Finite Group Databasebeta

← #356882

Subgroups — #356882

Order 512.

1402 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2369C211yesmaximal, characteristic
2C2×#1993C211yesmaximal, characteristic
3C2×#1988C211yesmaximal, characteristic
4C2×#1771C211yesmaximal, characteristic
5#13804C211yesmaximal, characteristic
6#10885C211yesmaximal, characteristic
7#10884C211yesmaximal, characteristic
8#10881C211yesmaximal, characteristic
9#10880C211yesmaximal, characteristic
10#10850C211yesmaximal, characteristic
11#10807C211yesmaximal, characteristic
12#10806C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic
14#10703C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×#97C2211yescharacteristic
19C22×#97C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2369—24no—
22#2369C418yescomplemented
23C2×#391—21no—
24C2×#391—21no—
25C2×#389—21no—
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#382C2211yescharacteristic
29C2×C4×C4⋊C4—21no—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37#1993C418yescomplemented
38#1988C418yescomplemented
39#1771—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#1436—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63C4×#95—21no—
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⋊Q8C2×C414yes—
74C2×C4⋊Q8C2×C414yes—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4D411yescharacteristic
79C22×C4⋊C4D411yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42—21no—
92C22×C42—21no—
93C22×C42—21no—
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×C4⋊C8—22no—
98C2×C4⋊C8—22no—
99C2×C4⋊C8C2×C414yes—
100C2×#97—22no—
101C2×#97—22no—
102C2×#97—22no—
103C2×#97—22no—
104C2×#97—41no—
105C2×#97C2×C414yes—
106C2×C4×C8—22no—
107C2×C4×C8—22no—
108C2×C4×C8—41no—
109#391—28no—
110#391—28no—
111#389—28no—
112#389—22no—
113#389—22no—
114#389C2×C414yes—
115#389C2×C414yes—
116#382—22no—
117#382C2×C414yes—
118C4×C4⋊C4—28no—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—41no—
126C4×C4⋊C4—41no—
127C4×C4⋊C4C2×C414yes—
128C4×C4⋊C4C2×C414yes—
129C4×C4⋊C4C2×C414yes—
130C4×C4⋊C4C2×C414yes—
131C4×C4⋊C4C2×C414yes—
132C4×C4⋊C4D414yes—
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—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—41no—
155#340—41no—
156#340C2×C414yes—
157#340C2×C414yes—
158#340C2×C414yes—
159#340C2×C414yes—
160#340C2×C414yes—
161#340C2×C414yes—
162#340C2×C414yes—
163#340C2×C414yes—
164#340Q814yescomplemented
165#336—22no—
166#336—22no—
167C22×Q8—24no—
168C22×Q8—24no—
169C22×Q8—24no—
170C22×Q8—81no—
171C22×Q8—81no—
172C22×Q8—81no—
173C22×Q8—81no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2411yescharacteristic
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×C8—21no—
211C22×C8C22×C412yes—
212C22×C8C22×C412yes—
213C22×C8C22×C412yes—
214C22×C8C22×C412yes—
215C22×C8C2×Q812yes—
216C22×C8#4112yes—
217C4⋊Q8—28no—
218C4⋊Q8—28no—
219C4⋊Q8—28no—
220C4⋊Q8C42116yescomplemented
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
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—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—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—41no—
262C2×C4⋊C4—81no—
263C2×C4⋊C4—81no—
264C2×C4⋊C4—81no—
265C2×C4⋊C4—81no—
266C2×C4⋊C4C22⋊C414yes—
267C2×C4⋊C4C22⋊C414yes—
268C2×C4⋊C4C22×C412yes—
269C2×C4⋊C4C22×C412yes—
270C2×C4⋊C4C22×C412yes—
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⋊C4C2×Q812yes—
281C2×C4⋊C4C2×Q812yes—
282C2×C4⋊C4#4112yes—
283C2×C4⋊C4#4112yes—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—24no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—81no—
303C2×C42—81no—
304C2×C42—81no—
305C2×C42—81no—
306C2×C42—81no—
307C2×C42—81no—
308C2×C42—81no—
309C2×C42—81no—
310C2×C42C22×C412yes—
311C2×C42C22×C412yes—
312C2×C42C22×C412yes—
313C2×C42C22×C412yes—
314C2×C42C22×C412yes—
315C2×C42C2×D412yes—
316C2×C42C2×D412yes—
317C2×C42C2×D412yes—
318C2×C42#4112yes—
319C2×C42#4112yes—
320C4⋊C8—28no—
321#97—28no—
322#97—44no—
323C4×C8—44no—
324#95—24no—
325#95—24no—
326#95—24no—
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—81no—
337#95—81no—
338#95C22⋊C414yes—
339#95C22⋊C414yes—
340C24C22×D411yescharacteristic
341C2×Q8—216no—
342C2×Q8—84no—
343C2×Q8—84no—
344C2×Q8—84no—
345C2×Q8—84no—
346C2×Q8—84no—
347C2×Q8—84no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
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—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
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—22no—
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×C4C2×C22⋊C412yes—
435C22×C4C2×C22⋊C412yes—
436C22×C4C2×C22⋊C412yes—
437C22×C4C2×C22⋊C412yes—
438C22×C4C2×C22⋊C412yes—
439C22×C4C2×C22⋊C412yes—
440C22×C4C4×D412yes—
441C22×C4C4×D412yes—
442C22×C4C4×D412yes—
443C22×C4C4×D412yes—
444C22×C4#13712yes—
445C22×C4#13712yes—
446C22×C4C23×C411yescharacteristic
447C22×C4C23×C411yescharacteristic
448C22×C4C23×C411yescharacteristic
449C22×C4C22×D411yescharacteristic
450C22×C4C22×Q811yescharacteristic
451C22×C4C2×#4111yescharacteristic
452C22×C4C2×#4111yescharacteristic
453C22×C4C2×#4111yescharacteristic
454C22×C4C2×#4111yescharacteristic
455C22×C4C2×#4111yescharacteristic
456C22×C4H(5,𝔽2)11yescharacteristic
457C22×C42−1+411yescharacteristic
458C22×C42−1+411yescharacteristic
459C22×C42−1+411yescharacteristic
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—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
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×C8C4×Q814yes—
488C4⋊C4—22no—
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—216no—
501C4⋊C4—28no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—44no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—84no—
520C4⋊C4—84no—
521C4⋊C4C2×C4214yes—
522C4⋊C4C2×C4214yes—
523C4⋊C4C4×Q814yes—
524C4⋊C4C4×Q814yes—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—48no—
534C42—84no—
535C42—84no—
536C42—84no—
537C42—84no—
538C42—84no—
539C42C2×C4214yes—
540C42#11714yes—
541C42C4×D414yes—
542C42C4×D414yes—
543C23C22×C22⋊C411yescharacteristic
544C23C2×C4×D411yescharacteristic
545C23C2×C4×D411yescharacteristic
546C23#54611yescharacteristic
547C23#54711yescharacteristic
548C23#54811yescharacteristic
549C23D4×Q811yescharacteristic
550C23C2×#13711yescharacteristic
551C23C2×#13711yescharacteristic
552C23#57511yescharacteristic
553C23#57511yescharacteristic
554C23#57611yescharacteristic
555C23#57611yescharacteristic
556C23#57711yescharacteristic
557C23#57711yescharacteristic
558Q8—816no—
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—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
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—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
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—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
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×C4C4×C22⋊C414yes—
655C2×C4C4×C22⋊C414yes—
656C2×C4#41914yes—
657C2×C4C22×C4211yescharacteristic
658C2×C4C2×#11711yescharacteristic
659C2×C4C2×C4×D411yescharacteristic
660C2×C4C2×C4×D411yescharacteristic
661C2×C4C2×C4×Q811yescharacteristic
662C2×C4C2×C4×Q811yescharacteristic
663C2×C4C2×C4×Q811yescharacteristic
664C2×C4C4×#4111yescharacteristic
665C2×C4C4×#4111yescharacteristic
666C2×C4C4×#4111yescharacteristic
667C2×C4#51911yescharacteristic
668C2×C4#51911yescharacteristic
669C2×C4#51911yescharacteristic
670C2×C4#52011yescharacteristic
671C2×C4#52011yescharacteristic
672C2×C4#52011yescharacteristic
673C2×C4#54611yescharacteristic
674C2×C4#54711yescharacteristic
675C2×C4#54811yescharacteristic
676C2×C4D4×Q811yescharacteristic
677C2×C4#55211yescharacteristic
678C2×C4#55211yescharacteristic
679C2×C4#55411yescharacteristic
680C2×C4#55611yescharacteristic
681C2×C4#55611yescharacteristic
682C2×C4#55611yescharacteristic
683C2×C4#55711yescharacteristic
684C2×C4#55911yescharacteristic
685C8—24no—
686C8—42no—
687C8—42no—
688C8—42no—
689C22C2×C4×C22⋊C411yescharacteristic
690C22#233911yescharacteristic
691C22Q8×C22⋊C411yescharacteristic
692C22#236011yescharacteristic
693C22#236211yescharacteristic
694C22#236511yescharacteristic
695C22#236711yescharacteristic
696C22C2×#41911yescharacteristic
697C22#289611yescharacteristic
698C22#289711yescharacteristic
699C22#289711yescharacteristic
700C22C4×#13711yescharacteristic
701C22C4×#13711yescharacteristic
702C22C4×#13711yescharacteristic
703C22C4×#13711yescharacteristic
704C22#294611yescharacteristic
705C22#294611yescharacteristic
706C22#294811yescharacteristic
707C22#294911yescharacteristic
708C22#331411yescharacteristic
709C22#331611yescharacteristic
710C22#331911yescharacteristic
711C22#332111yescharacteristic
712C22#334411yescharacteristic
713C22#334611yescharacteristic
714C22#334711yescharacteristic
715C22#334811yescharacteristic
716C22#336911yescharacteristic
717C22#337011yescharacteristic
718C22#337511yescharacteristic
719C22#337611yescharacteristic
720C22#338511yescharacteristic
721C22#338711yescharacteristic
722C22#338811yescharacteristic
723C22#338911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—44no—
728C4—44no—
729C4—44no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—44no—
734C4—82no—
735C4—82no—
736C4—82no—
737C4—82no—
738C4C42×Q811yescharacteristic
739C4#227611yescharacteristic
740C4#235511yescharacteristic
741C4#235611yescharacteristic
742C4#236011yescharacteristic
743C4#236211yescharacteristic
744C4#236511yescharacteristic
745C4#236711yescharacteristic
746C2#1381711yescharacteristic
747C2C4×#41911yescharacteristic
748C2#2041611yescharacteristic
749C2#2249211yescharacteristic
750C2#2249711yescharacteristic
751C2#2252511yescharacteristic
752C2#2252611yescharacteristic
753C2#2297911yescharacteristic
754C2#2298111yescharacteristic
755C2#2307711yescharacteristic
756C2#2307911yescharacteristic
757C2#2316711yescharacteristic
758C2#2316911yescharacteristic
759C2#2323011yescharacteristic
760C2#2323211yescharacteristic
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. #2369C4semidirect
37. #1993C4semidirect
38. #1988C4semidirect
164. #340Q8semidirect
220. C4⋊Q8C42semidirect

Maximal subgroups

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

subgroupindex
C2×#23692
C2×#19932
C2×#19882
C2×#17712
#138042
#108852
#108842
#108812
#108802
#108502
#108072
#108062
#107032
C4×#3402