Finite Group Databasebeta

← #857508

Subgroups — #857508

Order 512.

1934 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16966C212yesmaximal, complemented
2#16429C212yesmaximal
3#16221C212yesmaximal, complemented
4#16165C212yesmaximal, complemented
5#15557C212yesmaximal
6#15544C212yesmaximal
7#15233C211yesmaximal, characteristic
8#15232C211yesmaximal, characteristic, complemented
9#15221C211yesmaximal, characteristic, complemented
10#15221C211yesmaximal, characteristic, complemented
11#15200C211yesmaximal, characteristic, complemented
12#15150C211yesmaximal, characteristic
13#14697C211yesmaximal, characteristic
14#14682C211yesmaximal, characteristic
15#14541C212yesmaximal
16#14480C212yesmaximal, complemented
17#14029C211yesmaximal, characteristic, complemented
18#13994C211yesmaximal, characteristic
19#13993C211yesmaximal, characteristic
20#13982C211yesmaximal, characteristic, complemented
21#13936C211yesmaximal, characteristic, complemented
22#13911C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic
24C23×C42C2211yescharacteristic
25C2×#397C2212yes—
26C2×#397C2212yes—
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#388C2212yes—
32C2×#387C2212yes—
33C2×#385C2211yescharacteristic
34C2×#385C2211yescharacteristic
35C2×#385C2212yes—
36C2×#384C2211yescharacteristic
37C2×#382C2211yescharacteristic
38C2×#382C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50#1445C2212yes—
51#1445C2212yes—
52#1445C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1444C2212yes—
59#1444C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1443C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1441C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1439C2212yes—
84#1437C2212yes—
85#1436C2211yescharacteristic
86#1436C2212yes—
87#1436C2212yes—
88#1436C2211yescharacteristic
89#1436C2212yes—
90#1436C2211yescharacteristic
91#1436C2212yes—
92#1436C2212yes—
93#1436C2211yescharacteristic
94C4⋊#95C2212yes—
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2212yes—
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2211yescharacteristic
106C4⋊#95C2211yescharacteristic
107C4⋊#95C2211yescharacteristic
108C4⋊#95C2211yescharacteristic
109C4⋊#95C2211yescharacteristic
110#1434C2212yes—
111#1434C2212yes—
112#1434C2212yes—
113#1434C2212yes—
114#1434C2212yes—
115#1434C2212yes—
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2211yescharacteristic
123C24×C4C2311yescharacteristic
124C24×C4C2311yescharacteristic
125C24×C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C42—24no—
153C22×C42—42no—
154C22×C42—42no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165#397—28no—
166#397—44no—
167#389—24no—
168#389—42no—
169#389—42no—
170#389—42no—
171#388—44no—
172#387—28no—
173#385—24no—
174#385—24no—
175#385—44no—
176#384—24no—
177#382—42no—
178#382—42no—
179#382—42no—
180#380—24no—
181#380—24no—
182#380—24no—
183#380—42no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—42no—
187C4×C4⋊C4—42no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—42no—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2311yescharacteristic
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2311yescharacteristic
250C25C2411yescharacteristic
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4—41no—
268C23×C4—41no—
269C23×C4—41no—
270C23×C4—41no—
271C23×C4#4114yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4#4114yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—416no—
393C2×C42—41no—
394C2×C42—41no—
395C2×C42—41no—
396C2×C42—41no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42#4114yes—
402C2×C42#4114yes—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—22no—
422#95—24no—
423#95—41no—
424#95—41no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—41no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—41no—
441#95—41no—
442#95—41no—
443#95—41no—
444#95—42no—
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#4114yes—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24C2×#4112yes—
476C24C2×#4112yes—
477C24H(5,𝔽2)12yes—
478C24C2511yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2×#4112yes—
649C22×C4H(5,𝔽2)12yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C42−1+412yes—
652C22×C42−1+412yes—
653C22×C42−1+412yes—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—48no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—84no—
668C4⋊C4—84no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C22⋊C4—28no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—84no—
679C22⋊C4—84no—
680C42—28no—
681C42—28no—
682C42—44no—
683C42—44no—
684C42—44no—
685C42—44no—
686C42—44no—
687C42—44no—
688C42—84no—
689C42—84no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23#55914yes—
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4111yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×2−1+411yescharacteristic
734C23C2×2−1+411yescharacteristic
735C23C2×2−1+411yescharacteristic
736C23#58511yescharacteristic
737C23#58511yescharacteristic
738C23#58511yescharacteristic
739C23#58511yescharacteristic
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—416no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—42no—
889C2×C4#52914yes—
890C2×C4#53814yes—
891C2×C4#53914yes—
892C2×C4#54214yes—
893C2×C4#55214yes—
894C2×C4#55214yes—
895C2×C4#55314yes—
896C2×C4#56314yes—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C2×#52911yescharacteristic
913C22C2×#53811yescharacteristic
914C22C2×#53911yescharacteristic
915C22C2×#54211yescharacteristic
916C22#346111yescharacteristic
917C22C2×#55211yescharacteristic
918C22C2×#55211yescharacteristic
919C22C2×#55311yescharacteristic
920C22#347511yescharacteristic
921C22#347511yescharacteristic
922C22C2×#55911yescharacteristic
923C22#348011yescharacteristic
924C22#349411yescharacteristic
925C22#349411yescharacteristic
926C22#349511yescharacteristic
927C22#350611yescharacteristic
928C22#350611yescharacteristic
929C22#350711yescharacteristic
930C22#350911yescharacteristic
931C22#351011yescharacteristic
932C22#351011yescharacteristic
933C22#351511yescharacteristic
934C22#351511yescharacteristic
935C22#351511yescharacteristic
936C22#351911yescharacteristic
937C22#352011yescharacteristic
938C22C2×#56311yescharacteristic
939C22#353911yescharacteristic
940C22#354011yescharacteristic
941C22#354111yescharacteristic
942C22#354211yescharacteristic
943C22#354411yescharacteristic
944C22#355911yescharacteristic
945C22#356511yescharacteristic
946C22#356511yescharacteristic
947C4—24no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—82no—
957C4—82no—
958C4—81no—
959C4—82no—
960C4—82no—
961C4—81no—
962C4—82no—
963C4—81no—
964C4—82no—
965C4—82no—
966C4—81no—
967C4—82no—
968C4#277018yes—
969C2—44no—
970C2#3520611yescharacteristic
971C2#3617111yescharacteristic
972C2#3658711yescharacteristic
973C2#3736311yescharacteristic
974C2#3793911yescharacteristic
975C2#3919911yescharacteristic
976C2#3982211yescharacteristic
977C2#3990911yescharacteristic
978C2#3991111yescharacteristic
979C2#4003411yescharacteristic
980C2#4564811yescharacteristic
981C2#4570911yescharacteristic
982C2C2×#277011yescharacteristic
983C2#5933011yescharacteristic
984C2#5933211yescharacteristic
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
1. #16966C2semidirect
3. #16221C2semidirect
4. #16165C2semidirect
8. #15232C2semidirect
9. #15221C2semidirect
10. #15221C2semidirect
11. #15200C2semidirect
16. #14480C2semidirect
17. #14029C2semidirect
20. #13982C2semidirect
21. #13936C2semidirect
22. #13911C2semidirect

Maximal subgroups

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

subgroupindex
#169662
#164292
#162212
#161652
#155572
#155442
#152332
#152322
#152212
#152002
#151502
#146972
#146822
#145412
#144802
#140292
#139942
#139932
#139822
#139362
#139112
C4×#3852