Finite Group Databasebeta

← #7718242

Subgroups — #7718242

Order 512.

7002 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3561C212yesmaximal, complemented
2#51333C218yesmaximal, complemented
3#51332C218yesmaximal, complemented
4#45332C214yesmaximal, complemented
5#45303C214yesmaximal, complemented
6#45144C214yesmaximal, complemented
7#45077C214yesmaximal, complemented
8#39615C212yesmaximal, complemented
9#39486C212yesmaximal, complemented
10#39482C214yesmaximal, complemented
11#37861C214yesmaximal, complemented
12#36740C214yesmaximal, complemented
13Q8×#121C212yesmaximal, complemented
14#36153C212yesmaximal, complemented
15#35241C212yesmaximal, complemented
16#35173C211yesmaximal, characteristic, complemented
17#35003C212yesmaximal, complemented
18#35002C212yesmaximal, complemented
19#34594C211yesmaximal, characteristic, complemented
20C2×#2367C211yesmaximal, characteristic, complemented
21#3561—232no—
22C2×#563C2214yes—
23C2×#562C2214yes—
24C2×#556C2214yes—
25C2×#551C2218yes—
26C2×D4×Q8C2214yes—
27C2×D4×Q8C2212yescomplemented
28C2×#548C2214yes—
29C2×#547C2212yes—
30C2×#546C2214yes—
31C2×#543C2214yes—
32C2×#542C2214yes—
33C2×#542C2218yes—
34C2×#538C2214yes—
35C2×#536C2214yes—
36C2×#533C2212yes—
37C2×#529C2212yes—
38C22×#124C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41#2857C2212yes—
42#2857C2214yes—
43#2857C2212yes—
44#2857C2214yes—
45#2850C2214yes—
46#2847C2214yes—
47#2734C2214yescomplemented
48#2732C2214yescomplemented
49#2729C2218yescomplemented
50#2724C2214yes—
51#2722C2218yescomplemented
52#2718C2218yescomplemented
53#2715C2218yescomplemented
54#2710C2218yescomplemented
55#2701C2218yes—
56#2700C2218yescomplemented
57#2698C2218yescomplemented
58#2695C2218yescomplemented
59#2689C2218yescomplemented
60#2689C2218yescomplemented
61#2687C2218yescomplemented
62#2682C2214yes—
63#2681C2218yescomplemented
64#2680C2218yescomplemented
65#2674C2218yescomplemented
66#2674C2218yescomplemented
67#2672C2218yescomplemented
68#2672C2218yescomplemented
69#2664C2214yescomplemented
70#2664C2218yescomplemented
71#2662C2214yescomplemented
72#2659C2211yescharacteristic
73#2659C2212yes—
74#2659C2212yes—
75#2659C2214yes—
76#2656C2211yescharacteristic
77#2639C2212yes—
78#2618C2212yes—
79#2618C2212yes—
80#2617C2214yes—
81#2584C2218yescomplemented
82#2568C2212yescomplemented
83#2567C2214yescomplemented
84#2565C2214yescomplemented
85#2564C2218yes—
86#2555C2218yescomplemented
87#2553C2218yescomplemented
88#2549C2218yescomplemented
89#2549C2218yescomplemented
90#2547C2212yes—
91#2547C2212yescomplemented
92#2546C2214yescomplemented
93#2546C2212yescomplemented
94#2546C2212yescomplemented
95#2546C2214yescomplemented
96#2545C2214yescomplemented
97#2542C2212yescomplemented
98#2538C2214yescomplemented
99#2538C2212yescomplemented
100#2537C2212yes—
101#2521C2218yescomplemented
102#2498C2218yes—
103#2486C2214yes—
104#2478C2218yescomplemented
105#2470C2218yescomplemented
106#2466C2218yescomplemented
107#2464C2218yescomplemented
108#2455C2218yescomplemented
109#2449C2218yescomplemented
110#2447C2214yes—
111#2446C2214yescomplemented
112#2440C2218yescomplemented
113#2440C2218yescomplemented
114#2438C2218yescomplemented
115#2434C2214yescomplemented
116#2432C2214yes—
117#2429C2214yescomplemented
118#2429C2218yescomplemented
119#2427C2214yes—
120#2425C2218yes—
121#2425C2218yescomplemented
122#2423C2214yescomplemented
123#2422C2214yes—
124#2417C2214yes—
125#2417C2214yes—
126#2417C2218yes—
127#2416C2214yes—
128#2413C2218yescomplemented
129#2412C2218yes—
130#2412C2218yes—
131#2409C2214yescomplemented
132#2407C2214yes—
133#2396C2214yescomplemented
134#2392C2214yescomplemented
135#2367C2214yes—
136#2367C2214yes—
137#2367C2218yes—
138Q8×C4⋊C4C2212yescomplemented
139D4×C4⋊C4C2212yes—
140Q8×C22⋊C4C2214yescomplemented
141#2339C2214yes—
142#2325C2214yes—
143#2323C2214yescomplemented
144#2323C2214yescomplemented
145#2316C2212yes—
146#2316C2212yes—
147#2315C2214yes—
148C4×#121C2212yes—
149C4×#121C2212yes—
150C4×#121C2214yes—
151C2×#391C2211yescharacteristic
152C2×#390C2211yescharacteristic
153C2×#388C2212yes—
154C2×#388C2212yes—
155C2×#385C2212yes—
156C2×#380C2214yes—
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C4⋊C4C2211yescharacteristic
159C2×C4×C22⋊C4C2212yes—
160C22×#41C2314yes—
161C23×Q8C2314yes—
162C23×Q8C2311yescharacteristic
163C23×D4C2311yescharacteristic
164C24×C4C2312yes—
165#563—232no—
166#562—232no—
167#556—232no—
168#551—264no—
169D4×Q8—232no—
170D4×Q8—48no—
171#548—232no—
172#547—48no—
173#546—232no—
174#543—232no—
175#542—264no—
176#542—232no—
177#538—232no—
178#536—232no—
179#533—216no—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2318yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2314yes—
188#529—216no—
189C2×#126C2314yes—
190C2×#126C2318yes—
191C2×#126C2318yes—
192C2×#126C2318yes—
193C2×#125C2312yes—
194C2×#125C2314yes—
195C2×#124D4116yescomplemented
196C2×#124C2312yes—
197C2×#124C2318yes—
198C2×#124C2318yes—
199C2×#124C2314yes—
200C2×#124C2314yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#123C2314yes—
204C2×#123C2318yes—
205C2×#123C2318yes—
206C2×#123C2318yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2314yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#120C2318yes—
233C2×C4×Q8—44no—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×D4—44no—
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2318yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2318yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C42C2311yescharacteristic
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#399C2318yes—
278#399C2314yes—
279#399C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2314yes—
300#396C2314yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2314yes—
311#395C2318yes—
312#395C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2314yes—
316#394C2314yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#393C2318yes—
323#393C2314yes—
324#392C2318yes—
325#392C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2318yes—
335#391C2314yes—
336#391C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2312yes—
360#389C2312yes—
361#389C2314yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2314yes—
373#388C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#386C2314yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2314yes—
387#386C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#384C2314yes—
400#384C2312yes—
401#384C2312yes—
402#384C2314yes—
403#382C2314yes—
404#381C2318yes—
405#381C2318yes—
406#380C2314yes—
407#380C2318yes—
408#380C2312yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2318yes—
418#380C2312yes—
419#380C2314yes—
420#380C2318yes—
421#380C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C2×#95C2312yes—
436C2×#95C2312yes—
437C2×#95C2318yes—
438C2×#95C2311yescharacteristic
439C2×#95C2311yescharacteristic
440C2×#95C2312yes—
441C25C2412yes—
442C2×#41—216no—
443C2×#41—48no—
444C2×#41—48no—
445C22×Q8—216no—
446C22×Q8—42no—
447C22×Q8—42no—
448C22×Q8—48no—
449C22×Q8—48no—
450C22×Q8C2×D418yes—
451C22×Q8C2414yes—
452C22×Q8C2412yes—
453C22×Q8C2412yes—
454C22×Q8C2414yes—
455C22×Q8C2418yes—
456C22×Q8C2412yes—
457C22×D4—42no—
458C22×D4—42no—
459C22×D4C2×D418yes—
460C22×D4C2414yes—
461C22×D4C2412yes—
462C22×D4C2412yes—
463C22×D4C2418yes—
464C22×D4C2412yes—
465C22×D4C2412yes—
466C22×D4C2418yes—
467C22×D4C2412yes—
468C23×C4—28no—
469C23×C4—44no—
470C23×C4—82no—
471C23×C4C2414yes—
472C23×C4C2412yes—
473C23×C4C2414yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2418yes—
480C23×C4C2418yes—
481C23×C4C2418yes—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C4⋊Q8—216no—
488C4⋊Q8—232no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—48no—
492C4⋊Q8—44no—
493C4⋊Q8—44no—
494C4⋊Q8—84no—
495#126—232no—
496#126—232no—
497#126—232no—
498#126—216no—
499#125—28no—
500#125—216no—
501#124—216no—
502#124—232no—
503#124—232no—
504#124—28no—
505#124—84no—
506#124C2×D4132yes—
507#124C2×D4132yes—
508#123—232no—
509#123—216no—
510#123—232no—
511#123—232no—
512#123—232no—
513#123—416no—
514#123—88no—
515C22⋊Q8—216no—
516C22⋊Q8—232no—
517C22⋊Q8—28no—
518C22⋊Q8—216no—
519C22⋊Q8—216no—
520C22⋊Q8—232no—
521C22⋊Q8—216no—
522C22⋊Q8—232no—
523C22⋊Q8—232no—
524C22⋊Q8—232no—
525C22⋊Q8—232no—
526C22⋊Q8—232no—
527C22⋊Q8—416no—
528C22⋊Q8—48no—
529#121—216no—
530#121—232no—
531#121—28no—
532#121—28no—
533#121—28no—
534#121—232no—
535#121—48no—
536#121—84no—
537#120—232no—
538C4×Q8—216no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—48no—
544C4×Q8—44no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—232no—
548C4×D4—28no—
549C4×D4—232no—
550C4×D4—28no—
551C4×D4—48no—
552C4×D4—44no—
553C4×D4—44no—
554C4×D4—44no—
555C4×D4—48no—
556#117—216no—
557#117—232no—
558#117—216no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—42no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—48no—
565C2×C4⋊C4—84no—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C22⋊C4—232no—
610C2×C22⋊C4—28no—
611C2×C22⋊C4—44no—
612C2×C22⋊C4—82no—
613C2×C22⋊C4C2×D4116yes—
614C2×C22⋊C4C2×D4116yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C42—42no—
643C2×C42—42no—
644C2×C42—44no—
645C2×C42—82no—
646C2×C42C2×D418yes—
647C2×C42C2418yes—
648C2×C42C2414yes—
649C2×C42C2418yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660#95C2414yes—
661#95C2414yes—
662#95C2418yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2414yes—
672#95C2418yes—
673#95C2414yes—
674#95C2414yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684C24—24no—
685C24—24no—
686C24—42no—
687C24—42no—
688C24—42no—
689C24—42no—
690C24C22×D418yes—
691C24C2514yes—
692C24C2514yes—
693C24C2511yescharacteristic
694#41—832no—
695C2×Q8—28no—
696C2×Q8—24no—
697C2×Q8—28no—
698C2×Q8—216no—
699C2×Q8—24no—
700C2×Q8—28no—
701C2×Q8—24no—
702C2×Q8—28no—
703C2×Q8—42no—
704C2×Q8—42no—
705C2×Q8—48no—
706C2×Q8—44no—
707C2×Q8—42no—
708C2×Q8—48no—
709C2×Q8—42no—
710C2×Q8—44no—
711C2×Q8—416no—
712C2×Q8—832no—
713C2×Q8C22×D418yes—
714C2×Q8C22×D418yes—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—416no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—48no—
732C2×D4—42no—
733C2×D4—48no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4C22×D418yes—
739C2×D4C22×D418yes—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—24no—
745C22×C4—216no—
746C22×C4—216no—
747C22×C4—24no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—216no—
757C22×C4—28no—
758C22×C4—41no—
759C22×C4—42no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—42no—
763C22×C4—44no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—41no—
772C22×C4—48no—
773C22×C4—42no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—48no—
777C22×C4—44no—
778C22×C4—41no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—816no—
783C22×C4C22×D414yes—
784C22×C4C22×D414yes—
785C22×C4C22×D414yes—
786C22×C4C22×D418yes—
787C22×C42−1+414yes—
788C22×C42−1+414yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2518yes—
795C22×C4C2514yes—
796C22×C4C2518yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—216no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—24no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—28no—
817C4⋊C4—216no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—216no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—28no—
825C4⋊C4—216no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—42no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—42no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—42no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4H(5,𝔽2)14yes—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—216no—
852C22⋊C4—216no—
853C22⋊C4—216no—
854C22⋊C4—216no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—28no—
861C22⋊C4—216no—
862C22⋊C4—216no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—44no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4C22×D4132yes—
875C22⋊C4C22×D4132yes—
876C42—216no—
877C42—28no—
878C42—216no—
879C42—24no—
880C42—28no—
881C42—24no—
882C42—42no—
883C42—44no—
884C42—42no—
885C42—44no—
886C42—44no—
887C42C22×D418yes—
888C42C22×D418yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—216no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—48no—
908C23—48no—
909C23—84no—
910C23—84no—
911C23—84no—
912C23—84no—
913C23C23×D418yes—
914C23C23×D412yes—
915C23C2×2−1+412yes—
916C23C2×2−1+412yes—
917C23C2611yescharacteristic
918Q8—216no—
919Q8—48no—
920Q8—416no—
921Q8—84no—
922Q8—88no—
923Q8—816no—
924D4—216no—
925D4—48no—
926D4—48no—
927D4—416no—
928D4—84no—
929D4—84no—
930D4—816no—
931D4—816no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—28no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—48no—
978C2×C4—44no—
979C2×C4—416no—
980C2×C4—48no—
981C2×C4—416no—
982C2×C4—88no—
983C2×C4—816no—
984C2×C4—816no—
985C2×C4—82no—
986C2×C4—82no—
987C2×C4—84no—
988C2×C4—816no—
989C2×C4C23×D414yes—
990C2×C4C23×D418yes—
991C2×C4C23×D412yes—
992C2×C4C23×D414yes—
993C2×C4C23×D412yes—
994C2×C4C2×H(5,𝔽2)14yes—
995C2×C4C2×H(5,𝔽2)12yes—
996C2×C4C2×2−1+414yes—
997C2×C4C2×2−1+414yes—
998C2×C4#58512yes—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—28no—
1006C22—28no—
1007C22—28no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—816no—
1020C22#349914yes—
1021C22C24×D411yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C22×2−1+411yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C2×#58511yescharacteristic
1026C22H(7,𝔽2)11yescharacteristic
1027C222−1+611yescharacteristic
1028C4—22no—
1029C4—28no—
1030C4—24no—
1031C4—24no—
1032C4—24no—
1033C4—24no—
1034C4—24no—
1035C4—44no—
1036C4—48no—
1037C4—44no—
1038C4—44no—
1039C4—48no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4#349614yes—
1045C2—24no—
1046C2—48no—
1047C2—84no—
1048C2C2×#349611yescharacteristic
1049C2C2×#349911yescharacteristic
1050C2#6285311yescharacteristic
1051C2#6289311yescharacteristic
1052C2#6289411yescharacteristic
1053C2#6295911yescharacteristic
1054C2#6296211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3561C2semidirect
2. #51333C2semidirect
3. #51332C2semidirect
4. #45332C2semidirect
5. #45303C2semidirect
6. #45144C2semidirect
7. #45077C2semidirect
8. #39615C2semidirect
9. #39486C2semidirect
10. #39482C2semidirect
11. #37861C2semidirect
12. #36740C2semidirect
13. Q8×#121C2semidirect
14. #36153C2semidirect
15. #35241C2semidirect
16. #35173C2semidirect
17. #35003C2semidirect
18. #35002C2semidirect
19. #34594C2semidirect
20. C2×#2367C2semidirect
27. C2×D4×Q8C22semidirect
47. #2734C22semidirect
48. #2732C22semidirect
49. #2729C22semidirect
51. #2722C22semidirect
52. #2718C22semidirect
53. #2715C22semidirect
54. #2710C22semidirect
56. #2700C22semidirect
57. #2698C22semidirect
58. #2695C22semidirect
59. #2689C22semidirect
60. #2689C22semidirect
61. #2687C22semidirect
63. #2681C22semidirect
64. #2680C22semidirect
65. #2674C22semidirect
66. #2674C22semidirect
67. #2672C22semidirect
68. #2672C22semidirect
69. #2664C22semidirect
70. #2664C22semidirect
71. #2662C22semidirect
81. #2584C22semidirect
82. #2568C22semidirect
83. #2567C22semidirect
84. #2565C22semidirect
86. #2555C22semidirect
87. #2553C22semidirect
88. #2549C22semidirect
89. #2549C22semidirect
91. #2547C22semidirect
92. #2546C22semidirect
93. #2546C22semidirect
94. #2546C22semidirect
95. #2546C22semidirect
96. #2545C22semidirect
97. #2542C22semidirect
98. #2538C22semidirect
99. #2538C22semidirect
101. #2521C22semidirect
104. #2478C22semidirect
105. #2470C22semidirect
106. #2466C22semidirect
107. #2464C22semidirect
108. #2455C22semidirect
109. #2449C22semidirect
111. #2446C22semidirect
112. #2440C22semidirect
113. #2440C22semidirect
114. #2438C22semidirect
115. #2434C22semidirect
117. #2429C22semidirect
118. #2429C22semidirect
121. #2425C22semidirect
122. #2423C22semidirect
128. #2413C22semidirect
131. #2409C22semidirect
133. #2396C22semidirect
134. #2392C22semidirect
138. Q8×C4⋊C4C22semidirect
140. Q8×C22⋊C4C22semidirect
143. #2323C22semidirect
144. #2323C22semidirect
195. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35612
#513332
#513322
#453322
#453032
#451442
#450772
#396152
#394862
#394822
#378612
#367402
Q8×#1212
#361532
#352412
#351732
#350032
#350022
#345942
C2×#23672