Finite Group Databasebeta

← #165181

Subgroups — #165181

Order 512.

1250 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36258C211yesmaximal, characteristic
2#22532C211yesmaximal, characteristic, complemented
3#20720C211yesmaximal, characteristic, complemented
4#7724C211yesmaximal, characteristic, complemented
5#7714C211yesmaximal, characteristic, complemented
6#7704C211yesmaximal, characteristic, complemented
7#7698C211yesmaximal, characteristic, complemented
8#7674C211yesmaximal, characteristic, complemented
9#7658C211yesmaximal, characteristic, complemented
10#7640C211yesmaximal, characteristic, complemented
11#7626C211yesmaximal, characteristic, complemented
12#7620C211yesmaximal, characteristic, complemented
13#7599C211yesmaximal, characteristic, complemented
14#7572C211yesmaximal, characteristic, complemented
15#7572C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×D42C411yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#446—21no—
20C2×#433—21no—
21#2856C2211yescharacteristic
22#2854C2211yescharacteristic
23#2854C2211yescharacteristic
24#2548C411yescharacteristic
25#2538C411yescharacteristic
26#2426—21no—
27#2424—21no—
28#2424—21no—
29#2416C411yescharacteristic
30#2416C411yescharacteristic
31#2414—21no—
32#2411—21no—
33#2411—21no—
34#2408C411yescharacteristic
35#2408C411yescharacteristic
36D4×C4⋊C4C411yescharacteristic
37D4×C22⋊C4—21no—
38C4×#121C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41#1955—21no—
42#1955—21no—
43#1954—21no—
44#1817C2211yescharacteristic, complemented
45#1817C2211yescharacteristic, complemented
46#1798—21no—
47#1797C2211yescharacteristic, complemented
48#1797C2211yescharacteristic, complemented
49#1797C2211yescharacteristic, complemented
50#1797C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1780—21no—
53#1750—21no—
54#1749C2211yescharacteristic, complemented
55#1749C2211yescharacteristic, complemented
56#1749C2211yescharacteristic, complemented
57C4×C22⋊C8C2211yescharacteristic, complemented
58C4×C22⋊C8C2211yescharacteristic, complemented
59#1271C2211yescharacteristic, complemented
60#1271C2211yescharacteristic, complemented
61#1271C2211yescharacteristic, complemented
62#1271C2211yescharacteristic, complemented
63#1270C2211yescharacteristic
64#1270C2211yescharacteristic
65#1270C2211yescharacteristic
66#1270C2211yescharacteristic
67#1270C2211yescharacteristic, complemented
68#1270C2211yescharacteristic, complemented
69#1270C2211yescharacteristic, complemented
70#1270C2211yescharacteristic, complemented
71#1270C2211yescharacteristic, complemented
72#1270C2211yescharacteristic, complemented
73#1270C2211yescharacteristic, complemented
74#1270C2211yescharacteristic, complemented
75C22×#41D411yescharacteristic
76C23×D4—21no—
77C23×D4C2×C411yescharacteristic
78C23×D4C2×C411yescharacteristic
79#546—44no—
80#546—44no—
81D42—44no—
82C2×#127C2×C411yescharacteristic
83C2×#124—21no—
84C2×#123—21no—
85C2×#123—21no—
86C2×C22⋊Q8—21no—
87C2×#121—21no—
88C2×#121—21no—
89C2×#121—21no—
90C2×#121—21no—
91C2×#121—21no—
92C2×#121C2×C411yescharacteristic
93C2×#121C2×C411yescharacteristic
94C2×#121C2×C411yescharacteristic
95C2×#121C2×C411yescharacteristic
96C2×#121C2×C411yescharacteristic
97C2×#120—21no—
98C2×#120—21no—
99C2×#120—21no—
100C2×#120—21no—
101C4×#41—44no—
102C2×C4×Q8C2×C411yescharacteristic
103C2×C4×Q8D411yescharacteristic
104C2×C4×D4—21no—
105C2×C4×D4—21no—
106C2×C4×D4C2×C411yescharacteristic
107C2×C4×D4C2×C411yescharacteristic
108C2×C4×D4C2×C411yescharacteristic
109C2×C4×D4C2×C411yescharacteristic
110C2×C4×D4D411yescharacteristic
111C2×C4×D4D411yescharacteristic
112C2×C4×D4D411yescharacteristic
113C2×#117D411yescharacteristic
114C2×#117D411yescharacteristic
115C2×#117D411yescharacteristic
116C22×C4⋊C4C2×C411yescharacteristic
117C22×C4⋊C4C2×C411yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C42C2311yescharacteristic
123C22×C42C2311yescharacteristic
124C22×C42C2311yescharacteristic
125#446—44no—
126#433—44no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×#97—21no—
145C2×#97—21no—
146C2×#97—21no—
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149#396—21no—
150#396—21no—
151#396—21no—
152#396—21no—
153#394—21no—
154#394—21no—
155#394—21no—
156#394—21no—
157#394—21no—
158#394—21no—
159#392—21no—
160#392—21no—
161#390—21no—
162#390—21no—
163#390—21no—
164#390—21no—
165#390—21no—
166#390—21no—
167#390—21no—
168#390C2×C411yescharacteristic
169#390C2×C411yescharacteristic
170#390C2×C411yescharacteristic
171#390C2×C411yescharacteristic
172#390C2×C411yescharacteristic
173#390C2×C411yescharacteristic
174#390C2311yescharacteristic
175#390C2311yescharacteristic
176#390C2311yescharacteristic
177#389—21no—
178#389C2×C411yescharacteristic
179#389C2×C411yescharacteristic
180#389C2311yescharacteristic
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#386—21no—
187#386—21no—
188#386—21no—
189#386—21no—
190#386—21no—
191#385—21no—
192#385—21no—
193#384C2×C411yescharacteristic
194#380—21no—
195#380C2×C411yescharacteristic
196#380C2×C411yescharacteristic
197#380C2×C411yescharacteristic
198#379—21no—
199#379—21no—
200C4×C4⋊C4C2×C411yescharacteristic
201C4×C22⋊C4—21no—
202#336—21no—
203#336—21no—
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210#336C2311yescharacteristic
211#336C2311yescharacteristic
212C25—21no—
213C25—21no—
214C2×#41—22no—
215C2×#41—22no—
216C2×#41—42no—
217C2×#41—42no—
218C22×Q8C22⋊C411yescharacteristic
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—41no—
231C22×D4—41no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—81no—
238C22×D4—81no—
239C22×D4C22⋊C411yescharacteristic
240C22×D4C22⋊C411yescharacteristic
241C22×D4C22⋊C411yescharacteristic
242C22×D4C22×C411yescharacteristic
243C22×D4C22×C411yescharacteristic
244C22×D4C22×C411yescharacteristic
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265#127—42no—
266#124—44no—
267#123—42no—
268#123—42no—
269#123—42no—
270#123—42no—
271C22⋊Q8—44no—
272#121—22no—
273#121—41no—
274#121—42no—
275#121—42no—
276#121—44no—
277#121—44no—
278#121—44no—
279#121—42no—
280#121—42no—
281#121—81no—
282#121—81no—
283#121—81no—
284#121—81no—
285#120—44no—
286#120—44no—
287#120—44no—
288#120—44no—
289C4×Q8—24no—
290C4×Q8—42no—
291C4×D4—24no—
292C4×D4—42no—
293C4×D4—42no—
294C4×D4—42no—
295C4×D4—42no—
296C4×D4—42no—
297C4×D4—42no—
298C4×D4—42no—
299C4×D4—42no—
300C4×D4—44no—
301#117—24no—
302#117—42no—
303#117—42no—
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—81no—
312C2×C4⋊C4—81no—
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22⋊C411yescharacteristic
315C2×C4⋊C4C22⋊C411yescharacteristic
316C2×C4⋊C4C22⋊C411yescharacteristic
317C2×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22⋊C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C4⋊C4C22×C411yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—81no—
356C2×C22⋊C4—81no—
357C2×C22⋊C4—81no—
358C2×C22⋊C4—81no—
359C2×C22⋊C4C22⋊C411yescharacteristic
360C2×C22⋊C4C22⋊C411yescharacteristic
361C2×C22⋊C4C22⋊C411yescharacteristic
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C42—21no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42C22×C411yescharacteristic
370C2×C42C22×C411yescharacteristic
371C2×C42C22×C411yescharacteristic
372C2×C42C2×D411yescharacteristic
373C2×C42C2×D411yescharacteristic
374C2×C42C2×D411yescharacteristic
375C2×C42C2×D411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2411yescharacteristic
379C4⋊C8—42no—
380C4⋊C8—42no—
381C4⋊C8—42no—
382C4⋊C8—42no—
383C4⋊C8—42no—
384C22⋊C8—42no—
385C22⋊C8—42no—
386C22⋊C8—42no—
387C22⋊C8—42no—
388C22⋊C8—42no—
389C22⋊C8—42no—
390C22⋊C8—42no—
391C22⋊C8—42no—
392C22⋊C8—42no—
393C22⋊C8—81no—
394C22⋊C8—81no—
395C22⋊C8—81no—
396#97—42no—
397#97—42no—
398#97—42no—
399C4×C8—42no—
400C4×C8—42no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—81no—
420C24—81no—
421C24—81no—
422C24—81no—
423C24—81no—
424C24—81no—
425C24C2×C22⋊C411yescharacteristic
426C24C2×C22⋊C411yescharacteristic
427C24C2×C22⋊C411yescharacteristic
428#41—48no—
429#41—48no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—41no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—84no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—81no—
484C2×D4—816no—
485C2×D4#13112yes—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4C2×C22⋊C411yescharacteristic
542C22×C4C2×C22⋊C411yescharacteristic
543C22×C4AGL(1,ℤ/8)12yes—
544C22×C4AGL(1,ℤ/8)12yes—
545C22×C4C23×C411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C2×C8—22no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—42no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4—81no—
591C4⋊C4#9914yes—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23—162no—
691C23—162no—
692C23—162no—
693C23—162no—
694C23—162no—
695C23—162no—
696C23#41812yes—
697C23#42112yes—
698C23C22×C22⋊C411yescharacteristic
699Q8—44no—
700D4—28no—
701D4—44no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—84no—
706D4—84no—
707D4—81no—
708D4—81no—
709D4—81no—
710D4—81no—
711D4—84no—
712D4—84no—
713D4—84no—
714D4—84no—
715D4—162no—
716D4—162no—
717D4—162no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—84no—
781C2×C4—162no—
782C2×C4—162no—
783C2×C4C2×#9912yes—
784C2×C4C2×#9912yes—
785C2×C4C2×#9912yes—
786C2×C4#41812yes—
787C2×C4C2×#13111yescharacteristic
788C2×C4#56811yescharacteristic
789C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
790C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
791C2×C4#57611yescharacteristic
792C2×C4#57711yescharacteristic
793C8—42no—
794C8—81no—
795C8—81no—
796C8—81no—
797C8—81no—
798C8—81no—
799C8—81no—
800C8—81no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—168no—
844C22—168no—
845C22#288011yescharacteristic
846C22C22×#9911yescharacteristic
847C22#288811yescharacteristic
848C22C2×#41811yescharacteristic
849C22#289711yescharacteristic
850C22C2×#42111yescharacteristic
851C22#290111yescharacteristic
852C4—21no—
853C4—21no—
854C4—22no—
855C4—22no—
856C4—21no—
857C4—21no—
858C4—22no—
859C4—22no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C2—42no—
873C2—42no—
874C2—81no—
875C2—82no—
876C2—161no—
877C2—161no—
878C2#1741111yescharacteristic
879C2#1751111yescharacteristic
880C2#1752111yescharacteristic
881C2#1757711yescharacteristic
882C2#1761111yescharacteristic
883C2#1767911yescharacteristic
884C2#1775811yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36258C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22532C2semidirect
3. #20720C2semidirect
4. #7724C2semidirect
5. #7714C2semidirect
6. #7704C2semidirect
7. #7698C2semidirect
8. #7674C2semidirect
9. #7658C2semidirect
10. #7640C2semidirect
11. #7626C2semidirect
12. #7620C2semidirect
13. #7599C2semidirect
14. #7572C2semidirect
15. #7572C2semidirect
44. #1817C22semidirect
45. #1817C22semidirect
47. #1797C22semidirect
48. #1797C22semidirect
49. #1797C22semidirect
50. #1797C22semidirect
51. #1797C22semidirect
54. #1749C22semidirect
55. #1749C22semidirect
56. #1749C22semidirect
57. C4×C22⋊C8C22semidirect
58. C4×C22⋊C8C22semidirect
59. #1271C22semidirect
60. #1271C22semidirect
61. #1271C22semidirect
62. #1271C22semidirect
67. #1270C22semidirect
68. #1270C22semidirect
69. #1270C22semidirect
70. #1270C22semidirect
71. #1270C22semidirect
72. #1270C22semidirect
73. #1270C22semidirect
74. #1270C22semidirect

Maximal subgroups

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

subgroupindex
#362582
#225322
#207202
#77242
#77142
#77042
#76982
#76742
#76582
#76402
#76262
#76202
#75992
#75722