Finite Group Databasebeta

← #945727

Subgroups — #945727

Order 512.

2710 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2536C211yesmaximal, characteristic
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic, complemented
5#17118C214yesmaximal
6#16542C214yesmaximal, complemented
7#16332C214yesmaximal, complemented
8#15409C214yesmaximal, complemented
9#15240C211yesmaximal, characteristic, complemented
10#15231C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15182C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14024C211yesmaximal, characteristic, complemented
17#13976C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2621—28no—
30#2536—28no—
31#2499—28no—
32#2415—28no—
33C2×#398C2214yes—
34C2×#398C2212yes—
35C2×#397C2214yes—
36C2×#397C2212yes—
37C2×#397C2214yes—
38C2×#394C2212yes—
39C2×#394C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#387C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1445C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2212yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2212yes—
78#1439C2214yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1438C2212yes—
86#1436C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—42no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C2×C4×Q8—42no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4D418yes—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117—42no—
126C2×#117—42no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166#398—28no—
167#398—216no—
168#397—28no—
169#397—216no—
170#397—216no—
171#394—28no—
172#394—28no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—42no—
177#391—42no—
178#391—42no—
179#391D418yescomplemented
180#389—28no—
181#389—24no—
182#388—28no—
183#388—28no—
184#388—28no—
185#387—216no—
186#384—24no—
187#384—42no—
188#384—42no—
189#382—24no—
190#382—24no—
191#382—24no—
192#380—24no—
193#380—24no—
194#380—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—42no—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8C2×D414yes—
241C22×D4—41no—
242C22×D4—41no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4C2×D414yes—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C4⋊Q8—416no—
278C22⋊Q8—416no—
279C22⋊Q8—416no—
280C22⋊Q8—416no—
281C22⋊Q8—416no—
282C4×Q8—416no—
283C4×D4—416no—
284#117—416no—
285#117—416no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42C2×D414yes—
397C2×C42C2×D414yes—
398C2×C42#4114yes—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—42no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—42no—
421#95—42no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95C2×D4116yes—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24C22×D412yes—
447C24C22×D412yes—
448C24C2511yescharacteristic
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—28no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—48no—
467C2×D4—48no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4C22×D412yes—
569C22×C4C22×D414yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4112yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C42−1+414yes—
583C22×C42−1+414yes—
584C22×C42−1+412yes—
585C4⋊C4—28no—
586C4⋊C4—44no—
587C4⋊C4—416no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—416no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—88no—
602C4⋊C4—88no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C42—28no—
618C42—28no—
619C42—28no—
620C42—48no—
621C42—48no—
622C42—44no—
623C42—44no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C22×#4111yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×H(5,𝔽2)11yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×2−1+411yescharacteristic
677C23C2×2−1+412yes—
678C23C2×2−1+412yes—
679C23#58512yes—
680C23#58512yes—
681Q8—416no—
682Q8—88no—
683D4—416no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—42no—
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—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4#53414yes—
783C2×C4#53714yes—
784C2×C4#54014yes—
785C2×C4D4214yes—
786C2×C4#54614yes—
787C2×C4#54714yes—
788C2×C4#56214yes—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22C2×#53411yescharacteristic
812C22C2×#53711yescharacteristic
813C22#344911yescharacteristic
814C22#344911yescharacteristic
815C22C2×#54011yescharacteristic
816C22C2×D4211yescharacteristic
817C22C2×#54611yescharacteristic
818C22C2×#54711yescharacteristic
819C22#348912yes—
820C22#349512yes—
821C22#349712yes—
822C22#349911yescharacteristic
823C22#349911yescharacteristic
824C22#350712yes—
825C22C2×#56211yescharacteristic
826C22#353812yes—
827C22#353912yes—
828C22#354012yes—
829C22#355012yes—
830C22#355412yes—
831C22#355512yes—
832C22#356112yes—
833C22#356312yes—
834C4—42no—
835C4—44no—
836C4—44no—
837C4—44no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4#267118yes—
851C2—82no—
852C2—82no—
853C2#3738611yescharacteristic
854C2#3745511yescharacteristic
855C2#3768011yescharacteristic
856C2#3786811yescharacteristic
857C2#3935611yescharacteristic
858C2#3948411yescharacteristic
859C2#4266912yes—
860C2#4280312yes—
861C2#4532512yes—
862C2C2×#267111yescharacteristic
863C2#5307012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2499C2semidirect
4. C2×#2621C2semidirect
6. #16542C2semidirect
7. #16332C2semidirect
8. #15409C2semidirect
9. #15240C2semidirect
10. #15231C2semidirect
11. #15182C2semidirect
12. #15182C2semidirect
13. #15182C2semidirect
14. #15178C2semidirect
15. #14340C2semidirect
16. #14024C2semidirect
17. #13976C2semidirect
18. #13879C2semidirect
179. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25362
C2×#24992
C2×#24152
C2×#26212
#171182
#165422
#163322
#154092
#152402
#152312
#151822
#151782
#143402
#140242
#139762
#138792
#138392