Finite Group Databasebeta

← #7680734

Subgroups — #7680734

Order 512.

8320 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3508C212yesmaximal, complemented
2#59815C214yesmaximal, complemented
3#59641C214yesmaximal, complemented
4#59015C218yesmaximal, complemented
5#45421C214yesmaximal, complemented
6#44931C214yesmaximal, complemented
7#43079C218yesmaximal, complemented
8#39352C214yesmaximal, complemented
9#37792C218yesmaximal, complemented
10#36126C214yesmaximal, complemented
11#35554C212yesmaximal, complemented
12#35515C212yesmaximal, complemented
13#35272C211yesmaximal, characteristic, complemented
14#35254C212yesmaximal, complemented
15#34938C211yesmaximal, characteristic, complemented
16C2×#2541C211yesmaximal, characteristic, complemented
17#34210C211yesmaximal, characteristic, complemented
18#34181C211yesmaximal, characteristic, complemented
19C4⋊C4×#41C211yesmaximal, characteristic, complemented
20C4×#535C211yesmaximal, characteristic, complemented
21#3508—232no—
22C2×#559C2218yescomplemented
23C2×#550C2218yescomplemented
24C2×#547C2218yescomplemented
25C2×#546C22116yes—
26C2×#540C2218yescomplemented
27C2×#535C2212yes—
28C2×#535C2211yescharacteristic
29C2×#533C2212yes—
30C2×#532C2218yescomplemented
31C22×#127C2212yes—
32C22×#127C2211yescharacteristic
33C22×#121C2214yes—
34C2×#518C2212yes—
35C2×#518C2212yes—
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2212yes—
38C22×C4×D4C2211yescharacteristic
39#2856C2214yescomplemented
40#2854C2218yescomplemented
41#2710C22116yescomplemented
42#2706C22116yescomplemented
43#2682C22116yescomplemented
44#2672C22116yescomplemented
45#2671C22116yescomplemented
46#2671C22116yescomplemented
47#2624C2218yescomplemented
48#2619C2214yescomplemented
49#2580C2218yescomplemented
50#2552C2212yescomplemented
51#2551C2212yescomplemented
52#2550C2214yescomplemented
53#2549C2214yes—
54#2548C2212yescomplemented
55#2548C2212yescomplemented
56#2541C2212yes—
57#2541C2214yes—
58#2541C2214yes—
59#2541C2214yes—
60#2541C2212yes—
61#2541C2212yescomplemented
62#2541C2212yescomplemented
63#2538C2218yescomplemented
64#2537C2218yescomplemented
65#2501C2218yescomplemented
66#2491C2218yescomplemented
67#2461C22116yescomplemented
68#2455C22116yescomplemented
69#2454C2218yescomplemented
70#2452C2218yescomplemented
71#2448C2218yescomplemented
72#2445C2218yescomplemented
73#2445C2218yescomplemented
74#2445C2218yescomplemented
75#2445C2218yescomplemented
76#2445C2218yescomplemented
77#2440C2214yes—
78#2437C22116yes—
79#2430C22116yescomplemented
80#2430C22116yescomplemented
81#2425C22116yescomplemented
82#2422C2218yescomplemented
83#2418C22116yes—
84#2416C2218yescomplemented
85#2416C2218yescomplemented
86#2408C2214yes—
87#2408C2214yes—
88#2407C22116yescomplemented
89#2405C22116yes—
90#2399C2214yescomplemented
91C2×#392C2214yes—
92#2366C2214yescomplemented
93#2366C2214yescomplemented
94#2361C2218yescomplemented
95#2351C2212yescomplemented
96Q8×C4⋊C4C2212yescomplemented
97#2349C2214yes—
98#2349C2212yescomplemented
99#2349C2214yescomplemented
100#2349C2214yescomplemented
101D4×C4⋊C4C2214yes—
102D4×C4⋊C4C2214yescomplemented
103D4×C4⋊C4C2212yescomplemented
104D4×C4⋊C4C2214yescomplemented
105D4×C22⋊C4C2214yes—
106D4×C22⋊C4C2214yes—
107#2328C2212yescomplemented
108#2328C2214yescomplemented
109#2326C2212yescomplemented
110#2324C2214yescomplemented
111#2321C2214yes—
112#2317C2211yescharacteristic
113#2316C2212yes—
114#2315C2214yes—
115#2311C2211yescharacteristic
116#2309C2211yescharacteristic
117#2309C2212yes—
118#2309C2212yes—
119C4×C4⋊Q8C2214yescomplemented
120C4×#127C2212yescomplemented
121C4×#127C2214yescomplemented
122C4×#124C2212yescomplemented
123C4×#121C2214yescomplemented
124C4×#120C2214yes—
125#2296C2212yes—
126#2296C2212yes—
127#2296C2214yescomplemented
128C2×#390C2212yes—
129#2285C2211yescharacteristic
130#2285C2211yescharacteristic
131#2285C2212yescomplemented
132C2×#380C2214yes—
133C4×#117C2211yescharacteristic
134C2×C4×C4⋊C4C2211yescharacteristic
135C2×C4×C4⋊C4C2212yescomplemented
136C22×#41C2311yescharacteristic
137C22×#41C23116yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2318yes—
142C23×D4C2312yes—
143C24×C4C2312yes—
144#559—264no—
145#550—264no—
146#547—432no—
147#546—2128no—
148#540—264no—
149#535—216no—
150#535D4116yescomplemented
151#533—216no—
152#532—264no—
153C2×C4⋊Q8C2314yes—
154C2×C4⋊Q8C2314yes—
155C2×#127—216no—
156C2×#127—28no—
157C2×#127C2312yes—
158C2×#127C2312yes—
159C2×#127C2312yes—
160C2×#127C2312yes—
161C2×#127C2314yes—
162C2×#127C2314yes—
163C2×#127C2318yes—
164C2×#127C2314yes—
165C2×#127C2312yes—
166C2×#125C2314yes—
167C2×#124C23116yes—
168C2×#124C2314yes—
169C2×#124C2312yes—
170C2×#123C23116yes—
171C2×#123C23116yes—
172C2×#123C23116yes—
173C2×#123C23116yes—
174C2×#123C23116yes—
175C2×C22⋊Q8C2318yes—
176C2×C22⋊Q8C23116yes—
177C2×#121—416no—
178C2×#121C2318yes—
179C2×#121C2318yes—
180C2×#121C23116yes—
181C2×#121C23116yes—
182C2×#121C23116yes—
183C2×#121C2318yes—
184C2×#121C23116yes—
185C2×#121C2318yes—
186C2×#121C2318yes—
187C2×#121C2314yes—
188C2×#120C2318yes—
189C2×#120C2314yes—
190#518—216no—
191#518—216no—
192C4×#41—216no—
193C4×#41—28no—
194C2×C4×Q8C2318yes—
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2314yes—
198C2×C4×D4—28no—
199C2×C4×D4C2311yescharacteristic
200C2×C4×D4C2318yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2312yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C23116yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2318yes—
217C2×#117C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2318yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2318yes—
230C22×C22⋊C4C2318yes—
231C22×C22⋊C4C2318yes—
232C22×C42C2314yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236#399C23116yes—
237#399C23116yes—
238#398C2318yes—
239#398C2318yes—
240#397C23116yes—
241#396C23116yes—
242#396C23116yes—
243#395C2318yes—
244#395C2318yes—
245#394C2318yes—
246#394C2318yes—
247#394C23116yes—
248#394C23116yes—
249#394C23116yes—
250#394C23116yes—
251#394C23116yes—
252#394C23116yes—
253#393C23116yes—
254#392C2318yes—
255#392C2318yes—
256#392C23116yes—
257#392C2318yes—
258#392C2318yes—
259#391C2318yes—
260#391C2312yes—
261#390C2312yes—
262#390C2318yes—
263#390C2312yes—
264#390C2318yes—
265#390C2318yes—
266#390C2318yes—
267#390C2314yes—
268#390C2314yes—
269#390C2312yes—
270#390C2318yes—
271#390C2318yes—
272#390C2314yes—
273#390C2318yes—
274#390C2314yes—
275#390C2318yes—
276#390C2318yes—
277#390C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2318yes—
281#389C2318yes—
282#389C2318yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2314yes—
290#388C2318yes—
291#388C2318yes—
292#388C23116yes—
293#388C23116yes—
294#386C2314yes—
295#386C2318yes—
296#386C2318yes—
297#386C23116yes—
298#386C23116yes—
299#386C23116yes—
300#386C23116yes—
301#386C23116yes—
302#385C23116yes—
303#385C23116yes—
304#385C2314yes—
305#385C2318yes—
306#385C23116yes—
307#385C23116yes—
308#385C2318yes—
309#385C2318yes—
310#385C2318yes—
311#385C2318yes—
312#384C2312yes—
313#384C2312yes—
314#384C2314yes—
315#384C2312yes—
316#384C2314yes—
317#382C2312yes—
318#382C2312yes—
319#382C2314yes—
320#382C2312yes—
321#380C2314yes—
322#380C2312yes—
323#380C2312yes—
324#380C2318yes—
325#380C2312yes—
326#380C2314yes—
327#380C2318yes—
328#380C2314yes—
329#380C2318yes—
330#380C23116yes—
331#380C2312yes—
332#379C2314yes—
333#379C2318yes—
334#379C2318yes—
335C4×C4⋊C4C2312yes—
336C4×C4⋊C4C2312yes—
337C4×C4⋊C4C2318yes—
338C4×C4⋊C4C2312yes—
339C4×C4⋊C4C2314yes—
340C4×C4⋊C4C2312yes—
341C4×C4⋊C4C2314yes—
342C4×C4⋊C4C2312yes—
343C4×C4⋊C4C2312yes—
344C4×C4⋊C4C2312yes—
345C4×C4⋊C4C2312yes—
346C4×C4⋊C4C2314yes—
347C4×C4⋊C4C2314yes—
348C4×C4⋊C4C2311yescharacteristic
349C4×C4⋊C4C2311yescharacteristic
350C4×C4⋊C4C2312yes—
351C4×C22⋊C4C2312yes—
352C4×C22⋊C4C2312yes—
353C4×C22⋊C4C2318yes—
354#376C2312yes—
355C2×#95C2312yes—
356C2×#95C2314yes—
357C2×#95C2318yes—
358C43C2312yes—
359C25C2414yes—
360C25C2412yes—
361C2×#41—264no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—432no—
365C2×#41—816no—
366C2×#41C2×D418yes—
367C22×Q8C2418yes—
368C22×Q8C2411yescharacteristic
369C22×D4—232no—
370C22×D4—28no—
371C22×D4—24no—
372C22×D4—28no—
373C22×D4—28no—
374C22×D4—28no—
375C22×D4—24no—
376C22×D4—28no—
377C22×D4—48no—
378C22×D4—416no—
379C22×D4—84no—
380C22×D4—88no—
381C22×D4C2×D418yes—
382C22×D4C2414yes—
383C22×D4C2414yes—
384C22×D4C2414yes—
385C22×D4C24116yes—
386C22×D4C2412yes—
387C22×D4C2412yes—
388C22×D4C2412yes—
389C22×D4C2411yescharacteristic
390C22×D4C2414yes—
391C22×D4C24116yes—
392C22×D4C24116yes—
393C22×D4C2414yes—
394C22×D4C2414yes—
395C22×D4C2418yes—
396C23×C4—28no—
397C23×C4—48no—
398C23×C4C2412yes—
399C23×C4C2414yes—
400C23×C4C2414yes—
401C23×C4C2418yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C24116yes—
406C23×C4C24116yes—
407C23×C4C2414yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C4⋊Q8—216no—
412C4⋊Q8—216no—
413#127—216no—
414#127—216no—
415#127—232no—
416#127—216no—
417#127—28no—
418#127—28no—
419#127—28no—
420#127—28no—
421#127C2×D4116yescomplemented
422#125—216no—
423#124—216no—
424#124—264no—
425#124C2×D4116yescomplemented
426#123—264no—
427#123—264no—
428#123—432no—
429#123—432no—
430#123—816no—
431C22⋊Q8—232no—
432C22⋊Q8—432no—
433#121—264no—
434#121—264no—
435#121—264no—
436#121—232no—
437#121—232no—
438#121—432no—
439#121—416no—
440#121—416no—
441#121—88no—
442#121C2×D4132yescomplemented
443#120—232no—
444#120C2×D4132yes—
445C4×Q8—216no—
446C4×Q8—232no—
447C4×Q8—24no—
448C4×Q8—24no—
449C4×D4—232no—
450C4×D4—216no—
451C4×D4—232no—
452C4×D4—232no—
453C4×D4—28no—
454C4×D4—28no—
455C4×D4—232no—
456C4×D4—264no—
457C4×D4—232no—
458C4×D4—28no—
459C4×D4—28no—
460C4×D4—28no—
461C4×D4—28no—
462C4×D4—24no—
463C4×D4—24no—
464C4×D4—416no—
465C4×D4—416no—
466C4×D4—88no—
467#117—28no—
468#117—216no—
469#117—28no—
470#117—24no—
471#117—24no—
472#117—28no—
473#117C2×D418yes—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4—216no—
477C2×C4⋊C4—416no—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2412yes—
482C2×C4⋊C4C2412yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2411yescharacteristic
489C2×C4⋊C4C2411yescharacteristic
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C24116yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C22⋊C4—232no—
506C2×C22⋊C4—28no—
507C2×C22⋊C4—232no—
508C2×C22⋊C4—416no—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C24116yes—
512C2×C22⋊C4C24116yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C24116yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2412yes—
518C2×C22⋊C4C2412yes—
519C2×C22⋊C4C2412yes—
520C2×C22⋊C4C2412yes—
521C2×C22⋊C4C24116yes—
522C2×C22⋊C4C24116yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C24116yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C24116yes—
527C2×C22⋊C4C24116yes—
528C2×C22⋊C4C24116yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2418yes—
532C2×C42—28no—
533C2×C42—216no—
534C2×C42—28no—
535C2×C42#4118yescomplemented
536C2×C42C2414yes—
537C2×C42C2412yes—
538C2×C42C2412yes—
539C2×C42C2414yes—
540C2×C42C2412yes—
541C2×C42C2414yes—
542C2×C42C2418yes—
543C2×C42C2414yes—
544C2×C42C2412yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2414yes—
548C2×C42C2412yes—
549C2×C42C2411yescharacteristic
550C2×C42C2411yescharacteristic
551C2×C42C2411yescharacteristic
552C2×C42C2411yescharacteristic
553#95C2412yes—
554#95C2414yes—
555#95C2414yes—
556#95C2414yes—
557#95C2412yes—
558#95C2418yes—
559#95C2414yes—
560#95C24116yes—
561#95C2414yes—
562#95C2414yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2414yes—
567#95C2418yes—
568#95C2418yes—
569C24—24no—
570C24—24no—
571C24—28no—
572C24—28no—
573C24—28no—
574C24—44no—
575C24—44no—
576C24—48no—
577C24—48no—
578C24C22×D418yes—
579C24C2518yes—
580C24C2514yes—
581C24C2512yes—
582C24C2511yescharacteristic
583#41—232no—
584#41—8128no—
585C2×Q8—216no—
586C2×Q8—22no—
587C2×Q8—216no—
588C2×Q8—22no—
589C2×Q8—48no—
590C2×Q8C22×D414yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—232no—
594C2×D4—232no—
595C2×D4—232no—
596C2×D4—232no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—22no—
602C2×D4—28no—
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—216no—
609C2×D4—232no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—48no—
616C2×D4—48no—
617C2×D4—416no—
618C2×D4—48no—
619C2×D4—48no—
620C2×D4—416no—
621C2×D4—416no—
622C2×D4—48no—
623C2×D4—416no—
624C2×D4—416no—
625C2×D4—432no—
626C2×D4—816no—
627C2×D4—864no—
628C2×D4—816no—
629C2×D4C22×D418yes—
630C2×D4C22×D418yes—
631C2×D4C22×D418yes—
632C2×D4C22×D414yes—
633C2×D4C22×D4132yes—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—216no—
638C22×C4—28no—
639C22×C4—232no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—216no—
646C22×C4—216no—
647C22×C4—232no—
648C22×C4—24no—
649C22×C4—28no—
650C22×C4—42no—
651C22×C4—44no—
652C22×C4—48no—
653C22×C4—44no—
654C22×C4—416no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4—48no—
658C22×C4—44no—
659C22×C4—416no—
660C22×C4—816no—
661C22×C4C22×D418yes—
662C22×C4C22×D414yes—
663C22×C4C2×#4114yes—
664C22×C4C2×#4114yes—
665C22×C4C2×#4114yes—
666C22×C42−1+414yes—
667C22×C4C2514yes—
668C22×C4C2512yes—
669C22×C4C2514yes—
670C22×C4C2518yes—
671C22×C4C2514yes—
672C22×C4C2518yes—
673C22×C4C2512yes—
674C22×C4C2512yes—
675C22×C4C2514yes—
676C22×C4C2511yescharacteristic
677C22×C4C2511yescharacteristic
678C22×C4C2511yescharacteristic
679C22×C4C2514yes—
680C22×C4C2511yescharacteristic
681C22×C4C2511yescharacteristic
682C22×C4C2511yescharacteristic
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—216no—
686C4⋊C4—216no—
687C4⋊C4—216no—
688C4⋊C4—216no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—24no—
698C4⋊C4—216no—
699C4⋊C4—28no—
700C4⋊C4—216no—
701C4⋊C4—24no—
702C4⋊C4—416no—
703C4⋊C4—48no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4C22×D418yes—
709C4⋊C4H(5,𝔽2)18yes—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—232no—
713C22⋊C4—216no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—232no—
717C22⋊C4—232no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—232no—
723C22⋊C4—416no—
724C22⋊C4—48no—
725C22⋊C4—48no—
726C22⋊C4—416no—
727C22⋊C4—416no—
728C22⋊C4—416no—
729C22⋊C4—416no—
730C22⋊C4—48no—
731C22⋊C4C22×D418yes—
732C22⋊C4C22×D4132yes—
733C42—24no—
734C42—28no—
735C42—24no—
736C42—216no—
737C42—28no—
738C42—28no—
739C42—24no—
740C42—24no—
741C42—24no—
742C42—28no—
743C42—24no—
744C42—44no—
745C42C22×D418yes—
746C42C2×#4114yes—
747C42C2×#4114yes—
748C42C2×#4114yes—
749C42C2×#4114yes—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—24no—
754C23—24no—
755C23—28no—
756C23—22no—
757C23—24no—
758C23—28no—
759C23—24no—
760C23—216no—
761C23—28no—
762C23—28no—
763C23—216no—
764C23—28no—
765C23—216no—
766C23—416no—
767C23—416no—
768C23—84no—
769C23—84no—
770C23—88no—
771C23—816no—
772C23—88no—
773C23—88no—
774C23—816no—
775C23C23×D418yes—
776C23C23×D414yes—
777C23C23×D412yes—
778C23C22×#4112yes—
779C23C2×2−1+412yes—
780C23C2611yescharacteristic
781Q8—28no—
782Q8—432no—
783D4—216no—
784D4—216no—
785D4—216no—
786D4—28no—
787D4—432no—
788D4—464no—
789D4—416no—
790D4—416no—
791D4—416no—
792D4—416no—
793D4—88no—
794D4—88no—
795D4—832no—
796D4—832no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—44no—
827C2×C4—416no—
828C2×C4—432no—
829C2×C4—48no—
830C2×C4—416no—
831C2×C4—84no—
832C2×C4—88no—
833C2×C4—832no—
834C2×C4—84no—
835C2×C4—832no—
836C2×C4#547116yescomplemented
837C2×C4C23×D414yes—
838C2×C4C23×D418yes—
839C2×C4C23×D412yes—
840C2×C4C23×D412yes—
841C2×C4C22×#4112yes—
842C2×C4C22×#4112yes—
843C2×C4C22×#4112yes—
844C2×C4C22×#4112yes—
845C2×C4C22×#4112yes—
846C2×C4C22×#4112yes—
847C2×C4C2×H(5,𝔽2)18yes—
848C2×C4C2×H(5,𝔽2)14yes—
849C2×C4C2×2−1+412yes—
850C2×C4C2×2−1+412yes—
851C22—24no—
852C22—22no—
853C22—22no—
854C22—24no—
855C22—28no—
856C22—216no—
857C22—24no—
858C22—28no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22—48no—
865C22—416no—
866C22—48no—
867C22—48no—
868C22—416no—
869C22—48no—
870C22—816no—
871C22—1616no—
872C22C2×#54714yes—
873C22C24×D411yescharacteristic
874C22C23×#4111yescharacteristic
875C22C22×H(5,𝔽2)12yes—
876C22C22×2−1+411yescharacteristic
877C22H(7,𝔽2)12yes—
878C4—28no—
879C4—28no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—24no—
884C4—48no—
885C4—44no—
886C4—48no—
887C4—42no—
888C4—44no—
889C4—42no—
890C4—44no—
891C4C2×#54714yes—
892C4C2×#54714yes—
893C4#350814yescomplemented
894C2—24no—
895C2—44no—
896C2—48no—
897C2—88no—
898C2C22×#54711yescharacteristic
899C2C2×#350811yescharacteristic
900C2#6285511yescharacteristic
901C2#6291712yes—
902C2D4×H(5,𝔽2)12yes—
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×#3508C2semidirect
2. #59815C2semidirect
3. #59641C2semidirect
4. #59015C2semidirect
5. #45421C2semidirect
6. #44931C2semidirect
7. #43079C2semidirect
8. #39352C2semidirect
9. #37792C2semidirect
10. #36126C2semidirect
11. #35554C2semidirect
12. #35515C2semidirect
13. #35272C2semidirect
14. #35254C2semidirect
15. #34938C2semidirect
16. C2×#2541C2semidirect
17. #34210C2semidirect
18. #34181C2semidirect
19. C4⋊C4×#41C2semidirect
20. C4×#535C2semidirect
22. C2×#559C22semidirect
23. C2×#550C22semidirect
24. C2×#547C22semidirect
26. C2×#540C22semidirect
30. C2×#532C22semidirect
39. #2856C22semidirect
40. #2854C22semidirect
41. #2710C22semidirect
42. #2706C22semidirect
43. #2682C22semidirect
44. #2672C22semidirect
45. #2671C22semidirect
46. #2671C22semidirect
47. #2624C22semidirect
48. #2619C22semidirect
49. #2580C22semidirect
50. #2552C22semidirect
51. #2551C22semidirect
52. #2550C22semidirect
54. #2548C22semidirect
55. #2548C22semidirect
61. #2541C22semidirect
62. #2541C22semidirect
63. #2538C22semidirect
64. #2537C22semidirect
65. #2501C22semidirect
66. #2491C22semidirect
67. #2461C22semidirect
68. #2455C22semidirect
69. #2454C22semidirect
70. #2452C22semidirect
71. #2448C22semidirect
72. #2445C22semidirect
73. #2445C22semidirect
74. #2445C22semidirect
75. #2445C22semidirect
76. #2445C22semidirect
79. #2430C22semidirect
80. #2430C22semidirect
81. #2425C22semidirect
82. #2422C22semidirect
84. #2416C22semidirect
85. #2416C22semidirect
88. #2407C22semidirect
90. #2399C22semidirect
92. #2366C22semidirect
93. #2366C22semidirect
94. #2361C22semidirect
95. #2351C22semidirect
96. Q8×C4⋊C4C22semidirect
98. #2349C22semidirect
99. #2349C22semidirect
100. #2349C22semidirect
102. D4×C4⋊C4C22semidirect
103. D4×C4⋊C4C22semidirect
104. D4×C4⋊C4C22semidirect
107. #2328C22semidirect
108. #2328C22semidirect
109. #2326C22semidirect
110. #2324C22semidirect
119. C4×C4⋊Q8C22semidirect
120. C4×#127C22semidirect
121. C4×#127C22semidirect
122. C4×#124C22semidirect
123. C4×#121C22semidirect
127. #2296C22semidirect
131. #2285C22semidirect
135. C2×C4×C4⋊C4C22semidirect
150. #535D4semidirect
421. #127C2×D4semidirect
425. #124C2×D4semidirect
442. #121C2×D4semidirect
535. C2×C42#41semidirect
836. C2×C4#547semidirect
893. C4#3508semidirect

Maximal subgroups

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

subgroupindex
C2×#35082
#598152
#596412
#590152
#454212
#449312
#430792
#393522
#377922
#361262
#355542
#355152
#352722
#352542
#349382
C2×#25412
#342102
#341812
C4⋊C4×#412
C4×#5352