—
531C22⋊Q8—232no—
532C22⋊Q8—416no—
533#121—216no—
534#121—28no—
535C4×Q8—216no—
536C4×Q8—28no—
537C4×Q8—24no—
538C4×Q8—216no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—28no—
542C4×Q8—216no—
543C4×Q8—28no—
544C4×Q8—24no—
545C4×Q8—28no—
546C4×Q8—216no—
547C4×Q8—28no—
548C4×Q8—216no—
549C4×Q8C2×D418yes—
550C4×Q8C2×D418yes—
551C4×D4—28no—
552C4×D4—232no—
553C4×D4—216no—
554C4×D4—216no—
555C4×D4—28no—
556C4×D4—216no—
557C4×D4—28no—
558C4×D4—216no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4C2×D418yes—
562C4×D4C2×D4116yes—
563C4×D4C2×D418yes—
564C4×D4C2×D4116yes—
565#117—24no—
566#117—216no—
567#117—28no—
568#117—28no—
569#117—28no—
570#117—28no—
571#117—216no—
572#117—28no—
573#117—216no—
574#117—44no—
575#117C2×D4116yes—
576#117C2×D418yes—
577C2×C4⋊C4—28no—
578C2×C4⋊C4—216no—
579C2×C4⋊C4—216no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—216no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—432no—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C24116yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C24116yes—
623C2×C4⋊C4C24116yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C24116yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C24116yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C42—216no—
651C2×C42—28no—
652C2×C42—48no—
653C2×C42C2×D4116yes—
654C2×C42C2×D418yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2418yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2418yes—
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#95C2412yes—
677#95C2418yes—
678#95C2414yes—
679#95C2418yes—
680#95C24116yes—
681#95C24116yes—
682#95C24116yes—
683#95C2412yes—
684#95C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C24116yes—
693#95C24116yes—
694#95C24116yes—
695#95C24116yes—
696C24C2512yes—
697C24C2511yescharacteristic
698C24C2512yes—
699#41—232no—
700#41—416no—
701#41—432no—
702C2×Q8—22no—
703C2×Q8—24no—
704C2×Q8—28no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—28no—
708C2×Q8—24no—
709C2×Q8—28no—
710C2×Q8—216no—
711C2×Q8—28no—
712C2×Q8—24no—
713C2×Q8—28no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—28no—
717C2×Q8—28no—
718C2×Q8—22no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—48no—
725C2×Q8—44no—
726C2×Q8—48no—
727C2×Q8—432no—
728C2×Q8—832no—
729C2×Q8—816no—
730C2×Q8C22×D414yes—
731C2×Q8H(5,𝔽2)14yes—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—216no—
736C2×D4—22no—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—42no—
741C2×D4C22×D418yes—
742C2×D4C22×D414yes—
743C2×D42−1+418yes—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—216no—
755C22×C4—216no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—24no—
763C22×C4—216no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—48no—
767C22×C4—44no—
768C22×C4—42no—
769C22×C4—48no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—44no—
773C22×C4C22×D418yes—
774C22×C4C22×D418yes—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D418yes—
778C22×C4C22×D414yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2518yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C4⋊C4—24no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—28no—
805C4⋊C4—216no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—216no—
829C4⋊C4—216no—
830C4⋊C4—232no—
831C4⋊C4—216no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—216no—
836C4⋊C4—416no—
837C4⋊C4—416no—
838C4⋊C4—44no—
839C4⋊C4—416no—
840C4⋊C4C22×D414yes—
841C4⋊C4C22×D418yes—
842C4⋊C4C22×D414yes—
843C4⋊C4C22×D418yes—
844C4⋊C42−1+418yes—
845C22⋊C4—28no—
846C22⋊C4—216no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—216no—
858C22⋊C4—44no—
859C22⋊C4—416no—
860C22⋊C4—48no—
861C22⋊C4C22×D418yes—
862C22⋊C4C22×D418yes—
863C22⋊C4C22×D418yes—
864C42—24no—
865C42—24no—
866C42—28no—
867C42—28no—
868C42—24no—
869C42—28no—
870C42—216no—
871C42—28no—
872C42—24no—
873C42—28no—
874C42—28no—
875C42—28no—
876C42—24no—
877C42—48no—
878C42C22×D414yes—
879C42C22×D414yes—
880C42C22×D414yes—
881C42C22×D418yes—
882C42C22×D418yes—
883C42C22×D414yes—
884C42C22×D418yes—
885C23—22no—
886C23—24no—
887C23—22no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—21no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—24no—
896C23—22no—
897C23C23×D412yes—
898C23C23×D414yes—
899C23C2×2−1+418yes—
900C23C2611yescharacteristic
901Q8—28no—
902Q8—28no—
903Q8—416no—
904Q8—48no—
905Q8—48no—
906Q8—416no—
907Q8—48no—
908Q8—48no—
909Q8—88no—
910Q8—816no—
911D4—216no—
912D4—48no—
913D4—416no—
914D4—44no—
915D4#536116yescomplemented
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—216no—
929C2×C4—28no—
930C2×C4—216no—
931C2×C4—28no—
932C2×C4—216no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—28no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—28no—
957C2×C4—48no—
958C2×C4—432no—
959C2×C4—416no—
960C2×C4—416no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—816no—
964C2×C4—88no—
965C2×C4C23×D414yes—
966C2×C4C23×D414yes—
967C2×C4C23×D412yes—
968C2×C4C23×D412yes—
969C2×C4C23×D412yes—
970C2×C4C23×D414yes—
971C2×C4C23×D412yes—
972C2×C4C23×D412yes—
973C2×C4C23×D412yes—
974C2×C4C2×H(5,𝔽2)14yes—
975C2×C4C2×H(5,𝔽2)12yes—
976C2×C4C2×2−1+418yes—
977C2×C4C2×2−1+414yes—
978C2×C4C2×2−1+414yes—
979C2×C4#58512yes—
980C22—28no—
981C22—28no—
982C22—24no—
983C22—24no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—44no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22C2×#53618yes—
995C22C24×D411yescharacteristic
996C22C22×H(5,𝔽2)11yescharacteristic
997C22C22×2−1+412yes—
998C22C22×2−1+412yes—
999C22C2×#58511yescharacteristic
1000C4—28no—
1001C4—22no—
1002C4—24no—
1003C4—24no—
1004C4—22no—
1005C4—24no—
1006C4—22no—
1007C4—24no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—48no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4C2×#53614yes—
1018C4#348814yes—
1019C4#349914yes—
1020C2—28no—
1021C2—42no—
1022C2—82no—
1023C2C22×#53611yescharacteristic
1024C2C2×#348811yescharacteristic
1025C2C2×#349911yescharacteristic
1026C2#6301612yes—
1027C2#6303212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3482C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3503C2semidirect
3. #42918C2semidirect
4. #41939C2semidirect
5. #39744C2semidirect
6. #39597C2semidirect
7. #39170C2semidirect
8. #38081C2semidirect
9. #38040C2semidirect
10. #37675C2semidirect
11. #37641C2semidirect
12. #37617C2semidirect
13. #36303C2semidirect
14. #36275C2semidirect
15. D4×C4⋊Q8C2semidirect
16. #35998C2semidirect
17. #35316C2semidirect
18. #35281C2semidirect
19. #35248C2semidirect
20. #35241C2semidirect
21. #34979C2semidirect
22. C2×#2546C2semidirect
23. #34127C2semidirect
915. D4#536semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#34822
#429182
#419392
#397442
#395972
#391702
#380812
#380402
#376752
#376412
#376172
#363032
#362752
D4×C4⋊Q82
#359982
#353162
#352812
#352482
#352412
#349792
C2×#25462
#341272