Finite Group Databasebeta

← #356865

Subgroups — #356865

Order 512.

1380 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2370C211yesmaximal, characteristic
2C2×#1991C211yesmaximal, characteristic
3C2×#1989C211yesmaximal, characteristic
4C2×C8×C4⋊C4C211yesmaximal, characteristic
5#13804C211yesmaximal, characteristic
6#10885C211yesmaximal, characteristic
7#10884C211yesmaximal, characteristic
8#10880C211yesmaximal, characteristic
9#10880C211yesmaximal, characteristic
10#10850C211yesmaximal, characteristic
11#10807C211yesmaximal, characteristic
12#10806C211yesmaximal, characteristic
13C4×#340C211yesmaximal, characteristic
14C4×#340C211yesmaximal, characteristic
15C4×#340C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4⋊C8C2211yescharacteristic
18C22×C4×C8C2211yescharacteristic
19C22×C4×C8C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2370—24no—
22#2370C418yescomplemented
23C2×#389—21no—
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#387—21no—
27C2×#387—21no—
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#1991C418yescomplemented
38#1989C418yescomplemented
39C8×C4⋊C4—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×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×#125—22no—
69C2×#125—22no—
70C2×#125—22no—
71C2×#125C2×C414yes—
72C2×#125C2×C414yes—
73C2×#125C2×C414yes—
74C22×C4⋊C4—21no—
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×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—41no—
107C2×C4×C8—41no—
108C2×C4×C8C2×C414yes—
109#389—28no—
110#389—22no—
111#389—22no—
112#389C2×C414yes—
113#389C2×C414yes—
114#387—28no—
115#387—28no—
116#382—22no—
117#382C2×C414yes—
118C4×C4⋊C4—22no—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—28no—
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#340Q814yes—
165#336—22no—
166#336—22no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2411yescharacteristic
182C22×C8—21no—
183C22×C8—21no—
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×C8C22×C412yes—
205C22×C8C22×C412yes—
206C22×C8C22×C412yes—
207C22×C8C22×C412yes—
208C22×C8C2×Q812yes—
209C22×C8#4112yes—
210#125—28no—
211#125—28no—
212#125—28no—
213#125C42116yescomplemented
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
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—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—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—81no—
261C2×C4⋊C4—81no—
262C2×C4⋊C4C22⋊C414yes—
263C2×C4⋊C4C22⋊C414yes—
264C2×C4⋊C4C22×C412yes—
265C2×C4⋊C4C22×C412yes—
266C2×C4⋊C4C22×C412yes—
267C2×C4⋊C4C22×C412yes—
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⋊C4C2×Q812yes—
277C2×C4⋊C4C2×Q812yes—
278C2×C4⋊C4#4112yes—
279C2×C4⋊C4#4112yes—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—24no—
289C2×C42—24no—
290C2×C42—24no—
291C2×C42—24no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42—42no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—81no—
299C2×C42—81no—
300C2×C42—81no—
301C2×C42—81no—
302C2×C42—81no—
303C2×C42—81no—
304C2×C42—81no—
305C2×C42—81no—
306C2×C42C22×C412yes—
307C2×C42C22×C412yes—
308C2×C42C22×C412yes—
309C2×C42C22×C412yes—
310C2×C42C22×C412yes—
311C2×C42C2×D412yes—
312C2×C42C2×D412yes—
313C2×C42C2×D412yes—
314C2×C42#4112yes—
315C2×C42#4112yes—
316C4⋊C8—28no—
317C4×C8—28no—
318C4×C8—44no—
319C4×C8—44no—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—81no—
333#95—81no—
334#95C22⋊C414yes—
335#95C22⋊C414yes—
336C24C22×D411yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
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—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
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×C4C2×C22⋊C412yes—
422C22×C4C2×C22⋊C412yes—
423C22×C4C2×C22⋊C412yes—
424C22×C4C2×C22⋊C412yes—
425C22×C4C2×C22⋊C412yes—
426C22×C4C2×C22⋊C412yes—
427C22×C4C4×D412yes—
428C22×C4C4×D412yes—
429C22×C4C4×D412yes—
430C22×C4C4×D412yes—
431C22×C4#13512yes—
432C22×C4#13512yes—
433C22×C4#13512yes—
434C22×C4#13512yes—
435C22×C4C23×C411yescharacteristic
436C22×C4C23×C411yescharacteristic
437C22×C4C23×C411yescharacteristic
438C22×C4C22×D411yescharacteristic
439C22×C4C22×Q811yescharacteristic
440C22×C4C2×#4111yescharacteristic
441C22×C4C2×#4111yescharacteristic
442C22×C4C2×#4111yescharacteristic
443C22×C4C2×#4111yescharacteristic
444C22×C4C2×#4111yescharacteristic
445C22×C4H(5,𝔽2)11yescharacteristic
446C22×C42−1+411yescharacteristic
447C22×C42−1+411yescharacteristic
448C22×C42−1+411yescharacteristic
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
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×C8C4×Q814yes—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—216no—
490C4⋊C4—216no—
491C4⋊C4—28no—
492C4⋊C4—28no—
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—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—48no—
510C4⋊C4—84no—
511C4⋊C4C2×C4214yes—
512C4⋊C4C2×C4214yes—
513C4⋊C4C4×Q814yes—
514C4⋊C4C4×Q814yes—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—48no—
524C42—84no—
525C42—84no—
526C42—84no—
527C42—84no—
528C42—84no—
529C42C2×C4214yes—
530C42#11714yes—
531C42C4×D414yes—
532C42C4×D414yes—
533C23C22×C22⋊C411yescharacteristic
534C23C2×C4×D411yescharacteristic
535C23C2×C4×D411yescharacteristic
536C23#54611yescharacteristic
537C23#54711yescharacteristic
538C23#54811yescharacteristic
539C23D4×Q811yescharacteristic
540C23C2×#13511yescharacteristic
541C23C2×#13511yescharacteristic
542C23C2×#13511yescharacteristic
543C23C2×#13511yescharacteristic
544C23#57611yescharacteristic
545C23#57711yescharacteristic
546C23#57711yescharacteristic
547C23#57811yescharacteristic
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
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—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
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—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—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
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—81no—
627C2×C4—81no—
628C2×C4—81no—
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×C4C4×C22⋊C414yes—
643C2×C4C4×C22⋊C414yes—
644C2×C4#41614yes—
645C2×C4#41614yes—
646C2×C4C22×C4211yescharacteristic
647C2×C4C2×#11711yescharacteristic
648C2×C4C2×C4×D411yescharacteristic
649C2×C4C2×C4×D411yescharacteristic
650C2×C4C2×C4×Q811yescharacteristic
651C2×C4C2×C4×Q811yescharacteristic
652C2×C4C2×C4×Q811yescharacteristic
653C2×C4C4×#4111yescharacteristic
654C2×C4C4×#4111yescharacteristic
655C2×C4C4×#4111yescharacteristic
656C2×C4#51911yescharacteristic
657C2×C4#51911yescharacteristic
658C2×C4#51911yescharacteristic
659C2×C4#52011yescharacteristic
660C2×C4#52011yescharacteristic
661C2×C4#52011yescharacteristic
662C2×C4#54611yescharacteristic
663C2×C4#54711yescharacteristic
664C2×C4#54811yescharacteristic
665C2×C4D4×Q811yescharacteristic
666C2×C4#55211yescharacteristic
667C2×C4#55211yescharacteristic
668C2×C4#55411yescharacteristic
669C2×C4#55611yescharacteristic
670C2×C4#55611yescharacteristic
671C2×C4#55611yescharacteristic
672C2×C4#55711yescharacteristic
673C2×C4#55911yescharacteristic
674C8—24no—
675C8—42no—
676C8—42no—
677C8—42no—
678C22C2×C4×C22⋊C411yescharacteristic
679C22#233911yescharacteristic
680C22Q8×C22⋊C411yescharacteristic
681C22#236011yescharacteristic
682C22#236211yescharacteristic
683C22#236511yescharacteristic
684C22#236711yescharacteristic
685C22C2×#41611yescharacteristic
686C22C2×#41611yescharacteristic
687C22#289711yescharacteristic
688C22#289811yescharacteristic
689C22C4×#13511yescharacteristic
690C22C4×#13511yescharacteristic
691C22C4×#13511yescharacteristic
692C22C4×#13511yescharacteristic
693C22#294611yescharacteristic
694C22#294711yescharacteristic
695C22#295111yescharacteristic
696C22#295211yescharacteristic
697C22#329611yescharacteristic
698C22#329711yescharacteristic
699C22#330011yescharacteristic
700C22#330111yescharacteristic
701C22#333611yescharacteristic
702C22#333711yescharacteristic
703C22#333711yescharacteristic
704C22#333911yescharacteristic
705C22#336011yescharacteristic
706C22#336111yescharacteristic
707C22#336411yescharacteristic
708C22#336511yescharacteristic
709C22#338011yescharacteristic
710C22#338111yescharacteristic
711C22#338111yescharacteristic
712C22#338311yescharacteristic
713C4—24no—
714C4—24no—
715C4—24no—
716C4—24no—
717C4—44no—
718C4—44no—
719C4—44no—
720C4—42no—
721C4—42no—
722C4—44no—
723C4—82no—
724C4—82no—
725C4—82no—
726C4—82no—
727C4C42×Q811yescharacteristic
728C4#227611yescharacteristic
729C4#235511yescharacteristic
730C4#235611yescharacteristic
731C4#236011yescharacteristic
732C4#236211yescharacteristic
733C4#236511yescharacteristic
734C4#236711yescharacteristic
735C2#1381711yescharacteristic
736C2C4×#41611yescharacteristic
737C2#2041511yescharacteristic
738C2#2248611yescharacteristic
739C2#2248811yescharacteristic
740C2#2251911yescharacteristic
741C2#2252111yescharacteristic
742C2#2296611yescharacteristic
743C2#2296711yescharacteristic
744C2#2306411yescharacteristic
745C2#2306511yescharacteristic
746C2#2315911yescharacteristic
747C2#2316011yescharacteristic
748C2#2321811yescharacteristic
749C2#2321911yescharacteristic
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. #2370C4semidirect
37. #1991C4semidirect
38. #1989C4semidirect
213. #125C42semidirect

Maximal subgroups

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

subgroupindex
C2×#23702
C2×#19912
C2×#19892
C2×C8×C4⋊C42
#138042
#108852
#108842
#108802
#108502
#108072
#108062
C4×#3402