Finite Group Databasebeta

← #7631051

Subgroups — #7631051

Order 512.

7288 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C212yesmaximal, complemented
2#36645C211yesmaximal, characteristic, complemented
3#36631C211yesmaximal, characteristic, complemented
4#36631C212yesmaximal, complemented
5C2×#2859C212yesmaximal, complemented
6#36562C212yesmaximal, complemented
7#36560C211yesmaximal, characteristic, complemented
8#36559C211yesmaximal, characteristic, complemented
9#36272C214yesmaximal, complemented
10#36265C218yesmaximal, complemented
11#36259C214yesmaximal, complemented
12#36184C214yesmaximal, complemented
13#36182C212yesmaximal, complemented
14#36181C212yesmaximal, complemented
15#36180C211yesmaximal, characteristic, complemented
16#36179C211yesmaximal, characteristic, complemented
17#36164C212yesmaximal, complemented
18#35209C214yesmaximal, complemented
19#35201C212yesmaximal, complemented
20#35139C214yesmaximal, complemented
21#35008C218yesmaximal, complemented
22#34308C214yesmaximal, complemented
23C42×#41C211yesmaximal, characteristic, complemented
24#3515—232no—
25C2×#557C2212yes—
26C2×#554C2212yes—
27C2×#554C2212yes—
28C2×#553C2214yes—
29C2×#552C2214yes—
30C2×#552C2218yes—
31C2×#552C2214yes—
32C2×#547C2214yes—
33C2×#547C2212yes—
34C2×#547C2214yes—
35C2×#541C2214yes—
36C2×#539C2218yes—
37C2×#533C2212yes—
38C2×#529C2214yes—
39C2×#529C2212yes—
40C22×#125C2214yes—
41C2×#520C2214yes—
42C2×C4×#41C2212yes—
43C2×C4×#41C2211yescharacteristic
44#2868C2211yescharacteristic
45#2868C2211yescharacteristic
46#2862C2212yes—
47#2861C2212yes—
48#2861C2214yes—
49#2860C2218yes—
50#2860C2214yes—
51#2859C2211yescharacteristic
52#2859C2212yes—
53#2859C2214yes—
54#2859C2212yes—
55#2859C2212yes—
56#2859C2214yes—
57#2859C2218yes—
58#2859C2218yes—
59#2859C2212yes—
60#2858C2211yescharacteristic
61#2857C2212yes—
62#2857C2211yescharacteristic
63#2857C2214yes—
64#2857C2214yes—
65#2856C2212yes—
66#2856C2211yescharacteristic
67#2854C2218yes—
68#2854C2214yes—
69#2850C2214yes—
70#2850C2212yes—
71#2664C22116yes—
72#2663C2218yes—
73#2611C22116yes—
74#2604C2218yes—
75#2568C2212yes—
76#2567C2212yes—
77#2566C2214yes—
78#2566C2214yes—
79#2565C2214yes—
80#2565C2214yes—
81#2563C2212yes—
82#2556C22116yes—
83#2553C22116yes—
84#2552C2214yes—
85#2546C2214yes—
86#2542C2212yes—
87#2542C2214yes—
88#2538C2214yes—
89#2519C22116yes—
90#2512C2218yes—
91#2506C2218yes—
92#2506C2218yes—
93#2504C2214yes—
94#2503C2214yes—
95#2502C2214yes—
96#2501C2214yes—
97#2501C2218yes—
98#2500C2214yes—
99#2499C2214yes—
100#2496C2218yes—
101#2489C2218yes—
102#2488C22116yes—
103#2486C2218yes—
104#2452C2218yes—
105#2440C2218yes—
106#2429C2218yes—
107#2425C22116yes—
108#2422C2218yes—
109#2416C2218yes—
110#2415C2218yes—
111#2413C22116yes—
112#2365C2214yes—
113#2361C2218yes—
114#2360C2218yes—
115#2359C22116yes—
116D4×C4⋊C4C2214yes—
117D4×C4⋊C4C2214yes—
118#2344C2218yes—
119#2339C2218yes—
120#2323C2218yes—
121#2322C22116yes—
122C4×C4⋊Q8C2214yes—
123C4×C4⋊Q8C2211yescharacteristic
124C4×C4⋊Q8C2212yes—
125C4×C4⋊Q8C2214yes—
126C4×#127C2211yescharacteristic
127C4×#127C2212yes—
128C4×#124C2212yes—
129C4×#124C2214yes—
130C4×#121C2218yes—
131C4×#121C2214yes—
132#2293C2214yes—
133#2293C2218yes—
134C2×#389C2218yes—
135C2×#389C2218yes—
136#2285C2212yes—
137#2285C2212yes—
138C2×#384C2212yes—
139C2×#384C2212yes—
140C2×#382C2214yes—
141C42×Q8C2212yes—
142C42×Q8C2211yescharacteristic
143C42×Q8C2211yescharacteristic
144C42×D4C2212yes—
145C42×D4C2211yescharacteristic
146C42×D4C2211yescharacteristic
147C42×D4C2212yes—
148C42×D4C2212yes—
149C42×D4C2214yes—
150C4×#117C2212yes—
151C4×#117C2211yescharacteristic
152C4×#117C2214yes—
153C4×#117C2212yes—
154C2×C43C2212yes—
155C2×C43C2211yescharacteristic
156C22×#41C2314yes—
157C22×#41C2311yescharacteristic
158#557—216no—
159#554—216no—
160#554—216no—
161#553—232no—
162#552—232no—
163#552—264no—
164#552—232no—
165#547—232no—
166#547—216no—
167#547—232no—
168#541—232no—
169#539—264no—
170#533—216no—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×#127C2311yescharacteristic
178#529—232no—
179#529—216no—
180C2×#126C2314yes—
181C2×#126C2318yes—
182C2×#126C2318yes—
183C2×#126C2318yes—
184C2×#125—232no—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×#125C2312yes—
188C2×#125C2314yes—
189C2×#125C2318yes—
190C2×#125C2318yes—
191C2×#125C2318yes—
192C2×#125C2318yes—
193C2×#125C2314yes—
194C2×#124C2312yes—
195C2×#124C2312yes—
196C2×#123C23116yes—
197C2×#123C2314yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×#121C2314yes—
212C2×#121C2312yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216#520—232no—
217C4×#41—216no—
218C4×#41D4116yescomplemented
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×#117C2314yes—
245C2×#117C2318yes—
246C2×#117C2318yes—
247C2×#117C2314yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2311yescharacteristic
251C2×#117C2312yes—
252C22×C4⋊C4C2318yes—
253C22×C4⋊C4C2318yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2318yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2318yes—
259C22×C42C2312yes—
260C22×C42C2311yescharacteristic
261C22×C42C2314yes—
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267C22×C42C2312yes—
268C22×C42C2311yescharacteristic
269#400C2318yes—
270#400C23116yes—
271#399C2318yes—
272#399C23116yes—
273#398C23116yes—
274#398C23116yes—
275#398C23116yes—
276#397C23116yes—
277#397C23116yes—
278#396C23116yes—
279#396C23116yes—
280#395C2318yes—
281#394C23116yes—
282#393C2318yes—
283#391C2312yes—
284#391C2314yes—
285#391C2318yes—
286#391C2318yes—
287#391C2312yes—
288#391C2314yes—
289#391C2318yes—
290#390C2314yes—
291#390C2312yes—
292#390C2318yes—
293#390C2314yes—
294#390C2312yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C2314yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C23116yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2318yes—
312#389C2314yes—
313#389C23116yes—
314#389C23116yes—
315#389C2318yes—
316#389C2318yes—
317#389C23116yes—
318#389C2318yes—
319#388C2318yes—
320#388C23116yes—
321#388C23116yes—
322#388C2318yes—
323#388C23116yes—
324#388C23116yes—
325#388C23116yes—
326#388C2318yes—
327#388C2318yes—
328#387C23116yes—
329#387C23116yes—
330#387C23116yes—
331#386C23116yes—
332#386C23116yes—
333#386C2318yes—
334#385C23116yes—
335#385C23116yes—
336#385C23116yes—
337#384C2311yescharacteristic
338#384C2312yes—
339#384C2311yescharacteristic
340#384C2312yes—
341#384C2314yes—
342#384C2314yes—
343#384C2312yes—
344#384C2314yes—
345#384C2312yes—
346#384C2314yes—
347#384C2318yes—
348#384C2318yes—
349#382C2314yes—
350#382C2314yes—
351#382C2314yes—
352#382C2312yes—
353#382C2314yes—
354#382C23116yes—
355#381C23116yes—
356#380C2318yes—
357#380C2318yes—
358#380C2314yes—
359#380C2318yes—
360#380C2318yes—
361C4×C4⋊C4C2318yes—
362C4×C4⋊C4C2318yes—
363C4×C4⋊C4C2318yes—
364C4×C4⋊C4C2314yes—
365C4×C4⋊C4C2311yescharacteristic
366C4×C4⋊C4C2312yes—
367C4×C4⋊C4C2312yes—
368C4×C4⋊C4C2311yescharacteristic
369C4×C4⋊C4C2312yes—
370C4×C4⋊C4C2312yes—
371C4×C4⋊C4C2312yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2314yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2312yes—
378C4×C4⋊C4C2314yes—
379C4×C22⋊C4C2314yes—
380C4×C22⋊C4C2318yes—
381C4×C22⋊C4C2314yes—
382C4×C22⋊C4C2314yes—
383C4×C22⋊C4C23116yes—
384C4×C22⋊C4C2312yes—
385C4×C22⋊C4C2314yes—
386C4×C22⋊C4C2314yes—
387C4×C22⋊C4C2314yes—
388C4×C22⋊C4C2312yes—
389C4×C22⋊C4C2312yes—
390C4×C22⋊C4C2312yes—
391C4×C22⋊C4C2314yes—
392#376C2312yes—
393#376C2314yes—
394C2×#95C23116yes—
395C43C2312yes—
396C43C2311yescharacteristic
397C43C2312yes—
398C43C2312yes—
399C43C2311yescharacteristic
400C43C2314yes—
401C43C2312yes—
402C43C2311yescharacteristic
403C43C2314yes—
404C43C2312yes—
405C43C2311yescharacteristic
406C2×#41—216no—
407C2×#41—28no—
408C2×#41—232no—
409C2×#41C2×D418yes—
410C22×Q8C2412yes—
411C22×Q8C2414yes—
412C22×Q8C2411yescharacteristic
413C22×Q8C2414yes—
414C22×D4C2412yes—
415C22×D4C2414yes—
416C22×D4C2418yes—
417C22×D4C2412yes—
418C22×D4C2414yes—
419C22×D4C2411yescharacteristic
420C23×C4C2418yes—
421C23×C4C2414yes—
422C23×C4C2412yes—
423C23×C4C2414yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2414yes—
430C23×C4C2418yes—
431C23×C4C2418yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C4⋊Q8—216no—
435C4⋊Q8—28no—
436C4⋊Q8—28no—
437C4⋊Q8—216no—
438C4⋊Q8—24no—
439C4⋊Q8—48no—
440#127—24no—
441#126—232no—
442#126—232no—
443#126—232no—
444#126—216no—
445#125—232no—
446#125—232no—
447#125—216no—
448#125—28no—
449#125—216no—
450#125—232no—
451#125—232no—
452#125—216no—
453#125—216no—
454#124—28no—
455#124—28no—
456#123—232no—
457#123—216no—
458#123—232no—
459#123—232no—
460#123—232no—
461#123—264no—
462C22⋊Q8—216no—
463C22⋊Q8—28no—
464C22⋊Q8—216no—
465C22⋊Q8—216no—
466C22⋊Q8—216no—
467C22⋊Q8—232no—
468C22⋊Q8—216no—
469C22⋊Q8—232no—
470C22⋊Q8—232no—
471#121—232no—
472#121—216no—
473#121—28no—
474#121—232no—
475#121—48no—
476C4×Q8—216no—
477C4×Q8—28no—
478C4×Q8—216no—
479C4×Q8—216no—
480C4×Q8—28no—
481C4×Q8—216no—
482C4×Q8—28no—
483C4×Q8C2×D418yes—
484C4×Q8C2×D418yes—
485C4×D4—216no—
486C4×D4—28no—
487C4×D4—232no—
488C4×D4—216no—
489C4×D4—216no—
490C4×D4—232no—
491C4×D4—216no—
492C4×D4—28no—
493C4×D4—216no—
494C4×D4—216no—
495C4×D4—416no—
496C4×D4C2×D418yes—
497C4×D4C2×D4116yes—
498C4×D4C2×D418yes—
499C4×D4C2×D4116yes—
500C4×D4#41116yes—
501#117—216no—
502#117—28no—
503#117—232no—
504#117—216no—
505#117—216no—
506#117—232no—
507#117C2×D418yes—
508#117C2×D4116yes—
509C2×C4⋊C4—232no—
510C2×C4⋊C4—216no—
511C2×C4⋊C4—232no—
512C2×C4⋊C4—216no—
513C2×C4⋊C4—232no—
514C2×C4⋊C4—216no—
515C2×C4⋊C4—416no—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C24116yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C24116yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C24116yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C24116yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2414yes—
573C2×C42—216no—
574C2×C42—28no—
575C2×C42—28no—
576C2×C42—24no—
577C2×C42—28no—
578C2×C42—24no—
579C2×C42—48no—
580C2×C42—44no—
581C2×C42C2×D4116yes—
582C2×C42C2×D418yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2412yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2411yescharacteristic
600C2×C42C2414yes—
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617#95C2418yes—
618#95C24116yes—
619#95C24116yes—
620#95C24116yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2412yes—
625#95C2412yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C24116yes—
630#95C24116yes—
631#95C24116yes—
632#95C2418yes—
633C24C2514yes—
634C24C2511yescharacteristic
635C24C2512yes—
636#41—232no—
637#41—464no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—24no—
642C2×Q8—216no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—48no—
646C2×Q8C22×D414yes—
647C2×D4—28no—
648C2×D4—216no—
649C2×D4—232no—
650C2×D4—28no—
651C2×D4—24no—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—48no—
658C2×D4C22×D418yes—
659C2×D4C22×D414yes—
660C2×D4C2×#4118yes—
661C22×C4—28no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—28no—
668C22×C4—28no—
669C22×C4—216no—
670C22×C4—28no—
671C22×C4—232no—
672C22×C4—216no—
673C22×C4—28no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—216no—
677C22×C4—24no—
678C22×C4—28no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—216no—
682C22×C4—42no—
683C22×C4—44no—
684C22×C4—42no—
685C22×C4—44no—
686C22×C4—416no—
687C22×C4—416no—
688C22×C4C22×D418yes—
689C22×C4C22×D418yes—
690C22×C4C22×D414yes—
691C22×C4C22×D414yes—
692C22×C4C22×D418yes—
693C22×C4C22×D414yes—
694C22×C4C2×#41116yes—
695C22×C4C2514yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2518yes—
699C22×C4C2518yes—
700C22×C4C2514yes—
701C22×C4C2514yes—
702C22×C4C2511yescharacteristic
703C22×C4C2512yes—
704C22×C4C2512yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2511yescharacteristic
708C22×C4C2512yes—
709C22×C4C2512yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2511yescharacteristic
713C22×C4C2511yescharacteristic
714C22×C4C2512yes—
715C4⋊C4—216no—
716C4⋊C4—28no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—24no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—216no—
723C4⋊C4—28no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—216no—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—216no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—216no—
735C4⋊C4—28no—
736C4⋊C4—216no—
737C4⋊C4—232no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—24no—
741C4⋊C4—216no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—216no—
745C4⋊C4—416no—
746C4⋊C4—48no—
747C4⋊C4C22×D414yes—
748C4⋊C4C22×D418yes—
749C4⋊C4C22×D414yes—
750C4⋊C4C22×D418yes—
751C4⋊C4C2×#4118yes—
752C22⋊C4—216no—
753C22⋊C4—216no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—28no—
759C22⋊C4—216no—
760C22⋊C4—216no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—216no—
764C22⋊C4—232no—
765C22⋊C4—216no—
766C22⋊C4—416no—
767C22⋊C4—48no—
768C22⋊C4C22×D418yes—
769C22⋊C4C22×D418yes—
770C22⋊C4C22×D418yes—
771C22⋊C4C2×#41116yes—
772C42—216no—
773C42—216no—
774C42—28no—
775C42—24no—
776C42—28no—
777C42—24no—
778C42—28no—
779C42—24no—
780C42—28no—
781C42—24no—
782C42—24no—
783C42—22no—
784C42—28no—
785C42—28no—
786C42—24no—
787C42—22no—
788C42—24no—
789C42—24no—
790C42—28no—
791C42—24no—
792C42—42no—
793C42—44no—
794C42—42no—
795C42—44no—
796C42C22×D414yes—
797C42C22×D418yes—
798C42C22×D414yes—
799C42C22×D414yes—
800C42C22×D418yes—
801C42C22×D414yes—
802C42C22×D418yes—
803C42C2×#4118yes—
804C422−1+414yes—
805C422−1+414yes—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—22no—
813C23—24no—
814C23—28no—
815C23—24no—
816C23—24no—
817C23—28no—
818C23C23×D412yes—
819C23C23×D414yes—
820C23C22×#4118yes—
821C23C2611yescharacteristic
822Q8—28no—
823Q8—416no—
824Q8—48no—
825Q8—88no—
826D4—216no—
827D4—432no—
828D4—48no—
829D4—416no—
830D4—88no—
831D4#532116yes—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—216no—
848C2×C4—28no—
849C2×C4—216no—
850C2×C4—28no—
851C2×C4—232no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—216no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—28no—
868C2×C4—216no—
869C2×C4—48no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—416no—
873C2×C4—432no—
874C2×C4—416no—
875C2×C4—48no—
876C2×C4—816no—
877C2×C4—816no—
878C2×C4C23×D412yes—
879C2×C4C23×D414yes—
880C2×C4C23×D412yes—
881C2×C4C23×D412yes—
882C2×C4C23×D414yes—
883C2×C4C23×D412yes—
884C2×C4C23×D414yes—
885C2×C4C23×D412yes—
886C2×C4C23×D412yes—
887C2×C4C22×#4118yes—
888C2×C4C22×#4114yes—
889C2×C4C22×#4114yes—
890C2×C4C22×#4114yes—
891C2×C4C2×2−1+414yes—
892C2×C4C2×2−1+412yes—
893C2×C4C2×2−1+412yes—
894C2×C4C2×2−1+414yes—
895C2×C4#58514yes—
896C22—28no—
897C22—24no—
898C22—28no—
899C22—24no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—42no—
904C22—42no—
905C22—48no—
906C22—44no—
907C22—48no—
908C22—44no—
909C22—44no—
910C22C2×#53218yes—
911C22C24×D411yescharacteristic
912C22C23×#4112yes—
913C22C22×2−1+411yescharacteristic
914C22C22×2−1+411yescharacteristic
915C22C2×#58512yes—
916C4—28no—
917C4—22no—
918C4—24no—
919C4—24no—
920C4—24no—
921C4—22no—
922C4—24no—
923C4—22no—
924C4—22no—
925C4—24no—
926C4—42no—
927C4—44no—
928C4—44no—
929C4—44no—
930C4—48no—
931C4—44no—
932C4—48no—
933C4C2×#53214yes—
934C4#349914yes—
935C4#351518yescomplemented
936C2—28no—
937C2—42no—
938C2—84no—
939C2C22×#53211yescharacteristic
940C2C2×#351512yes—
941C2C2×#349911yescharacteristic
942C2#6280512yes—
943C2#6281211yescharacteristic
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×#3515C2semidirect
2. #36645C2semidirect
3. #36631C2semidirect
4. #36631C2semidirect
5. C2×#2859C2semidirect
6. #36562C2semidirect
7. #36560C2semidirect
8. #36559C2semidirect
9. #36272C2semidirect
10. #36265C2semidirect
11. #36259C2semidirect
12. #36184C2semidirect
13. #36182C2semidirect
14. #36181C2semidirect
15. #36180C2semidirect
16. #36179C2semidirect
17. #36164C2semidirect
18. #35209C2semidirect
19. #35201C2semidirect
20. #35139C2semidirect
21. #35008C2semidirect
22. #34308C2semidirect
23. C42×#41C2semidirect
218. C4×#41D4semidirect
935. C4#3515semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
#366452
#366312
C2×#28592
#365622
#365602
#365592
#362722
#362652
#362592
#361842
#361822
#361812
#361802
#361792
#361642
#352092
#352012
#351392
#350082
#343082
C42×#412