Finite Group Databasebeta

← #795109

Subgroups — #795109

Order 512.

2334 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2515C211yesmaximal, characteristic
2C2×#2362C211yesmaximal, characteristic
3#16983C211yesmaximal, characteristic, complemented
4#16364C211yesmaximal, characteristic
5#15574C212yesmaximal, complemented
6#15485C212yesmaximal
7#15433C212yesmaximal
8#15401C212yesmaximal, complemented
9#15214C211yesmaximal, characteristic, complemented
10#15114C211yesmaximal, characteristic
11#15089C211yesmaximal, characteristic, complemented
12#15088C211yesmaximal, characteristic, complemented
13#15068C211yesmaximal, characteristic, complemented
14#14901C211yesmaximal, characteristic, complemented
15#14758C211yesmaximal, characteristic
16#14225C212yesmaximal
17#14186C211yesmaximal, characteristic, complemented
18#13994C212yesmaximal
19#13893C212yesmaximal, complemented
20#13889C212yesmaximal, complemented
21#13878C211yesmaximal, characteristic
22#13856C211yesmaximal, characteristic, complemented
23#13809C211yesmaximal, characteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2515—28no—
28C2×#400C2211yescharacteristic
29C2×#398C2211yescharacteristic
30C2×#397C2211yescharacteristic
31C2×#397C2212yes—
32C2×#396C2211yescharacteristic
33C2×#395C2211yescharacteristic
34#2362—28no—
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2211yescharacteristic
41C2×#388C2211yescharacteristic
42C2×#387C2212yes—
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#385C2211yescharacteristic
49C2×#383C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#381C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×#376C2211yescharacteristic
62C22×#95C2211yescharacteristic
63#1446C2211yescharacteristic
64#1446C2211yescharacteristic
65#1446C2211yescharacteristic
66#1445C2212yes—
67#1445C2212yes—
68#1444C2211yescharacteristic
69#1444C2212yes—
70#1444C2211yescharacteristic
71#1444C2211yescharacteristic
72#1444C2212yes—
73#1444C2211yescharacteristic
74#1444C2212yes—
75#1444C2212yes—
76#1444C2211yescharacteristic
77#1444C2212yes—
78#1443C2212yes—
79#1442C2211yescharacteristic
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2211yescharacteristic
84#1442C2211yescharacteristic
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2211yescharacteristic
90#1441C2211yescharacteristic
91#1441C2211yescharacteristic
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2211yescharacteristic
98#1440C2212yes—
99#1440C2212yes—
100#1439C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107C4⋊#95C2212yes—
108C4⋊#95C2212yes—
109#1434C2212yes—
110#1434C2212yes—
111#1434C2212yes—
112#1434C2212yes—
113#1434C2212yes—
114#1434C2212yes—
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2211yescharacteristic
119#1434C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C24×C4C2312yes—
127C24×C4C2311yescharacteristic
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—28no—
130C2×C4×Q8—24no—
131C2×C4×Q8—44no—
132C2×#117—24no—
133C2×#117—44no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172#400—24no—
173#398—24no—
174#397—24no—
175#397—28no—
176#396—24no—
177#395—24no—
178#391—24no—
179#389—24no—
180#389—44no—
181#388—28no—
182#388—28no—
183#388—24no—
184#388—24no—
185#387—24no—
186#387—24no—
187#387—24no—
188#387—28no—
189#387—44no—
190#387—44no—
191#385—24no—
192#383—24no—
193#382—24no—
194#381—24no—
195#380—28no—
196#380—44no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4—28no—
200C4×C4⋊C4—28no—
201C4×C4⋊C4—28no—
202C4×C22⋊C4—28no—
203C4×C22⋊C4D418yes—
204#376—24no—
205C2×#95—24no—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2311yescharacteristic
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C25C2411yescharacteristic
265C22×Q8—22no—
266C22×Q8—24no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—42no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2×D414yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C22⋊Q8—232no—
305C4×Q8—416no—
306#117—416no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4#4118yes—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42#4118yes—
408#95—22no—
409#95—22no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—24no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—24no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—22no—
446#95—24no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95C2×D414yes—
464#95C2×D414yes—
465#95#4114yes—
466C24—22no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24C22×D412yes—
476C24C2×#4114yes—
477C24C2511yescharacteristic
478C2×Q8—28no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—44no—
482C2×Q8—44no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—28no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4H(5,𝔽2)14yes—
622C22×C42−1+412yes—
623C22×C42−1+412yes—
624C22×C42−1+414yes—
625C4⋊C4—216no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—84no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C22⋊C4—216no—
646C22⋊C4—28no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—82no—
654C42—28no—
655C42—216no—
656C42—44no—
657C42—48no—
658C42—48no—
659C42—48no—
660C42—44no—
661C42—44no—
662C42—84no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23#52514yes—
686C23C23×D411yescharacteristic
687C23C22×#4112yes—
688C23C22×#4112yes—
689C23C22×#4111yescharacteristic
690C23C2×H(5,𝔽2)12yes—
691C23C2×2−1+411yescharacteristic
692C23C2×2−1+412yes—
693C23C2×2−1+411yescharacteristic
694C23#58511yescharacteristic
695C23#58511yescharacteristic
696C23#58511yescharacteristic
697Q8—416no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—416no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—816no—
827C2×C4#53214yes—
828C2×C4#54714yes—
829C2×C4#55218yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—44no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22C2×#52511yescharacteristic
842C22C2×#53211yescharacteristic
843C22#344911yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#55212yes—
846C22#347512yes—
847C22#347512yes—
848C22#348112yes—
849C22#348411yescharacteristic
850C22#348911yescharacteristic
851C22#349212yes—
852C22#349412yes—
853C22#349512yes—
854C22#349911yescharacteristic
855C22#350912yes—
856C22#350912yes—
857C22#351811yescharacteristic
858C22#352012yes—
859C22#352111yescharacteristic
860C22#354712yes—
861C22#355511yescharacteristic
862C22#356112yes—
863C22#356511yescharacteristic
864C4—24no—
865C4—28no—
866C4—24no—
867C4—44no—
868C4—42no—
869C4—42no—
870C4—44no—
871C4—42no—
872C4—44no—
873C4—42no—
874C4—42no—
875C4—44no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—82no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—44no—
887C2#3487611yescharacteristic
888C2#3592311yescharacteristic
889C2#3608611yescharacteristic
890C2#3618111yescharacteristic
891C2#3631711yescharacteristic
892C2#3805111yescharacteristic
893C2#4231111yescharacteristic
894C2#4485012yes—
895C2#4485512yes—
896C2#5928312yes—
897C2#5929412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #16983C2semidirect
5. #15574C2semidirect
8. #15401C2semidirect
9. #15214C2semidirect
11. #15089C2semidirect
12. #15088C2semidirect
13. #15068C2semidirect
14. #14901C2semidirect
17. #14186C2semidirect
19. #13893C2semidirect
20. #13889C2semidirect
22. #13856C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25152
C2×#23622
#169832
#163642
#155742
#154852
#154332
#154012
#152142
#151142
#150892
#150882
#150682
#149012
#147582
#142252
#141862
#139942
#138932
#138892
#138782
#138562
#138092