Finite Group Databasebeta

← #440918

Subgroups — #440918

Order 512.

1296 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2441C211yesmaximal, characteristic
2C2×#2059C211yesmaximal, characteristic, complemented
3C2×#1992C211yesmaximal, characteristic, complemented
4#15216C211yesmaximal, characteristic
5#11385C211yesmaximal, characteristic, complemented
6#11385C211yesmaximal, characteristic, complemented
7#11357C211yesmaximal, characteristic, complemented
8#11220C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic
11#11095C211yesmaximal, characteristic
12#10922C211yesmaximal, characteristic
13#10881C211yesmaximal, characteristic, complemented
14#10731C211yesmaximal, characteristic
15#10731C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#125C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×#97C2211yescharacteristic
24#2441—24no—
25#2441—24no—
26C2×#399—21no—
27C2×#396—21no—
28C2×#389—21no—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#387—21no—
32C2×#384C2211yescharacteristic
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#2059—24no—
38#1992—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×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1442—21no—
57#1442—21no—
58#1439—21no—
59#1439—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×#125—22no—
69C2×#125—22no—
70C2×#125—22no—
71C2×#125—22no—
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—22no—
75C2×#125—22no—
76C2×#125—41no—
77C2×#125—41no—
78C2×#125—41no—
79C2×#125—41no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—41no—
85C2×#117—41no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4D411yescharacteristic
107C22×C22⋊C4D411yescharacteristic
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—41no—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—41no—
117C2×C22⋊C8—41no—
118C2×C22⋊C8—41no—
119C2×C22⋊C8—41no—
120C2×C22⋊C8—41no—
121C2×C22⋊C8Q814yes—
122C2×C22⋊C8Q814yes—
123C2×#97—22no—
124C2×#97—41no—
125C2×#97—41no—
126#399—28no—
127#396—28no—
128#389—28no—
129#389—22no—
130#389—22no—
131#389—22no—
132#389D414yes—
133#387—28no—
134#384—22no—
135#384D414yes—
136#380—22no—
137#380—22no—
138#380—22no—
139#380—22no—
140#380—41no—
141#380—41no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—22no—
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×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—41no—
166#340—41no—
167#340—41no—
168#340—41no—
169#340—41no—
170#340—41no—
171#336—22no—
172#336—41no—
173#336—41no—
174C25C2×D411yescharacteristic
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×C4—21no—
194C23×C4—21no—
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×Q812yes—
201C23×C4C2×Q812yes—
202C23×C4C2411yescharacteristic
203C22×C8—21no—
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×C8C2×Q812yes—
228C22×C8C2×Q812yes—
229C22×C8C2×Q812yes—
230C22×C8C2×Q812yes—
231#125—28no—
232#125—44no—
233#125—44no—
234#125—44no—
235#125—44no—
236#125—44no—
237#125—44no—
238#125—44no—
239#117—44no—
240#117—44no—
241#117—44no—
242#117—44no—
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—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
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—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—42no—
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—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—81no—
304C2×C4⋊C4—81no—
305C2×C4⋊C4—81no—
306C2×C4⋊C4—81no—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4#4112yes—
312C2×C4⋊C4#4112yes—
313C2×C4⋊C4#4112yes—
314C2×C4⋊C4#4112yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—41no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—81no—
330C2×C22⋊C4—81no—
331C2×C22⋊C4—81no—
332C2×C22⋊C4—81no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—24no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42C2×D412yes—
347C2×C42C2×D412yes—
348#107—44no—
349#106—44no—
350C22⋊C8—44no—
351C22⋊C8—44no—
352#97—44no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—22no—
357#95—22no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—81no—
363#95—81no—
364#95—81no—
365#95—81no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24C4⋊Q812yes—
381C24C22×D411yescharacteristic
382C22×C4—21no—
383C22×C4—22no—
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—22no—
394C22×C4—22no—
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—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—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
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—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
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×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4#12012yes—
499C22×C4#12012yes—
500C22×C4C4⋊Q812yes—
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×Q811yescharacteristic
504C22×C4C22×Q811yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C4H(5,𝔽2)11yescharacteristic
513C22×C42−1+411yescharacteristic
514C22×C42−1+411yescharacteristic
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C4⋊C4#12414yes—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C22⋊C4—48no—
586C22⋊C4—84no—
587C22⋊C4—84no—
588C22⋊C4—84no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—48no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×#12011yescharacteristic
634C23C2×C4⋊Q811yescharacteristic
635C23#53611yescharacteristic
636C23#54611yescharacteristic
637C23#54611yescharacteristic
638C23#54611yescharacteristic
639C23#54611yescharacteristic
640C23#57511yescharacteristic
641C23#57511yescharacteristic
642C23#57511yescharacteristic
643C23#57511yescharacteristic
644C23#57611yescharacteristic
645C23#57711yescharacteristic
646C23#57711yescharacteristic
647C23#57811yescharacteristic
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
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—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
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—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4#52511yescharacteristic
748C2×C4C2×#12411yescharacteristic
749C2×C4#53311yescharacteristic
750C2×C4#53311yescharacteristic
751C2×C4#53511yescharacteristic
752C2×C4#53511yescharacteristic
753C2×C4#54211yescharacteristic
754C2×C4#54211yescharacteristic
755C2×C4#54211yescharacteristic
756C2×C4#54211yescharacteristic
757C2×C4#54311yescharacteristic
758C2×C4#54311yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54611yescharacteristic
763C2×C4D4×Q811yescharacteristic
764C2×C4D4×Q811yescharacteristic
765C2×C4D4×Q811yescharacteristic
766C2×C4D4×Q811yescharacteristic
767C2×C4#55411yescharacteristic
768C2×C4#55411yescharacteristic
769C2×C4#55411yescharacteristic
770C2×C4#55411yescharacteristic
771C2×C4#55611yescharacteristic
772C2×C4#55611yescharacteristic
773C2×C4#56211yescharacteristic
774C2×C4#56211yescharacteristic
775C8—42no—
776C8—42no—
777C8—42no—
778C8—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22#240411yescharacteristic
795C22#243411yescharacteristic
796C22#243511yescharacteristic
797C22#254911yescharacteristic
798C22#254911yescharacteristic
799C22#270011yescharacteristic
800C22#270011yescharacteristic
801C22#300511yescharacteristic
802C22#300511yescharacteristic
803C22#301211yescharacteristic
804C22#301311yescharacteristic
805C22#316211yescharacteristic
806C22#316311yescharacteristic
807C22#316411yescharacteristic
808C22#316611yescharacteristic
809C22#324011yescharacteristic
810C22#324011yescharacteristic
811C22#324111yescharacteristic
812C22#324211yescharacteristic
813C22#330711yescharacteristic
814C22#330711yescharacteristic
815C22#330711yescharacteristic
816C22#330911yescharacteristic
817C22#330911yescharacteristic
818C22#330911yescharacteristic
819C22#331511yescharacteristic
820C22#331511yescharacteristic
821C22#331511yescharacteristic
822C22#331711yescharacteristic
823C22#331711yescharacteristic
824C22#331711yescharacteristic
825C22#332211yescharacteristic
826C22#332311yescharacteristic
827C22#332611yescharacteristic
828C22#332711yescharacteristic
829C4—44no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—161no—
841C4—161no—
842C4#246511yescharacteristic
843C4#246511yescharacteristic
844C4#249211yescharacteristic
845C4#249211yescharacteristic
846C4#269211yescharacteristic
847C4#269211yescharacteristic
848C4#269211yescharacteristic
849C4#269211yescharacteristic
850C2—82no—
851C2#1567111yescharacteristic
852C2#2397511yescharacteristic
853C2#2397811yescharacteristic
854C2#2581711yescharacteristic
855C2#2582211yescharacteristic
856C2#2589211yescharacteristic
857C2#2589311yescharacteristic
858C2#2877811yescharacteristic
859C2#2878011yescharacteristic
860C2#2878611yescharacteristic
861C2#2878811yescharacteristic
862C2#3175511yescharacteristic
863C2#3175711yescharacteristic
864C2#3175911yescharacteristic
865C2#3176111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×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
2. C2×#2059C2semidirect
3. C2×#1992C2semidirect
5. #11385C2semidirect
6. #11385C2semidirect
7. #11357C2semidirect
8. #11220C2semidirect
9. #11219C2semidirect
13. #10881C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24412
C2×#20592
C2×#19922
#152162
#113852
#113572
#112202
#112192
#110962
#110952
#109222
#108812
#107312