Finite Group Databasebeta

← #363141

Subgroups — #363141

Order 512.

1410 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×#2365C211yesmaximal, characteristic
2C2×#1993C211yesmaximal, characteristic
3C2×#1987C211yesmaximal, characteristic
4C2×#1940C211yesmaximal, characteristic
5#13909C211yesmaximal, characteristic
6#11228C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11208C211yesmaximal, characteristic
9#11207C211yesmaximal, characteristic
10#10850C211yesmaximal, characteristic
11#10850C211yesmaximal, characteristic
12#10849C211yesmaximal, characteristic
13#10807C211yesmaximal, characteristic
14#10806C211yesmaximal, characteristic
15#10703C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4×Q8—21no—
18C22×C4⋊C8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#97C2211yescharacteristic
22#2365—24no—
23#2365C418yescomplemented
24C2×#391—21no—
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#387—21no—
28C2×#387—21no—
29C2×#384C2211yescharacteristic
30C2×#382C2211yescharacteristic
31C2×#382C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#1993—24no—
38#1987—24no—
39#1940—24no—
40C2×#340C2211yescharacteristic
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×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1441—21no—
59#1441—21no—
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C23×Q8—21no—
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8C2×C414yes—
73C2×C4⋊Q8D414yes—
74C2×C4⋊Q8Q814yes—
75C2×C4×Q8—28no—
76C2×C4×Q8—44no—
77C2×C4×Q8—44no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4D411yescharacteristic
84C22×C4⋊C4D411yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C42—21no—
94C22×C42—21no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—41no—
108C2×C4⋊C8—41no—
109C2×#97—22no—
110C2×#97—22no—
111C2×#97—22no—
112#391—28no—
113#389—22no—
114#389—22no—
115#389C2×C414yes—
116#389C2×C414yes—
117#387—28no—
118#387—28no—
119#384—22no—
120#384—41no—
121#382—22no—
122#382—22no—
123#382—22no—
124#382—41no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129C4×C4⋊C4—22no—
130C4×C4⋊C4C2×C414yes—
131C4×C4⋊C4C2×C414yes—
132C4×C4⋊C4C2×C414yes—
133C4×C4⋊C4C2×C414yes—
134C4×C4⋊C4D414yes—
135C2×#95—21no—
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×#95—21no—
149C2×#95D411yescharacteristic
150C2×#95D411yescharacteristic
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
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—41no—
165#340—41no—
166#340Q814yescomplemented
167#336—22no—
168#336—22no—
169C22×Q8—24no—
170C22×Q8—24no—
171C22×Q8—24no—
172C22×Q8—42no—
173C22×Q8—42no—
174C22×Q8—42no—
175C22×Q8—42no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2411yescharacteristic
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×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8C2×Q812yes—
218C22×C8#4112yes—
219C4⋊Q8—28no—
220C4⋊Q8—28no—
221C4⋊Q8—28no—
222C4⋊Q8C4⋊C4116yescomplemented
223C4×Q8—432no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
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—24no—
251C2×C4⋊C4—24no—
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—41no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—42no—
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—81no—
278C2×C4⋊C4—81no—
279C2×C4⋊C4C22⋊C414yes—
280C2×C4⋊C4C22⋊C414yes—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C22×C412yes—
283C2×C4⋊C4C22×C412yes—
284C2×C4⋊C4C22×C412yes—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×Q812yes—
288C2×C4⋊C4C2×Q812yes—
289C2×C4⋊C4C2×Q812yes—
290C2×C4⋊C4C2×Q812yes—
291C2×C4⋊C4#4112yes—
292C2×C4⋊C4#4112yes—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—24no—
302C2×C42—24no—
303C2×C42—24no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42—42no—
308C2×C42—42no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—81no—
312C2×C42—81no—
313C2×C42C22×C412yes—
314C2×C42C22×C412yes—
315C2×C42C22×C412yes—
316C2×C42C2×D412yes—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319C2×C42C2×D412yes—
320C2×C42C2×Q812yes—
321C2×C42#4112yes—
322C2×C42#4112yes—
323C4⋊C8—44no—
324C4⋊C8—44no—
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—42no—
338#95—42no—
339#95—81no—
340#95—81no—
341#95C22⋊C414yes—
342#95C22⋊C414yes—
343C24C22×D411yescharacteristic
344C2×Q8—216no—
345C2×Q8—48no—
346C2×Q8—48no—
347C2×Q8—48no—
348C2×Q8—48no—
349C2×Q8—48no—
350C2×Q8—48no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
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—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
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—21no—
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×C4C2×C22⋊C412yes—
438C22×C4C2×C22⋊C412yes—
439C22×C4C2×C22⋊C412yes—
440C22×C4C2×C22⋊C412yes—
441C22×C4C2×C22⋊C412yes—
442C22×C4C2×C22⋊C412yes—
443C22×C4#12112yes—
444C22×C4#12112yes—
445C22×C4C22⋊Q812yes—
446C22×C4C22⋊Q812yes—
447C22×C4AGL(1,ℤ/8)12yes—
448C22×C4AGL(1,ℤ/8)12yes—
449C22×C4C23×C411yescharacteristic
450C22×C4C22×D411yescharacteristic
451C22×C4C22×D411yescharacteristic
452C22×C4C22×Q811yescharacteristic
453C22×C4C22×Q811yescharacteristic
454C22×C4C2×#4111yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4H(5,𝔽2)11yescharacteristic
460C22×C42−1+411yescharacteristic
461C22×C42−1+411yescharacteristic
462C22×C42−1+411yescharacteristic
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×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
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—216no—
501C4⋊C4—28no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—44no—
509C4⋊C4—48no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—48no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—84no—
526C4⋊C4—84no—
527C4⋊C4C2×C4⋊C414yes—
528C4⋊C4C2×C4⋊C414yes—
529C4⋊C4C4×Q814yes—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—22no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—48no—
539C42—48no—
540C42—48no—
541C42—84no—
542C42C2×C4⋊C414yes—
543C42#11714yes—
544C42#12114yes—
545C42C22⋊Q814yes—
546C23C22×C22⋊C411yescharacteristic
547C23C2×#12111yescharacteristic
548C23C2×C22⋊Q811yescharacteristic
549C23#54611yescharacteristic
550C23#54711yescharacteristic
551C23#54811yescharacteristic
552C23D4×Q811yescharacteristic
553C23C2×AGL(1,ℤ/8)11yescharacteristic
554C23C2×AGL(1,ℤ/8)11yescharacteristic
555C23#57511yescharacteristic
556C23#57511yescharacteristic
557C23#57711yescharacteristic
558C23#57711yescharacteristic
559C23#57811yescharacteristic
560C23#57811yescharacteristic
561Q8—432no—
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—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
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—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
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—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#38014yes—
658C2×C4#38014yes—
659C2×C4#41814yes—
660C2×C4C22×C4⋊C411yescharacteristic
661C2×C4C2×#11711yescharacteristic
662C2×C4C2×C4×Q811yescharacteristic
663C2×C4C4×#4111yescharacteristic
664C2×C4#51911yescharacteristic
665C2×C4#52011yescharacteristic
666C2×C4C2×#12111yescharacteristic
667C2×C4C2×C22⋊Q811yescharacteristic
668C2×C4#52911yescharacteristic
669C2×C4#52911yescharacteristic
670C2×C4#53311yescharacteristic
671C2×C4#53311yescharacteristic
672C2×C4#54111yescharacteristic
673C2×C4#54111yescharacteristic
674C2×C4#54211yescharacteristic
675C2×C4#54211yescharacteristic
676C2×C4#54611yescharacteristic
677C2×C4#54711yescharacteristic
678C2×C4#54811yescharacteristic
679C2×C4#54811yescharacteristic
680C2×C4#54811yescharacteristic
681C2×C4D4×Q811yescharacteristic
682C2×C4D4×Q811yescharacteristic
683C2×C4#55011yescharacteristic
684C2×C4#55711yescharacteristic
685C2×C4#55711yescharacteristic
686C2×C4#55711yescharacteristic
687C2×C4Q8211yescharacteristic
688C8—42no—
689C8—42no—
690C8—81no—
691C8—81no—
692C22C2×#38011yescharacteristic
693C22#233911yescharacteristic
694C22Q8×C22⋊C411yescharacteristic
695C22#242611yescharacteristic
696C22#242911yescharacteristic
697C22#245111yescharacteristic
698C22#245311yescharacteristic
699C22C2×#41811yescharacteristic
700C22#289611yescharacteristic
701C22#289811yescharacteristic
702C22#289811yescharacteristic
703C22#303611yescharacteristic
704C22#303611yescharacteristic
705C22#304311yescharacteristic
706C22#304411yescharacteristic
707C22#307711yescharacteristic
708C22#307711yescharacteristic
709C22#308211yescharacteristic
710C22#308211yescharacteristic
711C22#330611yescharacteristic
712C22#330811yescharacteristic
713C22#331111yescharacteristic
714C22#331311yescharacteristic
715C22#334311yescharacteristic
716C22#334511yescharacteristic
717C22#334911yescharacteristic
718C22#335011yescharacteristic
719C22#336711yescharacteristic
720C22#337111yescharacteristic
721C22#337311yescharacteristic
722C22#337711yescharacteristic
723C22#338411yescharacteristic
724C22#338611yescharacteristic
725C22#338811yescharacteristic
726C22#339011yescharacteristic
727C4—24no—
728C4—24no—
729C4—24no—
730C4—44no—
731C4—44no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—44no—
736C4—82no—
737C4—82no—
738C4—82no—
739C4—161no—
740C4—161no—
741C4#229511yescharacteristic
742C4#232011yescharacteristic
743C4Q8×C4⋊C411yescharacteristic
744C4#235111yescharacteristic
745C4#242611yescharacteristic
746C4#242911yescharacteristic
747C4#245111yescharacteristic
748C4#245311yescharacteristic
749C2#1393511yescharacteristic
750C2#2064611yescharacteristic
751C2#2065111yescharacteristic
752C2#2249411yescharacteristic
753C2#2249511yescharacteristic
754C2#2252311yescharacteristic
755C2#2252711yescharacteristic
756C2#2528411yescharacteristic
757C2#2528611yescharacteristic
758C2#2546111yescharacteristic
759C2#2546311yescharacteristic
760C2#2645211yescharacteristic
761C2#2645511yescharacteristic
762C2#2651811yescharacteristic
763C2#2652111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×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
23. #2365C4semidirect
166. #340Q8semidirect
222. C4⋊Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23652
C2×#19932
C2×#19872
C2×#19402
#139092
#112282
#112272
#112082
#112072
#108502
#108492
#108072
#108062
#107032