Finite Group Databasebeta

← #365356

Subgroups — #365356

Order 512.

1764 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2362C211yesmaximal, characteristic
2C2×#1894C211yesmaximal, characteristic
3C2×#1872C211yesmaximal, characteristic
4C2×#1863C211yesmaximal, characteristic, complemented
5C2×#1854C211yesmaximal, characteristic
6C2×#1736C211yesmaximal, characteristic
7#13907C211yesmaximal, characteristic
8#11327C211yesmaximal, characteristic, complemented
9#11293C211yesmaximal, characteristic, complemented
10#11122C211yesmaximal, characteristic, complemented
11#11067C211yesmaximal, characteristic, complemented
12#10907C211yesmaximal, characteristic, complemented
13#10884C211yesmaximal, characteristic, complemented
14#10789C211yesmaximal, characteristic, complemented
15#10715C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C22×#107C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28#2362—24no—
29#2362—24no—
30C2×#391C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#388—21no—
35C2×#388—21no—
36C2×#387—21no—
37C2×#380—21no—
38C2×#380C2211yescharacteristic
39C2×C4×C4⋊C4—21no—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42#1894—24no—
43#1872C418yescomplemented
44#1863—24no—
45#1854—24no—
46#1736—24no—
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61#1441—21no—
62#1441—21no—
63C4⋊#95C2211yescharacteristic
64C4⋊#95C2211yescharacteristic
65C22⋊#95—21no—
66C23×Q8C2311yescharacteristic
67C24×C4—21no—
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—41no—
75C22×M16—41no—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×C22⋊Q8—22no—
81C2×C22⋊Q8—22no—
82C2×C22⋊Q8—22no—
83C2×C22⋊Q8C2×C414yes—
84C2×C22⋊Q8D414yes—
85C2×C22⋊Q8Q814yes—
86C2×C4×Q8—22no—
87C2×C4×Q8—22no—
88C2×C4×Q8—22no—
89C2×C4×Q8—22no—
90C2×C4×Q8—41no—
91C2×C4×Q8—41no—
92C2×#117—22no—
93C2×#117—22no—
94C2×#117—22no—
95C2×#117—41no—
96C2×#117—41no—
97C2×#117D414yes—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—22no—
100C22×C4⋊C4—22no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—22no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—41no—
108C22×C4⋊C4—41no—
109C22×C4⋊C4C2×C414yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4D411yescharacteristic
121C22×C22⋊C4D411yescharacteristic
122C22×C42—21no—
123C22×C42—21no—
124C22×C42—21no—
125C22×C42C2311yescharacteristic
126C22×C42C2311yescharacteristic
127C2×#107—22no—
128C2×#107—22no—
129C2×#107—22no—
130C2×#106—22no—
131C2×#106—41no—
132C2×#106—41no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—41no—
140C2×#103—41no—
141C2×#103—41no—
142C2×#103—41no—
143C2×#103C2×C414yes—
144C2×#103C2×C414yes—
145C2×C22⋊C8—22no—
146C2×C22⋊C8—22no—
147C2×C22⋊C8C2×C414yes—
148#391—22no—
149#391—22no—
150#389—22no—
151#389—22no—
152#389—22no—
153#389—22no—
154#389—41no—
155#389—41no—
156#388—28no—
157#388—28no—
158#387—28no—
159#380—22no—
160#380—22no—
161#380—44no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—22no—
164C4×C4⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—21no—
171C2×#95—21no—
172C2×#95—21no—
173C2×#95—21no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95—21no—
177C2×#95—21no—
178C2×#95D411yescharacteristic
179C2×#95D411yescharacteristic
180#340—22no—
181#340—22no—
182#340—22no—
183#340—22no—
184#340—22no—
185#340—22no—
186#340—22no—
187#340C2×C414yes—
188#340C2×C414yes—
189#340D414yes—
190#336—22no—
191#336—22no—
192#336—41no—
193#336—41no—
194C25C2×D411yescharacteristic
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8C22×C412yes—
207C22×Q8C2×D412yes—
208C22×Q8C2×Q812yes—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—24no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—42no—
227C23×C4—42no—
228C23×C4—42no—
229C23×C4—42no—
230C23×C4—81no—
231C23×C4—81no—
232C23×C4C22×C412yes—
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C23×C4C2×D411yescharacteristic
237C23×C4C2×D412yes—
238C23×C4C2×D411yescharacteristic
239C23×C4C2×D412yes—
240C23×C4C2×Q812yes—
241C23×C4#4112yes—
242C23×C4#4112yes—
243C23×C4C2411yescharacteristic
244C2×M16—28no—
245C2×M16—44no—
246C2×M16—44no—
247C2×M16—44no—
248C2×M16—44no—
249C2×M16—44no—
250C2×M16—44no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C2×D412yes—
278C22×C8#4112yes—
279C22⋊Q8—28no—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8C4⋊C4116yescomplemented
283C4×Q8—44no—
284C4×Q8—44no—
285C4×Q8—44no—
286C4×Q8—44no—
287#117—28no—
288#117—44no—
289#117—44no—
290#117—44no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—81no—
343C2×C4⋊C4—81no—
344C2×C4⋊C4C22×C412yes—
345C2×C4⋊C4C22×C412yes—
346C2×C4⋊C4C22×C412yes—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2×D412yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×Q812yes—
353C2×C4⋊C4#4112yes—
354C2×C4⋊C4#4112yes—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391#107—44no—
392#106—44no—
393#103—28no—
394#103—44no—
395#103—44no—
396#103—44no—
397C22⋊C8—28no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—81no—
410#95—81no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24C4×D412yes—
424C24#12012yes—
425C24C22⋊Q812yes—
426C24C22×D411yescharacteristic
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8C2×C4⋊C414yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—48no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—48no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—84no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—84no—
572C22×C4C2×C4⋊C414yes—
573C22×C4C4×D414yes—
574C22×C4C4×D412yes—
575C22×C4#12012yes—
576C22×C4C22⋊Q814yes—
577C22×C4C22⋊Q812yes—
578C22×C4#12314yes—
579C22×C4AGL(1,ℤ/8)12yes—
580C22×C4#13712yes—
581C22×C4C23×C411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×Q811yescharacteristic
586C22×C4C2×#4111yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591C22×C4H(5,𝔽2)11yescharacteristic
592C22×C4H(5,𝔽2)11yescharacteristic
593C22×C4H(5,𝔽2)11yescharacteristic
594C22×C42−1+411yescharacteristic
595M16—416no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—216no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—41no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C4⋊C4C2×C4⋊C414yes—
656C4⋊C4C4×D414yes—
657C4⋊C4#12114yes—
658C22⋊C4—216no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—48no—
662C22⋊C4—84no—
663C42—48no—
664C42—48no—
665C42—48no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—41no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23#38514yes—
709C23C2×C4×D411yescharacteristic
710C23C2×#12011yescharacteristic
711C23C2×C22⋊Q811yescharacteristic
712C23D4211yescharacteristic
713C23#54611yescharacteristic
714C23#54611yescharacteristic
715C23#54711yescharacteristic
716C23C2×AGL(1,ℤ/8)11yescharacteristic
717C23C2×#13711yescharacteristic
718C23#57511yescharacteristic
719C23#57511yescharacteristic
720C23#57711yescharacteristic
721C23#57711yescharacteristic
722C23#57811yescharacteristic
723C23#57811yescharacteristic
724Q8—24no—
725Q8—24no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—42no—
730Q8—42no—
731Q8—42no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—816no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4#38514yes—
832C2×C4C22×C4⋊C411yescharacteristic
833C2×C4C2×C4×D411yescharacteristic
834C2×C4C2×C4×D411yescharacteristic
835C2×C4C4×#4111yescharacteristic
836C2×C4#51811yescharacteristic
837C2×C4#52011yescharacteristic
838C2×C4C2×#12111yescharacteristic
839C2×C4C2×C22⋊Q811yescharacteristic
840C2×C4C2×#12311yescharacteristic
841C2×C4#52511yescharacteristic
842C2×C4#52911yescharacteristic
843C2×C4#53211yescharacteristic
844C2×C4#53411yescharacteristic
845C2×C4#53711yescharacteristic
846C2×C4#53811yescharacteristic
847C2×C4#53911yescharacteristic
848C2×C4D4211yescharacteristic
849C2×C4#54611yescharacteristic
850C2×C4#54611yescharacteristic
851C2×C4#54611yescharacteristic
852C2×C4#54711yescharacteristic
853C2×C4D4×Q811yescharacteristic
854C2×C4#55111yescharacteristic
855C2×C4#55111yescharacteristic
856C2×C4#55211yescharacteristic
857C2×C4#55411yescharacteristic
858C2×C4#55411yescharacteristic
859C2×C4#55411yescharacteristic
860C8—42no—
861C8—42no—
862C8—42no—
863C8—42no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22C2×#38511yescharacteristic
880C22#235811yescharacteristic
881C22#235911yescharacteristic
882C22#241011yescharacteristic
883C22#243011yescharacteristic
884C22#244911yescharacteristic
885C22#245011yescharacteristic
886C22C4×AGL(1,ℤ/8)11yescharacteristic
887C22C4×#13711yescharacteristic
888C22#294911yescharacteristic
889C22#295011yescharacteristic
890C22#300611yescharacteristic
891C22#300711yescharacteristic
892C22#301311yescharacteristic
893C22#301311yescharacteristic
894C22#307911yescharacteristic
895C22#308011yescharacteristic
896C22#308211yescharacteristic
897C22#308211yescharacteristic
898C22#326911yescharacteristic
899C22#327011yescharacteristic
900C22#327211yescharacteristic
901C22#327511yescharacteristic
902C22#330711yescharacteristic
903C22#331011yescharacteristic
904C22#331111yescharacteristic
905C22#331611yescharacteristic
906C22#332711yescharacteristic
907C22#332711yescharacteristic
908C22#332811yescharacteristic
909C22#333011yescharacteristic
910C22#334311yescharacteristic
911C22#334911yescharacteristic
912C22#335111yescharacteristic
913C22#335611yescharacteristic
914C4—24no—
915C4—44no—
916C4—42no—
917C4—44no—
918C4—44no—
919C4—44no—
920C4—42no—
921C4—82no—
922C4—82no—
923C4—81no—
924C4—81no—
925C4—161no—
926C4—161no—
927C4C4×#12111yescharacteristic
928C4#232511yescharacteristic
929C4D4×C4⋊C411yescharacteristic
930C4#234911yescharacteristic
931C4#241711yescharacteristic
932C4#241811yescharacteristic
933C4#241911yescharacteristic
934C4#256411yescharacteristic
935C2—44no—
936C2#1397511yescharacteristic
937C2#2087511yescharacteristic
938C2#2088011yescharacteristic
939C2#2286411yescharacteristic
940C2#2288111yescharacteristic
941C2#2292711yescharacteristic
942C2#2294711yescharacteristic
943C2#2444911yescharacteristic
944C2#2445411yescharacteristic
945C2#2555811yescharacteristic
946C2#2556011yescharacteristic
947C2#2635511yescharacteristic
948C2#2636711yescharacteristic
949C2#2642911yescharacteristic
950C2#2643311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1863C2semidirect
8. #11327C2semidirect
9. #11293C2semidirect
10. #11122C2semidirect
11. #11067C2semidirect
12. #10907C2semidirect
13. #10884C2semidirect
14. #10789C2semidirect
43. #1872C4semidirect
282. C22⋊Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23622
C2×#18942
C2×#18722
C2×#18632
C2×#18542
C2×#17362
#139072
#113272
#112932
#111222
#110672
#109072
#108842
#107892
#107152