Finite Group Databasebeta

← #369009

Subgroups — #369009

Order 512.

1432 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#446C211yesmaximal, characteristic
2C2×#2584C211yesmaximal, characteristic
3C2×#1992C211yesmaximal, characteristic
4C2×#1989C211yesmaximal, characteristic
5#13926C211yesmaximal, characteristic
6#11228C211yesmaximal, characteristic
7#11228C211yesmaximal, characteristic
8#11227C211yesmaximal, characteristic
9#11227C211yesmaximal, characteristic
10#10881C211yesmaximal, characteristic
11#10881C211yesmaximal, characteristic
12#10880C211yesmaximal, characteristic
13#10880C211yesmaximal, characteristic
14#10849C211yesmaximal, characteristic
15#10703C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C2×#446—24no—
19C2×#446—24no—
20C2×#446—24no—
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×#97C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2584—24no—
28#2584C418yescomplemented
29C2×#398—21no—
30C2×#395—21no—
31C2×#391—21no—
32C2×#389—21no—
33C2×#389—21no—
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#1992—24no—
42#1989—24no—
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×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#340C2211yescharacteristic
59#1441—21no—
60#1441—21no—
61C4⋊#95—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8D411yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—22no—
75C2×#125—22no—
76C2×#125C2×C414yes—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8C2×C414yes—
82C2×C4×Q8D414yes—
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×C42—21no—
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107#446—232no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—22no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8D414yes—
117C2×#97—22no—
118C2×#97—22no—
119C2×#97—22no—
120C2×#97—22no—
121C2×#97—22no—
122C2×#97D414yes—
123C2×C4×C8—22no—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126#398—28no—
127#395—28no—
128#391—44no—
129#389—28no—
130#389—28no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—22no—
135#389C2×C414yes—
136#389C2×C414yes—
137#389C2×C414yes—
138#389C2×C414yes—
139#384—22no—
140#384—22no—
141C4×C4⋊C4—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4C2×C414yes—
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—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340Q814yescomplemented
174#340Q814yescomplemented
175C22×Q8—22no—
176C22×Q8—22no—
177C22×Q8—22no—
178C22×Q8—22no—
179C22×Q8—41no—
180C22×Q8—41no—
181C22×Q8C22⋊C414yes—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2411yescharacteristic
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×C8—21no—
219C22×C8C2×D412yes—
220C22×C8C2×D412yes—
221C22×C8C2×D412yes—
222C22×C8C2×D412yes—
223C22×C8C2×Q812yes—
224C22×C8C2×Q812yes—
225#125—28no—
226#125—28no—
227#125—44no—
228#125—44no—
229C4×Q8—28no—
230C4×Q8—28no—
231C4×Q8—28no—
232C4×Q8—28no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
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—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
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—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
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—81no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4—81no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4C22⋊C414yes—
302C2×C4⋊C4C22⋊C414yes—
303C2×C4⋊C4C22⋊C414yes—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C2×Q812yes—
309C2×C4⋊C4C2×Q812yes—
310C2×C4⋊C4C2×Q812yes—
311C2×C4⋊C4C2×Q812yes—
312C2×C4⋊C4#4112yes—
313C2×C4⋊C4#4112yes—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—24no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—81no—
327C2×C42—81no—
328C2×C42C22×C412yes—
329C2×C42C22×C412yes—
330C2×C42C22×C412yes—
331C2×C42C2×D412yes—
332C2×C42C2×D412yes—
333C2×C42C2×D412yes—
334C2×C42C2×D412yes—
335C2×C42C2×D412yes—
336C2×C42#4112yes—
337C2×C42#4112yes—
338C4⋊C8—28no—
339C4⋊C8—28no—
340C4⋊C8—28no—
341#97—28no—
342#97—28no—
343C4×C8—28no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—81no—
355#95—81no—
356#95—81no—
357#95—81no—
358C24C22×D411yescharacteristic
359C2×Q8—28no—
360C2×Q8—28no—
361C2×Q8—44no—
362C2×Q8—44no—
363C2×Q8—44no—
364C2×Q8—44no—
365C2×Q8—44no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
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—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
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—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
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×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×C4C2×C22⋊C412yes—
453C22×C4C2×C22⋊C412yes—
454C22×C4C2×C22⋊C412yes—
455C22×C4C2×C22⋊C412yes—
456C22×C4C2×C22⋊C412yes—
457C22×C4C2×C22⋊C412yes—
458C22×C4#12112yes—
459C22×C4#12112yes—
460C22×C4#12112yes—
461C22×C4#12112yes—
462C22×C4AGL(1,ℤ/8)12yes—
463C22×C4#13712yes—
464C22×C4C23×C411yescharacteristic
465C22×C4C22×D411yescharacteristic
466C22×C4C22×D411yescharacteristic
467C22×C4C22×D411yescharacteristic
468C22×C4C22×Q811yescharacteristic
469C22×C4C22×Q811yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C42−1+411yescharacteristic
475C22×C42−1+411yescharacteristic
476C22×C42−1+411yescharacteristic
477C22×C42−1+411yescharacteristic
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—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
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×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8C4⋊Q814yes—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—28no—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—48no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—48no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—84no—
546C4⋊C4—84no—
547C4⋊C4C4×Q814yes—
548C4⋊C4C4×Q814yes—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—84no—
558C42—84no—
559C42C4×D414yes—
560C42C4×D414yes—
561C42#12014yes—
562C42#12314yes—
563C23C22×C22⋊C411yescharacteristic
564C23C2×#12111yescharacteristic
565C23C2×#12111yescharacteristic
566C23#54811yescharacteristic
567C23#54811yescharacteristic
568C23D4×Q811yescharacteristic
569C23D4×Q811yescharacteristic
570C23C2×AGL(1,ℤ/8)11yescharacteristic
571C23C2×#13711yescharacteristic
572C23#57511yescharacteristic
573C23#57511yescharacteristic
574C23#57611yescharacteristic
575C23#57711yescharacteristic
576C23#57711yescharacteristic
577C23#57811yescharacteristic
578Q8—416no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
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—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
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—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
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—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—81no—
674C2×C4#38614yes—
675C2×C4#38614yes—
676C2×C4#41714yes—
677C2×C4C2×C4×D411yescharacteristic
678C2×C4C2×C4×D411yescharacteristic
679C2×C4C2×C4×Q811yescharacteristic
680C2×C4C2×C4×Q811yescharacteristic
681C2×C4#51911yescharacteristic
682C2×C4#51911yescharacteristic
683C2×C4C2×#12011yescharacteristic
684C2×C4C2×#12311yescharacteristic
685C2×C4C2×C4⋊Q811yescharacteristic
686C2×C4#53211yescharacteristic
687C2×C4#53311yescharacteristic
688C2×C4#53311yescharacteristic
689C2×C4#53611yescharacteristic
690C2×C4#53611yescharacteristic
691C2×C4#54111yescharacteristic
692C2×C4#54111yescharacteristic
693C2×C4#54711yescharacteristic
694C2×C4#54711yescharacteristic
695C2×C4#54811yescharacteristic
696C2×C4#54811yescharacteristic
697C2×C4D4×Q811yescharacteristic
698C2×C4D4×Q811yescharacteristic
699C2×C4D4×Q811yescharacteristic
700C2×C4D4×Q811yescharacteristic
701C2×C4#55611yescharacteristic
702C2×C4#55611yescharacteristic
703C2×C4#55711yescharacteristic
704C2×C4#55711yescharacteristic
705C8—24no—
706C8—42no—
707C8—42no—
708C8—42no—
709C22C2×#38611yescharacteristic
710C22Q8×C22⋊C411yescharacteristic
711C22Q8×C22⋊C411yescharacteristic
712C22#242911yescharacteristic
713C22#242911yescharacteristic
714C22#254511yescharacteristic
715C22#254611yescharacteristic
716C22C2×#41711yescharacteristic
717C22#289611yescharacteristic
718C22#289711yescharacteristic
719C22#289811yescharacteristic
720C22#305511yescharacteristic
721C22#305511yescharacteristic
722C22#305611yescharacteristic
723C22#305611yescharacteristic
724C22#306011yescharacteristic
725C22#306111yescharacteristic
726C22#306211yescharacteristic
727C22#306311yescharacteristic
728C22#336611yescharacteristic
729C22#336811yescharacteristic
730C22#337011yescharacteristic
731C22#337111yescharacteristic
732C22#337211yescharacteristic
733C22#337411yescharacteristic
734C22#337611yescharacteristic
735C22#337711yescharacteristic
736C22#338411yescharacteristic
737C22#338511yescharacteristic
738C22#338611yescharacteristic
739C22#338711yescharacteristic
740C22#338811yescharacteristic
741C22#338811yescharacteristic
742C22#338911yescharacteristic
743C22#339011yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—44no—
751C4—44no—
752C4—82no—
753C4—82no—
754C4—82no—
755C4—82no—
756C4—161no—
757C4—161no—
758C4C4×C4⋊Q811yescharacteristic
759C4#232711yescharacteristic
760C4#236511yescharacteristic
761C4#236511yescharacteristic
762C4#243211yescharacteristic
763C4#243411yescharacteristic
764C4#244611yescharacteristic
765C4#244611yescharacteristic
766C2#1402411yescharacteristic
767C2#2097111yescharacteristic
768C2#2097611yescharacteristic
769C2#2252211yescharacteristic
770C2#2252411yescharacteristic
771C2#2252611yescharacteristic
772C2#2252711yescharacteristic
773C2#2548211yescharacteristic
774C2#2548411yescharacteristic
775C2#2548611yescharacteristic
776C2#2548811yescharacteristic
777C2#2865011yescharacteristic
778C2#2865211yescharacteristic
779C2#2868511yescharacteristic
780C2#2868611yescharacteristic
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
28. #2584C4semidirect
173. #340Q8semidirect
174. #340Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#4462
C2×#25842
C2×#19922
C2×#19892
#139262
#112282
#112272
#108812
#108802
#108492
#107032