Finite Group Databasebeta

← #360471

Subgroups — #360471

Order 512.

1292 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1847C211yesmaximal, characteristic, complemented
2C2×#1809C211yesmaximal, characteristic
3C2×#1809C211yesmaximal, characteristic
4C2×C4×#107C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic
6#13876C211yesmaximal, characteristic
7#13875C211yesmaximal, characteristic
8#11268C211yesmaximal, characteristic, complemented
9#11267C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic
11#11095C211yesmaximal, characteristic
12#10908C211yesmaximal, characteristic, complemented
13#10907C211yesmaximal, characteristic, complemented
14#10863C211yesmaximal, characteristic, complemented
15#10861C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×#97C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#388—21no—
27C2×#384C2211yescharacteristic
28C2×#382C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36#1847—24no—
37#1809—24no—
38#1809—24no—
39C4×#107—24no—
40#1753C418yescomplemented
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53#1443—21no—
54#1442—21no—
55#1440—21no—
56#1439—21no—
57#1437—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—21no—
64C24×C4C2311yescharacteristic
65C22×M16—22no—
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16C2×C414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4D411yescharacteristic
91C22×C22⋊C4D411yescharacteristic
92C22×C42—21no—
93C22×C42—21no—
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C2×#107—22no—
97C2×#107—22no—
98C2×#107—22no—
99C2×#107—22no—
100C2×#107—22no—
101C2×#107—22no—
102C2×#107—41no—
103C2×#107D414yes—
104C2×#107D414yes—
105C2×#106—22no—
106C2×#106—22no—
107C2×#106—22no—
108C2×#106—22no—
109C2×#106—22no—
110C2×#106—22no—
111C2×#106—22no—
112C2×#106—22no—
113C2×#106—41no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8C2×C414yes—
117C2×#97—22no—
118C2×#97—22no—
119C2×#97C2×C414yes—
120C2×C4×C8—22no—
121C2×C4×C8—22no—
122C2×C4×C8C2×C414yes—
123#388—44no—
124#384—22no—
125#384—41no—
126#382—22no—
127#382—41no—
128#380—22no—
129#380—22no—
130#380—22no—
131#380—22no—
132#380—41no—
133#380—41no—
134#380—41no—
135#380—41no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—41no—
139C4×C4⋊C4—41no—
140C4×C22⋊C4C2×C414yes—
141C4×C22⋊C4Q814yes—
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—
157C2×#95—21no—
158C2×#95D411yescharacteristic
159C2×#95D411yescharacteristic
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—41no—
169#340—41no—
170#336C2×C414yes—
171#336C2×C414yes—
172C25C2×D411yescharacteristic
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
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×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4C22×C412yes—
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×Q812yes—
200C23×C4C2411yescharacteristic
201C2×M16—28no—
202C2×M16—28no—
203C2×M16—28no—
204C2×M16—44no—
205C2×M16—44no—
206C2×M16—44no—
207C2×M16—44no—
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×C8C22×C412yes—
225C22×C8C22×C412yes—
226C22×C8C22×C412yes—
227C22×C8C22×C412yes—
228C22×C8C2×D412yes—
229C22×C8C2×D412yes—
230C22×C8#4112yes—
231C22×C8#4112yes—
232C22×C8#4112yes—
233C22×C8#4112yes—
234C22×C8#4112yes—
235C22×C8#4112yes—
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—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—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—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×D412yes—
289C2×C4⋊C4C2×D412yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—41no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—81no—
303C2×C22⋊C4—81no—
304C2×C22⋊C4—81no—
305C2×C22⋊C4—81no—
306C2×C22⋊C4C4⋊C414yes—
307C2×C22⋊C4C4⋊C414yes—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—81no—
321C2×C42—81no—
322C2×C42C22×C412yes—
323C2×C42C22×C412yes—
324C2×C42C2×Q812yes—
325C2×C42C2×Q812yes—
326#107—28no—
327#107—28no—
328#107—44no—
329#106—44no—
330#106—44no—
331#106—44no—
332C22⋊C8—28no—
333#97—28no—
334C4×C8—28no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—81no—
348#95—81no—
349#95—81no—
350#95—81no—
351#95C4⋊C414yes—
352#95C4⋊C414yes—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24C2×C4⋊C412yes—
368C24C22×D411yescharacteristic
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—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
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—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
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×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×C4C2×C4⋊C412yes—
482C22×C4C2×C4⋊C412yes—
483C22×C4C2×C4⋊C412yes—
484C22×C4C2×C4⋊C412yes—
485C22×C4C2×C4⋊C412yes—
486C22×C4AGL(1,ℤ/8)12yes—
487C22×C4#13712yes—
488C22×C4C23×C411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C22×D411yescharacteristic
491C22×C4C22×Q811yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C42−1+411yescharacteristic
501C22×C42−1+411yescharacteristic
502M16—416no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
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#11714yes—
524C2×C8#11714yes—
525C2×C8C4×D414yes—
526C2×C8C4×D414yes—
527C2×C8#12114yes—
528C2×C8#12314yes—
529C2×C8#12414yes—
530C2×C8#12614yes—
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—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
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—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—84no—
568C22⋊C4—84no—
569C22⋊C4—84no—
570C22⋊C4—84no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—84no—
580C42—84no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23C22×C4⋊C411yescharacteristic
617C23#53211yescharacteristic
618C23#53211yescharacteristic
619C23D4211yescharacteristic
620C23D4211yescharacteristic
621C23#54711yescharacteristic
622C23#54711yescharacteristic
623C23C2×AGL(1,ℤ/8)11yescharacteristic
624C23C2×#13711yescharacteristic
625C23#57511yescharacteristic
626C23#57511yescharacteristic
627C23#57611yescharacteristic
628C23#57711yescharacteristic
629C23#57711yescharacteristic
630C23#57811yescharacteristic
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
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—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
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—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4#42814yes—
730C2×C4C2×#11711yescharacteristic
731C2×C4C2×#11711yescharacteristic
732C2×C4C2×C4×D411yescharacteristic
733C2×C4C2×C4×D411yescharacteristic
734C2×C4#52011yescharacteristic
735C2×C4#52011yescharacteristic
736C2×C4C2×#12111yescharacteristic
737C2×C4C2×#12311yescharacteristic
738C2×C4C2×#12411yescharacteristic
739C2×C4C2×#12611yescharacteristic
740C2×C4#53311yescharacteristic
741C2×C4#53311yescharacteristic
742C2×C4#54011yescharacteristic
743C2×C4#54111yescharacteristic
744C2×C4#54211yescharacteristic
745C2×C4#54211yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54711yescharacteristic
748C2×C4#54811yescharacteristic
749C2×C4D4×Q811yescharacteristic
750C2×C4D4×Q811yescharacteristic
751C2×C4#55011yescharacteristic
752C2×C4#55211yescharacteristic
753C2×C4#55311yescharacteristic
754C2×C4#55411yescharacteristic
755C2×C4#55411yescharacteristic
756C2×C4#55511yescharacteristic
757C2×C4#55611yescharacteristic
758C8—24no—
759C8—42no—
760C8—42no—
761C8#38818yescomplemented
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22#228511yescharacteristic
778C22D4×C4⋊C411yescharacteristic
779C22D4×C4⋊C411yescharacteristic
780C22#242211yescharacteristic
781C22#242811yescharacteristic
782C22#249111yescharacteristic
783C22#249611yescharacteristic
784C22C2×#42811yescharacteristic
785C22#291111yescharacteristic
786C22#291211yescharacteristic
787C22#291311yescharacteristic
788C22#317111yescharacteristic
789C22#317111yescharacteristic
790C22#317211yescharacteristic
791C22#317211yescharacteristic
792C22#317811yescharacteristic
793C22#317811yescharacteristic
794C22#317911yescharacteristic
795C22#317911yescharacteristic
796C22#326411yescharacteristic
797C22#326711yescharacteristic
798C22#327011yescharacteristic
799C22#327111yescharacteristic
800C22#327211yescharacteristic
801C22#327311yescharacteristic
802C22#327711yescharacteristic
803C22#327811yescharacteristic
804C22#334311yescharacteristic
805C22#334611yescharacteristic
806C22#334811yescharacteristic
807C22#335011yescharacteristic
808C22#335211yescharacteristic
809C22#335411yescharacteristic
810C22#335511yescharacteristic
811C22#335611yescharacteristic
812C4—24no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—161no—
822C4—161no—
823C4—161no—
824C4—161no—
825C4C2×#38811yescharacteristic
826C4#231411yescharacteristic
827C4#235211yescharacteristic
828C4#235411yescharacteristic
829C4#242311yescharacteristic
830C4#242911yescharacteristic
831C4#249211yescharacteristic
832C4#249711yescharacteristic
833C2—82no—
834C2#1387611yescharacteristic
835C2#2081911yescharacteristic
836C2#2082211yescharacteristic
837C2#2266111yescharacteristic
838C2#2266211yescharacteristic
839C2#2266311yescharacteristic
840C2#2266411yescharacteristic
841C2#2503811yescharacteristic
842C2#2503911yescharacteristic
843C2#2541811yescharacteristic
844C2#2541911yescharacteristic
845C2#2779511yescharacteristic
846C2#2779611yescharacteristic
847C2#2784311yescharacteristic
848C2#2784411yescharacteristic
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
1. C2×#1847C2semidirect
4. C2×C4×#107C2semidirect
8. #11268C2semidirect
9. #11267C2semidirect
12. #10908C2semidirect
13. #10907C2semidirect
14. #10863C2semidirect
15. #10861C2semidirect
40. #1753C4semidirect
761. C8#388semidirect

Maximal subgroups

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

subgroupindex
C2×#18472
C2×#18092
C2×C4×#1072
C2×#17532
#138762
#138752
#112682
#112672
#110962
#110952
#109082
#109072
#108632
#108612