Finite Group Databasebeta

← #7680791

Subgroups — #7680791

Order 512.

7700 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3506C211yesmaximal, characteristic, complemented
3#59125C214yesmaximal, complemented
4#59050C214yesmaximal, complemented
5#59005C218yesmaximal, complemented
6#44973C218yesmaximal, complemented
7#44103C218yesmaximal, complemented
8#39174C212yesmaximal, complemented
9#39168C214yesmaximal, complemented
10#39167C212yesmaximal, complemented
11#39161C214yesmaximal, complemented
12#36508C212yesmaximal, complemented
13#36465C212yesmaximal, complemented
14#35533C212yesmaximal, complemented
15#35532C212yesmaximal, complemented
16#35289C211yesmaximal, characteristic, complemented
17#35264C212yesmaximal, complemented
18#34937C211yesmaximal, characteristic, complemented
19C2×#2542C211yesmaximal, characteristic, complemented
20#34207C212yesmaximal, complemented
21#34145C211yesmaximal, characteristic, complemented
22C4×#535C211yesmaximal, characteristic, complemented
23#3506—216no—
24#3503—216no—
25C2×#559C2214yes—
26C2×Q82C2212yescomplemented
27C2×#557C2212yescomplemented
28C2×#556C2212yes—
29C2×#555C2212yes—
30C2×#554C2214yes—
31C2×#554C2212yescomplemented
32C2×#553C2214yes—
33C2×#550C2212yes—
34C2×D4×Q8C2214yes—
35C2×D4×Q8C2212yescomplemented
36C2×#548C2218yescomplemented
37C2×#547C2212yes—
38C2×#544C2212yes—
39C2×#544C2214yescomplemented
40C2×#538C2214yes—
41C2×#535C2211yescharacteristic
42C2×#535C2212yes—
43C2×#533C2211yescharacteristic
44C2×#533C2212yescomplemented
45C2×#532C2211yescharacteristic
46C2×#532C2212yes—
47C22×C4⋊Q8C2211yescharacteristic
48C22×C4⋊Q8C2212yescomplemented
49C2×#525C2214yes—
50C22×C22⋊Q8C2214yes—
51C2×#520C2212yes—
52C2×#520C2212yes—
53C2×C4×#41C2211yescharacteristic
54C22×C4×D4C2211yescharacteristic
55#2862C2212yescomplemented
56#2861C2214yes—
57#2858C2214yes—
58#2858C2212yescomplemented
59#2730C22116yescomplemented
60#2723C22116yescomplemented
61#2711C22116yescomplemented
62#2681C22116yescomplemented
63#2674C22116yescomplemented
64#2674C22116yescomplemented
65#2641C2214yes—
66#2640C2214yes—
67#2640C2214yescomplemented
68#2567C2214yescomplemented
69#2566C2214yescomplemented
70#2565C2214yescomplemented
71#2563C2214yescomplemented
72#2548C2214yes—
73#2548C2211yescharacteristic, complemented
74#2547C2211yescharacteristic, complemented
75#2547C2214yescomplemented
76#2546C2211yescharacteristic, complemented
77#2545C2214yes—
78#2545C2212yescomplemented
79#2544C2214yes—
80#2544C2212yescomplemented
81#2543C2214yes—
82#2542C2214yes—
83#2542C2212yes—
84#2542C2212yes—
85#2542C2214yes—
86#2542C2214yes—
87#2542C2214yescomplemented
88#2541C2214yes—
89#2541C2211yescharacteristic, complemented
90#2540C22116yescomplemented
91#2540C2218yescomplemented
92#2519C22116yescomplemented
93#2504C2214yes—
94#2491C2218yes—
95#2490C2218yes—
96#2472C22116yes—
97#2463C22116yescomplemented
98#2452C22116yescomplemented
99#2449C22116yes—
100#2448C22116yescomplemented
101#2443C22116yescomplemented
102#2441C2218yescomplemented
103#2440C2218yescomplemented
104#2436C2214yes—
105#2432C2218yescomplemented
106#2429C2218yescomplemented
107#2426C2218yescomplemented
108#2424C22116yes—
109#2416C2214yes—
110#2416C2218yes—
111#2415C2218yescomplemented
112#2414C2218yes—
113#2409C2218yescomplemented
114C2×#399C2214yes—
115#2392C2214yescomplemented
116#2370C2214yescomplemented
117#2369C2212yescomplemented
118#2368C2214yes—
119#2365C2212yescomplemented
120#2362C2218yescomplemented
121#2361C22116yes—
122#2360C2214yes—
123#2354C2218yescomplemented
124D4×C4⋊C4C2218yescomplemented
125#2328C2212yes—
126#2326C2212yes—
127#2326C2214yescomplemented
128#2326C2214yescomplemented
129#2324C2214yes—
130#2321C2214yes—
131#2317C2211yescharacteristic
132#2311C2211yescharacteristic
133#2311C2212yes—
134#2311C2212yes—
135#2309C2211yescharacteristic
136C4×C4⋊Q8C2214yescomplemented
137C4×#127C2212yes—
138C4×#127C2214yescomplemented
139C4×#124C2212yes—
140C4×#121C2214yes—
141C4×#121C2214yescomplemented
142C4×#120C2214yes—
143#2297C2212yes—
144#2296C2212yes—
145#2295C2214yescomplemented
146#2295C2212yescomplemented
147C2×#390C2212yes—
148C2×#384C2212yes—
149C42×Q8C2212yescomplemented
150C4×#117C2211yescharacteristic
151C4×#117C2212yes—
152C2×C4×C4⋊C4C2211yescharacteristic
153C22×#41C2312yes—
154C22×#41C2311yescharacteristic
155C22×#41C2314yes—
156C23×Q8C2314yes—
157C23×Q8C2312yes—
158C23×D4C2311yescharacteristic
159C24×C4C2312yes—
160#559—232no—
161Q82—216no—
162#557—216no—
163#556—216no—
164#555—216no—
165#554—232no—
166#554—216no—
167#553—232no—
168#550—216no—
169D4×Q8—232no—
170D4×Q8—216no—
171#548—432no—
172#547—216no—
173#544—232no—
174#544—216no—
175#538—232no—
176#535—28no—
177#535—216no—
178#533—216no—
179#533D4116yescomplemented
180#532—216no—
181#532—28no—
182C2×C4⋊Q8—216no—
183C2×C4⋊Q8—28no—
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2318yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2311yescharacteristic
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2314yes—
200C2×#127C2311yescharacteristic
201C2×#126C2318yes—
202C2×#125C2314yes—
203C2×#125C2314yes—
204C2×#125C2318yes—
205C2×#125C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2314yes—
210C2×#124C2312yes—
211C2×#124C2318yes—
212C2×#124C23116yes—
213C2×#124C2318yes—
214#525—232no—
215C2×#123C2318yes—
216C2×#123C2318yes—
217C2×C22⋊Q8—416no—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C23116yes—
227C2×C22⋊Q8C23116yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2314yes—
231C2×#121C2318yes—
232C2×#121C2312yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2318yes—
239C2×#121C23116yes—
240C2×#120C2314yes—
241C2×#120C2318yes—
242#520—216no—
243#520—216no—
244C4×#41—28no—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×D4—28no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2318yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2318yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C23116yes—
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2318yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2318yes—
291C22×C42C2312yes—
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294#399C23116yes—
295#399C2318yes—
296#399C2318yes—
297#399C23116yes—
298#398C23116yes—
299#398C2314yes—
300#397C23116yes—
301#397C23116yes—
302#397C2314yes—
303#396C23116yes—
304#396C2318yes—
305#396C23116yes—
306#395C23116yes—
307#394C23116yes—
308#394C23116yes—
309#394C2318yes—
310#394C2314yes—
311#394C23116yes—
312#394C23116yes—
313#393C23116yes—
314#393C23116yes—
315#392C2314yes—
316#392C23116yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2312yes—
322#391C2318yes—
323#391C2314yes—
324#391C2318yes—
325#390C2312yes—
326#390C2312yes—
327#390C2318yes—
328#390C2314yes—
329#390C23116yes—
330#390C2318yes—
331#390C2314yes—
332#390C2312yes—
333#390C2312yes—
334#390C2314yes—
335#390C2312yes—
336#390C2314yes—
337#390C23116yes—
338#390C2314yes—
339#390C2318yes—
340#390C23116yes—
341#390C2314yes—
342#389C23116yes—
343#389C23116yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#388C2318yes—
351#388C2318yes—
352#388C23116yes—
353#388C23116yes—
354#388C23116yes—
355#388C23116yes—
356#388C23116yes—
357#388C2318yes—
358#387C23116yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C23116yes—
368#386C2318yes—
369#386C2318yes—
370#385C23116yes—
371#385C2314yes—
372#385C2318yes—
373#385C23116yes—
374#385C23116yes—
375#385C2318yes—
376#384C2312yes—
377#384C2314yes—
378#384C2314yes—
379#384C2318yes—
380#382C2318yes—
381#382C2312yes—
382#380C2318yes—
383#380C2318yes—
384#380C2314yes—
385#380C2314yes—
386#379C2314yes—
387C4×C4⋊C4C23116yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2311yescharacteristic
401C4×C22⋊C4C2312yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2318yes—
406#376C2312yes—
407#376C2314yes—
408C2×#95C2312yes—
409C43C2312yes—
410C43C2314yes—
411C25C2412yes—
412C2×#41—216no—
413C2×#41—24no—
414C2×#41—28no—
415C2×#41—28no—
416C2×#41—24no—
417C2×#41—28no—
418C2×#41—416no—
419C2×#41#4118yescomplemented
420C22×Q8—216no—
421C22×Q8—28no—
422C22×Q8—48no—
423C22×Q8—416no—
424C22×Q8C2412yes—
425C22×Q8C2414yes—
426C22×Q8C2412yes—
427C22×Q8C2411yescharacteristic
428C22×Q8C2414yes—
429C22×Q8C2418yes—
430C22×Q8C2412yes—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4—24no—
434C22×D4C2414yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2412yes—
438C22×D4C2412yes—
439C22×D4C2418yes—
440C22×D4C2412yes—
441C22×D4C2411yescharacteristic
442C22×D4C2418yes—
443C22×D4C2418yes—
444C22×D4C2412yes—
445C22×D4C2418yes—
446C23×C4—28no—
447C23×C4—48no—
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C2412yes—
451C23×C4C2414yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2414yes—
455C23×C4C2412yes—
456C23×C4C2418yes—
457C23×C4C2412yes—
458C23×C4C2418yes—
459C23×C4C2414yes—
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C4⋊Q8—216no—
463C4⋊Q8—28no—
464C4⋊Q8—216no—
465C4⋊Q8—216no—
466C4⋊Q8—232no—
467C4⋊Q8—28no—
468C4⋊Q8—28no—
469C4⋊Q8—28no—
470C4⋊Q8—28no—
471C4⋊Q8—24no—
472C4⋊Q8—216no—
473C4⋊Q8C2×D418yes—
474C4⋊Q8C2×D418yes—
475#127—28no—
476#127—28no—
477#127—24no—
478#127—216no—
479#126—232no—
480#125—216no—
481#125—232no—
482#125—216no—
483#125C2×D4116yes—
484#124—232no—
485#124—28no—
486#124—28no—
487#124—28no—
488#124—28no—
489#124—216no—
490#124—432no—
491#124—416no—
492#123—232no—
493#123—232no—
494C22⋊Q8—216no—
495C22⋊Q8—216no—
496C22⋊Q8—216no—
497C22⋊Q8—232no—
498C22⋊Q8—232no—
499C22⋊Q8—232no—
500C22⋊Q8—232no—
501C22⋊Q8—432no—
502C22⋊Q8—432no—
503C22⋊Q8—416no—
504C22⋊Q8C2×D4116yes—
505C22⋊Q8C2×D4116yes—
506#121—232no—
507#121—28no—
508#121—28no—
509#121—216no—
510#121—216no—
511#121—216no—
512#121—216no—
513#121—232no—
514#121—216no—
515#121—432no—
516#120—216no—
517#120—232no—
518C4×Q8—216no—
519C4×Q8—216no—
520C4×Q8—216no—
521C4×Q8—24no—
522C4×Q8—24no—
523C4×Q8—216no—
524C4×Q8—216no—
525C4×Q8C2×D4116yes—
526C4×Q8C2×D4116yes—
527C4×D4—28no—
528C4×D4—28no—
529C4×D4—232no—
530C4×D4—232no—
531C4×D4—232no—
532C4×D4—232no—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—24no—
538C4×D4—24no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—432no—
544C4×D4—416no—
545#117—24no—
546#117—24no—
547#117—24no—
548#117—216no—
549#117—216no—
550#117—216no—
551#117—28no—
552#117C2×D4116yes—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—28no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—216no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—216no—
559C2×C4⋊C4—28no—
560C2×C4⋊C4—416no—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C24116yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C24116yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C22⋊C4—28no—
596C2×C22⋊C4—416no—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C24116yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C24116yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C24116yes—
619C2×C22⋊C4C24116yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C42—28no—
624C2×C42—28no—
625C2×C42C2×D418yes—
626C2×C42C2418yes—
627C2×C42C2412yes—
628C2×C42C2418yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2414yes—
632C2×C42C2418yes—
633C2×C42C2414yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2418yes—
639C2×C42C2414yes—
640C2×C42C2411yescharacteristic
641C2×C42C2414yes—
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#95C2412yes—
646#95C2414yes—
647#95C2412yes—
648#95C2418yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C24116yes—
658#95C2418yes—
659#95C24116yes—
660C24—24no—
661C24—24no—
662C24—24no—
663C24—44no—
664C24—44no—
665C24C2514yes—
666C24C2514yes—
667C24C2512yes—
668C24C2511yescharacteristic
669#41—232no—
670#41—432no—
671#41—832no—
672C2×Q8—22no—
673C2×Q8—24no—
674C2×Q8—28no—
675C2×Q8—216no—
676C2×Q8—28no—
677C2×Q8—24no—
678C2×Q8—28no—
679C2×Q8—216no—
680C2×Q8—22no—
681C2×Q8—24no—
682C2×Q8—44no—
683C2×Q8—48no—
684C2×Q8—416no—
685C2×Q8—816no—
686C2×Q8—832no—
687C2×Q8C22×D418yes—
688C2×Q8C22×D418yes—
689C2×Q8C2×#4114yes—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—216no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—216no—
697C2×D4—22no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—216no—
703C2×D4—24no—
704C2×D4—216no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—216no—
709C2×D4—28no—
710C2×D4—22no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—416no—
717C2×D4—44no—
718C2×D4—416no—
719C2×D4—48no—
720C2×D4—416no—
721C2×D4C2×#4118yes—
722C2×D4C2×#4114yes—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—24no—
728C22×C4—28no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—216no—
737C22×C4—28no—
738C22×C4—216no—
739C22×C4—216no—
740C22×C4—28no—
741C22×C4—42no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—44no—
746C22×C4—416no—
747C22×C4—416no—
748C22×C4—48no—
749C22×C4—816no—
750C22×C4C22×D414yes—
751C22×C4C22×D414yes—
752C22×C4C22×D414yes—
753C22×C4C2×#4118yes—
754C22×C4C2×#4114yes—
755C22×C42−1+414yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2514yes—
759C22×C4C2514yes—
760C22×C4C2512yes—
761C22×C4C2512yes—
762C22×C4C2514yes—
763C22×C4C2518yes—
764C22×C4C2511yescharacteristic
765C22×C4C2514yes—
766C22×C4C2511yescharacteristic
767C22×C4C2514yes—
768C22×C4C2511yescharacteristic
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C4⋊C4—24no—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—216no—
779C4⋊C4—216no—
780C4⋊C4—28no—
781C4⋊C4—216no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—22no—
786C4⋊C4—24no—
787C4⋊C4—22no—
788C4⋊C4—24no—
789C4⋊C4—216no—
790C4⋊C4—216no—
791C4⋊C4—24no—
792C4⋊C4—216no—
793C4⋊C4—28no—
794C4⋊C4—24no—
795C4⋊C4—232no—
796C4⋊C4—216no—
797C4⋊C4—24no—
798C4⋊C4—416no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4C22×D418yes—
802C4⋊C4C22×D418yes—
803C4⋊C4C22×D418yes—
804C4⋊C4C22×D418yes—
805C4⋊C4C22×D4116yes—
806C4⋊C4C22×D4116yes—
807C4⋊C4H(5,𝔽2)18yes—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—216no—
811C22⋊C4—24no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—216no—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—28no—
820C22⋊C4—216no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—216no—
824C22⋊C4—232no—
825C22⋊C4—216no—
826C22⋊C4—416no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—416no—
832C22⋊C4—416no—
833C22⋊C4C22×D4116yes—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—216no—
838C42—216no—
839C42—28no—
840C42—24no—
841C42—24no—
842C42—24no—
843C42—216no—
844C42—28no—
845C42—24no—
846C42—48no—
847C42—44no—
848C42C22×D414yes—
849C42C22×D414yes—
850C42C22×D414yes—
851C42C22×D414yes—
852C42C22×D4116yes—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—28no—
864C23—28no—
865C23—24no—
866C23—24no—
867C23—28no—
868C23—28no—
869C23—416no—
870C23—48no—
871C23—84no—
872C23—88no—
873C23—84no—
874C23C23×D412yes—
875C23C22×#4114yes—
876C23C22×#4112yes—
877C23C2×2−1+412yes—
878C23C2611yescharacteristic
879Q8—28no—
880Q8—216no—
881Q8—48no—
882Q8—48no—
883Q8—416no—
884Q8—88no—
885Q8—816no—
886D4—216no—
887D4—28no—
888D4—432no—
889D4—416no—
890D4—48no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—84no—
895D4—816no—
896D4—816no—
897D4—816no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—28no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—28no—
906C2×C4—22no—
907C2×C4—216no—
908C2×C4—28no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—216no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—44no—
930C2×C4—416no—
931C2×C4—48no—
932C2×C4—416no—
933C2×C4—416no—
934C2×C4—48no—
935C2×C4—88no—
936C2×C4—816no—
937C2×C4—816no—
938C2×C4—84no—
939C2×C4—88no—
940C2×C4#548116yescomplemented
941C2×C4C23×D418yes—
942C2×C4C23×D412yes—
943C2×C4C23×D412yes—
944C2×C4C23×D412yes—
945C2×C4C23×D418yes—
946C2×C4C23×D412yes—
947C2×C4C23×D412yes—
948C2×C4C23×D412yes—
949C2×C4C22×#4114yes—
950C2×C4C22×#4112yes—
951C2×C4C22×#4112yes—
952C2×C4C2×H(5,𝔽2)18yes—
953C2×C4C2×H(5,𝔽2)14yes—
954C2×C4C2×2−1+412yes—
955C2×C4C2×2−1+412yes—
956C22—24no—
957C22—22no—
958C22—22no—
959C22—24no—
960C22—28no—
961C22—24no—
962C22—42no—
963C22—42no—
964C22—44no—
965C22—48no—
966C22—48no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—48no—
972C22—48no—
973C22—44no—
974C22—44no—
975C22—816no—
976C22C2×#54814yes—
977C22C24×D411yescharacteristic
978C22C23×#4111yescharacteristic
979C22C22×H(5,𝔽2)12yes—
980C22C22×2−1+411yescharacteristic
981C222−1+612yes—
982C4—28no—
983C4—22no—
984C4—28no—
985C4—22no—
986C4—22no—
987C4—28no—
988C4—24no—
989C4—44no—
990C4—44no—
991C4—44no—
992C4—42no—
993C4—48no—
994C4—42no—
995C4—44no—
996C4—44no—
997C4C2×#54814yes—
998C4C2×#54814yes—
999C4#349814yes—
1000C2—24no—
1001C2—44no—
1002C2—84no—
1003C2—84no—
1004C2C22×#54811yescharacteristic
1005C2C2×#349811yescharacteristic
1006C2#6285911yescharacteristic
1007C2#6291312yes—
1008C2#6298512yes—
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×#3503C2semidirect
2. C2×#3506C2semidirect
3. #59125C2semidirect
4. #59050C2semidirect
5. #59005C2semidirect
6. #44973C2semidirect
7. #44103C2semidirect
8. #39174C2semidirect
9. #39168C2semidirect
10. #39167C2semidirect
11. #39161C2semidirect
12. #36508C2semidirect
13. #36465C2semidirect
14. #35533C2semidirect
15. #35532C2semidirect
16. #35289C2semidirect
17. #35264C2semidirect
18. #34937C2semidirect
19. C2×#2542C2semidirect
20. #34207C2semidirect
21. #34145C2semidirect
22. C4×#535C2semidirect
26. C2×Q82C22semidirect
27. C2×#557C22semidirect
31. C2×#554C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
39. C2×#544C22semidirect
44. C2×#533C22semidirect
48. C22×C4⋊Q8C22semidirect
55. #2862C22semidirect
58. #2858C22semidirect
59. #2730C22semidirect
60. #2723C22semidirect
61. #2711C22semidirect
62. #2681C22semidirect
63. #2674C22semidirect
64. #2674C22semidirect
67. #2640C22semidirect
68. #2567C22semidirect
69. #2566C22semidirect
70. #2565C22semidirect
71. #2563C22semidirect
73. #2548C22semidirect
74. #2547C22semidirect
75. #2547C22semidirect
76. #2546C22semidirect
78. #2545C22semidirect
80. #2544C22semidirect
87. #2542C22semidirect
89. #2541C22semidirect
90. #2540C22semidirect
91. #2540C22semidirect
92. #2519C22semidirect
97. #2463C22semidirect
98. #2452C22semidirect
100. #2448C22semidirect
101. #2443C22semidirect
102. #2441C22semidirect
103. #2440C22semidirect
105. #2432C22semidirect
106. #2429C22semidirect
107. #2426C22semidirect
111. #2415C22semidirect
113. #2409C22semidirect
115. #2392C22semidirect
116. #2370C22semidirect
117. #2369C22semidirect
119. #2365C22semidirect
120. #2362C22semidirect
123. #2354C22semidirect
124. D4×C4⋊C4C22semidirect
127. #2326C22semidirect
128. #2326C22semidirect
136. C4×C4⋊Q8C22semidirect
138. C4×#127C22semidirect
141. C4×#121C22semidirect
145. #2295C22semidirect
146. #2295C22semidirect
149. C42×Q8C22semidirect
179. #533D4semidirect
419. C2×#41#41semidirect
940. C2×C4#548semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#35062
#591252
#590502
#590052
#449732
#441032
#391742
#391682
#391672
#391612
#365082
#364652
#355332
#355322
#352892
#352642
#349372
C2×#25422
#342072
#341452
C4×#5352