Finite Group Databasebeta

← #7643427

Subgroups — #7643427

Order 512.

8252 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3444C211yesmaximal, characteristic, complemented
3#39596C214yesmaximal, complemented
4#39471C214yesmaximal, complemented
5#39124C214yesmaximal, complemented
6#38920C214yesmaximal, complemented
7#38041C218yesmaximal, complemented
8#37839C218yesmaximal, complemented
9#37379C218yesmaximal, complemented
10#36624C211yesmaximal, characteristic, complemented
11C2×#2857C211yesmaximal, characteristic, complemented
12#35660C212yesmaximal, complemented
13#35659C212yesmaximal, complemented
14#35634C212yesmaximal, complemented
15#35628C212yesmaximal, complemented
16#35316C211yesmaximal, characteristic, complemented
17#35292C214yesmaximal, complemented
18#35279C214yesmaximal, complemented
19#35273C211yesmaximal, characteristic, complemented
20#34188C211yesmaximal, characteristic, complemented
21C22×2−1+4C2212yes—
22#3499—216no—
23C2×D4×Q8C2214yescomplemented
24C2×#547C2218yes—
25C2×#547C2214yescomplemented
26C2×#537C2212yes—
27C2×#536C2212yes—
28C2×#536C2212yes—
29C2×#536C2214yescomplemented
30#3444—216no—
31C2×#533C2211yescharacteristic
32C2×#533C2212yes—
33C2×#532C2211yescharacteristic
34C2×#532C2212yes—
35C2×#532C2211yescharacteristic
36C2×#532C2212yescomplemented
37C22×C4⋊Q8C2211yescharacteristic
38C22×C4⋊Q8C2212yescomplemented
39C2×#529C2214yes—
40C2×#529C2212yes—
41C2×#529C2214yes—
42C2×#529C2212yes—
43C2×#525C2211yescharacteristic
44C2×#525C2211yescharacteristic
45C2×#525C2214yes—
46C2×#525C2212yes—
47C22×C22⋊Q8C2212yes—
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2214yes—
50C2×C4×#41C2211yescharacteristic
51C23×C42C2211yescharacteristic
52#2857C2214yes—
53#2857C2214yes—
54#2857C2214yes—
55#2857C2214yes—
56#2857C2212yes—
57#2857C2212yescomplemented
58#2857C2214yescomplemented
59#2856C2212yes—
60#2856C2212yescomplemented
61#2854C2214yes—
62#2850C2214yes—
63#2847C2214yes—
64#2723C22116yescomplemented
65#2720C22116yescomplemented
66#2718C22116yescomplemented
67#2710C22116yescomplemented
68#2706C22116yes—
69#2703C22116yes—
70#2696C22116yes—
71#2692C22116yes—
72#2628C2218yes—
73#2628C2218yescomplemented
74#2624C2218yescomplemented
75#2621C2214yescomplemented
76#2620C2214yescomplemented
77#2615C2218yes—
78#2592C2218yescomplemented
79#2580C2218yescomplemented
80#2568C2218yescomplemented
81#2567C2218yescomplemented
82#2563C2218yes—
83#2547C2214yescomplemented
84#2546C2214yescomplemented
85#2542C2218yes—
86#2542C2218yes—
87#2540C2218yes—
88#2540C2218yes—
89#2539C2218yes—
90#2538C2214yescomplemented
91#2537C2214yescomplemented
92#2535C2218yes—
93#2501C2218yes—
94#2492C2218yescomplemented
95#2489C2218yescomplemented
96#2488C22116yes—
97#2487C2218yes—
98#2487C2218yescomplemented
99#2486C2218yes—
100#2436C2214yescomplemented
101#2434C2214yescomplemented
102#2432C2214yescomplemented
103#2431C2214yescomplemented
104#2430C22116yes—
105#2416C2218yes—
106#2414C2218yes—
107#2414C2218yescomplemented
108#2409C2218yes—
109#2409C2218yes—
110#2409C2218yescomplemented
111#2407C2218yes—
112#2407C2218yes—
113#2407C2218yescomplemented
114#2406C2218yes—
115#2404C2218yes—
116#2355C2214yescomplemented
117#2354C2214yescomplemented
118#2352C2218yes—
119#2324C2218yes—
120#2324C2218yescomplemented
121#2317C2218yescomplemented
122#2314C2214yescomplemented
123#2311C2212yes—
124#2311C2218yes—
125#2311C2212yes—
126#2310C2212yes—
127C4×#121C2214yes—
128C4×#121C2214yes—
129#2297C2212yes—
130C2×#391C2212yes—
131C2×#389C2214yes—
132#2285C2211yescharacteristic
133#2285C2214yescomplemented
134C2×#384C2211yescharacteristic
135C2×#380C2214yes—
136#2274C2212yes—
137C2×2−1+4—216no—
138C2×2−1+4—48no—
139C2×2−1+4—48no—
140C22×#41C2312yes—
141C22×#41C2311yescharacteristic
142C22×#41C2314yes—
143C22×#41C2311yescharacteristic
144C22×#41C2318yes—
145C22×#41C2314yes—
146C22×#41C2314yes—
147C23×Q8C2312yes—
148C23×Q8C2314yes—
149C23×Q8C2314yes—
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152D4×Q8—232no—
153#547—264no—
154#547—232no—
155#537—48no—
156#536—216no—
157#536—232no—
158#536—48no—
159#533—216no—
160#533—28no—
161#532—28no—
162#532—216no—
163#532—28no—
164#532—216no—
165C2×C4⋊Q8—28no—
166C2×C4⋊Q8—216no—
167C2×C4⋊Q8C2318yes—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×#127C2311yescharacteristic
177C2×#127C2311yescharacteristic
178#529—216no—
179#529—232no—
180#529—216no—
181#529—232no—
182C2×#126C2314yes—
183C2×#126C2314yes—
184C2×#125C2314yes—
185C2×#125C2312yes—
186C2×#124C2314yes—
187C2×#124C2312yes—
188C2×#124C2311yescharacteristic
189C2×#124C2311yescharacteristic
190C2×#124C2314yes—
191C2×#124C2314yes—
192#525—28no—
193#525—232no—
194#525—28no—
195#525—48no—
196C2×#123C2312yes—
197C2×#123C2314yes—
198C2×#123C2314yes—
199C2×#123C2312yes—
200C2×#123C2318yes—
201C2×#123C23116yes—
202C2×#123C2314yes—
203C2×#123C2318yes—
204C2×C22⋊Q8—48no—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C23116yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2312yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2312yes—
224C2×#121C2318yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C2×#121C2318yes—
229C2×#121C2314yes—
230C2×#120C2312yes—
231C2×#120C2312yes—
232C2×#120C2314yes—
233C4×#41—28no—
234C4×#41—232no—
235C4×#41D4116yescomplemented
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2314yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2318yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2318yes—
260C2×#117C2312yes—
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2318yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C22⋊C4C2314yes—
268C22×C42—28no—
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2312yes—
278#400C23116yes—
279#400C23116yes—
280#399C23116yes—
281#399C23116yes—
282#399C23116yes—
283#398C23116yes—
284#397C23116yes—
285#397C23116yes—
286#396C23116yes—
287#395C23116yes—
288#395C23116yes—
289#394C23116yes—
290#394C23116yes—
291#394C23116yes—
292#393C23116yes—
293#393C23116yes—
294#393C23116yes—
295#392C23116yes—
296#392C23116yes—
297#392C23116yes—
298#391C2318yes—
299#391C2318yes—
300#391C23116yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2314yes—
306#391C2314yes—
307#390C23116yes—
308#390C2314yes—
309#390C2314yes—
310#390C2318yes—
311#390C23116yes—
312#390C2314yes—
313#390C23116yes—
314#390C2314yes—
315#390C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2314yes—
321#389C2318yes—
322#389C2318yes—
323#389C2318yes—
324#389C2318yes—
325#388C23116yes—
326#388C23116yes—
327#388C23116yes—
328#388C2318yes—
329#388C2318yes—
330#387C23116yes—
331#386C2318yes—
332#386C2318yes—
333#386C23116yes—
334#386C23116yes—
335#386C23116yes—
336#386C23116yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#385C23116yes—
341#385C23116yes—
342#385C23116yes—
343#385C23116yes—
344#384C23116yes—
345#384C2312yes—
346#384C2312yes—
347#384C2312yes—
348#384C2314yes—
349#382C23116yes—
350#382C2312yes—
351#382C2318yes—
352#381C2318yes—
353#380C2314yes—
354#380C2318yes—
355#380C2318yes—
356#380C2318yes—
357#380C2314yes—
358#380C2318yes—
359#380C2318yes—
360#380C2318yes—
361#380C2318yes—
362#380C2314yes—
363#380C2318yes—
364#380C2318yes—
365#380C2318yes—
366C4×C4⋊C4C2318yes—
367C4×C4⋊C4C2318yes—
368C4×C4⋊C4C2318yes—
369C4×C4⋊C4C2314yes—
370C4×C22⋊C4C2318yes—
371C4×C22⋊C4C2314yes—
372C4×C22⋊C4C2314yes—
373C2×#95C2318yes—
374C25C2411yescharacteristic
3752−1+4—4128no—
376C2×#41—232no—
377C2×#41—216no—
378C2×#41—216no—
379C2×#41—24no—
380C2×#41—216no—
381C2×#41—28no—
382C2×#41—24no—
383C2×#41—24no—
384C2×#41—28no—
385C2×#41—24no—
386C2×#41—24no—
387C2×#41—28no—
388C2×#41—216no—
389C2×#41—48no—
390C2×#41—416no—
391C2×#41—416no—
392C2×#41—48no—
393C2×#41—48no—
394C2×#41—48no—
395C2×#41—48no—
396C2×#41C2×D418yes—
397C22×Q8—216no—
398C22×Q8—216no—
399C22×Q8—28no—
400C22×Q8—28no—
401C22×Q8—28no—
402C22×Q8—48no—
403C22×Q8—48no—
404C22×Q8—48no—
405C22×Q8—48no—
406C22×Q8C2411yescharacteristic
407C22×Q8C2414yes—
408C22×Q8C2414yes—
409C22×Q8C2412yes—
410C22×Q8C2414yes—
411C22×Q8C2411yescharacteristic
412C22×Q8C2418yes—
413C22×D4C2414yes—
414C22×D4C2412yes—
415C22×D4C2411yescharacteristic
416C22×D4C2414yes—
417C22×D4C2412yes—
418C22×D4C2414yes—
419C22×D4C2414yes—
420C22×D4C2414yes—
421C22×D4C2412yes—
422C22×D4C2411yescharacteristic
423C22×D4C2418yes—
424C22×D4C2418yes—
425C22×D4C2418yes—
426C23×C4—28no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—28no—
431C23×C4—44no—
432C23×C4C2414yes—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2414yes—
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2414yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2414yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2414yes—
448C23×C4C2418yes—
449C23×C4C2418yes—
450C23×C4C2411yescharacteristic
451C4⋊Q8—24no—
452C4⋊Q8—28no—
453C4⋊Q8—28no—
454C4⋊Q8—24no—
455C4⋊Q8—28no—
456C4⋊Q8—216no—
457C4⋊Q8—216no—
458C4⋊Q8—232no—
459C4⋊Q8—48no—
460#127—24no—
461#127—24no—
462#126—216no—
463#126—216no—
464#125—216no—
465#125—28no—
466#124—24no—
467#124—24no—
468#124—216no—
469#124—28no—
470#124—216no—
471#124—48no—
472#123—28no—
473#123—216no—
474#123—216no—
475#123—28no—
476#123—232no—
477#123—264no—
478#123—48no—
479#123—416no—
480C22⋊Q8—28no—
481C22⋊Q8—216no—
482C22⋊Q8—28no—
483C22⋊Q8—232no—
484C22⋊Q8—264no—
485C22⋊Q8—216no—
486C22⋊Q8—416no—
487C22⋊Q8—416no—
488C22⋊Q8—48no—
489C22⋊Q8—416no—
490C22⋊Q8—48no—
491C22⋊Q8—48no—
492#121—28no—
493#121—216no—
494#121—216no—
495#121—232no—
496#121—216no—
497#121—28no—
498#121—216no—
499#121—416no—
500#121—48no—
501#121—48no—
502#121—48no—
503#121—48no—
504#121—416no—
505#120—28no—
506#120—28no—
507#120—48no—
508C4×Q8—216no—
509C4×Q8—216no—
510C4×Q8—28no—
511C4×Q8C2×D4116yes—
512C4×D4—216no—
513C4×D4—216no—
514C4×D4—216no—
515C4×D4—216no—
516C4×D4—216no—
517C4×D4—216no—
518C4×D4—216no—
519C4×D4—28no—
520C4×D4—216no—
521C4×D4—232no—
522C4×D4—416no—
523C4×D4C2×D4132yes—
524C4×D4C2×D4116yes—
525#117—24no—
526#117—216no—
527#117—28no—
528#117—216no—
529#117—216no—
530#117—28no—
531#117—416no—
532#117C2×D418yes—
533#117C2×D4116yes—
534C2×C4⋊C4—216no—
535C2×C4⋊C4—232no—
536C2×C4⋊C4—28no—
537C2×C4⋊C4—48no—
538C2×C4⋊C4—48no—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C24116yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C24116yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C24116yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C22⋊C4—48no—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C24116yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C24116yes—
578C2×C22⋊C4C24116yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C24116yes—
585C2×C22⋊C4C24116yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2414yes—
588C2×C42—28no—
589C2×C42—24no—
590C2×C42—28no—
591C2×C42—28no—
592C2×C42—28no—
593C2×C42—28no—
594C2×C42—28no—
595C2×C42C2×D4116yes—
596C2×C42C2×D418yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2411yescharacteristic
604C2×C42C2412yes—
605C2×C42C2412yes—
606C2×C42C2411yescharacteristic
607C2×C42C24116yes—
608C2×C42C2411yescharacteristic
609C2×C42C2414yes—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613#95C24116yes—
614#95C24116yes—
615#95C24116yes—
616#95C2418yes—
617#95C2418yes—
618#95C24116yes—
619#95C2418yes—
620#95C24116yes—
621#95C24116yes—
622#95C24116yes—
623C24—22no—
624C24—24no—
625C24—22no—
626C24—22no—
627C24—42no—
628C24C2512yes—
629C24C2514yes—
630C24C2512yes—
631C24C2512yes—
632C24C2511yescharacteristic
633#41—232no—
634#41—464no—
635#41—464no—
636#41—4128no—
637#41—464no—
638#41—416no—
639#41—432no—
640C2×Q8—28no—
641C2×Q8—22no—
642C2×Q8—216no—
643C2×Q8—28no—
644C2×Q8—28no—
645C2×Q8—24no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—28no—
650C2×Q8—28no—
651C2×Q8—28no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—28no—
655C2×Q8—22no—
656C2×Q8—28no—
657C2×Q8—48no—
658C2×Q8—48no—
659C2×Q8—44no—
660C2×Q8—464no—
661C2×Q8—464no—
662C2×Q8—432no—
663C2×Q8C22×D414yes—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—28no—
667C2×D4—24no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—216no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—22no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—22no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—416no—
700C2×D4C22×D418yes—
701C2×D4C22×D414yes—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—28no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—216no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—28no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—216no—
728C22×C4—28no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—48no—
749C22×C4—48no—
750C22×C4—432no—
751C22×C4—48no—
752C22×C4—416no—
753C22×C4C22×D418yes—
754C22×C4C22×D4116yes—
755C22×C4C22×D418yes—
756C22×C4C22×D414yes—
757C22×C4H(5,𝔽2)14yes—
758C22×C4H(5,𝔽2)14yes—
759C22×C42−1+418yescomplemented
760C22×C4C2512yes—
761C22×C4C2518yes—
762C22×C4C2514yes—
763C22×C4C2518yes—
764C22×C4C2514yes—
765C22×C4C2518yes—
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2512yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2512yes—
772C22×C4C2511yescharacteristic
773C22×C4C2511yescharacteristic
774C22×C4C2512yes—
775C4⋊C4—216no—
776C4⋊C4—28no—
777C4⋊C4—216no—
778C4⋊C4—232no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—48no—
794C4⋊C4—416no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—416no—
798C4⋊C4C22×D418yes—
799C4⋊C4C22×D4116yes—
800C22⋊C4—24no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—216no—
810C22⋊C4—232no—
811C22⋊C4—216no—
812C22⋊C4—416no—
813C22⋊C4—416no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—416no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—416no—
821C22⋊C4C22×D418yes—
822C22⋊C4C22×D4116yes—
823C42—24no—
824C42—24no—
825C42—24no—
826C42—24no—
827C42—22no—
828C42—24no—
829C42—22no—
830C42—24no—
831C42—28no—
832C42—28no—
833C42—416no—
834C42C22×D414yes—
835C42C22×D414yes—
836C42C22×D418yes—
837C42C22×D4116yes—
838C42C22×D418yes—
839C23—22no—
840C23—22no—
841C23—28no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—24no—
854C23—22no—
855C23—22no—
856C23—24no—
857C23—24no—
858C23—28no—
859C23—24no—
860C23—28no—
861C23—24no—
862C23—48no—
863C23—48no—
864C23—44no—
865C23—44no—
866C23C23×D414yes—
867C23C23×D412yes—
868C23C2×H(5,𝔽2)12yes—
869C23C2×H(5,𝔽2)12yes—
870C23C2×2−1+414yes—
871C23C2611yescharacteristic
872Q8—28no—
873Q8—416no—
874Q8—432no—
875Q8—416no—
876Q8—48no—
877Q8—416no—
878Q8—44no—
879D4—216no—
880D4—28no—
881D4—416no—
882D4—416no—
883D4—416no—
884D4—432no—
885D4—48no—
886D4—416no—
887D4—44no—
888D4—48no—
889D4—416no—
890D4—816no—
891D4—168no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—216no—
901C2×C4—216no—
902C2×C4—216no—
903C2×C4—232no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—28no—
917C2×C4—28no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—216no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—48no—
928C2×C4—48no—
929C2×C4—48no—
930C2×C4—432no—
931C2×C4—432no—
932C2×C4—44no—
933C2×C4—416no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—416no—
937C2×C4—48no—
938C2×C4—48no—
939C2×C4—416no—
940C2×C4—88no—
941C2×C4#535116yes—
942C2×C4C23×D414yes—
943C2×C4C23×D418yes—
944C2×C4C23×D414yes—
945C2×C4C23×D412yes—
946C2×C4C23×D412yes—
947C2×C4C23×D414yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)12yes—
950C2×C4C2×H(5,𝔽2)12yes—
951C2×C4C2×H(5,𝔽2)12yes—
952C2×C4C2×2−1+414yes—
953C2×C4C2×2−1+414yes—
954C2×C4#58514yes—
955C22—24no—
956C22—22no—
957C22—24no—
958C22—22no—
959C22—24no—
960C22—28no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—416no—
965C22—42no—
966C22—42no—
967C22—44no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—44no—
973C22—48no—
974C22—42no—
975C22—44no—
976C22—48no—
977C22—44no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—42no—
982C22C2×#53514yes—
983C22C24×D411yescharacteristic
984C22C22×H(5,𝔽2)11yescharacteristic
985C22C22×H(5,𝔽2)11yescharacteristic
986C22C22×2−1+412yes—
987C22C2×#58512yes—
988C4—24no—
989C4—24no—
990C4—28no—
991C4—24no—
992C4—42no—
993C4—44no—
994C4—48no—
995C4—48no—
996C4—42no—
997C4—44no—
998C4—48no—
999C4—42no—
1000C4C2×#53514yes—
1001C4C2×#53514yes—
1002C4#348918yes—
1003C2—24no—
1004C2—44no—
1005C2—44no—
1006C2—82no—
1007C2—84no—
1008C2C22×#53511yescharacteristic
1009C2C2×#348912yes—
1010C2#6283311yescharacteristic
1011C2#6283512yes—
1012C2#6283611yescharacteristic
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×#3499C2semidirect
2. C2×#3444C2semidirect
3. #39596C2semidirect
4. #39471C2semidirect
5. #39124C2semidirect
6. #38920C2semidirect
7. #38041C2semidirect
8. #37839C2semidirect
9. #37379C2semidirect
10. #36624C2semidirect
11. C2×#2857C2semidirect
12. #35660C2semidirect
13. #35659C2semidirect
14. #35634C2semidirect
15. #35628C2semidirect
16. #35316C2semidirect
17. #35292C2semidirect
18. #35279C2semidirect
19. #35273C2semidirect
20. #34188C2semidirect
23. C2×D4×Q8C22semidirect
25. C2×#547C22semidirect
29. C2×#536C22semidirect
36. C2×#532C22semidirect
38. C22×C4⋊Q8C22semidirect
57. #2857C22semidirect
58. #2857C22semidirect
60. #2856C22semidirect
64. #2723C22semidirect
65. #2720C22semidirect
66. #2718C22semidirect
67. #2710C22semidirect
73. #2628C22semidirect
74. #2624C22semidirect
75. #2621C22semidirect
76. #2620C22semidirect
78. #2592C22semidirect
79. #2580C22semidirect
80. #2568C22semidirect
81. #2567C22semidirect
83. #2547C22semidirect
84. #2546C22semidirect
90. #2538C22semidirect
91. #2537C22semidirect
94. #2492C22semidirect
95. #2489C22semidirect
98. #2487C22semidirect
100. #2436C22semidirect
101. #2434C22semidirect
102. #2432C22semidirect
103. #2431C22semidirect
107. #2414C22semidirect
110. #2409C22semidirect
113. #2407C22semidirect
116. #2355C22semidirect
117. #2354C22semidirect
120. #2324C22semidirect
121. #2317C22semidirect
122. #2314C22semidirect
133. #2285C22semidirect
235. C4×#41D4semidirect
759. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34442
#395962
#394712
#391242
#389202
#380412
#378392
#373792
#366242
C2×#28572
#356602
#356592
#356342
#356282
#353162
#352922
#352792
#352732
#341882