Finite Group Databasebeta

← #356883

Subgroups — #356883

Order 512.

1392 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2370C211yesmaximal, characteristic
2C2×#1992C211yesmaximal, characteristic
3C2×#1989C211yesmaximal, characteristic
4C2×#1771C211yesmaximal, characteristic
5C4⋊C42C211yesmaximal, characteristic
6#10885C211yesmaximal, characteristic
7#10885C211yesmaximal, characteristic
8#10881C211yesmaximal, characteristic
9#10880C211yesmaximal, characteristic
10#10849C211yesmaximal, characteristic
11#10806C211yesmaximal, characteristic
12#10806C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic
14#10703C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×#97C2211yescharacteristic
19C22×#97C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2370—24no—
22#2370C418yescomplemented
23C2×#389—21no—
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#387—21no—
27C2×#387—21no—
28C2×#384C2211yescharacteristic
29C2×C4×C4⋊C4—21no—
30C2×C4×C4⋊C4—21no—
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#1992C418yescomplemented
39#1989C418yescomplemented
40#1771—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1436—21no—
60#1436—21no—
61C4⋊#95—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×#125—22no—
69C2×#125—22no—
70C2×#125—22no—
71C2×#125C2×C414yes—
72C2×#125C2×C414yes—
73C2×#125C2×C414yes—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4D411yescharacteristic
81C22×C4⋊C4D411yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C42—21no—
91C22×C42—21no—
92C22×C42—21no—
93C22×C42—21no—
94C22×C42—21no—
95C22×C42—21no—
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×C4⋊C8—22no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8C2×C414yes—
102C2×#97—22no—
103C2×#97—22no—
104C2×#97—22no—
105C2×#97—22no—
106C2×#97—41no—
107C2×#97C2×C414yes—
108C2×C4×C8—22no—
109C2×C4×C8—22no—
110C2×C4×C8—41no—
111#389—28no—
112#389—22no—
113#389—22no—
114#389C2×C414yes—
115#389C2×C414yes—
116#387—28no—
117#387—28no—
118#384—22no—
119#384C2×C414yes—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—28no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—41no—
128C4×C4⋊C4—41no—
129C4×C4⋊C4—44no—
130C4×C4⋊C4C2×C414yes—
131C4×C4⋊C4C2×C414yes—
132C4×C4⋊C4C2×C414yes—
133C4×C4⋊C4C2×C414yes—
134C4×C4⋊C4C2×C414yes—
135C4×C4⋊C4D414yes—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—41no—
156#340—41no—
157#340C2×C414yes—
158#340C2×C414yes—
159#340C2×C414yes—
160#340C2×C414yes—
161#340C2×C414yes—
162#340C2×C414yes—
163#340C2×C414yes—
164#340C2×C414yes—
165#340Q814yes—
166#336—22no—
167#336—22no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2411yescharacteristic
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8C22×C412yes—
206C22×C8C22×C412yes—
207C22×C8C22×C412yes—
208C22×C8C22×C412yes—
209C22×C8C2×Q812yes—
210C22×C8#4112yes—
211#125—28no—
212#125—28no—
213#125—28no—
214#125C42116yescomplemented
215C2×C4⋊C4—24no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—41no—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—81no—
266C2×C4⋊C4—81no—
267C2×C4⋊C4—81no—
268C2×C4⋊C4—81no—
269C2×C4⋊C4C22⋊C414yes—
270C2×C4⋊C4C22⋊C414yes—
271C2×C4⋊C4C22×C412yes—
272C2×C4⋊C4C22×C412yes—
273C2×C4⋊C4C22×C412yes—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C22×C412yes—
279C2×C4⋊C4C22×C412yes—
280C2×C4⋊C4C22×C412yes—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C22×C412yes—
283C2×C4⋊C4C2×Q812yes—
284C2×C4⋊C4C2×Q812yes—
285C2×C4⋊C4#4112yes—
286C2×C4⋊C4#4112yes—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—24no—
296C2×C42—24no—
297C2×C42—24no—
298C2×C42—24no—
299C2×C42—42no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42—42no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—81no—
308C2×C42—81no—
309C2×C42—81no—
310C2×C42—81no—
311C2×C42—81no—
312C2×C42—81no—
313C2×C42C22×C412yes—
314C2×C42C22×C412yes—
315C2×C42C22×C412yes—
316C2×C42C22×C412yes—
317C2×C42C22×C412yes—
318C2×C42C2×D412yes—
319C2×C42C2×D412yes—
320C2×C42C2×D412yes—
321C2×C42#4112yes—
322C2×C42#4112yes—
323C4⋊C8—28no—
324#97—28no—
325#97—44no—
326C4×C8—44no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—81no—
338#95—81no—
339#95C22⋊C414yes—
340#95C22⋊C414yes—
341C24C22×D411yescharacteristic
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C2×C22⋊C412yes—
429C22×C4C2×C22⋊C412yes—
430C22×C4C2×C22⋊C412yes—
431C22×C4C2×C22⋊C412yes—
432C22×C4C2×C22⋊C412yes—
433C22×C4C2×C22⋊C412yes—
434C22×C4C4×D412yes—
435C22×C4C4×D412yes—
436C22×C4C4×D412yes—
437C22×C4C4×D412yes—
438C22×C4AGL(1,ℤ/8)12yes—
439C22×C4#13712yes—
440C22×C4C23×C411yescharacteristic
441C22×C4C23×C411yescharacteristic
442C22×C4C23×C411yescharacteristic
443C22×C4C22×D411yescharacteristic
444C22×C4C22×Q811yescharacteristic
445C22×C4C2×#4111yescharacteristic
446C22×C4C2×#4111yescharacteristic
447C22×C4C2×#4111yescharacteristic
448C22×C4C2×#4111yescharacteristic
449C22×C4C2×#4111yescharacteristic
450C22×C4H(5,𝔽2)11yescharacteristic
451C22×C42−1+411yescharacteristic
452C22×C42−1+411yescharacteristic
453C22×C42−1+411yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8C4×Q814yes—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—216no—
495C4⋊C4—216no—
496C4⋊C4—28no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—44no—
506C4⋊C4—48no—
507C4⋊C4—48no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—84no—
517C4⋊C4—84no—
518C4⋊C4C2×C4214yes—
519C4⋊C4C2×C4214yes—
520C4⋊C4C4×Q814yes—
521C4⋊C4C4×Q814yes—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—48no—
531C42—48no—
532C42—84no—
533C42—84no—
534C42—84no—
535C42—84no—
536C42C2×C4214yes—
537C42#11714yes—
538C42C4×D414yes—
539C42C4×D414yes—
540C23C22×C22⋊C411yescharacteristic
541C23C2×C4×D411yescharacteristic
542C23C2×C4×D411yescharacteristic
543C23#54611yescharacteristic
544C23#54711yescharacteristic
545C23#54811yescharacteristic
546C23D4×Q811yescharacteristic
547C23C2×AGL(1,ℤ/8)11yescharacteristic
548C23C2×#13711yescharacteristic
549C23#57511yescharacteristic
550C23#57511yescharacteristic
551C23#57611yescharacteristic
552C23#57711yescharacteristic
553C23#57711yescharacteristic
554C23#57811yescharacteristic
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4C4×C22⋊C414yes—
651C2×C4C4×C22⋊C414yes—
652C2×C4#41714yes—
653C2×C4C22×C4211yescharacteristic
654C2×C4C2×#11711yescharacteristic
655C2×C4C2×C4×D411yescharacteristic
656C2×C4C2×C4×D411yescharacteristic
657C2×C4C2×C4×Q811yescharacteristic
658C2×C4C2×C4×Q811yescharacteristic
659C2×C4C2×C4×Q811yescharacteristic
660C2×C4C4×#4111yescharacteristic
661C2×C4C4×#4111yescharacteristic
662C2×C4C4×#4111yescharacteristic
663C2×C4#51911yescharacteristic
664C2×C4#51911yescharacteristic
665C2×C4#51911yescharacteristic
666C2×C4#52011yescharacteristic
667C2×C4#52011yescharacteristic
668C2×C4#52011yescharacteristic
669C2×C4#54611yescharacteristic
670C2×C4#54711yescharacteristic
671C2×C4#54811yescharacteristic
672C2×C4D4×Q811yescharacteristic
673C2×C4#55211yescharacteristic
674C2×C4#55211yescharacteristic
675C2×C4#55411yescharacteristic
676C2×C4#55611yescharacteristic
677C2×C4#55611yescharacteristic
678C2×C4#55611yescharacteristic
679C2×C4#55711yescharacteristic
680C2×C4#55911yescharacteristic
681C8—24no—
682C8—42no—
683C8—42no—
684C8—42no—
685C22C2×C4×C22⋊C411yescharacteristic
686C22#233911yescharacteristic
687C22Q8×C22⋊C411yescharacteristic
688C22#236011yescharacteristic
689C22#236211yescharacteristic
690C22#236511yescharacteristic
691C22#236711yescharacteristic
692C22C2×#41711yescharacteristic
693C22#289611yescharacteristic
694C22#289711yescharacteristic
695C22#289811yescharacteristic
696C22C4×AGL(1,ℤ/8)11yescharacteristic
697C22C4×AGL(1,ℤ/8)11yescharacteristic
698C22C4×#13711yescharacteristic
699C22C4×#13711yescharacteristic
700C22#294611yescharacteristic
701C22#294711yescharacteristic
702C22#295111yescharacteristic
703C22#295211yescharacteristic
704C22#330711yescharacteristic
705C22#330911yescharacteristic
706C22#331011yescharacteristic
707C22#331211yescharacteristic
708C22#334311yescharacteristic
709C22#334411yescharacteristic
710C22#334711yescharacteristic
711C22#335011yescharacteristic
712C22#336611yescharacteristic
713C22#337111yescharacteristic
714C22#337211yescharacteristic
715C22#337711yescharacteristic
716C22#338411yescharacteristic
717C22#338511yescharacteristic
718C22#338811yescharacteristic
719C22#339011yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—44no—
724C4—44no—
725C4—44no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—44no—
730C4—82no—
731C4—82no—
732C4—82no—
733C4—82no—
734C4C42×Q811yescharacteristic
735C4#227611yescharacteristic
736C4#235511yescharacteristic
737C4#235611yescharacteristic
738C4#236011yescharacteristic
739C4#236211yescharacteristic
740C4#236511yescharacteristic
741C4#236711yescharacteristic
742C2#1381711yescharacteristic
743C2C4×#41711yescharacteristic
744C2#2041511yescharacteristic
745C2#2249111yescharacteristic
746C2#2249811yescharacteristic
747C2#2252211yescharacteristic
748C2#2252711yescharacteristic
749C2#2297811yescharacteristic
750C2#2298011yescharacteristic
751C2#2307611yescharacteristic
752C2#2307811yescharacteristic
753C2#2316611yescharacteristic
754C2#2316911yescharacteristic
755C2#2323111yescharacteristic
756C2#2323311yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
22. #2370C4semidirect
38. #1992C4semidirect
39. #1989C4semidirect
214. #125C42semidirect

Maximal subgroups

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

subgroupindex
C2×#23702
C2×#19922
C2×#19892
C2×#17712
C4⋊C422
#108852
#108812
#108802
#108492
#108062
#107032
C4×#3402