Finite Group Databasebeta

← #424028

Subgroups — #424028

Order 512.

1256 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2584C211yesmaximal, characteristic
2C2×#2086C211yesmaximal, characteristic
3C2×#2059C211yesmaximal, characteristic
4C2×#1984C211yesmaximal, characteristic
5C2×#1941C211yesmaximal, characteristic
6#15158C211yesmaximal, characteristic
7#11385C211yesmaximal, characteristic
8#11328C211yesmaximal, characteristic
9#11327C211yesmaximal, characteristic
10#11293C211yesmaximal, characteristic
11#11228C211yesmaximal, characteristic
12#11220C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic
14#10885C211yesmaximal, characteristic
15#10880C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23#2584—24no—
24#2584—24no—
25C2×#398—21no—
26C2×#395—21no—
27C2×#395—21no—
28C2×#389—21no—
29C2×#389—21no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#2086—24no—
39#2059—24no—
40#1984—24no—
41#1941—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
59#1441—21no—
60#1441—21no—
61#1441—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C23×Q8D411yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×#125—22no—
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—41no—
75C2×#125—41no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4D411yescharacteristic
93C22×C4⋊C4D411yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×#107—22no—
107C2×#107—22no—
108C2×#107—41no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—22no—
113C2×#106—41no—
114C2×#106Q814yescomplemented
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—41no—
118C2×C4×C8—22no—
119C2×C4×C8—22no—
120C2×C4×C8—41no—
121#398—28no—
122#395—28no—
123#395—44no—
124#389—28no—
125#389—28no—
126#389—22no—
127#389—22no—
128#389—22no—
129#389—22no—
130#389—22no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—22no—
135#389—22no—
136#389—41no—
137#389—41no—
138#389D414yes—
139#389D414yes—
140C4×C4⋊C4—22no—
141C4×C4⋊C4—22no—
142C2×#95—21no—
143C2×#95—21no—
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×#95—21no—
156#340—22no—
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—41no—
166#340—41no—
167#340Q814yescomplemented
168#340Q814yescomplemented
169#336—22no—
170#336—22no—
171#336—22no—
172#336D414yes—
173C22×Q8—22no—
174C22×Q8—22no—
175C22×Q8—22no—
176C22×Q8—22no—
177C22×Q8—22no—
178C22×Q8—41no—
179C22×Q8—41no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2411yescharacteristic
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×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×C8C2×D412yes—
219C22×C8C2×D412yes—
220C22×C8C2×Q812yes—
221C22×C8C2×Q812yes—
222C22×C8C2×Q812yes—
223#125—44no—
224#125—44no—
225#125—44no—
226#125—44no—
227C4×Q8—44no—
228C4×Q8—44no—
229C4×Q8—44no—
230C4×Q8—44no—
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—21no—
252C2×C4⋊C4—21no—
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—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
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—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4C2×D412yes—
305C2×C4⋊C4C2×D412yes—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×Q812yes—
309C2×C4⋊C4C2×Q812yes—
310C2×C4⋊C4C2×Q812yes—
311C2×C4⋊C4C2×Q812yes—
312C2×C4⋊C4C2×Q812yes—
313C2×C4⋊C4C2×Q812yes—
314C2×C4⋊C4#4112yes—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—24no—
330C2×C42—81no—
331C2×C42—81no—
332C2×C42C2×D412yes—
333C2×C42C2×D412yes—
334C2×C42C2×D412yes—
335C2×C42#4112yes—
336#107—44no—
337#106—28no—
338#106—44no—
339C4⋊C8—44no—
340C4×C8—44no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—81no—
353#95—81no—
354#95—81no—
355C24C22×D411yescharacteristic
356C2×Q8—28no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—44no—
360C2×Q8—44no—
361C2×Q8—44no—
362C2×Q8—44no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
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×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#12012yes—
455C22×C4#12012yes—
456C22×C4#12112yes—
457C22×C4#12112yes—
458C22×C4#13512yes—
459C22×C4#13512yes—
460C22×C4AGL(1,ℤ/8)12yes—
461C22×C4C22×D411yescharacteristic
462C22×C4C22×D411yescharacteristic
463C22×C4C22×D411yescharacteristic
464C22×C4C22×Q811yescharacteristic
465C22×C4C22×Q811yescharacteristic
466C22×C4C22×Q811yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4H(5,𝔽2)11yescharacteristic
470C22×C4H(5,𝔽2)11yescharacteristic
471C22×C42−1+411yescharacteristic
472C22×C42−1+411yescharacteristic
473C22×C42−1+411yescharacteristic
474C22×C42−1+411yescharacteristic
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8C4⋊Q814yes—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—44no—
520C4⋊C4—44no—
521C4⋊C4—44no—
522C4⋊C4—48no—
523C4⋊C4—48no—
524C4⋊C4—48no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—48no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—84no—
541C4⋊C4—84no—
542C4⋊C4—84no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4C22⋊Q814yes—
546C4⋊C4C4⋊Q814yes—
547C42—22no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—84no—
560C23C2×#12011yescharacteristic
561C23C2×#12111yescharacteristic
562C23#53411yescharacteristic
563C23#54811yescharacteristic
564C23D4×Q811yescharacteristic
565C23D4×Q811yescharacteristic
566C23D4×Q811yescharacteristic
567C23C2×#13511yescharacteristic
568C23C2×#13511yescharacteristic
569C23C2×AGL(1,ℤ/8)11yescharacteristic
570C23#57511yescharacteristic
571C23#57711yescharacteristic
572C23#57711yescharacteristic
573C23#57711yescharacteristic
574C23#57811yescharacteristic
575Q8—416no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
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—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
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#44914yes—
674C2×C4C2×C22⋊Q811yescharacteristic
675C2×C4C2×C4⋊Q811yescharacteristic
676C2×C4C2×C4⋊Q811yescharacteristic
677C2×C4#53311yescharacteristic
678C2×C4#53611yescharacteristic
679C2×C4#53611yescharacteristic
680C2×C4#53611yescharacteristic
681C2×C4#54111yescharacteristic
682C2×C4#54211yescharacteristic
683C2×C4#54411yescharacteristic
684C2×C4#54411yescharacteristic
685C2×C4#54411yescharacteristic
686C2×C4D4211yescharacteristic
687C2×C4D4211yescharacteristic
688C2×C4#54611yescharacteristic
689C2×C4#54611yescharacteristic
690C2×C4#54711yescharacteristic
691C2×C4#54811yescharacteristic
692C2×C4D4×Q811yescharacteristic
693C2×C4D4×Q811yescharacteristic
694C2×C4D4×Q811yescharacteristic
695C2×C4D4×Q811yescharacteristic
696C2×C4#55411yescharacteristic
697C2×C4#55711yescharacteristic
698C2×C4#55711yescharacteristic
699C2×C4Q8211yescharacteristic
700C2×C4#56311yescharacteristic
701C2×C4#56311yescharacteristic
702C8—24no—
703C8—42no—
704C8—42no—
705C8—81no—
706C22#240911yescharacteristic
707C22#241011yescharacteristic
708C22#242911yescharacteristic
709C22#243411yescharacteristic
710C22#254611yescharacteristic
711C22#272911yescharacteristic
712C22#273411yescharacteristic
713C22C2×#44911yescharacteristic
714C22#300211yescharacteristic
715C22#300911yescharacteristic
716C22#301311yescharacteristic
717C22#305011yescharacteristic
718C22#305511yescharacteristic
719C22#306011yescharacteristic
720C22#306311yescharacteristic
721C22#318811yescharacteristic
722C22#319111yescharacteristic
723C22#320111yescharacteristic
724C22#320411yescharacteristic
725C22#336011yescharacteristic
726C22#336411yescharacteristic
727C22#336811yescharacteristic
728C22#337611yescharacteristic
729C22#338111yescharacteristic
730C22#338111yescharacteristic
731C22#338111yescharacteristic
732C22#338111yescharacteristic
733C22#338111yescharacteristic
734C22#338311yescharacteristic
735C22#338411yescharacteristic
736C22#338411yescharacteristic
737C22#338611yescharacteristic
738C22#338811yescharacteristic
739C22#338811yescharacteristic
740C22#339011yescharacteristic
741C4—24no—
742C4—44no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—44no—
748C4—82no—
749C4—82no—
750C4—82no—
751C4—81no—
752C4—82no—
753C4—82no—
754C4—161no—
755C4#244011yescharacteristic
756C4#245111yescharacteristic
757C4#255011yescharacteristic
758C4#255111yescharacteristic
759C4#267411yescharacteristic
760C4#267711yescharacteristic
761C4#271311yescharacteristic
762C4#271311yescharacteristic
763C2#1531811yescharacteristic
764C2#2432811yescharacteristic
765C2#2433711yescharacteristic
766C2#2438211yescharacteristic
767C2#2439511yescharacteristic
768C2#2547411yescharacteristic
769C2#2548611yescharacteristic
770C2#2583511yescharacteristic
771C2#2584211yescharacteristic
772C2#2867811yescharacteristic
773C2#2868511yescharacteristic
774C2#3257111yescharacteristic
775C2#3257211yescharacteristic
776C2#3268511yescharacteristic
777C2#3268811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
114. C2×#106Q8semidirect
167. #340Q8semidirect
168. #340Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25842
C2×#20862
C2×#20592
C2×#19842
C2×#19412
#151582
#113852
#113282
#113272
#112932
#112282
#112202
#109082
#108852
#108802