Finite Group Databasebeta

← #423992

Subgroups — #423992

Order 512.

1412 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2551C211yesmaximal, characteristic
2C2×#2086C211yesmaximal, characteristic
3C2×#2057C211yesmaximal, characteristic
4C2×#2057C211yesmaximal, characteristic
5C2×#1988C211yesmaximal, characteristic
6#14046C211yesmaximal, characteristic
7#11384C211yesmaximal, characteristic
8#11328C211yesmaximal, characteristic
9#11324C211yesmaximal, characteristic
10#11292C211yesmaximal, characteristic
11#11207C211yesmaximal, characteristic
12#11202C211yesmaximal, characteristic
13#10907C211yesmaximal, characteristic
14#10884C211yesmaximal, characteristic
15#10884C211yesmaximal, characteristic
16C22×C4⋊Q8—21no—
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23#2551—24no—
24#2551—24no—
25C2×#395—21no—
26C2×#395—21no—
27C2×#389—21no—
28C2×#389—21no—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#2086—24no—
39#2057—24no—
40#2057—24no—
41#1988—24no—
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×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1442—21no—
61#1441—21no—
62#1436—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×Q8—21no—
66C23×Q8—21no—
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C4⋊Q8—28no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8—22no—
76C2×C4⋊Q8—22no—
77C2×C4⋊Q8—22no—
78C2×C4⋊Q8—22no—
79C2×C4⋊Q8—41no—
80C2×C4⋊Q8—41no—
81C2×C4⋊Q8—41no—
82C2×C4⋊Q8—41no—
83C2×C4⋊Q8—44no—
84C2×C4⋊Q8—44no—
85C2×C4⋊Q8D414yes—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4D411yescharacteristic
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C42—21no—
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—41no—
117C2×#107—41no—
118C2×#107—41no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—41no—
122#395—28no—
123#395—28no—
124#389—28no—
125#389—22no—
126#389—22no—
127#389—22no—
128#389—22no—
129#389—22no—
130#389—22no—
131#389—22no—
132#389—41no—
133#389—44no—
134#389D414yes—
135#389Q814yescomplemented
136#384—22no—
137#384—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—41no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—41no—
167#340D414yes—
168#340Q814yescomplemented
169#340Q814yescomplemented
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—41no—
175C22×Q8—24no—
176C22×Q8—24no—
177C22×Q8—42no—
178C22×Q8—42no—
179C22×Q8—42no—
180C22×Q8—42no—
181C22×Q8—42no—
182C22×Q8—42no—
183C22×Q8—42no—
184C22×Q8—42no—
185C22×Q8—81no—
186C22×Q8—81no—
187C22×Q8—81no—
188C22×Q8—81no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8C2×D412yes—
230C22×C8C2×Q812yes—
231C22×C8C2×Q812yes—
232C4⋊Q8—28no—
233C4⋊Q8—44no—
234C4⋊Q8—44no—
235C4⋊Q8—44no—
236C4⋊Q8—44no—
237C4⋊Q8—44no—
238C4⋊Q8—432no—
239C4⋊Q8—44no—
240C4⋊Q8—44no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4—81no—
308C2×C4⋊C4D814yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C4⋊C4C2×D412yes—
314C2×C4⋊C4C2×D412yes—
315C2×C4⋊C4C2×Q812yes—
316C2×C4⋊C4C2×Q812yes—
317C2×C4⋊C4C2×Q812yes—
318C2×C4⋊C4C2×Q812yes—
319C2×C4⋊C4C2×Q812yes—
320C2×C4⋊C4C2×Q812yes—
321C2×C4⋊C4#4112yes—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—24no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—81no—
342C2×C42C2×D412yes—
343C2×C42C2×D412yes—
344C2×C42C2×Q812yes—
345C2×C42#4112yes—
346#107—44no—
347#107—44no—
348#107—44no—
349C4⋊C8—44no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—22no—
354#95—22no—
355#95—24no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—81no—
363C24C22×D411yescharacteristic
364C2×Q8—48no—
365C2×Q8—48no—
366C2×Q8—48no—
367C2×Q8—48no—
368C2×Q8—84no—
369C2×Q8—84no—
370C2×Q8—84no—
371C2×Q8—84no—
372C2×Q8—84no—
373C2×Q8—84no—
374C2×Q8—84no—
375C2×Q8—84no—
376C2×Q8—84no—
377C2×Q8—84no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4#12012yes—
467C22×C4#12012yes—
468C22×C4C22⋊Q812yes—
469C22×C4C22⋊Q812yes—
470C22×C4C2×D812yes—
471C22×C4C2×D812yes—
472C22×C4C2×D812yes—
473C22×C4AGL(1,ℤ/8)12yes—
474C22×C4#13712yes—
475C22×C4#13712yes—
476C22×C4C22×D411yescharacteristic
477C22×C4C22×D411yescharacteristic
478C22×C4C22×D411yescharacteristic
479C22×C4C22×Q811yescharacteristic
480C22×C4C22×Q811yescharacteristic
481C22×C4C22×Q811yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C4H(5,𝔽2)11yescharacteristic
486C22×C42−1+411yescharacteristic
487C22×C42−1+411yescharacteristic
488C22×C42−1+411yescharacteristic
489C22×C42−1+411yescharacteristic
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—28no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—84no—
556C4⋊C4—84no—
557C4⋊C4—84no—
558C4⋊C4#12114yes—
559C4⋊C4C4⋊Q814yes—
560C4⋊C4C4⋊Q814yescomplemented
561C42—22no—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—48no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—84no—
575C23C2×#12011yescharacteristic
576C23C2×C22⋊Q811yescharacteristic
577C23#53611yescharacteristic
578C23D4211yescharacteristic
579C23#54611yescharacteristic
580C23D4×Q811yescharacteristic
581C23D4×Q811yescharacteristic
582C23C22×D811yescharacteristic
583C23C2×AGL(1,ℤ/8)11yescharacteristic
584C23C2×#13711yescharacteristic
585C23C2×#13711yescharacteristic
586C23#57611yescharacteristic
587C23#57711yescharacteristic
588C23#57811yescharacteristic
589C23#57811yescharacteristic
590Q8—816no—
591Q8—816no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4#44714yes—
689C2×C4#47414yes—
690C2×C4C2×#12111yescharacteristic
691C2×C4C2×C4⋊Q811yescharacteristic
692C2×C4C2×C4⋊Q811yescharacteristic
693C2×C4#53311yescharacteristic
694C2×C4#53411yescharacteristic
695C2×C4#53611yescharacteristic
696C2×C4#53611yescharacteristic
697C2×C4#54111yescharacteristic
698C2×C4#54211yescharacteristic
699C2×C4#54411yescharacteristic
700C2×C4#54411yescharacteristic
701C2×C4#54411yescharacteristic
702C2×C4D4211yescharacteristic
703C2×C4#54611yescharacteristic
704C2×C4#54711yescharacteristic
705C2×C4#54811yescharacteristic
706C2×C4#54811yescharacteristic
707C2×C4D4×Q811yescharacteristic
708C2×C4D4×Q811yescharacteristic
709C2×C4D4×Q811yescharacteristic
710C2×C4D4×Q811yescharacteristic
711C2×C4D4×Q811yescharacteristic
712C2×C4#55411yescharacteristic
713C2×C4#55711yescharacteristic
714C2×C4#55711yescharacteristic
715C2×C4Q8211yescharacteristic
716C2×C4#56311yescharacteristic
717C2×C4#56311yescharacteristic
718C8—42no—
719C8—42no—
720C8—42no—
721C8—81no—
722C22#240911yescharacteristic
723C22#241011yescharacteristic
724C22#243411yescharacteristic
725C22#244011yescharacteristic
726C22#245111yescharacteristic
727C22#267711yescharacteristic
728C22#271311yescharacteristic
729C22C2×#44711yescharacteristic
730C22#300411yescharacteristic
731C22#301111yescharacteristic
732C22#301211yescharacteristic
733C22C2×#47411yescharacteristic
734C22#307911yescharacteristic
735C22#308211yescharacteristic
736C22#308311yescharacteristic
737C22#322611yescharacteristic
738C22#323911yescharacteristic
739C22#324211yescharacteristic
740C22#324311yescharacteristic
741C22#326511yescharacteristic
742C22#327011yescharacteristic
743C22#327611yescharacteristic
744C22D4×D811yescharacteristic
745C22#329411yescharacteristic
746C22#331211yescharacteristic
747C22#331811yescharacteristic
748C22#332811yescharacteristic
749C22Q8×D811yescharacteristic
750C22Q8×D811yescharacteristic
751C22#338511yescharacteristic
752C22#338511yescharacteristic
753C22#338611yescharacteristic
754C22#338611yescharacteristic
755C22#338711yescharacteristic
756C22#338711yescharacteristic
757C4—24no—
758C4—24no—
759C4—42no—
760C4—44no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4—44no—
765C4—42no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—161no—
771C4#242911yescharacteristic
772C4#254611yescharacteristic
773C4#255011yescharacteristic
774C4#255111yescharacteristic
775C4#267411yescharacteristic
776C4#271311yescharacteristic
777C4#272911yescharacteristic
778C4#273411yescharacteristic
779C2#1531811yescharacteristic
780C2#2429811yescharacteristic
781C2#2431111yescharacteristic
782C2#2442411yescharacteristic
783C2#2445311yescharacteristic
784C2#2583811yescharacteristic
785C2#2584711yescharacteristic
786C2#2604011yescharacteristic
787C2#2605611yescharacteristic
788C2#2644011yescharacteristic
789C2#2645611yescharacteristic
790C2#3094611yescharacteristic
791C2#3096511yescharacteristic
792C2#3213011yescharacteristic
793C2#3214611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×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
135. #389Q8semidirect
168. #340Q8semidirect
169. #340Q8semidirect
560. C4⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25512
C2×#20862
C2×#20572
C2×#19882
#140462
#113842
#113282
#113242
#112922
#112072
#112022
#109072
#108842