Finite Group Databasebeta

← #375892

Subgroups — #375892

Order 512.

1388 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#125C211yesmaximal, characteristic
2C2×#2026C211yesmaximal, characteristic
3C2×#1865C211yesmaximal, characteristic
4C2×#1863C211yesmaximal, characteristic
5C4×#391C211yesmaximal, characteristic
6#11385C211yesmaximal, characteristic
7#11325C211yesmaximal, characteristic
8#11052C211yesmaximal, characteristic
9#10932C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic
11#10908C211yesmaximal, characteristic
12#10907C211yesmaximal, characteristic
13#10885C211yesmaximal, characteristic
14#10884C211yesmaximal, characteristic
15#10795C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C4×#125—24no—
25C4×#125—24no—
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#387—21no—
31C2×#387—21no—
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4—21no—
34C2×C4×C4⋊C4—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C43C2211yescharacteristic
39#2026C418yescomplemented
40#1865—24no—
41#1863—24no—
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1436—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4×#95—21no—
63C4×#95—21no—
64C23×Q8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×#125—22no—
70C2×#125—22no—
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125C2×C414yes—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
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×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42D411yescharacteristic
100C22×C42D411yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×#107—22no—
105C2×#107—22no—
106C2×#107—41no—
107C2×#106—22no—
108C2×#106—22no—
109C2×#106—41no—
110C2×#103—22no—
111C2×#103—22no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—41no—
119C2×#103—41no—
120C2×#103C2×C414yes—
121C2×#103C2×C414yes—
122#391—22no—
123#391—22no—
124#391C2×C414yes—
125#391Q814yes—
126#389—22no—
127#389—22no—
128#389D414yes—
129#389D414yes—
130#387—28no—
131#387—28no—
132#382—22no—
133#382—22no—
134C4×C4⋊C4—28no—
135C4×C4⋊C4—28no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—22no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
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—
157C43—22no—
158C43—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—41no—
164#340—41no—
165#340—41no—
166#340—41no—
167#340C2×C414yes—
168#340C2×C414yes—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336C2×C414yes—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8C22×C412yes—
187C22×Q8C2×Q812yes—
188C22×Q8#4112yes—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
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×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8C22×C412yes—
231C22×C8C22×C412yes—
232#125—28no—
233#125—28no—
234#125—28no—
235#125—28no—
236C4×Q8—44no—
237C4×Q8—44no—
238C4×Q8—44no—
239C4×Q8—44no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
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—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
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—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4C22×C412yes—
287C2×C4⋊C4C22×C412yes—
288C2×C4⋊C4C22×C412yes—
289C2×C4⋊C4C2×D412yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4C2×Q812yes—
294C2×C4⋊C4#4112yes—
295C2×C4⋊C4#4112yes—
296C2×C4⋊C4#4112yes—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
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—24no—
310C2×C42—24no—
311C2×C42—24no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—41no—
321C2×C42—41no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42C22×C412yes—
334C2×C42C2×D412yes—
335C2×C42C2×D412yes—
336C2×C42C2×Q812yes—
337C2×C42#4112yes—
338C2×C42#4112yes—
339#107—44no—
340#106—44no—
341#103—28no—
342#103—28no—
343#103—44no—
344#103—44no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360C24C22×D411yescharacteristic
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—41no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8C4×Q814yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
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×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4C4×D412yes—
478C22×C4C4×D412yes—
479C22×C4#12012yes—
480C22×C4#12012yes—
481C22×C4C22⋊Q812yes—
482C22×C4C22⋊Q812yes—
483C22×C4#13512yes—
484C22×C4#13512yes—
485C22×C4#13712yes—
486C22×C4#13712yes—
487C22×C4C23×C411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×Q811yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4H(5,𝔽2)11yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C42−1+411yescharacteristic
500C22×C42−1+411yescharacteristic
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C4⋊C4—216no—
530C4⋊C4—216no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—48no—
560C4⋊C4C4×D414yes—
561C4⋊C4C4×D414yes—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—44no—
575C42—44no—
576C42—48no—
577C42—48no—
578C42—44no—
579C42—48no—
580C42—44no—
581C42—84no—
582C23C2×C4×D411yescharacteristic
583C23C2×#12011yescharacteristic
584C23C2×C22⋊Q811yescharacteristic
585C23#52511yescharacteristic
586C23#52511yescharacteristic
587C23#53511yescharacteristic
588C23#53611yescharacteristic
589C23C2×#13511yescharacteristic
590C23C2×#13511yescharacteristic
591C23C2×#13711yescharacteristic
592C23C2×#13711yescharacteristic
593C23#57511yescharacteristic
594C23#57511yescharacteristic
595C23#57511yescharacteristic
596C23#57511yescharacteristic
597Q8—24no—
598Q8—24no—
599Q8—42no—
600Q8—42no—
601Q8—42no—
602Q8—42no—
603Q8—42no—
604Q8—42no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4#45214yes—
702C2×C4#47914yes—
703C2×C4C2×C4×D411yescharacteristic
704C2×C4C2×C4×D411yescharacteristic
705C2×C4C2×C4×Q811yescharacteristic
706C2×C4C4×#4111yescharacteristic
707C2×C4#52011yescharacteristic
708C2×C4#52011yescharacteristic
709C2×C4#52511yescharacteristic
710C2×C4#52511yescharacteristic
711C2×C4#52911yescharacteristic
712C2×C4#53311yescharacteristic
713C2×C4#54211yescharacteristic
714C2×C4#54211yescharacteristic
715C2×C4#54611yescharacteristic
716C2×C4#54611yescharacteristic
717C2×C4#54611yescharacteristic
718C2×C4#54611yescharacteristic
719C2×C4#54811yescharacteristic
720C2×C4#54811yescharacteristic
721C2×C4D4×Q811yescharacteristic
722C2×C4D4×Q811yescharacteristic
723C2×C4#55211yescharacteristic
724C2×C4#55211yescharacteristic
725C2×C4#55411yescharacteristic
726C2×C4#55411yescharacteristic
727C2×C4#55611yescharacteristic
728C2×C4#55611yescharacteristic
729C2×C4#55911yescharacteristic
730C2×C4#55911yescharacteristic
731C8—42no—
732C8—42no—
733C8—81no—
734C8—81no—
735C22C4×#12011yescharacteristic
736C22C4×C22⋊Q811yescharacteristic
737C22#232611yescharacteristic
738C22#240411yescharacteristic
739C22#240911yescharacteristic
740C22#258011yescharacteristic
741C22#259911yescharacteristic
742C22C4×#13511yescharacteristic
743C22#294311yescharacteristic
744C22C4×#13711yescharacteristic
745C22C4×#13711yescharacteristic
746C22C2×#45211yescharacteristic
747C22#300211yescharacteristic
748C22#300511yescharacteristic
749C22#300711yescharacteristic
750C22C2×#47911yescharacteristic
751C22#307611yescharacteristic
752C22#307811yescharacteristic
753C22#308011yescharacteristic
754C22#310211yescharacteristic
755C22#310211yescharacteristic
756C22#310711yescharacteristic
757C22#310811yescharacteristic
758C22#311111yescharacteristic
759C22#311111yescharacteristic
760C22#311611yescharacteristic
761C22#311711yescharacteristic
762C22#321111yescharacteristic
763C22#321211yescharacteristic
764C22#321811yescharacteristic
765C22#321911yescharacteristic
766C22#323211yescharacteristic
767C22#323311yescharacteristic
768C22#323611yescharacteristic
769C22#323711yescharacteristic
770C4—24no—
771C4—24no—
772C4—44no—
773C4—42no—
774C4—42no—
775C4—44no—
776C4—42no—
777C4—44no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4#236011yescharacteristic
785C4#236011yescharacteristic
786C4#236711yescharacteristic
787C4#236711yescharacteristic
788C4#245811yescharacteristic
789C4#245811yescharacteristic
790C4#246511yescharacteristic
791C4#246511yescharacteristic
792C2#1417211yescharacteristic
793C2C4×#45211yescharacteristic
794C2#2145711yescharacteristic
795C2C4×#47911yescharacteristic
796C2#2161811yescharacteristic
797C2#2222211yescharacteristic
798C2#2222511yescharacteristic
799C2#2393711yescharacteristic
800C2#2393811yescharacteristic
801C2#2430311yescharacteristic
802C2#2430711yescharacteristic
803C2#2925711yescharacteristic
804C2#2926111yescharacteristic
805C2#2939811yescharacteristic
806C2#2939911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
39. #2026C4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1252
C2×#20262
C2×#18652
C2×#18632
C4×#3912
#113852
#113252
#110522
#109322
#109082
#109072
#108852
#108842
#107952