Finite Group Databasebeta

← #6393854

Subgroups — #6393854

Order 512.

3111 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3559C211yesmaximal, characteristic
2#34378C211yesmaximal, characteristic, complemented
3#34239C211yesmaximal, characteristic, complemented
4#22535C214yesmaximal, complemented
5#22406C214yesmaximal, complemented
6#22406C218yesmaximal, complemented
7#21877C212yesmaximal, complemented
8#21875C211yesmaximal, characteristic, complemented
9#21796C212yesmaximal, complemented
10#21794C211yesmaximal, characteristic, complemented
11#21423C212yesmaximal, complemented
12#21421C211yesmaximal, characteristic, complemented
13#21214C212yesmaximal, complemented
14#21212C211yesmaximal, characteristic, complemented
15#3559—22no—
16#3559—22no—
17#3559—22no—
18#3559—22no—
19#3559—22no—
20#3559—22no—
21#3559—22no—
22#3559—22no—
23C2×#563C412yescomplemented
24C2×#562C412yescomplemented
25C2×#554C412yescomplemented
26C2×#553C412yescomplemented
27C2×#553C2212yes—
28C2×#547C2214yes—
29C2×#547C2212yes—
30C2×#544C412yescomplemented
31C2×#540C412yescomplemented
32C2×#539C414yescomplemented
33C2×#539C2212yes—
34C2×#537C2212yes—
35C2×#532C2211yescharacteristic
36C2×#529C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C2×#410C2214yes—
39C2×#410C2218yes—
40#2382—22no—
41#2371—22no—
42#2370—22no—
43#2370—22no—
44#2345C2212yes—
45#2345C2212yes—
46#2344C2212yes—
47#2344C2214yes—
48#2344C2214yes—
49#2344C2212yes—
50#2336—22no—
51#2336—22no—
52#2330—22no—
53#2316C2212yes—
54#2313C2212yes—
55#2313C2212yes—
56C4×#125—22no—
57#2285C2211yescharacteristic
58#2283C2211yescharacteristic
59#2283C2211yescharacteristic
60#2274C2212yes—
61C4×#117C2211yescharacteristic
62#1996C2212yes—
63#1996C2211yescharacteristic
64#1996C2211yescharacteristic
65#1964C2214yes—
66#1964C2218yes—
67#1964C2214yes—
68#1964C2218yes—
69#1964C2212yes—
70#1964C2212yes—
71#1964C2211yescharacteristic
72#1964C2212yes—
73#1964C2212yes—
74#1964C2211yescharacteristic
75#1964C2212yes—
76#1899C2214yes—
77#1899C2218yes—
78#1899C2214yes—
79#1899C2218yes—
80#1799C2214yes—
81#1799C2218yes—
82#1782C2214yes—
83#1782C2218yes—
84C4×#99C2214yes—
85C4×#99C2218yes—
86C22×#41C2312yes—
87C22×#41C2314yes—
88#563—24no—
89#563—24no—
90#563—24no—
91#563—24no—
92#562—24no—
93#562—24no—
94#562—24no—
95#562—24no—
96#554—24no—
97#554—24no—
98#554—24no—
99#554—24no—
100#553—24no—
101#553—24no—
102#553—24no—
103#553—24no—
104#553—24no—
105#553—24no—
106#553—24no—
107#553—24no—
108#547—28no—
109#547—28no—
110#547—28no—
111#547—28no—
112#547—24no—
113#547—24no—
114#547—24no—
115#547—24no—
116#544—24no—
117#544—24no—
118#544—24no—
119#544—24no—
120#540—24no—
121#540—24no—
122#540—24no—
123#540—24no—
124#539—28no—
125#539—28no—
126#539—28no—
127#539—28no—
128#539—24no—
129#539—24no—
130#539—24no—
131#539—24no—
132#537—24no—
133#537—24no—
134#537—24no—
135#537—24no—
136#532—21no—
137#532—21no—
138#532—21no—
139#532—21no—
140#532—21no—
141#532—21no—
142#532—21no—
143#532—21no—
144C2×C4⋊Q8C2×C411yescharacteristic
145C2×C4⋊Q8C2×C412yes—
146C2×C4⋊Q8C2×C414yes—
147C2×#127C2×C411yescharacteristic
148#529—21no—
149#529—21no—
150#529—21no—
151#529—21no—
152#529—21no—
153#529—21no—
154#529—21no—
155#529—21no—
156C2×#126C2×C412yes—
157C2×#126C2×C414yes—
158C2×#126C2×C414yes—
159C2×#125C2×C411yescharacteristic
160C2×#125C2×C414yes—
161C2×#125C2×C412yes—
162C2×#125C2×C412yes—
163C2×#125C2×C412yes—
164C2×#125C2×C412yes—
165C2×#125C2×C412yes—
166C2×#125D412yes—
167C2×#125D412yes—
168C2×#125D412yes—
169C2×#125D412yes—
170C2×#125D412yes—
171C2×#125D412yes—
172C2×#125D412yes—
173C2×#125D412yes—
174C2×#124C2×C411yescharacteristic
175C2×#124C2×C412yes—
176C2×#123C2×C414yes—
177C2×#123C2×C414yes—
178C2×#123C2×C414yes—
179C2×#123C2×C414yes—
180C2×#123C2×C414yes—
181C2×#123C2312yes—
182C2×#123C2314yes—
183C2×C22⋊Q8C2×C414yes—
184C2×C22⋊Q8C2×C414yes—
185C2×C22⋊Q8C2×C414yes—
186C2×C22⋊Q8C2×C414yes—
187C2×C22⋊Q8C2×C414yes—
188C2×C22⋊Q8C2×C414yes—
189C2×C22⋊Q8C2311yescharacteristic
190C2×#121C2×C414yes—
191C2×#121C2×C414yes—
192C2×#121C2×C412yes—
193C2×#121C2×C414yes—
194C2×#121C2×C412yes—
195C2×#121C2311yescharacteristic
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2314yes—
199C2×C4×Q8C2×C411yescharacteristic
200C2×C4×D4C2×C411yescharacteristic
201C2×C4×D4C2×C412yes—
202C2×C4×D4C2×C412yes—
203C2×C4×D4C2×C414yes—
204C2×C4×D4C2×C412yes—
205C2×C4×D4C2×C412yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×#117C2×C412yes—
209C2×#117C2×C412yes—
210C2×#117C2312yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2312yes—
214C22×C4⋊C4C2×C414yes—
215C22×C4⋊C4C2×C412yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2311yescharacteristic
220C22×C42C2311yescharacteristic
221#410—48no—
222#410—416no—
223C2×#99C2318yes—
224C2×#99C2314yes—
225C2×#99C2318yes—
226C2×#99C2318yes—
227C2×#99C2318yes—
228C2×#99C2314yes—
229C2×#99C2318yes—
230#389—22no—
231#389—22no—
232#389—24no—
233#389—24no—
234#389—22no—
235#389—24no—
236#389—22no—
237#389—24no—
238#387—24no—
239#387—24no—
240#387—24no—
241#387—24no—
242#387—24no—
243#387—24no—
244#387—24no—
245#387—24no—
246#387—24no—
247#387—24no—
248#387—24no—
249#387—24no—
250#384—21no—
251#383—21no—
252#383—21no—
253#382—21no—
254#382—21no—
255#382—21no—
256#381C2314yes—
257#381C2314yes—
258#381C2312yes—
259#381C2312yes—
260#380C2314yes—
261#380C2314yes—
262#380C2312yes—
263#380C2312yes—
264#380C2311yescharacteristic
265#380C2312yes—
266#380C2311yescharacteristic
267C4×C4⋊C4—24no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—22no—
271C4×C4⋊C4—22no—
272C4×C4⋊C4—22no—
273C4×C4⋊C4—24no—
274C4×C4⋊C4—24no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2314yes—
283C4×C22⋊C4C2312yes—
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2314yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2311yescharacteristic
288#376—21no—
289#376—21no—
290#376—21no—
291C43—21no—
292#342C2318yes—
293#342C2314yes—
294#342C2314yes—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—28no—
300C2×#41—28no—
301C2×#41—44no—
302C2×#41—48no—
303C2×#41—44no—
304C2×#41—48no—
305C22×Q8C22×C414yes—
306C22×Q8C22×C412yes—
307C22×Q8C22×C411yescharacteristic
308C22×D4C22×C412yes—
309C22×D4C22×C414yes—
310C22×D4C22×C412yes—
311C22×D4C22×C414yes—
312C22×D4C22×C411yescharacteristic
313C22×D4C22×C412yes—
314C22×D4C2412yes—
315C22×D4C2414yes—
316C23×C4C22×C412yes—
317C23×C4C22×C414yes—
318C23×C4C22×C414yes—
319C23×C4C22×C414yes—
320C23×C4C22×C414yes—
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2412yes—
325C23×C4C2411yescharacteristic
326C4⋊Q8—24no—
327C4⋊Q8—24no—
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334#127—21no—
335#127—21no—
336#127—21no—
337#127—21no—
338#126—28no—
339#126—28no—
340#126—28no—
341#126—28no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—22no—
346#125—28no—
347#125—28no—
348#125—24no—
349#125—24no—
350#125—21no—
351#125—21no—
352#125—21no—
353#125—21no—
354#125C22⋊C414yes—
355#125C22⋊C414yes—
356#125C22⋊C414yes—
357#125C22⋊C414yes—
358#125C22⋊C414yes—
359#125C22⋊C414yes—
360#125C22⋊C414yes—
361#125C22⋊C414yes—
362#125C22⋊C414yes—
363#125C22⋊C414yes—
364#125C22⋊C414yes—
365#125C22⋊C414yes—
366#125C22⋊C414yes—
367#125C22⋊C414yes—
368#125C22⋊C414yes—
369#125C22⋊C414yes—
370#124—21no—
371#124—21no—
372#124—21no—
373#124—21no—
374#124—22no—
375#124—22no—
376#124—22no—
377#124—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—28no—
383#123—28no—
384#123—28no—
385#123—28no—
386#123—28no—
387#123—28no—
388#123—28no—
389#123—28no—
390#123—28no—
391#123—28no—
392#123—28no—
393#123—28no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—28no—
399C22⋊Q8—28no—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8—28no—
403C22⋊Q8—28no—
404C22⋊Q8—28no—
405C22⋊Q8—28no—
406C22⋊Q8—28no—
407C22⋊Q8—28no—
408C22⋊Q8—28no—
409C22⋊Q8—28no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—22no—
421#121—22no—
422#121—28no—
423#121—28no—
424#121—28no—
425#121—28no—
426#121—28no—
427#121—28no—
428#121—24no—
429#121—24no—
430#121—28no—
431#121—28no—
432#121—24no—
433#121—24no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—28no—
443C4×D4—28no—
444C4×D4—28no—
445C4×D4—28no—
446C4×D4—24no—
447C4×D4—24no—
448C4×D4—24no—
449C4×D4—24no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462#117—24no—
463#117—24no—
464#117—22no—
465#117—22no—
466#117—22no—
467#117—22no—
468#117—24no—
469#117—28no—
470#117—42no—
471#117—44no—
472#117—48no—
473#117—44no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4C22×C412yes—
490C2×C4⋊C4C22×C412yes—
491C2×C4⋊C4C22×C414yes—
492C2×C4⋊C4C22×C414yes—
493C2×C4⋊C4C22×C414yes—
494C2×C4⋊C4C22×C412yes—
495C2×C4⋊C4C22×C412yes—
496C2×C4⋊C4C22×C412yes—
497C2×C4⋊C4C22×C411yescharacteristic
498C2×C4⋊C4C22×C414yes—
499C2×C4⋊C4C22×C412yes—
500C2×C4⋊C4C22×C411yescharacteristic
501C2×C4⋊C4C22×C412yes—
502C2×C4⋊C4C22×C414yes—
503C2×C4⋊C4C22×C412yes—
504C2×C4⋊C4C22×C414yes—
505C2×C4⋊C4C22×C414yes—
506C2×C4⋊C4C22×C414yes—
507C2×C4⋊C4C22×C412yes—
508C2×C4⋊C4C22×C412yes—
509C2×C4⋊C4C2×D414yes—
510C2×C4⋊C4C2×D414yes—
511C2×C4⋊C4C2×D414yes—
512C2×C4⋊C4C2×D414yes—
513C2×C4⋊C4C2×D414yes—
514C2×C4⋊C4C2×D414yes—
515C2×C4⋊C4C2×D412yes—
516C2×C4⋊C4C2×D412yes—
517C2×C4⋊C4C2×D412yes—
518C2×C4⋊C4C2×D412yes—
519C2×C4⋊C4C2×D414yes—
520C2×C4⋊C4C2×D414yes—
521C2×C4⋊C4C2×D412yes—
522C2×C4⋊C4C2×D412yes—
523C2×C4⋊C4C2×D412yes—
524C2×C4⋊C4C2×D412yes—
525C2×C22⋊C4C22×C412yes—
526C2×C22⋊C4C22×C412yes—
527C2×C22⋊C4C22×C414yes—
528C2×C22⋊C4C22×C412yes—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C414yes—
533C2×C22⋊C4C22×C414yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C22×C412yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2412yes—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—24no—
549C2×C42—21no—
550C2×C42—21no—
551C2×C42—22no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42C22×C412yes—
555C2×C42C22×C414yes—
556C2×C42C22×C411yescharacteristic
557C2×C42C22×C411yescharacteristic
558C2×C42C22×C411yescharacteristic
559C2×C42C22×C411yescharacteristic
560C2×C42C2×D411yescharacteristic
561C2×C42C2×D411yescharacteristic
562C2×C42C2×D411yescharacteristic
563C2×C42C2×D411yescharacteristic
564C2×C42C2×D411yescharacteristic
565C2×C42C2×D411yescharacteristic
566C2×C42C2×D411yescharacteristic
567C2×C42C2×D411yescharacteristic
568#99—216no—
569#99—28no—
570#99—44no—
571#99—48no—
572#99—48no—
573#99—48no—
574#99—48no—
575#95—21no—
576#95—22no—
577#95—21no—
578#95—22no—
579#95—21no—
580#95—22no—
581#95—21no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—22no—
586#95—24no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—22no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597C24C23×C412yes—
598C24C23×C414yes—
599C24C2511yescharacteristic
600#41—84no—
601#41—88no—
602#41—84no—
603#41—88no—
604#41—82no—
605#41—88no—
606#41—82no—
607#41—82no—
608#41—82no—
609#41—88no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—28no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—48no—
616C2×Q8—44no—
617C2×Q8—81no—
618C2×D4—22no—
619C2×D4—24no—
620C2×D4—22no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—28no—
624C2×D4—24no—
625C2×D4—28no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—28no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—28no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—44no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—84no—
640C2×D4—82no—
641C2×D4—81no—
642C22×C4—22no—
643C22×C4—24no—
644C22×C4—22no—
645C22×C4—24no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—24no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—42no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—81no—
665C22×C4—82no—
666C22×C4—84no—
667C22×C4C23×C412yes—
668C22×C4C23×C414yes—
669C22×C4C23×C411yescharacteristic
670C22×C4C23×C411yescharacteristic
671C22×C4C23×C411yescharacteristic
672C22×C4C23×C414yes—
673C22×C4C23×C412yes—
674C22×C4C23×C412yes—
675C22×C4C23×C411yescharacteristic
676C22×C4C23×C411yescharacteristic
677C22×C4C23×C411yescharacteristic
678C22×C4C23×C414yes—
679C22×C4C22×D411yescharacteristic
680C22×C4C22×D411yescharacteristic
681C22×C4C22×D414yes—
682C22×C4C22×D414yes—
683C22×C4C22×D411yescharacteristic
684C22×C4C22×D411yescharacteristic
685C22×C4C22×D411yescharacteristic
686C22×C4C22×D411yescharacteristic
687C22×C4C22×D411yescharacteristic
688C22×C4C22×D411yescharacteristic
689C22×C4C22×D411yescharacteristic
690C22×C4C22×D411yescharacteristic
691C22×C4C22×D414yes—
692C22×C4C22×D414yes—
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D411yescharacteristic
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—28no—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—28no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—44no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—84no—
720C4⋊C4—82no—
721C4⋊C4—84no—
722C4⋊C4—84no—
723C4⋊C4—81no—
724C4⋊C4—82no—
725C4⋊C4—81no—
726C4⋊C4C2×C22⋊C414yes—
727C4⋊C4C2×C22⋊C414yes—
728C4⋊C4C2×C22⋊C418yes—
729C4⋊C4C2×C22⋊C418yes—
730C4⋊C4C2×C22⋊C414yes—
731C4⋊C4C2×C22⋊C414yes—
732C4⋊C4C2×C22⋊C418yes—
733C4⋊C4C2×C22⋊C418yes—
734C4⋊C4C2×C22⋊C418yes—
735C4⋊C4C2×C22⋊C418yes—
736C4⋊C4C2×C22⋊C418yes—
737C4⋊C4C2×C22⋊C418yes—
738C4⋊C4C2×C22⋊C414yes—
739C4⋊C4C2×C22⋊C414yes—
740C4⋊C4C2×C22⋊C414yes—
741C4⋊C4C2×C22⋊C414yes—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—28no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—28no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—28no—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—28no—
764C22⋊C4—22no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4H(5,𝔽2)14yes—
770C42—22no—
771C42—22no—
772C42—28no—
773C42—44no—
774C42—48no—
775C42—44no—
776C42—44no—
777C42—82no—
778C42—84no—
779C42—81no—
780C42—82no—
781C42—81no—
782C42—84no—
783C42—84no—
784C42C2×C22⋊C411yescharacteristic
785C42C2×C22⋊C411yescharacteristic
786C42C2×C22⋊C411yescharacteristic
787C42C2×C22⋊C411yescharacteristic
788C42C2×C22⋊C411yescharacteristic
789C42C2×C22⋊C411yescharacteristic
790C42C2×C22⋊C411yescharacteristic
791C42C2×C22⋊C411yescharacteristic
792C42C2×C22⋊C411yescharacteristic
793C42C2×C22⋊C411yescharacteristic
794C42C2×C22⋊C411yescharacteristic
795C42C2×C22⋊C411yescharacteristic
796C42C2×C22⋊C411yescharacteristic
797C42C2×C22⋊C411yescharacteristic
798C42C2×C22⋊C411yescharacteristic
799C42C2×C22⋊C411yescharacteristic
800C23—22no—
801C23—24no—
802C23—24no—
803C23—28no—
804C23—41no—
805C23—41no—
806C23—42no—
807C23—44no—
808C23—44no—
809C23—42no—
810C23C24×C411yescharacteristic
811C23C23×D411yescharacteristic
812C23C23×D411yescharacteristic
813C23C2×H(5,𝔽2)12yes—
814C23#58512yes—
815Q8—88no—
816Q8—82no—
817Q8—82no—
818Q8—81no—
819Q8—81no—
820D4—44no—
821D4—44no—
822D4—48no—
823D4—42no—
824D4—44no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—88no—
829D4—82no—
830D4—82no—
831D4—88no—
832D4—82no—
833D4—82no—
834D4—81no—
835D4—81no—
836C2×C4—22no—
837C2×C4—28no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—21no—
844C2×C4—24no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—44no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—44no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—42no—
892C2×C4—84no—
893C2×C4—84no—
894C2×C4—88no—
895C2×C4—88no—
896C2×C4—88no—
897C2×C4C22×C22⋊C411yescharacteristic
898C2×C4C22×C22⋊C418yes—
899C2×C4C22×C22⋊C411yescharacteristic
900C2×C4C22×C22⋊C411yescharacteristic
901C2×C4C22×C22⋊C411yescharacteristic
902C2×C4C22×C22⋊C411yescharacteristic
903C2×C4C22×C22⋊C411yescharacteristic
904C2×C4C22×C22⋊C411yescharacteristic
905C2×C4C22×C22⋊C411yescharacteristic
906C2×C4C22×C22⋊C411yescharacteristic
907C2×C4C22×C22⋊C411yescharacteristic
908C2×C4C22×C22⋊C411yescharacteristic
909C2×C4C22×C22⋊C418yes—
910C2×C4C22×C22⋊C411yescharacteristic
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—42no—
923C22—42no—
924C22—44no—
925C22—84no—
926C22—88no—
927C22C23×C22⋊C411yescharacteristic
928C22C4×H(5,𝔽2)12yes—
929C22#348812yes—
930C22#349811yescharacteristic
931C22#350011yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—28no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—28no—
943C4—21no—
944C4—21no—
945C4—44no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—44no—
950C4—82no—
951C4—84no—
952C4—82no—
953C4—84no—
954C4—82no—
955C4#288412yes—
956C2—22no—
957C2—21no—
958C2—21no—
959C2—22no—
960C2—82no—
961C2—84no—
962C2#3425811yescharacteristic
963C2C2×#288411yescharacteristic
964C2#6007011yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#3559C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×#125 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #34378C2semidirect
3. #34239C2semidirect
4. #22535C2semidirect
5. #22406C2semidirect
6. #22406C2semidirect
7. #21877C2semidirect
8. #21875C2semidirect
9. #21796C2semidirect
10. #21794C2semidirect
11. #21423C2semidirect
12. #21421C2semidirect
13. #21214C2semidirect
14. #21212C2semidirect
23. C2×#563C4semidirect
24. C2×#562C4semidirect
25. C2×#554C4semidirect
26. C2×#553C4semidirect
30. C2×#544C4semidirect
31. C2×#540C4semidirect
32. C2×#539C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35592
#343782
#342392
#225352
#224062
#218772
#218752
#217962
#217942
#214232
#214212
#212142
#212122