Finite Group Databasebeta

← #7678016

Subgroups — #7678016

Order 512.

7344 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C22×#555C211yesmaximal, characteristic, complemented
3#59659C214yesmaximal, complemented
4#59652C214yesmaximal, complemented
5#59135C214yesmaximal, complemented
6#59050C214yesmaximal, complemented
7#45270C214yesmaximal, complemented
8#44938C214yesmaximal, complemented
9#44893C218yesmaximal, complemented
10#39123C218yesmaximal, complemented
11#39120C214yesmaximal, complemented
12#36516C214yesmaximal, complemented
13#35584C212yesmaximal, complemented
14#35563C212yesmaximal, complemented
15#35172C211yesmaximal, characteristic, complemented
16#35151C212yesmaximal, complemented
17#34946C211yesmaximal, characteristic, complemented
18#34935C211yesmaximal, characteristic, complemented
19#34216C211yesmaximal, characteristic, complemented
20#34201C212yesmaximal, complemented
21C4×#535C211yesmaximal, characteristic, complemented
22#3503—216no—
23C2×Q82C2212yescomplemented
24C2×#557C2212yescomplemented
25C2×#555—216no—
26C2×#555C2214yes—
27C2×#555C2214yes—
28C2×#555C2214yes—
29C2×#555C2214yes—
30C2×#554C2214yes—
31C2×#554C2212yescomplemented
32C2×D4×Q8C2214yes—
33C2×D4×Q8C2212yescomplemented
34C2×#544C2212yes—
35C2×#544C2214yescomplemented
36C2×#535C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#533C2212yescomplemented
39C22×C4⋊Q8C2211yescharacteristic
40C22×C4⋊Q8C2212yescomplemented
41C22×#124C2214yes—
42C2×#525C2212yes—
43C22×#121C2212yes—
44C22×#121C2212yes—
45C2×#520C2212yes—
46C2×C4×#41C2211yescharacteristic
47C22×C4×D4C2211yescharacteristic
48C22×C4×D4C2211yescharacteristic
49C22×#117C2212yes—
50C22×#117C2212yes—
51#2855C2218yes—
52#2848C2214yes—
53#2731C22116yescomplemented
54#2731C22116yescomplemented
55#2730C22116yescomplemented
56#2730C22116yescomplemented
57#2711C22116yescomplemented
58#2676C22116yescomplemented
59#2626C2218yes—
60#2626C2214yes—
61#2580C2214yescomplemented
62#2566C2214yescomplemented
63#2563C2212yescomplemented
64#2563C2212yescomplemented
65#2562C2214yescomplemented
66#2561C2218yes—
67#2561C2214yes—
68#2547C2212yescomplemented
69#2545C22116yescomplemented
70#2542C2212yescomplemented
71#2540C2218yescomplemented
72#2538C2214yescomplemented
73#2538C2212yescomplemented
74#2537C2212yescomplemented
75#2536C2212yescomplemented
76#2535C2212yescomplemented
77#2534C2214yes—
78#2534C2218yes—
79#2503C2212yes—
80#2491C2218yescomplemented
81#2491C2218yescomplemented
82#2491C2218yescomplemented
83#2490C2218yescomplemented
84#2490C2218yescomplemented
85#2486C2212yes—
86#2477C22116yescomplemented
87#2475C22116yescomplemented
88#2448C22116yescomplemented
89#2441C2218yescomplemented
90#2441C2218yescomplemented
91#2439C2218yescomplemented
92#2439C2218yescomplemented
93#2439C2218yescomplemented
94#2436C22116yescomplemented
95#2435C2218yes—
96#2435C2212yes—
97#2428C2218yescomplemented
98#2426C22116yescomplemented
99#2426C2218yescomplemented
100#2426C2218yescomplemented
101#2416C2218yescomplemented
102#2416C2218yescomplemented
103#2415C2218yescomplemented
104#2414C2218yescomplemented
105#2408C2212yes—
106#2408C2218yes—
107#2398C2214yescomplemented
108#2392C2214yescomplemented
109#2369C2214yescomplemented
110#2365C2214yescomplemented
111#2363C2218yescomplemented
112#2362C2218yescomplemented
113#2362C2218yescomplemented
114#2354C2218yescomplemented
115#2352C2218yescomplemented
116#2352C2218yescomplemented
117#2345C2214yes—
118Q8×C22⋊C4C2214yes—
119#2331C2214yescomplemented
120#2328C2212yescomplemented
121#2326C2212yescomplemented
122#2324C2214yescomplemented
123#2321C2214yes—
124#2321C2218yes—
125#2317C2211yescharacteristic
126#2317C2212yes—
127#2316C2212yes—
128#2311C2211yescharacteristic
129#2309C2211yescharacteristic
130#2309C2212yes—
131C4×C4⋊Q8C2214yescomplemented
132C4×#127C2212yescomplemented
133C4×#124C2214yescomplemented
134C4×#124C2212yescomplemented
135C4×#123C2218yes—
136C4×#121C2214yescomplemented
137C4×#121C2214yescomplemented
138C4×#120C2214yes—
139#2285C2211yescharacteristic
140#2280C2212yes—
141#2280C2212yes—
142#2280C2212yes—
143#2274C2212yes—
144C4×#117C2211yescharacteristic
145C22×#41C2311yescharacteristic
146C23×Q8C2314yes—
147C23×Q8C2312yes—
148C23×D4C2311yescharacteristic
149C23×D4C2311yescharacteristic
150C23×D4C2314yes—
151C24×C4C2312yes—
152C24×C4C2312yes—
153Q82—216no—
154#557—216no—
155#555—232no—
156#555—232no—
157#555—232no—
158#555—232no—
159#554—216no—
160#554—232no—
161D4×Q8—232no—
162D4×Q8—216no—
163#544—232no—
164#544—216no—
165#535—28no—
166#533—216no—
167#533—28no—
168C2×C4⋊Q8—216no—
169C2×C4⋊Q8D4116yescomplemented
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2318yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2312yes—
180C2×C4⋊Q8C2312yes—
181C2×#127C2312yes—
182C2×#125C2312yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×#124—232no—
187C2×#124C2312yes—
188C2×#124C23116yes—
189C2×#124C23116yes—
190C2×#124C2314yes—
191C2×#124C23116yes—
192#525—216no—
193C2×#123C2314yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×#121—216no—
204C2×#121—216no—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C2×#121C23116yes—
213C2×#120C2314yes—
214C2×#120C2314yes—
215#520—216no—
216C4×#41—28no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2318yes—
225C2×C4×D4—28no—
226C2×C4×D4—28no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2318yes—
243C2×#117—216no—
244C2×#117—216no—
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2318yes—
252C2×#117C2318yes—
253C2×#117C2314yes—
254C2×#117C2318yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2312yes—
266C22×C42C2314yes—
267C22×C42C2312yes—
268C22×C42C2311yescharacteristic
269#400C2318yes—
270#399C2318yes—
271#399C23116yes—
272#398C2314yes—
273#397C2318yes—
274#397C23116yes—
275#397C2314yes—
276#396C23116yes—
277#396C23116yes—
278#396C23116yes—
279#396C2318yes—
280#396C23116yes—
281#394C2318yes—
282#394C2314yes—
283#394C2318yes—
284#394C23116yes—
285#394C23116yes—
286#394C23116yes—
287#394C23116yes—
288#393C2318yes—
289#393C23116yes—
290#393C2318yes—
291#393C23116yes—
292#392C2314yes—
293#392C23116yes—
294#391C2318yes—
295#391C2312yes—
296#391C23116yes—
297#391C23116yes—
298#391C2314yes—
299#390C2312yes—
300#390C2312yes—
301#390C2318yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2318yes—
307#390C2312yes—
308#390C23116yes—
309#390C23116yes—
310#390C2314yes—
311#390C23116yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#389C2314yes—
316#389C2318yes—
317#389C23116yes—
318#389C2314yes—
319#388C2318yes—
320#388C2318yes—
321#388C23116yes—
322#388C23116yes—
323#388C2318yes—
324#388C2318yes—
325#388C23116yes—
326#388C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C2318yes—
330#387C23116yes—
331#387C23116yes—
332#387C23116yes—
333#387C23116yes—
334#386C2314yes—
335#386C2318yes—
336#386C23116yes—
337#386C2318yes—
338#386C23116yes—
339#386C2318yes—
340#385C23116yes—
341#385C2318yes—
342#385C2314yes—
343#385C2318yes—
344#384C2312yes—
345#384C2312yes—
346#384C2314yes—
347#382C2314yes—
348#382C2314yes—
349#382C2312yes—
350#382C2312yes—
351#381C2314yes—
352#381C2314yes—
353#381C2314yes—
354#380C2314yes—
355#380C2314yes—
356#380C2314yes—
357#380C2314yes—
358#380C2318yes—
359#380C2314yes—
360#380C2318yes—
361#380C2312yes—
362#380C2312yes—
363#380C2314yes—
364#380C2314yes—
365#380C2314yes—
366#379C2314yes—
367#379C2318yes—
368#379C2314yes—
369#379C2314yes—
370#379C2314yes—
371C4×C4⋊C4C2312yes—
372C4×C4⋊C4C2318yes—
373C4×C4⋊C4C2318yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2312yes—
376C4×C4⋊C4C2312yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C23116yes—
379C4×C22⋊C4C2312yes—
380C4×C22⋊C4C2318yes—
381C4×C22⋊C4C2312yes—
382C4×C22⋊C4C23116yes—
383C4×C22⋊C4C2318yes—
384C4×C22⋊C4C2318yes—
385C4×C22⋊C4C2318yes—
386C4×C22⋊C4C2318yes—
387#376C2312yes—
388C43C2312yes—
389C25C2412yes—
390C25C2412yes—
391C2×#41—24no—
392C2×#41—24no—
393C2×#41#4118yes—
394C22×Q8—216no—
395C22×Q8—84no—
396C22×Q8—88no—
397C22×Q8C2×D4116yes—
398C22×Q8C2412yes—
399C22×Q8C2411yescharacteristic
400C22×Q8C2412yes—
401C22×Q8C2418yes—
402C22×Q8C2414yes—
403C22×Q8C2414yes—
404C22×D4—24no—
405C22×D4—24no—
406C22×D4—216no—
407C22×D4—24no—
408C22×D4—24no—
409C22×D4—44no—
410C22×D4—88no—
411C22×D4C2412yes—
412C22×D4C2412yes—
413C22×D4C2412yes—
414C22×D4C2412yes—
415C22×D4C2411yescharacteristic
416C22×D4C2412yes—
417C22×D4C2418yes—
418C22×D4C2418yes—
419C22×D4C24116yes—
420C23×C4—28no—
421C23×C4—28no—
422C23×C4—28no—
423C23×C4—28no—
424C23×C4—48no—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2414yes—
428C23×C4C2414yes—
429C23×C4C2414yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2418yes—
434C23×C4C2414yes—
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2414yes—
438C23×C4C2411yescharacteristic
439C4⋊Q8—216no—
440C4⋊Q8—232no—
441C4⋊Q8—216no—
442C4⋊Q8—216no—
443C4⋊Q8—216no—
444C4⋊Q8—24no—
445C4⋊Q8—24no—
446C4⋊Q8C2×D4116yes—
447C4⋊Q8C2×D4116yes—
448C4⋊Q8C2×D4116yes—
449C4⋊Q8C2×D4116yes—
450#127—28no—
451#125—216no—
452#125—232no—
453#125—216no—
454#125—28no—
455#124—264no—
456#124—264no—
457#124—28no—
458#124—48no—
459#124—816no—
460#123—216no—
461C22⋊Q8—216no—
462C22⋊Q8—232no—
463C22⋊Q8—216no—
464C22⋊Q8—28no—
465C22⋊Q8—28no—
466C22⋊Q8—232no—
467C22⋊Q8—216no—
468C22⋊Q8—232no—
469C22⋊Q8—416no—
470#121—216no—
471#121—216no—
472#121—232no—
473#121—232no—
474#121—232no—
475#121—232no—
476#121—48no—
477#121—816no—
478#120—216no—
479#120—216no—
480C4×Q8—216no—
481C4×Q8—216no—
482C4×Q8—216no—
483C4×Q8—24no—
484C4×Q8—24no—
485C4×Q8—28no—
486C4×Q8—28no—
487C4×Q8—88no—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—232no—
491C4×D4—232no—
492C4×D4—216no—
493C4×D4—28no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—28no—
498C4×D4—28no—
499C4×D4—28no—
500C4×D4—28no—
501C4×D4—24no—
502C4×D4—24no—
503C4×D4—416no—
504#117—24no—
505#117—28no—
506#117—28no—
507#117—24no—
508#117—24no—
509#117—232no—
510#117—232no—
511#117—232no—
512#117—232no—
513#117—216no—
514#117—28no—
515C2×C4⋊C4—24no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—216no—
518C2×C4⋊C4—216no—
519C2×C4⋊C4C2×D4116yes—
520C2×C4⋊C4C2×D4116yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2411yescharacteristic
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C24116yes—
547C2×C4⋊C4C24116yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C22⋊C4—216no—
553C2×C22⋊C4—216no—
554C2×C22⋊C4—28no—
555C2×C22⋊C4—28no—
556C2×C22⋊C4C24116yes—
557C2×C22⋊C4C24116yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C24116yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C24116yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C42—216no—
585C2×C42—28no—
586C2×C42C2×D418yes—
587C2×C42C24116yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2418yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C24116yes—
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603#95C2414yes—
604#95C2414yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C24116yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C24116yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C24116yes—
618C24—24no—
619C24—24no—
620C24—24no—
621C24—24no—
622C24—24no—
623C24—24no—
624C24—44no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24C2514yes—
629C24C2514yes—
630C24C2512yes—
631C24C2511yescharacteristic
632#41—232no—
633C2×Q8—22no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—216no—
637C2×Q8—22no—
638C2×Q8—28no—
639C2×Q8—48no—
640C2×Q8—48no—
641C2×Q8—44no—
642C2×Q8—416no—
643C2×Q8—816no—
644C2×Q8—832no—
645C2×Q8C22×D4116yes—
646C2×Q8C22×D4116yes—
647C2×Q8C2×#4114yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—216no—
651C2×D4—216no—
652C2×D4—22no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—232no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—44no—
666C2×D4—416no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—416no—
672C2×D4—416no—
673C2×D4—416no—
674C2×D4—832no—
675C2×D4C2×#4118yes—
676C2×D4C2×#4114yes—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—216no—
696C22×C4—216no—
697C22×C4—48no—
698C22×C4—44no—
699C22×C4—48no—
700C22×C4—42no—
701C22×C4—44no—
702C22×C4—416no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4C22×D414yes—
706C22×C4C22×D4116yes—
707C22×C4C22×D414yes—
708C22×C4C22×D414yes—
709C22×C4C2×#4118yes—
710C22×C4C2×#4114yes—
711C22×C42−1+414yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2518yes—
716C22×C4C2514yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2512yes—
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C22×C4C2518yes—
724C22×C4C2511yescharacteristic
725C22×C4C2512yes—
726C22×C4C2511yescharacteristic
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—22no—
740C4⋊C4—24no—
741C4⋊C4—22no—
742C4⋊C4—24no—
743C4⋊C4—216no—
744C4⋊C4—28no—
745C4⋊C4—216no—
746C4⋊C4—28no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—216no—
750C4⋊C4—24no—
751C4⋊C4—28no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—416no—
755C4⋊C4—416no—
756C4⋊C4C22×D4116yes—
757C4⋊C4C22×D4116yes—
758C4⋊C4C22×D4116yes—
759C4⋊C4C22×D4116yes—
760C22⋊C4—28no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—24no—
766C22⋊C4—232no—
767C22⋊C4—232no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—216no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—416no—
782C22⋊C4—416no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C42—232no—
789C42—24no—
790C42—24no—
791C42—24no—
792C42—216no—
793C42—28no—
794C42—28no—
795C42—24no—
796C42—24no—
797C42—28no—
798C42—44no—
799C42—416no—
800C42C22×D414yes—
801C42C22×D414yes—
802C42C22×D414yes—
803C42C22×D414yes—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—28no—
818C23—24no—
819C23—24no—
820C23—28no—
821C23—24no—
822C23—48no—
823C23—48no—
824C23—48no—
825C23—48no—
826C23—48no—
827C23—48no—
828C23—88no—
829C23—88no—
830C23—88no—
831C23—88no—
832C23C23×D412yes—
833C23C22×#4114yes—
834C23C22×#4112yes—
835C23C2×2−1+412yes—
836C23C2611yescharacteristic
837Q8—28no—
838Q8—416no—
839Q8—416no—
840Q8—48no—
841Q8—48no—
842Q8—816no—
843D4—216no—
844D4—28no—
845D4—48no—
846D4—48no—
847D4—48no—
848D4—48no—
849D4—832no—
850D4—816no—
851D4—816no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—216no—
857C2×C4—22no—
858C2×C4—216no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—28no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—28no—
879C2×C4—24no—
880C2×C4—28no—
881C2×C4—24no—
882C2×C4—416no—
883C2×C4—44no—
884C2×C4—416no—
885C2×C4—48no—
886C2×C4—48no—
887C2×C4—48no—
888C2×C4—416no—
889C2×C4—416no—
890C2×C4—48no—
891C2×C4—416no—
892C2×C4—816no—
893C2×C4#548116yes—
894C2×C4C23×D4116yes—
895C2×C4C23×D412yes—
896C2×C4C23×D412yes—
897C2×C4C23×D412yes—
898C2×C4C23×D412yes—
899C2×C4C23×D412yes—
900C2×C4C23×D412yes—
901C2×C4C22×#4114yes—
902C2×C4C22×#4112yes—
903C2×C4C22×#4112yes—
904C2×C4C2×2−1+412yes—
905C2×C4C2×2−1+412yes—
906C2×C4#58514yes—
907C22—24no—
908C22—22no—
909C22—22no—
910C22—24no—
911C22—28no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—48no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—48no—
926C22—44no—
927C22—44no—
928C22—816no—
929C22—816no—
930C22C2×#54814yes—
931C22C24×D411yescharacteristic
932C22C23×#4111yescharacteristic
933C22C22×2−1+411yescharacteristic
934C22C2×#58512yes—
935C22H(7,𝔽2)12yes—
936C4—22no—
937C4—22no—
938C4—216no—
939C4—22no—
940C4—24no—
941C4—48no—
942C4—44no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4—42no—
947C4—44no—
948C4—44no—
949C4—44no—
950C4C2×#54814yes—
951C4C2×#54814yes—
952C4#348714yes—
953C2—24no—
954C2—44no—
955C2—84no—
956C2—84no—
957C2C22×#54811yescharacteristic
958C2C2×#348711yescharacteristic
959C2#6284211yescharacteristic
960C2#6292912yes—
961C2#6299412yes—
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. C22×#555C2semidirect
3. #59659C2semidirect
4. #59652C2semidirect
5. #59135C2semidirect
6. #59050C2semidirect
7. #45270C2semidirect
8. #44938C2semidirect
9. #44893C2semidirect
10. #39123C2semidirect
11. #39120C2semidirect
12. #36516C2semidirect
13. #35584C2semidirect
14. #35563C2semidirect
15. #35172C2semidirect
16. #35151C2semidirect
17. #34946C2semidirect
18. #34935C2semidirect
19. #34216C2semidirect
20. #34201C2semidirect
21. C4×#535C2semidirect
23. C2×Q82C22semidirect
24. C2×#557C22semidirect
31. C2×#554C22semidirect
33. C2×D4×Q8C22semidirect
35. C2×#544C22semidirect
38. C2×#533C22semidirect
40. C22×C4⋊Q8C22semidirect
53. #2731C22semidirect
54. #2731C22semidirect
55. #2730C22semidirect
56. #2730C22semidirect
57. #2711C22semidirect
58. #2676C22semidirect
61. #2580C22semidirect
62. #2566C22semidirect
63. #2563C22semidirect
64. #2563C22semidirect
65. #2562C22semidirect
68. #2547C22semidirect
69. #2545C22semidirect
70. #2542C22semidirect
71. #2540C22semidirect
72. #2538C22semidirect
73. #2538C22semidirect
74. #2537C22semidirect
75. #2536C22semidirect
76. #2535C22semidirect
80. #2491C22semidirect
81. #2491C22semidirect
82. #2491C22semidirect
83. #2490C22semidirect
84. #2490C22semidirect
86. #2477C22semidirect
87. #2475C22semidirect
88. #2448C22semidirect
89. #2441C22semidirect
90. #2441C22semidirect
91. #2439C22semidirect
92. #2439C22semidirect
93. #2439C22semidirect
94. #2436C22semidirect
97. #2428C22semidirect
98. #2426C22semidirect
99. #2426C22semidirect
100. #2426C22semidirect
101. #2416C22semidirect
102. #2416C22semidirect
103. #2415C22semidirect
104. #2414C22semidirect
107. #2398C22semidirect
108. #2392C22semidirect
109. #2369C22semidirect
110. #2365C22semidirect
111. #2363C22semidirect
112. #2362C22semidirect
113. #2362C22semidirect
114. #2354C22semidirect
115. #2352C22semidirect
116. #2352C22semidirect
119. #2331C22semidirect
120. #2328C22semidirect
121. #2326C22semidirect
122. #2324C22semidirect
131. C4×C4⋊Q8C22semidirect
132. C4×#127C22semidirect
133. C4×#124C22semidirect
134. C4×#124C22semidirect
136. C4×#121C22semidirect
137. C4×#121C22semidirect
169. C2×C4⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C22×#5552
#596592
#596522
#591352
#590502
#452702
#449382
#448932
#391232
#391202
#365162
#355842
#355632
#351722
#351512
#349462
#349352
#342162
#342012
C4×#5352