Finite Group Databasebeta

← #387087

Subgroups — #387087

Order 512.

1276 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2582C211yesmaximal, characteristic
2C2×#1985C211yesmaximal, characteristic
3#13926C211yesmaximal, characteristic
4#11373C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11227C211yesmaximal, characteristic
7#11207C211yesmaximal, characteristic
8#11077C211yesmaximal, characteristic
9#11050C211yesmaximal, characteristic
10#10932C211yesmaximal, characteristic
11#10928C211yesmaximal, characteristic
12#10885C211yesmaximal, characteristic
13#10881C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#97C2211yescharacteristic
24#2582—24no—
25#2582C418yescomplemented
26C2×#398—21no—
27C2×#398—21no—
28C2×#391—21no—
29C2×#391—21no—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#389—21no—
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#384C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38#1985—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1441—21no—
56#1441—21no—
57C4⋊#95—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8D411yescharacteristic
63C23×Q8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4×Q8—22no—
69C2×C4×Q8—41no—
70C2×C4×Q8—41no—
71C2×C4×Q8—41no—
72C2×C4×Q8—41no—
73C2×C4×Q8—41no—
74C2×C4×Q8—41no—
75C2×C4×Q8—41no—
76C2×C4×Q8—41no—
77C2×C4×Q8C2×C414yes—
78C2×C4×Q8C2×C414yes—
79C2×C4×Q8D414yes—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4D411yescharacteristic
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C42—21no—
98C22×C42—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C2×C4⋊C8—22no—
103C2×C4⋊C8—41no—
104C2×C4⋊C8—41no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—41no—
111C2×#103—41no—
112C2×#103—41no—
113C2×#103—41no—
114C2×#103—41no—
115C2×#103—41no—
116C2×#103Q814yescomplemented
117C2×#97—22no—
118C2×#97—41no—
119C2×#97—41no—
120#398—28no—
121#398—28no—
122#391—28no—
123#391—22no—
124#391—22no—
125#391—44no—
126#391C2×C414yes—
127#391C2×C414yes—
128#389—28no—
129#389—22no—
130#389—22no—
131#389C2×C414yes—
132#389C2×C414yes—
133#384—22no—
134#384—41no—
135#384—41no—
136#384C2×C414yes—
137C4×C4⋊C4—41no—
138C4×C4⋊C4—41no—
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×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340—41no—
163#340—41no—
164#340—41no—
165#340—41no—
166#336—22no—
167#336—22no—
168#336—22no—
169#336—22no—
170C22×Q8—22no—
171C22×Q8—22no—
172C22×Q8—22no—
173C22×Q8—22no—
174C22×Q8—21no—
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—41no—
186C22×Q8—41no—
187C22×Q8C22⋊C414yes—
188C22×Q8C22×C412yes—
189C22×Q8C2×Q812yes—
190C22×Q8#4112yes—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2411yescharacteristic
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×C8—21no—
231C22×C8—21no—
232C22×C8C2×Q812yes—
233C22×C8#4112yes—
234C4×Q8—44no—
235C4×Q8—44no—
236C4×Q8—44no—
237C4×Q8—44no—
238C4×Q8—44no—
239C4×Q8—44no—
240C4×Q8—44no—
241C4×Q8—44no—
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—21no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
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—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—24no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—81no—
299C2×C4⋊C4—81no—
300C2×C4⋊C4—81no—
301C2×C4⋊C4—81no—
302C2×C4⋊C4—81no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4C22⋊C414yes—
307C2×C4⋊C4C22⋊C414yes—
308C2×C4⋊C4C22⋊C414yes—
309C2×C4⋊C4C22×C412yes—
310C2×C4⋊C4C22×C412yes—
311C2×C4⋊C4C22×C412yes—
312C2×C4⋊C4C2×Q812yes—
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—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—24no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42C22×C412yes—
333C2×C42C22×C412yes—
334C2×C42C22×C412yes—
335C2×C42C2×D412yes—
336C2×C42C2×D412yes—
337C2×C42C2×D412yes—
338C4⋊C8—44no—
339#103—44no—
340#103—44no—
341#103—44no—
342#103—44no—
343#97—44no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—81no—
356#95—81no—
357#95—81no—
358#95—81no—
359C24C22×D411yescharacteristic
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—28no—
364C2×Q8—28no—
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—22no—
377C2×Q8—44no—
378C2×Q8—44no—
379C2×Q8—44no—
380C2×Q8—44no—
381C2×Q8—44no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8C4×Q814yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
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×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4C2×C22⋊C412yes—
484C22×C4C2×C22⋊C412yes—
485C22×C4C2×C22⋊C412yes—
486C22×C4C2×C22⋊C412yes—
487C22×C4C2×C22⋊C412yes—
488C22×C4C2×C22⋊C412yes—
489C22×C4AGL(1,ℤ/8)12yes—
490C22×C4#13712yes—
491C22×C4#13712yes—
492C22×C4#13712yes—
493C22×C4C23×C411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4C22×Q811yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C4H(5,𝔽2)11yescharacteristic
504C22×C42−1+411yescharacteristic
505C22×C42−1+411yescharacteristic
506C22×C42−1+411yescharacteristic
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
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—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
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—44no—
546C4⋊C4—44no—
547C4⋊C4—44no—
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⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—84no—
572C4⋊C4—84no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—48no—
586C42—84no—
587C23C22×C22⋊C411yescharacteristic
588C23#53411yescharacteristic
589C23#53411yescharacteristic
590C23#54811yescharacteristic
591C23#54811yescharacteristic
592C23D4×Q811yescharacteristic
593C23#55011yescharacteristic
594C23C2×AGL(1,ℤ/8)11yescharacteristic
595C23C2×#13711yescharacteristic
596C23C2×#13711yescharacteristic
597C23C2×#13711yescharacteristic
598C23#57611yescharacteristic
599C23#57711yescharacteristic
600C23#57711yescharacteristic
601C23#57811yescharacteristic
602Q8—24no—
603Q8—24no—
604Q8—416no—
605Q8—42no—
606Q8—42no—
607Q8—42no—
608Q8—42no—
609Q8—42no—
610Q8—42no—
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—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
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—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
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—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#41714yes—
708C2×C4#41914yes—
709C2×C4C2×C4×Q811yescharacteristic
710C2×C4C4×#4111yescharacteristic
711C2×C4#51811yescharacteristic
712C2×C4#51811yescharacteristic
713C2×C4#51911yescharacteristic
714C2×C4#52011yescharacteristic
715C2×C4#53411yescharacteristic
716C2×C4#53411yescharacteristic
717C2×C4#53811yescharacteristic
718C2×C4#53911yescharacteristic
719C2×C4#53911yescharacteristic
720C2×C4#53911yescharacteristic
721C2×C4#54211yescharacteristic
722C2×C4#54211yescharacteristic
723C2×C4#54311yescharacteristic
724C2×C4#54411yescharacteristic
725C2×C4#54811yescharacteristic
726C2×C4#54811yescharacteristic
727C2×C4D4×Q811yescharacteristic
728C2×C4#55011yescharacteristic
729C2×C4#55111yescharacteristic
730C2×C4#55111yescharacteristic
731C2×C4#55411yescharacteristic
732C2×C4#55411yescharacteristic
733C2×C4#56211yescharacteristic
734C2×C4#56211yescharacteristic
735C2×C4#56311yescharacteristic
736C2×C4#56311yescharacteristic
737C8—42no—
738C8—42no—
739C8—81no—
740C8—81no—
741C22#230811yescharacteristic
742C22Q8×C22⋊C411yescharacteristic
743C22#234111yescharacteristic
744C22#272811yescharacteristic
745C22#272911yescharacteristic
746C22#273011yescharacteristic
747C22#273211yescharacteristic
748C22C2×#41911yescharacteristic
749C22C2×#41711yescharacteristic
750C22#289711yescharacteristic
751C22#289811yescharacteristic
752C22#319311yescharacteristic
753C22#319311yescharacteristic
754C22#319511yescharacteristic
755C22#319511yescharacteristic
756C22#319811yescharacteristic
757C22#320111yescharacteristic
758C22#320311yescharacteristic
759C22#320411yescharacteristic
760C22#336811yescharacteristic
761C22#336911yescharacteristic
762C22#337211yescharacteristic
763C22#337311yescharacteristic
764C22#337411yescharacteristic
765C22#337411yescharacteristic
766C22#337511yescharacteristic
767C22#337511yescharacteristic
768C22#338511yescharacteristic
769C22#338611yescharacteristic
770C22#338711yescharacteristic
771C22#338711yescharacteristic
772C22#339811yescharacteristic
773C22#339911yescharacteristic
774C22#340011yescharacteristic
775C22#340011yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—161no—
789C4—161no—
790C4#232911yescharacteristic
791C4#233211yescharacteristic
792C4#236811yescharacteristic
793C4#237811yescharacteristic
794C4#272811yescharacteristic
795C4#272911yescharacteristic
796C4#273011yescharacteristic
797C4#273211yescharacteristic
798C2#1444911yescharacteristic
799C2#2176511yescharacteristic
800C2#2177211yescharacteristic
801C2#2252411yescharacteristic
802C2#2252511yescharacteristic
803C2#2254611yescharacteristic
804C2#2254711yescharacteristic
805C2#3256111yescharacteristic
806C2#3256311yescharacteristic
807C2#3259111yescharacteristic
808C2#3259511yescharacteristic
809C2#3262511yescharacteristic
810C2#3262711yescharacteristic
811C2#3266511yescharacteristic
812C2#3266711yescharacteristic
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
25. #2582C4semidirect
116. C2×#103Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25822
C2×#19852
#139262
#113732
#113572
#112272
#112072
#110772
#110502
#109322
#109282
#108852
#108812
#107892