Finite Group Databasebeta

← #793199

Subgroups — #793199

Order 512.

2526 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C2×#2344C211yesmaximal, characteristic
3#16983C211yesmaximal, characteristic, complemented
4#16965C211yesmaximal, characteristic, complemented
5#15897C212yesmaximal, complemented
6#15877C212yesmaximal, complemented
7#15876C212yesmaximal, complemented
8#15870C212yesmaximal, complemented
9#15212C211yesmaximal, characteristic, complemented
10#15102C211yesmaximal, characteristic, complemented
11#15073C211yesmaximal, characteristic
12#15068C211yesmaximal, characteristic, complemented
13#15019C211yesmaximal, characteristic
14#14903C211yesmaximal, characteristic, complemented
15#14766C211yesmaximal, characteristic
16#14244C211yesmaximal, characteristic, complemented
17#13992C212yesmaximal
18#13952C211yesmaximal, characteristic, complemented
19#13904C212yesmaximal
20#13878C212yesmaximal
21#13870C212yesmaximal
22C2×#1444C211yesmaximal, characteristic
23#13809C211yesmaximal, characteristic
24C22×#117C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27#2493—28no—
28C2×#401C2211yescharacteristic
29C2×#400C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2211yescharacteristic
32C2×#398C2211yescharacteristic
33#2344—28no—
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#387C2212yes—
37C2×#387C2212yes—
38C2×#387C2211yescharacteristic
39C2×#387C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2211yescharacteristic
43C2×#383C2211yescharacteristic
44C2×#381C2211yescharacteristic
45C2×#381C2212yes—
46C2×#381C2212yes—
47C2×#381C2211yescharacteristic
48C2×#381C2212yes—
49C2×#381C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×#376C2211yescharacteristic
58C22×#95C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1445C2212yes—
62#1445C2212yes—
63#1445C2212yes—
64#1445C2211yescharacteristic
65#1445C2211yescharacteristic
66#1445C2211yescharacteristic
67#1445C2212yes—
68#1444C2212yes—
69#1444C2212yes—
70#1444C2212yes—
71#1444C2211yescharacteristic
72#1444C2211yescharacteristic
73#1444C2211yescharacteristic
74#1444C2211yescharacteristic
75#1444C2212yes—
76#1444C2211yescharacteristic
77#1443C2212yes—
78#1443C2212yes—
79#1443C2212yes—
80#1443C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1442C2211yescharacteristic
87#1442C2211yescharacteristic
88#1442C2211yescharacteristic
89#1442C2212yes—
90#1442C2211yescharacteristic
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2211yescharacteristic
98#1441C2211yescharacteristic
99#1441C2211yescharacteristic
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110C4⋊#95C2212yes—
111C4⋊#95C2212yes—
112C4⋊#95C2212yes—
113C4⋊#95C2212yes—
114#1434C2212yes—
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2211yescharacteristic
119#1434C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C4×#95C2211yescharacteristic
125C24×C4C2311yescharacteristic
126C24×C4C2312yes—
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2312yes—
130C2×#117—28no—
131C2×#117—44no—
132C2×#117—44no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—28no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—28no—
137C22×C4⋊C4—44no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169#401—24no—
170#400—24no—
171#400—24no—
172#400—24no—
173#398—24no—
174#389—24no—
175#389—24no—
176#387—24no—
177#387—24no—
178#387—24no—
179#387—28no—
180#387—28no—
181#385—24no—
182#385—24no—
183#383—24no—
184#381—28no—
185#381—28no—
186#381—24no—
187#381—24no—
188#381—44no—
189#381—44no—
190#380—24no—
191#380—24no—
192#380—44no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—28no—
196C4×C22⋊C4D418yes—
197#376—24no—
198C2×#95—24no—
199C2×#95—28no—
200C2×#95—24no—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
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
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—41no—
291C23×C4C2×D414yes—
292C23×C4#4118yes—
293C23×C4#4118yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2412yes—
316#117—432no—
317C2×C4⋊C4—232no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—432no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4C2×D414yes—
385C2×C22⋊C4C2×D414yes—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C2×D414yes—
402C2×C42C2×D414yes—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—24no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—24no—
427#95—22no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—22no—
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—22no—
444#95—24no—
445#95—42no—
446#95—42no—
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—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—22no—
471C24—21no—
472C24C22×D412yes—
473C24C2×#4114yes—
474C24C2×#4114yes—
475C24H(5,𝔽2)12yes—
476C24H(5,𝔽2)12yes—
477C24C2511yescharacteristic
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
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—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—28no—
534C22×C4—216no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—82no—
621C22×C4—84no—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C42−1+412yes—
635C22×C42−1+412yes—
636C22×C42−1+414yes—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—216no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—44no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C42—28no—
663C42—44no—
664C42—48no—
665C42—48no—
666C42—48no—
667C42—84no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23#52514yes—
687C23#53214yes—
688C23#53514yes—
689C23#55118yes—
690C23#55318yes—
691C23C23×D411yescharacteristic
692C23C22×#4112yes—
693C23C22×#4112yes—
694C23C22×#4111yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×2−1+411yescharacteristic
698C23C2×2−1+412yes—
699C23C2×2−1+411yescharacteristic
700C23#58512yes—
701C23#58511yescharacteristic
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—432no—
739C2×C4—416no—
740C2×C4—432no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
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—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—88no—
834C2×C4—88no—
835C2×C4#54714yes—
836C2×C4#55218yes—
837C22—28no—
838C22—24no—
839C22—24no—
840C22—28no—
841C22—24no—
842C22—28no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—28no—
847C22#260318yes—
848C22C2×#52511yescharacteristic
849C22C2×#53211yescharacteristic
850C22C2×#53511yescharacteristic
851C22C2×#54711yescharacteristic
852C22C2×#55112yes—
853C22C2×#55212yes—
854C22C2×#55312yes—
855C22#347512yes—
856C22#348511yescharacteristic
857C22#348911yescharacteristic
858C22#349112yes—
859C22#349512yes—
860C22#349512yes—
861C22#349512yes—
862C22#349911yescharacteristic
863C22#350912yes—
864C22#350912yes—
865C22#351311yescharacteristic
866C22#352211yescharacteristic
867C22#353512yes—
868C22#354411yescharacteristic
869C22#355911yescharacteristic
870C22#355912yes—
871C4—28no—
872C4—24no—
873C4—44no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—81no—
883C4—81no—
884C4—82no—
885C4—81no—
886C4—82no—
887C4—82no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—81no—
893C2—28no—
894C2C2×#260311yescharacteristic
895C2#3606111yescharacteristic
896C2#3608611yescharacteristic
897C2#3618111yescharacteristic
898C2#3634111yescharacteristic
899C2#3804111yescharacteristic
900C2#4137511yescharacteristic
901C2#4446212yes—
902C2#4479512yes—
903C2#5919612yes—
904C2#5928912yes—
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
4. #16965C2semidirect
5. #15897C2semidirect
6. #15877C2semidirect
7. #15876C2semidirect
8. #15870C2semidirect
9. #15212C2semidirect
10. #15102C2semidirect
12. #15068C2semidirect
14. #14903C2semidirect
16. #14244C2semidirect
18. #13952C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C2×#23442
#169832
#169652
#158972
#158772
#158762
#158702
#152122
#151022
#150732
#150682
#150192
#149032
#147662
#142442
#139922
#139522
#139042
#138782
#138702
C2×#14442
#138092