Finite Group Databasebeta

← #7631041

Subgroups — #7631041

Order 512.

8186 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C23×C4×Q8C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#36621C214yesmaximal, complemented
6#36580C214yesmaximal, complemented
7#36579C214yesmaximal, complemented
8#36545C214yesmaximal, complemented
9#36544C214yesmaximal, complemented
10#36233C218yesmaximal, complemented
11#36232C218yesmaximal, complemented
12#35242C212yesmaximal, complemented
13#35182C212yesmaximal, complemented
14#35179C211yesmaximal, characteristic, complemented
15#35178C211yesmaximal, characteristic, complemented
16#35111C214yesmaximal, complemented
17#35092C214yesmaximal, complemented
18#34989C214yesmaximal, complemented
19#34266C212yesmaximal, complemented
20#34200C212yesmaximal, complemented
21#34187C211yesmaximal, characteristic, complemented
22C24×Q8C2211yescharacteristic
23#3507—216no—
24C2×#559C2212yescomplemented
25C2×#557C2212yescomplemented
26C2×#556C2214yescomplemented
27C2×#556C2212yescomplemented
28C2×#554C2212yescomplemented
29C2×#552C2214yescomplemented
30C2×#539C2214yes—
31C2×#536C2212yes—
32C2×#536C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×#529C2214yes—
36C2×#525C2212yes—
37C2×#520C2212yes—
38C22×C4×Q8—216no—
39C22×C4×Q8C2212yes—
40C22×C4×Q8C2212yes—
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2214yes—
44C22×C4×Q8C2214yes—
45C22×C4×Q8C2214yes—
46C22×C4×Q8C2214yes—
47C22×C4×Q8C2211yescharacteristic
48C22×C4×Q8C2211yescharacteristic
49C23×C4⋊C4C2211yescharacteristic
50C23×C4⋊C4C2212yes—
51C23×C42C2212yes—
52C23×C42C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2856C2212yes—
57#2855C2214yes—
58#2855C2212yes—
59#2855C2212yes—
60#2854C2214yes—
61#2854C2212yes—
62#2854C2212yes—
63#2853C2218yes—
64#2852C22116yes—
65#2851C2218yes—
66#2851C2214yes—
67#2850C2218yes—
68#2850C2214yes—
69#2849C2218yes—
70#2848C2212yes—
71#2848C2212yes—
72#2847C2212yes—
73#2847C2212yes—
74#2627C2214yes—
75#2623C2218yes—
76#2618C2214yes—
77#2614C2218yes—
78#2604C22116yescomplemented
79#2599C22116yescomplemented
80#2592C2218yescomplemented
81#2584C2218yescomplemented
82#2582C2214yescomplemented
83#2581C2218yescomplemented
84#2581C2214yescomplemented
85#2580C2218yescomplemented
86#2568C2212yescomplemented
87#2567C2212yescomplemented
88#2565C2214yescomplemented
89#2548C2212yescomplemented
90#2546C2212yescomplemented
91#2545C2214yescomplemented
92#2538C2214yescomplemented
93#2536C2214yescomplemented
94#2481C22116yes—
95#2473C22116yes—
96#2469C22116yescomplemented
97#2465C22116yescomplemented
98#2462C22116yescomplemented
99#2458C22116yescomplemented
100#2449C22116yes—
101#2448C2218yescomplemented
102#2446C2218yescomplemented
103#2443C22116yes—
104#2436C2218yes—
105#2434C2218yes—
106#2423C2218yescomplemented
107#2421C2218yescomplemented
108#2409C2218yes—
109#2409C2218yes—
110#2367C2218yescomplemented
111#2365C2218yescomplemented
112#2362C2218yescomplemented
113#2361C2218yes—
114#2360C2218yes—
115#2360C2218yescomplemented
116#2356C2214yescomplemented
117#2356C2214yescomplemented
118#2355C2214yescomplemented
119#2355C2214yescomplemented
120#2352C2218yes—
121D4×C4⋊C4C2218yes—
122#2322C2218yes—
123#2322C2218yes—
124#2317C2212yes—
125#2313C2214yes—
126#2311C2212yes—
127#2310C2212yes—
128#2310C2212yes—
129C4×C22⋊Q8C2218yes—
130C4×C22⋊Q8C2214yes—
131C4×C22⋊Q8C2214yes—
132C4×#123C2218yes—
133C4×#121C2218yes—
134C4×#121C2214yes—
135C4×#121C2214yes—
136C4×#120C2218yes—
137#2297C2212yes—
138#2296C2212yes—
139#2290C22116yes—
140#2285C2211yescharacteristic
141#2285C2211yescharacteristic
142#2283C2214yes—
143#2280C2212yes—
144#2274C2212yes—
145C22×#41C2312yes—
146C23×Q8—28no—
147C23×Q8—28no—
148C23×Q8—28no—
149C23×Q8C2312yes—
150C23×Q8C2314yes—
151C23×Q8C2314yes—
152C23×Q8C2311yescharacteristic
153C23×Q8C2311yescharacteristic
154C24×C4C2312yes—
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2312yes—
159#559—216no—
160#557—216no—
161#556—216no—
162#556—232no—
163#554—216no—
164#552—232no—
165#539—232no—
166#536—216no—
167#536—216no—
168#533—28no—
169#532—28no—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×#127C2311yescharacteristic
176#529—232no—
177C2×#126C2318yes—
178C2×#126C2318yes—
179C2×#125C2312yes—
180C2×#125C2314yes—
181C2×#125C2318yes—
182C2×#124C2314yes—
183C2×#124C2312yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186#525—216no—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2314yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#120C2314yes—
206#520—216no—
207C2×C4×Q8—28no—
208C2×C4×Q8—232no—
209C2×C4×Q8—232no—
210C2×C4×Q8—232no—
211C2×C4×Q8—232no—
212C2×C4×Q8—28no—
213C2×C4×Q8—216no—
214C2×C4×Q8—216no—
215C2×C4×Q8—28no—
216C2×C4×Q8D4116yescomplemented
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2318yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2318yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2318yes—
232C2×C4×Q8C2318yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C23116yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2318yes—
248C2×#117C2314yes—
249C22×C4⋊C4—28no—
250C22×C4⋊C4—216no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2318yes—
260C22×C4⋊C4C2318yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C42—216no—
264C22×C42—28no—
265C22×C42C2312yes—
266C22×C42C2318yes—
267C22×C42C2312yes—
268C22×C42C2318yes—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279#400C2318yes—
280#400C23116yes—
281#399C23116yes—
282#398C23116yes—
283#398C23116yes—
284#398C2318yes—
285#397C23116yes—
286#396C23116yes—
287#395C2318yes—
288#395C23116yes—
289#395C23116yes—
290#394C2318yes—
291#393C23116yes—
292#393C23116yes—
293#391C2314yes—
294#391C2314yes—
295#391C2318yes—
296#391C2318yes—
297#391C2318yes—
298#391C2314yes—
299#391C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2318yes—
306#390C2314yes—
307#390C2314yes—
308#389C2318yes—
309#389C2318yes—
310#389C23116yes—
311#389C23116yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2314yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#388C23116yes—
320#388C23116yes—
321#388C23116yes—
322#388C23116yes—
323#388C2318yes—
324#388C2318yes—
325#388C23116yes—
326#388C23116yes—
327#387C23116yes—
328#387C23116yes—
329#387C23116yes—
330#387C23116yes—
331#387C23116yes—
332#387C23116yes—
333#387C23116yes—
334#387C2318yes—
335#387C2318yes—
336#387C23116yes—
337#386C2318yes—
338#386C2314yes—
339#386C2318yes—
340#386C2318yes—
341#386C2314yes—
342#386C23116yes—
343#386C23116yes—
344#386C23116yes—
345#385C2318yes—
346#385C2314yes—
347#385C23116yes—
348#385C23116yes—
349#385C2318yes—
350#385C2318yes—
351#385C2314yes—
352#385C23116yes—
353#385C23116yes—
354#385C23116yes—
355#384C2314yes—
356#384C2312yes—
357#384C2312yes—
358#383C2318yes—
359#382C2314yes—
360#382C2318yes—
361#382C2312yes—
362#382C2312yes—
363#381C2318yes—
364#381C2318yes—
365#381C2314yes—
366#380C2318yes—
367#380C2312yes—
368#380C2312yes—
369#380C2314yes—
370#380C2312yes—
371#380C2314yes—
372#380C2314yes—
373#380C2312yes—
374#380C2314yes—
375#380C2314yes—
376#380C2314yes—
377#379C2314yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2318yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C23116yes—
386C4×C4⋊C4C2318yes—
387C4×C22⋊C4C2318yes—
388C4×C22⋊C4C23116yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C23116yes—
392#376C2318yes—
393C25C2411yescharacteristic
394C2×#41—28no—
395C2×#41—28no—
396C2×#41—28no—
397C22×Q8—2128no—
398C22×Q8—216no—
399C22×Q8—216no—
400C22×Q8—216no—
401C22×Q8—216no—
402C22×Q8—28no—
403C22×Q8—24no—
404C22×Q8—216no—
405C22×Q8—216no—
406C22×Q8—28no—
407C22×Q8—28no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8C2×D418yes—
412C22×Q8#4118yes—
413C22×Q8C2418yes—
414C22×Q8C2412yes—
415C22×Q8C2412yes—
416C22×Q8C2412yes—
417C22×Q8C2412yes—
418C22×Q8C2412yes—
419C22×Q8C2412yes—
420C22×Q8C2412yes—
421C22×D4C2418yes—
422C22×D4C2412yes—
423C22×D4C2414yes—
424C22×D4C2412yes—
425C22×D4C2412yes—
426C23×C4—28no—
427C23×C4—28no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—28no—
431C23×C4—24no—
432C23×C4—28no—
433C23×C4—28no—
434C23×C4—24no—
435C23×C4—48no—
436C23×C4—44no—
437C23×C4#4118yes—
438C23×C4C2418yes—
439C23×C4C2414yes—
440C23×C4C2411yescharacteristic
441C23×C4C2412yes—
442C23×C4C2418yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C23×C4C2418yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C4⋊Q8—216no—
459C4⋊Q8—216no—
460C4⋊Q8—24no—
461C4⋊Q8—24no—
462C4⋊Q8—24no—
463#127—24no—
464#126—232no—
465#126—232no—
466#125—232no—
467#125—216no—
468#125—28no—
469#124—216no—
470#124—216no—
471#124—216no—
472#124—28no—
473#123—232no—
474#123—216no—
475#123—232no—
476#123—232no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479C22⋊Q8—232no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8—216no—
483C22⋊Q8—216no—
484C22⋊Q8—232no—
485C22⋊Q8—48no—
486#121—28no—
487#121—28no—
488#121—216no—
489#121—216no—
490#121—48no—
491#120—216no—
492C4×Q8—216no—
493C4×Q8—216no—
494C4×Q8—216no—
495C4×Q8—216no—
496C4×Q8—232no—
497C4×Q8—232no—
498C4×Q8—216no—
499C4×Q8—232no—
500C4×Q8—28no—
501C4×Q8—28no—
502C4×Q8—232no—
503C4×Q8—28no—
504C4×Q8—28no—
505C4×Q8—216no—
506C4×Q8—28no—
507C4×Q8—28no—
508C4×Q8C2×D4116yes—
509C4×Q8C2×D4116yes—
510C4×Q8C2×D4116yes—
511C4×Q8C2×D4116yes—
512C4×D4—232no—
513C4×D4—232no—
514C4×D4—216no—
515C4×D4—216no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—432no—
519#117—28no—
520#117—28no—
521#117—28no—
522#117—216no—
523#117—232no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—216no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4—232no—
532C2×C4⋊C4—232no—
533C2×C4⋊C4—216no—
534C2×C4⋊C4C2×D418yes—
535C2×C4⋊C4C2×D4116yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C24116yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C24116yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C24116yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C24116yes—
584C2×C22⋊C4C2418yes—
585C2×C42—28no—
586C2×C42—24no—
587C2×C42—28no—
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—28no—
591C2×C42—232no—
592C2×C42—28no—
593C2×C42—28no—
594C2×C42—232no—
595C2×C42—28no—
596C2×C42—28no—
597C2×C42C2×D4116yes—
598C2×C42C2×D418yes—
599C2×C42C2418yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2412yes—
604C2×C42C2418yes—
605C2×C42C2412yes—
606C2×C42C2414yes—
607C2×C42C2412yes—
608C2×C42C2418yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C24116yes—
614C2×C42C2414yes—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2414yes—
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620#95C2414yes—
621#95C2414yes—
622#95C24116yes—
623#95C2418yes—
624#95C2418yes—
625#95C24116yes—
626#95C2418yes—
627#95C2418yes—
628#95C24116yes—
629#95C2418yes—
630#95C24116yes—
631#95C24116yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C24116yes—
636#95C24116yes—
637C24—22no—
638C24—22no—
639C24—24no—
640C24—24no—
641C24C2×#4114yes—
642C24C2514yes—
643C24C2511yescharacteristic
644C24C2512yes—
645#41—432no—
646C2×Q8—2128no—
647C2×Q8—2128no—
648C2×Q8—264no—
649C2×Q8—232no—
650C2×Q8—232no—
651C2×Q8—216no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—24no—
656C2×Q8—24no—
657C2×Q8—216no—
658C2×Q8—216no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—24no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—24no—
667C2×Q8—28no—
668C2×Q8—44no—
669C2×Q8C22×D418yes—
670C2×Q8C22×D418yes—
671C2×Q8C2×#4118yes—
672C2×Q8C2×#4118yes—
673C2×D4—28no—
674C2×D4—216no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—216no—
678C2×D4—216no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—28no—
685C2×D4—44no—
686C22×C4—232no—
687C22×C4—264no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—216no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—232no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—216no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—216no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—216no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—216no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—216no—
722C22×C4—44no—
723C22×C4—48no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—44no—
729C22×C4—416no—
730C22×C4—432no—
731C22×C4—416no—
732C22×C4C22×D414yes—
733C22×C4C22×D418yes—
734C22×C4C22×D418yes—
735C22×C4C22×D414yes—
736C22×C4C22×D414yes—
737C22×C4C2×#4118yes—
738C22×C4C2×#4118yes—
739C22×C4C2×#4118yes—
740C22×C4C2×#4114yes—
741C22×C4C2×#4114yes—
742C22×C4C2×#4114yes—
743C22×C42−1+418yes—
744C22×C4C2518yes—
745C22×C4C2518yes—
746C22×C4C2514yes—
747C22×C4C2512yes—
748C22×C4C2514yes—
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2511yescharacteristic
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2511yescharacteristic
755C22×C4C2511yescharacteristic
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2512yes—
759C22×C4C2511yescharacteristic
760C22×C4C2511yescharacteristic
761C22×C4C2511yescharacteristic
762C4⋊C4—216no—
763C4⋊C4—216no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—216no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—216no—
771C4⋊C4—24no—
772C4⋊C4—28no—
773C4⋊C4—216no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—216no—
779C4⋊C4—24no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—216no—
783C4⋊C4—232no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—216no—
787C4⋊C4—416no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4C22×D418yes—
792C4⋊C4C22×D418yes—
793C4⋊C4C22×D4116yes—
794C4⋊C4C22×D4116yes—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—216no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—216no—
803C22⋊C4—216no—
804C22⋊C4—28no—
805C22⋊C4—216no—
806C22⋊C4—216no—
807C22⋊C4—232no—
808C22⋊C4—216no—
809C22⋊C4—416no—
810C22⋊C4—48no—
811C42—216no—
812C42—24no—
813C42—24no—
814C42—216no—
815C42—24no—
816C42—24no—
817C42—28no—
818C42—24no—
819C42—24no—
820C42—28no—
821C42—216no—
822C42—28no—
823C42—28no—
824C42—28no—
825C42—416no—
826C42C22×D4116yes—
827C42C22×D414yes—
828C42C22×D414yes—
829C42C22×D4116yes—
830C42C22×D414yes—
831C42C22×D414yes—
832C23—28no—
833C23—28no—
834C23—216no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—28no—
842C23—216no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—28no—
847C23—28no—
848C23C23×D412yes—
849C23C22×#4112yes—
850C23C22×#4112yes—
851C23C22×#4114yes—
852C23C2×2−1+414yes—
853C23#58514yes—
854C23C2611yescharacteristic
855Q8—264no—
856Q8—216no—
857Q8—216no—
858Q8—216no—
859Q8—216no—
860Q8—48no—
861Q8—48no—
862Q8—84no—
863D4—416no—
864D4—432no—
865D4—48no—
866D4—48no—
867D4—84no—
868C2×C4—216no—
869C2×C4—28no—
870C2×C4—264no—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—28no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—216no—
884C2×C4—216no—
885C2×C4—28no—
886C2×C4—216no—
887C2×C4—216no—
888C2×C4—28no—
889C2×C4—216no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—48no—
909C2×C4—44no—
910C2×C4—432no—
911C2×C4—48no—
912C2×C4—48no—
913C2×C4—44no—
914C2×C4—48no—
915C2×C4—416no—
916C2×C4—816no—
917C2×C4#525116yes—
918C2×C4C23×D412yes—
919C2×C4C23×D418yes—
920C2×C4C23×D412yes—
921C2×C4C23×D418yes—
922C2×C4C23×D412yes—
923C2×C4C23×D412yes—
924C2×C4C23×D412yes—
925C2×C4C23×D412yes—
926C2×C4C22×#4118yes—
927C2×C4C22×#4114yes—
928C2×C4C22×#4112yes—
929C2×C4C22×#4112yes—
930C2×C4C22×#4112yes—
931C2×C4C22×#4112yes—
932C2×C4C2×2−1+414yes—
933C2×C4C2×2−1+414yes—
934C22—232no—
935C22—24no—
936C22—24no—
937C22—22no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—22no—
943C22—24no—
944C22—24no—
945C22—48no—
946C22—44no—
947C22—48no—
948C22—44no—
949C22—44no—
950C22C2×#52514yes—
951C22#350718yescomplemented
952C22C24×D411yescharacteristic
953C22C23×#4111yescharacteristic
954C22C23×#4111yescharacteristic
955C22C22×2−1+412yes—
956C22C2×#58512yes—
957C4—22no—
958C4—24no—
959C4—28no—
960C4—22no—
961C4—22no—
962C4—28no—
963C4—28no—
964C4—24no—
965C4—48no—
966C4—44no—
967C4—48no—
968C4—42no—
969C4—44no—
970C4—44no—
971C4—44no—
972C4C2×#52514yes—
973C4C2×#52514yes—
974C4#348614yes—
975C2—24no—
976C2—28no—
977C2—84no—
978C2C22×#52511yescharacteristic
979C2C2×#350712yes—
980C2C2×#348611yescharacteristic
981C2#6278812yes—
982C2#6281111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36624C2
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×#3507C2semidirect
2. C23×C4×Q8C2semidirect
3. #36625C2semidirect
5. #36621C2semidirect
6. #36580C2semidirect
7. #36579C2semidirect
8. #36545C2semidirect
9. #36544C2semidirect
10. #36233C2semidirect
11. #36232C2semidirect
12. #35242C2semidirect
13. #35182C2semidirect
14. #35179C2semidirect
15. #35178C2semidirect
16. #35111C2semidirect
17. #35092C2semidirect
18. #34989C2semidirect
19. #34266C2semidirect
20. #34200C2semidirect
21. #34187C2semidirect
24. C2×#559C22semidirect
25. C2×#557C22semidirect
26. C2×#556C22semidirect
27. C2×#556C22semidirect
28. C2×#554C22semidirect
29. C2×#552C22semidirect
78. #2604C22semidirect
79. #2599C22semidirect
80. #2592C22semidirect
81. #2584C22semidirect
82. #2582C22semidirect
83. #2581C22semidirect
84. #2581C22semidirect
85. #2580C22semidirect
86. #2568C22semidirect
87. #2567C22semidirect
88. #2565C22semidirect
89. #2548C22semidirect
90. #2546C22semidirect
91. #2545C22semidirect
92. #2538C22semidirect
93. #2536C22semidirect
96. #2469C22semidirect
97. #2465C22semidirect
98. #2462C22semidirect
99. #2458C22semidirect
101. #2448C22semidirect
102. #2446C22semidirect
106. #2423C22semidirect
107. #2421C22semidirect
110. #2367C22semidirect
111. #2365C22semidirect
112. #2362C22semidirect
115. #2360C22semidirect
116. #2356C22semidirect
117. #2356C22semidirect
118. #2355C22semidirect
119. #2355C22semidirect
216. C2×C4×Q8D4semidirect
951. C22#3507semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C23×C4×Q82
#366252
#366242
#366212
#365802
#365792
#365452
#365442
#362332
#362322
#352422
#351822
#351792
#351782
#351112
#350922
#349892
#342662
#342002
#341872