Finite Group Databasebeta

← #387117

Subgroups — #387117

Order 512.

1200 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2584C211yesmaximal, characteristic
2C2×#1985C211yesmaximal, characteristic
3#13926C211yesmaximal, characteristic
4#11385C211yesmaximal, characteristic
5#11385C211yesmaximal, characteristic
6#11228C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11207C211yesmaximal, characteristic
9#11207C211yesmaximal, characteristic
10#10885C211yesmaximal, characteristic
11#10884C211yesmaximal, characteristic
12#10881C211yesmaximal, characteristic
13#10881C211yesmaximal, characteristic
14#10807C211yesmaximal, characteristic
15#10806C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#97C2211yescharacteristic
20#2584—24no—
21#2584C418yescomplemented
22C2×#398—21no—
23C2×#395—21no—
24C2×#391—21no—
25C2×#389—21no—
26C2×#389—21no—
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34#1985—24no—
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1441—21no—
56#1441—21no—
57C4⋊#95—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8D411yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×#125—22no—
68C2×#125—41no—
69C2×#125—41no—
70C2×#125—41no—
71C2×#125—41no—
72C2×#125C2×C414yes—
73C2×C4×Q8—41no—
74C2×C4×Q8—41no—
75C2×C4×Q8—41no—
76C2×C4×Q8—41no—
77C2×C4×Q8C2×C414yes—
78C2×C4×Q8D414yes—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4D411yescharacteristic
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C42—21no—
99C22×C42—21no—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C2×C4⋊C8—22no—
104C2×C4⋊C8—41no—
105C2×C4⋊C8—41no—
106C2×#97—22no—
107C2×#97—41no—
108C2×#97—41no—
109#398—28no—
110#395—28no—
111#391—44no—
112#389—28no—
113#389—28no—
114#389—22no—
115#389—22no—
116#389—22no—
117#389—22no—
118#389C2×C414yes—
119#389C2×C414yes—
120#389C2×C414yes—
121#389C2×C414yes—
122#384—41no—
123#384—41no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—41no—
126C4×C4⋊C4—41no—
127C4×C4⋊C4C2×C414yes—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142#340—22no—
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—41no—
149#340—41no—
150#340—41no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340Q814yescomplemented
157#340Q814yescomplemented
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162C22×Q8—22no—
163C22×Q8—22no—
164C22×Q8—41no—
165C22×Q8—41no—
166C22×Q8—41no—
167C22×Q8—41no—
168C22×Q8C22⋊C414yes—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2411yescharacteristic
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×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8C2×Q812yes—
211C22×C8C2×Q812yes—
212#125—44no—
213#125—44no—
214#125—44no—
215#125—44no—
216C4×Q8—44no—
217C4×Q8—44no—
218C4×Q8—44no—
219C4×Q8—44no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
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—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
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—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—41no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4C22⋊C414yes—
289C2×C4⋊C4C22⋊C414yes—
290C2×C4⋊C4C22⋊C414yes—
291C2×C4⋊C4C22×C412yes—
292C2×C4⋊C4C22×C412yes—
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C412yes—
295C2×C4⋊C4C2×Q812yes—
296C2×C4⋊C4C2×Q812yes—
297C2×C4⋊C4C2×Q812yes—
298C2×C4⋊C4C2×Q812yes—
299C2×C4⋊C4#4112yes—
300C2×C4⋊C4#4112yes—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—24no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—81no—
318C2×C42—81no—
319C2×C42C22×C412yes—
320C2×C42C22×C412yes—
321C2×C42C22×C412yes—
322C2×C42C2×D412yes—
323C2×C42C2×D412yes—
324C2×C42C2×D412yes—
325C4⋊C8—44no—
326#97—44no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—81no—
338#95—81no—
339#95—81no—
340#95—81no—
341C24C22×D411yescharacteristic
342C2×Q8—28no—
343C2×Q8—44no—
344C2×Q8—44no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—44no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
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—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—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
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×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×C4C2×C22⋊C412yes—
440C22×C4C2×C22⋊C412yes—
441C22×C4C2×C22⋊C412yes—
442C22×C4C2×C22⋊C412yes—
443C22×C4C2×C22⋊C412yes—
444C22×C4C2×C22⋊C412yes—
445C22×C4AGL(1,ℤ/8)12yes—
446C22×C4#13712yes—
447C22×C4C23×C411yescharacteristic
448C22×C4C22×D411yescharacteristic
449C22×C4C22×Q811yescharacteristic
450C22×C4C22×Q811yescharacteristic
451C22×C4C2×#4111yescharacteristic
452C22×C4C2×#4111yescharacteristic
453C22×C4H(5,𝔽2)11yescharacteristic
454C22×C4H(5,𝔽2)11yescharacteristic
455C22×C4H(5,𝔽2)11yescharacteristic
456C22×C4H(5,𝔽2)11yescharacteristic
457C22×C42−1+411yescharacteristic
458C22×C42−1+411yescharacteristic
459C22×C42−1+411yescharacteristic
460C22×C42−1+411yescharacteristic
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—41no—
468C2×C8—41no—
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×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—44no—
504C4⋊C4—44no—
505C4⋊C4—44no—
506C4⋊C4—48no—
507C4⋊C4—48no—
508C4⋊C4—48no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—48no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—84no—
527C4⋊C4—84no—
528C4⋊C4—84no—
529C4⋊C4—84no—
530C4⋊C4C4×Q814yes—
531C4⋊C4C4×Q814yes—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42—84no—
545C42—84no—
546C23C22×C22⋊C411yescharacteristic
547C23#53411yescharacteristic
548C23#53411yescharacteristic
549C23#54811yescharacteristic
550C23#54811yescharacteristic
551C23D4×Q811yescharacteristic
552C23D4×Q811yescharacteristic
553C23C2×AGL(1,ℤ/8)11yescharacteristic
554C23C2×#13711yescharacteristic
555C23#57511yescharacteristic
556C23#57511yescharacteristic
557C23#57611yescharacteristic
558C23#57711yescharacteristic
559C23#57711yescharacteristic
560C23#57811yescharacteristic
561Q8—416no—
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—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
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—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
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×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#41714yes—
660C2×C4C2×C4×Q811yescharacteristic
661C2×C4C2×C4×Q811yescharacteristic
662C2×C4#51811yescharacteristic
663C2×C4#51811yescharacteristic
664C2×C4#51911yescharacteristic
665C2×C4#51911yescharacteristic
666C2×C4#53411yescharacteristic
667C2×C4#53411yescharacteristic
668C2×C4#54211yescharacteristic
669C2×C4#54211yescharacteristic
670C2×C4#54211yescharacteristic
671C2×C4#54211yescharacteristic
672C2×C4#54411yescharacteristic
673C2×C4#54411yescharacteristic
674C2×C4#54411yescharacteristic
675C2×C4#54411yescharacteristic
676C2×C4#54811yescharacteristic
677C2×C4#54811yescharacteristic
678C2×C4D4×Q811yescharacteristic
679C2×C4D4×Q811yescharacteristic
680C2×C4#55411yescharacteristic
681C2×C4#55411yescharacteristic
682C2×C4#55511yescharacteristic
683C2×C4Q8211yescharacteristic
684C2×C4#56311yescharacteristic
685C2×C4#56311yescharacteristic
686C2×C4#56311yescharacteristic
687C2×C4#56311yescharacteristic
688C8—42no—
689C8—42no—
690C8—81no—
691C8—81no—
692C22#230811yescharacteristic
693C22Q8×C22⋊C411yescharacteristic
694C22Q8×C22⋊C411yescharacteristic
695C22#272911yescharacteristic
696C22#272911yescharacteristic
697C22#273111yescharacteristic
698C22#273411yescharacteristic
699C22C2×#41711yescharacteristic
700C22#289611yescharacteristic
701C22#289711yescharacteristic
702C22#289811yescharacteristic
703C22#319411yescharacteristic
704C22#319411yescharacteristic
705C22#319611yescharacteristic
706C22#319611yescharacteristic
707C22#319811yescharacteristic
708C22#320111yescharacteristic
709C22#320311yescharacteristic
710C22#320411yescharacteristic
711C22#336611yescharacteristic
712C22#336811yescharacteristic
713C22#337011yescharacteristic
714C22#337111yescharacteristic
715C22#337211yescharacteristic
716C22#337411yescharacteristic
717C22#337611yescharacteristic
718C22#337711yescharacteristic
719C22#338411yescharacteristic
720C22#338511yescharacteristic
721C22#338611yescharacteristic
722C22#338711yescharacteristic
723C22#338811yescharacteristic
724C22#338811yescharacteristic
725C22#338911yescharacteristic
726C22#339011yescharacteristic
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—44no—
734C4—44no—
735C4—82no—
736C4—82no—
737C4—82no—
738C4—82no—
739C4—161no—
740C4—161no—
741C4#233111yescharacteristic
742C4#233111yescharacteristic
743C4#236911yescharacteristic
744C4#238111yescharacteristic
745C4#272911yescharacteristic
746C4#272911yescharacteristic
747C4#273111yescharacteristic
748C4#273411yescharacteristic
749C2#1445011yescharacteristic
750C2#2176911yescharacteristic
751C2#2177211yescharacteristic
752C2#2252211yescharacteristic
753C2#2252411yescharacteristic
754C2#2252611yescharacteristic
755C2#2252711yescharacteristic
756C2#3258111yescharacteristic
757C2#3258311yescharacteristic
758C2#3258511yescharacteristic
759C2#3258711yescharacteristic
760C2#3264011yescharacteristic
761C2#3264111yescharacteristic
762C2#3268911yescharacteristic
763C2#3269011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×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
21. #2584C4semidirect
156. #340Q8semidirect
157. #340Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25842
C2×#19852
#139262
#113852
#112282
#112272
#112072
#108852
#108842
#108812
#108072
#108062