Finite Group Databasebeta

← #7671951

Subgroups — #7671951

Order 512.

8058 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic, complemented
2C2×#3501C211yesmaximal, characteristic, complemented
3#59657C218yesmaximal, complemented
4#59654C214yesmaximal, complemented
5#59652C214yesmaximal, complemented
6#39420C218yesmaximal, complemented
7#39169C212yesmaximal, complemented
8#39167C212yesmaximal, complemented
9#39161C214yesmaximal, complemented
10#36639C211yesmaximal, characteristic, complemented
11#36534C212yesmaximal, complemented
12#36496C214yesmaximal, complemented
13#36465C212yesmaximal, complemented
14#36097C218yesmaximal, complemented
15#35532C212yesmaximal, complemented
16#35528C212yesmaximal, complemented
17#35264C212yesmaximal, complemented
18#35172C211yesmaximal, characteristic, complemented
19#35165C211yesmaximal, characteristic, complemented
20#34275C212yesmaximal, complemented
21C4×#533C211yesmaximal, characteristic, complemented
22C2×C4×#127C211yesmaximal, characteristic, complemented
23#3506—216no—
24#3501—216no—
25C2×#559C2214yescomplemented
26C2×#556C2212yescomplemented
27C2×#555C2212yescomplemented
28C2×#554C2212yescomplemented
29C2×#554C2212yescomplemented
30C2×#554C2214yescomplemented
31C2×#554C2214yescomplemented
32C2×#553C2214yescomplemented
33C2×#550C2212yescomplemented
34C2×D4×Q8C2212yescomplemented
35C2×D4×Q8C2212yescomplemented
36C2×#548C2218yescomplemented
37C2×#547C2212yescomplemented
38C2×#544C2212yes—
39C2×#543C2214yes—
40C2×#538C2214yes—
41C2×#535C2212yes—
42C2×#535C2212yes—
43C2×#533C2211yescharacteristic
44C2×#533C2211yescharacteristic
45C2×#532C2211yescharacteristic
46C22×#127C2211yescharacteristic
47C2×#525C2214yes—
48C22×C22⋊Q8C2214yes—
49C2×#520C2212yes—
50C2×#518C2212yes—
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic
53C22×C4×D4C2214yes—
54#2862C2211yescharacteristic, complemented
55#2862C2211yescharacteristic, complemented
56#2861C2212yescomplemented
57#2861C2212yescomplemented
58#2861C2214yescomplemented
59#2858C2211yescharacteristic, complemented
60#2858C2211yescharacteristic, complemented
61#2858C2214yescomplemented
62#2850C2214yes—
63#2850C2214yes—
64#2848C2214yes—
65#2847C2214yes—
66#2730C22116yescomplemented
67#2723C22116yescomplemented
68#2681C22116yescomplemented
69#2676C22116yescomplemented
70#2641C2214yescomplemented
71#2640C2214yescomplemented
72#2626C2214yes—
73#2617C2214yes—
74#2580C2214yescomplemented
75#2567C2214yescomplemented
76#2566C2214yescomplemented
77#2566C2214yescomplemented
78#2565C2214yescomplemented
79#2563C2212yescomplemented
80#2560C22116yescomplemented
81#2547C2212yescomplemented
82#2544C2214yes—
83#2544C2214yes—
84#2544C2214yescomplemented
85#2542C2212yescomplemented
86#2542C2214yescomplemented
87#2541C2214yes—
88#2541C2214yes—
89#2541C2212yescomplemented
90#2540C2218yescomplemented
91#2540C22116yescomplemented
92#2538C2214yescomplemented
93#2537C2214yescomplemented
94#2536C2218yescomplemented
95#2535C2214yescomplemented
96#2491C2218yescomplemented
97#2490C2218yescomplemented
98#2472C22116yes—
99#2463C22116yescomplemented
100#2461C22116yescomplemented
101#2461C22116yescomplemented
102#2449C22116yes—
103#2443C22116yescomplemented
104#2441C2218yescomplemented
105#2440C2218yescomplemented
106#2428C2218yes—
107#2428C2218yes—
108#2426C22116yescomplemented
109#2416C2218yescomplemented
110#2415C2218yescomplemented
111#2410C22116yes—
112#2409C2218yescomplemented
113#2407C2218yescomplemented
114#2363C2218yescomplemented
115#2361C22116yescomplemented
116#2361C2218yescomplemented
117#2358C22116yes—
118#2352C2218yescomplemented
119#2328C2214yescomplemented
120#2326C2214yescomplemented
121#2317C2212yes—
122#2311C2212yes—
123#2309C2212yes—
124C4×C4⋊Q8C2212yescomplemented
125C4×C4⋊Q8C2212yescomplemented
126C4×#127C2212yes—
127C4×#127C2214yes—
128C4×#127C2214yes—
129C4×#127C2212yes—
130C4×#127C2212yes—
131C4×#127C2212yes—
132C4×#127C2214yescomplemented
133C4×#125C2214yescomplemented
134C4×#124C2214yescomplemented
135C4×#124C2214yescomplemented
136C4×#124C2214yescomplemented
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2214yes—
139#2297C2212yes—
140#2297C2212yes—
141#2296C2212yes—
142#2295C2212yescomplemented
143#2295C2212yescomplemented
144C2×#390C2211yescharacteristic
145C2×#390C2211yescharacteristic
146C2×#390C2214yes—
147#2285C2211yescharacteristic
148C2×#384C2211yescharacteristic
149C42×Q8C2212yescomplemented
150C42×Q8C2212yescomplemented
151C4×#117C2212yes—
152C2×C43C2211yescharacteristic
153C22×#41C2312yes—
154C22×#41C2314yes—
155C23×Q8C2314yes—
156C23×D4C2311yescharacteristic
157C23×D4C2311yescharacteristic
158C23×D4C2314yes—
159C24×C4C2312yes—
160C24×C4C2312yes—
161#559—232no—
162#556—216no—
163#555—216no—
164#554—216no—
165#554—232no—
166#554—216no—
167#554—232no—
168#553—232no—
169#550—216no—
170D4×Q8—216no—
171D4×Q8—216no—
172#548—432no—
173#547—216no—
174#544—216no—
175#543—232no—
176#538—232no—
177#535—216no—
178#535—216no—
179#533—28no—
180#533D4116yescomplemented
181#532—28no—
182C2×C4⋊Q8C2311yescharacteristic
183C2×C4⋊Q8C2314yes—
184C2×C4⋊Q8C2311yescharacteristic
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2311yescharacteristic
189C2×#127—28no—
190C2×#127C2314yes—
191C2×#127C2312yes—
192C2×#127C2312yes—
193C2×#127C2314yes—
194C2×#127C2311yescharacteristic
195C2×#127C2314yes—
196C2×#126C2318yes—
197C2×#125C2314yes—
198C2×#125C2312yes—
199C2×#125C2314yes—
200C2×#125C2312yes—
201C2×#124C2314yes—
202C2×#124C2314yes—
203C2×#124C2312yes—
204C2×#124C2314yes—
205C2×#124C2318yes—
206C2×#124C2314yes—
207C2×#124C23116yes—
208#525—232no—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×C22⋊Q8—232no—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C23116yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2318yes—
230C2×#121C2314yes—
231C2×#121C2318yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2318yes—
235C2×#121C23116yes—
236C2×#121C23116yes—
237C2×#120C2318yes—
238C2×#120C2318yes—
239#520—216no—
240#518—216no—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×D4—28no—
249C2×C4×D4—28no—
250C2×C4×D4—416no—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2318yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2318yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C23116yes—
273C2×#117C2312yes—
274C2×#117C2312yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2312yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2318yes—
283C22×C4⋊C4C2314yes—
284C22×C22⋊C4C2318yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2314yes—
288C22×C22⋊C4C2314yes—
289C22×C42C2312yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2312yes—
293C22×C42C2311yescharacteristic
294#399C2318yes—
295#399C23116yes—
296#398C23116yes—
297#397C2318yes—
298#397C23116yes—
299#396C23116yes—
300#396C23116yes—
301#395C23116yes—
302#394C23116yes—
303#394C23116yes—
304#394C23116yes—
305#394C23116yes—
306#394C23116yes—
307#393C2318yes—
308#393C23116yes—
309#392C2318yes—
310#392C23116yes—
311#392C23116yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#390C2318yes—
322#390C2312yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2312yes—
327#390C2318yes—
328#390C2318yes—
329#390C2318yes—
330#390C2314yes—
331#390C2312yes—
332#390C23116yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2312yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C23116yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C23116yes—
348#389C2318yes—
349#388C23116yes—
350#388C23116yes—
351#388C23116yes—
352#388C23116yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#387C23116yes—
358#387C2318yes—
359#387C2318yes—
360#386C23116yes—
361#386C2318yes—
362#386C23116yes—
363#386C23116yes—
364#386C23116yes—
365#386C2318yes—
366#386C2318yes—
367#386C23116yes—
368#385C23116yes—
369#385C23116yes—
370#385C2318yes—
371#385C23116yes—
372#385C2318yes—
373#384C2312yes—
374#384C2312yes—
375#384C2314yes—
376#384C2314yes—
377#384C2312yes—
378#382C2312yes—
379#382C2314yes—
380#382C2314yes—
381#382C2314yes—
382#380C2318yes—
383#380C2318yes—
384#380C2312yes—
385#380C2318yes—
386#380C2312yes—
387#379C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2314yes—
398C4×C22⋊C4C23116yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2318yes—
401C4×C22⋊C4C2318yes—
402#376C2314yes—
403C43C2312yes—
404C43C2312yes—
405C43C2311yescharacteristic
406C43C2311yescharacteristic
407C43C2311yescharacteristic
408C43C2311yescharacteristic
409C43C2314yes—
410C25C2412yes—
411C25C2412yes—
412C2×#41—216no—
413C2×#41—28no—
414C2×#41—28no—
415C2×#41—28no—
416C2×#41—416no—
417C22×Q8—216no—
418C22×Q8—416no—
419C22×Q8C2412yes—
420C22×Q8C2412yes—
421C22×Q8C2412yes—
422C22×Q8C2412yes—
423C22×Q8C2418yes—
424C22×Q8C2412yes—
425C22×D4—216no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4—48no—
432C22×D4—48no—
433C22×D4#4118yescomplemented
434C22×D4C2414yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2412yes—
438C22×D4C2412yes—
439C22×D4C2418yes—
440C22×D4C2418yes—
441C22×D4C2412yes—
442C22×D4C2412yes—
443C22×D4C2418yes—
444C22×D4C24116yes—
445C22×D4C2412yes—
446C22×D4C2418yes—
447C23×C4—28no—
448C23×C4—28no—
449C23×C4—48no—
450C23×C4—48no—
451C23×C4C2412yes—
452C23×C4C2414yes—
453C23×C4C2414yes—
454C23×C4C2414yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2418yes—
460C23×C4C2418yes—
461C23×C4C2414yes—
462C23×C4C2418yes—
463C23×C4C2414yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C4⋊Q8—216no—
467C4⋊Q8—24no—
468C4⋊Q8—24no—
469C4⋊Q8—24no—
470C4⋊Q8—216no—
471C4⋊Q8C2×D418yescomplemented
472C4⋊Q8C2×D418yescomplemented
473#127—216no—
474#127—28no—
475#127—28no—
476#127—216no—
477#127—24no—
478#127—216no—
479#126—232no—
480#125—216no—
481#125—28no—
482#125—216no—
483#125C2×D4116yescomplemented
484#124—232no—
485#124—216no—
486#124—28no—
487#124—216no—
488#124—216no—
489#124—48no—
490#124—432no—
491#123—232no—
492#123—232no—
493C22⋊Q8—216no—
494C22⋊Q8—216no—
495C22⋊Q8—232no—
496C22⋊Q8—28no—
497C22⋊Q8—28no—
498C22⋊Q8—216no—
499C22⋊Q8—232no—
500C22⋊Q8—232no—
501C22⋊Q8—232no—
502C22⋊Q8—232no—
503C22⋊Q8—232no—
504C22⋊Q8—432no—
505C22⋊Q8—416no—
506C22⋊Q8C2×D4116yes—
507C22⋊Q8C2×D4116yes—
508#121—232no—
509#121—28no—
510#121—28no—
511#121—216no—
512#121—216no—
513#121—216no—
514#121—232no—
515#121—432no—
516#121—432no—
517#121—416no—
518#120—232no—
519#120—232no—
520C4×Q8—216no—
521C4×Q8—28no—
522C4×Q8—28no—
523C4×Q8—216no—
524C4×Q8—48no—
525C4×Q8C2×D4116yescomplemented
526C4×Q8C2×D4116yescomplemented
527C4×D4—216no—
528C4×D4—216no—
529C4×D4—232no—
530C4×D4—232no—
531C4×D4—28no—
532C4×D4—28no—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—28no—
538C4×D4—28no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—216no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—232no—
545C4×D4—416no—
546C4×D4—432no—
547C4×D4—416no—
548C4×D4—416no—
549#117—28no—
550#117—28no—
551#117—216no—
552#117—216no—
553#117C2×D4116yes—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—216no—
557C2×C4⋊C4—232no—
558C2×C4⋊C4—216no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C24116yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C22⋊C4—28no—
591C2×C22⋊C4—28no—
592C2×C22⋊C4—232no—
593C2×C22⋊C4—48no—
594C2×C22⋊C4—48no—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C24116yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C24116yes—
617C2×C22⋊C4C24116yes—
618C2×C22⋊C4C24116yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C42—24no—
622C2×C42—24no—
623C2×C42—28no—
624C2×C42—44no—
625C2×C42C2×D418yes—
626C2×C42C2418yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2418yes—
633C2×C42C2412yes—
634C2×C42C2412yes—
635C2×C42C2412yes—
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2412yes—
641C2×C42C2418yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2414yes—
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2412yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C24116yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2418yes—
660#95C2418yes—
661#95C24116yes—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24C2×#4118yes—
672C24C2514yes—
673C24C2514yes—
674C24C2514yes—
675C24C2511yescharacteristic
676#41—432no—
677#41—832no—
678C2×Q8—24no—
679C2×Q8—24no—
680C2×Q8—24no—
681C2×Q8—216no—
682C2×Q8—24no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—24no—
686C2×Q8—44no—
687C2×Q8—416no—
688C2×Q8—44no—
689C2×Q8—832no—
690C2×Q8C22×D418yes—
691C2×Q8C22×D418yes—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—216no—
695C2×D4—216no—
696C2×D4—28no—
697C2×D4—232no—
698C2×D4—232no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—216no—
706C2×D4—24no—
707C2×D4—216no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—216no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—464no—
722C2×D4—416no—
723C2×D4—416no—
724C2×D4—416no—
725C2×D4—416no—
726C2×D4—44no—
727C2×D4—416no—
728C2×D4C2×#4118yes—
729C2×D4C2×#4118yes—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—216no—
743C22×C4—216no—
744C22×C4—28no—
745C22×C4—216no—
746C22×C4—216no—
747C22×C4—28no—
748C22×C4—216no—
749C22×C4—28no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—48no—
755C22×C4—48no—
756C22×C4—416no—
757C22×C4—416no—
758C22×C4—416no—
759C22×C4—816no—
760C22×C4—816no—
761C22×C4C22×D414yes—
762C22×C4C22×D414yes—
763C22×C4C22×D414yes—
764C22×C4C2×#4114yes—
765C22×C42−1+414yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2518yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2511yescharacteristic
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—216no—
791C4⋊C4—216no—
792C4⋊C4—216no—
793C4⋊C4—216no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—28no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—28no—
804C4⋊C4—216no—
805C4⋊C4—48no—
806C4⋊C4—416no—
807C4⋊C4—44no—
808C4⋊C4C22×D418yes—
809C4⋊C4C22×D418yes—
810C4⋊C4C22×D4116yes—
811C4⋊C4C22×D418yes—
812C4⋊C4C22×D4116yes—
813C4⋊C4C22×D418yes—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—232no—
817C22⋊C4—28no—
818C22⋊C4—216no—
819C22⋊C4—216no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—216no—
824C22⋊C4—216no—
825C22⋊C4—28no—
826C22⋊C4—216no—
827C22⋊C4—28no—
828C22⋊C4—216no—
829C22⋊C4—216no—
830C22⋊C4—216no—
831C22⋊C4—216no—
832C22⋊C4—216no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—416no—
836C22⋊C4—416no—
837C22⋊C4—416no—
838C22⋊C4—48no—
839C22⋊C4C22×D4116yes—
840C42—216no—
841C42—28no—
842C42—22no—
843C42—22no—
844C42—24no—
845C42—28no—
846C42—24no—
847C42—24no—
848C42—24no—
849C42—216no—
850C42—22no—
851C42—24no—
852C42—22no—
853C42—24no—
854C42—24no—
855C42—42no—
856C42—42no—
857C42—48no—
858C42C22×D414yes—
859C42C22×D414yes—
860C42C22×D414yes—
861C42C22×D414yes—
862C42C22×D4116yes—
863C42H(5,𝔽2)18yes—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—28no—
868C23—24no—
869C23—28no—
870C23—216no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—28no—
876C23—28no—
877C23—24no—
878C23—24no—
879C23—28no—
880C23—28no—
881C23—416no—
882C23—416no—
883C23—48no—
884C23—84no—
885C23—84no—
886C23—84no—
887C23—84no—
888C23—88no—
889C23—88no—
890C23C23×D412yes—
891C23C22×#4118yes—
892C23C22×#4112yes—
893C23C2×2−1+412yes—
894C23C2611yescharacteristic
895Q8—216no—
896Q8—48no—
897Q8—48no—
898Q8—48no—
899Q8—84no—
900Q8—816no—
901D4—216no—
902D4—216no—
903D4—432no—
904D4—432no—
905D4—416no—
906D4—48no—
907D4—48no—
908D4—48no—
909D4—48no—
910D4—84no—
911D4—816no—
912D4—816no—
913D4—832no—
914C2×C4—216no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—28no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—44no—
945C2×C4—48no—
946C2×C4—416no—
947C2×C4—416no—
948C2×C4—416no—
949C2×C4—816no—
950C2×C4—88no—
951C2×C4—88no—
952C2×C4—816no—
953C2×C4—816no—
954C2×C4—84no—
955C2×C4—84no—
956C2×C4#548116yescomplemented
957C2×C4C23×D418yes—
958C2×C4C23×D412yes—
959C2×C4C23×D412yes—
960C2×C4C23×D412yes—
961C2×C4C23×D418yes—
962C2×C4C23×D412yes—
963C2×C4C23×D412yes—
964C2×C4C23×D412yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×H(5,𝔽2)14yes—
969C2×C4C2×H(5,𝔽2)14yes—
970C2×C4C2×2−1+412yes—
971C2×C4C2×2−1+412yes—
972C2×C4#58514yes—
973C22—24no—
974C22—22no—
975C22—22no—
976C22—24no—
977C22—216no—
978C22—28no—
979C22—44no—
980C22—44no—
981C22—48no—
982C22—48no—
983C22—48no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—44no—
988C22—48no—
989C22—48no—
990C22—44no—
991C22—44no—
992C22—816no—
993C22—816no—
994C22C2×#54814yes—
995C22C24×D411yescharacteristic
996C22C23×#4111yescharacteristic
997C22C22×H(5,𝔽2)12yes—
998C22C22×2−1+411yescharacteristic
999C22C2×#58512yes—
1000C4—24no—
1001C4—24no—
1002C4—22no—
1003C4—28no—
1004C4—22no—
1005C4—22no—
1006C4—28no—
1007C4—24no—
1008C4—48no—
1009C4—44no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—42no—
1014C4—44no—
1015C4C2×#54814yes—
1016C4C2×#54814yes—
1017C4#349814yes—
1018C2—24no—
1019C2—48no—
1020C2—84no—
1021C2—84no—
1022C2C22×#54811yescharacteristic
1023C2#6277312yes—
1024C2C2×#349811yescharacteristic
1025C2#6281211yescharacteristic
1026C2#6283512yes—
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×#3506C2semidirect
2. C2×#3501C2semidirect
3. #59657C2semidirect
4. #59654C2semidirect
5. #59652C2semidirect
6. #39420C2semidirect
7. #39169C2semidirect
8. #39167C2semidirect
9. #39161C2semidirect
10. #36639C2semidirect
11. #36534C2semidirect
12. #36496C2semidirect
13. #36465C2semidirect
14. #36097C2semidirect
15. #35532C2semidirect
16. #35528C2semidirect
17. #35264C2semidirect
18. #35172C2semidirect
19. #35165C2semidirect
20. #34275C2semidirect
21. C4×#533C2semidirect
22. C2×C4×#127C2semidirect
25. C2×#559C22semidirect
26. C2×#556C22semidirect
27. C2×#555C22semidirect
28. C2×#554C22semidirect
29. C2×#554C22semidirect
30. C2×#554C22semidirect
31. C2×#554C22semidirect
32. C2×#553C22semidirect
33. C2×#550C22semidirect
34. C2×D4×Q8C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
37. C2×#547C22semidirect
54. #2862C22semidirect
55. #2862C22semidirect
56. #2861C22semidirect
57. #2861C22semidirect
58. #2861C22semidirect
59. #2858C22semidirect
60. #2858C22semidirect
61. #2858C22semidirect
66. #2730C22semidirect
67. #2723C22semidirect
68. #2681C22semidirect
69. #2676C22semidirect
70. #2641C22semidirect
71. #2640C22semidirect
74. #2580C22semidirect
75. #2567C22semidirect
76. #2566C22semidirect
77. #2566C22semidirect
78. #2565C22semidirect
79. #2563C22semidirect
80. #2560C22semidirect
81. #2547C22semidirect
84. #2544C22semidirect
85. #2542C22semidirect
86. #2542C22semidirect
89. #2541C22semidirect
90. #2540C22semidirect
91. #2540C22semidirect
92. #2538C22semidirect
93. #2537C22semidirect
94. #2536C22semidirect
95. #2535C22semidirect
96. #2491C22semidirect
97. #2490C22semidirect
99. #2463C22semidirect
100. #2461C22semidirect
101. #2461C22semidirect
103. #2443C22semidirect
104. #2441C22semidirect
105. #2440C22semidirect
108. #2426C22semidirect
109. #2416C22semidirect
110. #2415C22semidirect
112. #2409C22semidirect
113. #2407C22semidirect
114. #2363C22semidirect
115. #2361C22semidirect
116. #2361C22semidirect
118. #2352C22semidirect
119. #2328C22semidirect
120. #2326C22semidirect
124. C4×C4⋊Q8C22semidirect
125. C4×C4⋊Q8C22semidirect
132. C4×#127C22semidirect
133. C4×#125C22semidirect
134. C4×#124C22semidirect
135. C4×#124C22semidirect
136. C4×#124C22semidirect
142. #2295C22semidirect
143. #2295C22semidirect
149. C42×Q8C22semidirect
150. C42×Q8C22semidirect
180. #533D4semidirect
433. C22×D4#41semidirect
471. C4⋊Q8C2×D4semidirect
472. C4⋊Q8C2×D4semidirect
483. #125C2×D4semidirect
525. C4×Q8C2×D4semidirect
526. C4×Q8C2×D4semidirect
956. C2×C4#548semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C2×#35012
#596572
#596542
#596522
#394202
#391692
#391672
#391612
#366392
#365342
#364962
#364652
#360972
#355322
#355282
#352642
#351722
#351652
#342752
C4×#5332
C2×C4×#1272