Finite Group Databasebeta

← #360887

Subgroups — #360887

Order 512.

1346 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1798C211yesmaximal, characteristic
2C2×#1750C211yesmaximal, characteristic
3#13756C211yesmaximal, characteristic
4#11298C211yesmaximal, characteristic, complemented
5#11298C211yesmaximal, characteristic, complemented
6#11255C211yesmaximal, characteristic, complemented
7#11255C211yesmaximal, characteristic, complemented
8#10877C211yesmaximal, characteristic, complemented
9#10876C211yesmaximal, characteristic, complemented
10#10798C211yesmaximal, characteristic, complemented
11#10797C211yesmaximal, characteristic, complemented
12#10713C211yesmaximal, characteristic
13#10713C211yesmaximal, characteristic
14#10712C211yesmaximal, characteristic
15#10712C211yesmaximal, characteristic
16C22×#117C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#1798—24no—
28#1750—24no—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31C2×#336C2211yescharacteristic
32C2×#336C2211yescharacteristic
33C2×#336C2211yescharacteristic
34C2×#336C2211yescharacteristic
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C4⋊#95C411yescharacteristic
50C4⋊#95C411yescharacteristic
51C4⋊#95C411yescharacteristic
52C4⋊#95C411yescharacteristic
53C22⋊#95C411yescharacteristic
54C22⋊#95C411yescharacteristic
55C22⋊#95C411yescharacteristic
56C22⋊#95C411yescharacteristic
57C4×#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59C4×#95C2211yescharacteristic
60C4×#95C2211yescharacteristic
61C24×C4C2×C411yescharacteristic
62C24×C4C2×C411yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×#117—22no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—22no—
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—41no—
81C2×#117—41no—
82C2×#117—41no—
83C2×#117—41no—
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C22⋊C4C2×C411yescharacteristic
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C42—22no—
93C22×C42—22no—
94C22×C42—41no—
95C22×C42—41no—
96C22×C42—41no—
97C22×C42—41no—
98C22×C42C2×C411yescharacteristic
99C22×C42C2×C411yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—22no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—41no—
111C2×C4⋊C8—41no—
112C2×C22⋊C8—22no—
113C2×C22⋊C8—22no—
114C2×C22⋊C8—22no—
115C2×C22⋊C8—22no—
116C2×C22⋊C8—22no—
117C2×C22⋊C8—22no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8D414yes—
123C2×C22⋊C8Q814yes—
124C2×#97—22no—
125C2×#97—22no—
126C2×#97—41no—
127C2×C4×C8—22no—
128C2×C4×C8—22no—
129C2×C4×C8—41no—
130C2×#95C2×C411yescharacteristic
131C2×#95C2×C411yescharacteristic
132C2×#95C2×C411yescharacteristic
133C2×#95C2×C411yescharacteristic
134C2×#95C2×C411yescharacteristic
135C2×#95C2×C411yescharacteristic
136C2×#95C2×C411yescharacteristic
137C2×#95C2×C411yescharacteristic
138C2×#95C2×C411yescharacteristic
139C2×#95C2×C411yescharacteristic
140C2×#95C2×C411yescharacteristic
141C2×#95C2×C411yescharacteristic
142C2×#95C2×C411yescharacteristic
143C2×#95C2×C411yescharacteristic
144C2×#95C2×C411yescharacteristic
145C2×#95C2×C411yescharacteristic
146#336—22no—
147#336—22no—
148#336—22no—
149#336—22no—
150#336—22no—
151#336—22no—
152#336—22no—
153#336—22no—
154#336—41no—
155#336—41no—
156#336—41no—
157#336—41no—
158#336—41no—
159#336—41no—
160#336—41no—
161#336—41no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336—41no—
166C25C22×C411yescharacteristic
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—41no—
182C23×C4—41no—
183C23×C4—41no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—41no—
187C23×C4—41no—
188C23×C4—41no—
189C23×C4C22×C411yescharacteristic
190C23×C4C22×C411yescharacteristic
191C23×C4C22×C411yescharacteristic
192C23×C4C22×C411yescharacteristic
193C23×C4C22×C411yescharacteristic
194C23×C4C22×C411yescharacteristic
195C23×C4C22×C411yescharacteristic
196C23×C4C22×C411yescharacteristic
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C2×D412yes—
203C23×C4C2×Q812yes—
204C23×C4#4112yes—
205C23×C4#4112yes—
206C23×C4#4112yes—
207C23×C4#4112yes—
208C23×C4C2411yescharacteristic
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×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
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×C8C2×D412yes—
262C22×C8C2×D412yes—
263C22×C8C2×Q812yes—
264C22×C8C2×Q812yes—
265#117—44no—
266#117—44no—
267#117—44no—
268#117—44no—
269#117—44no—
270#117—44no—
271#117—44no—
272#117—44no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—41no—
295C2×C22⋊C4—41no—
296C2×C22⋊C4—41no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—22no—
306C2×C42—22no—
307C2×C42—21no—
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—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—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—41no—
332C2×C42—41no—
333C2×C42—41no—
334C2×C42—41no—
335C2×C42—44no—
336C2×C42—44no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42#4112yes—
340C2×C42#4112yes—
341C2×C42#4112yes—
342C2×C42#4112yes—
343C4⋊C8—44no—
344C4⋊C8—44no—
345C22⋊C8—28no—
346C22⋊C8—28no—
347C22⋊C8—44no—
348C22⋊C8—44no—
349#97—44no—
350C4×C8—44no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—22no—
358#95—22no—
359#95—41no—
360#95—41no—
361#95—41no—
362#95—41no—
363#95—41no—
364#95—41no—
365#95—41no—
366#95—41no—
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#11712yes—
380C24C4×D412yes—
381C24C4×Q812yes—
382C24C23×C411yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
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—21no—
412C22×C4—21no—
413C22×C4—21no—
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—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4#11712yes—
502C22×C4#11712yes—
503C22×C4#11712yes—
504C22×C4#11712yes—
505C22×C4#11712yes—
506C22×C4C4×D412yes—
507C22×C4C4×Q812yes—
508C22×C4C22⋊Q814yes—
509C22×C4#12314yes—
510C22×C4#12514yes—
511C22×C4#12614yes—
512C22×C4#13112yes—
513C22×C4#13112yes—
514C22×C4#13112yes—
515C22×C4#13112yes—
516C22×C4C22×D411yescharacteristic
517C22×C4C22×Q811yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C4H(5,𝔽2)11yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C4H(5,𝔽2)11yescharacteristic
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
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—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—44no—
603C42—44no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23#38714yes—
655C23C2×#11711yescharacteristic
656C23C2×#11711yescharacteristic
657C23C2×#11711yescharacteristic
658C23C2×C4×D411yescharacteristic
659C23C2×C4×Q811yescharacteristic
660C23#51811yescharacteristic
661C23#51811yescharacteristic
662C23C2×#13111yescharacteristic
663C23C2×#13111yescharacteristic
664C23C2×#13111yescharacteristic
665C23C2×#13111yescharacteristic
666C23#56811yescharacteristic
667C23#56811yescharacteristic
668C23#56811yescharacteristic
669C23#56811yescharacteristic
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—416no—
709C2×C4—416no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
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#38714yes—
771C2×C4C2×C22⋊Q811yescharacteristic
772C2×C4C2×#12311yescharacteristic
773C2×C4C2×#12511yescharacteristic
774C2×C4C2×#12611yescharacteristic
775C2×C4#52911yescharacteristic
776C2×C4#52911yescharacteristic
777C2×C4#52911yescharacteristic
778C2×C4#52911yescharacteristic
779C2×C4#53811yescharacteristic
780C2×C4#53811yescharacteristic
781C2×C4#53811yescharacteristic
782C2×C4#53811yescharacteristic
783C2×C4#54611yescharacteristic
784C2×C4#54611yescharacteristic
785C2×C4#54611yescharacteristic
786C2×C4#54611yescharacteristic
787C2×C4#55111yescharacteristic
788C2×C4#55111yescharacteristic
789C2×C4#55111yescharacteristic
790C2×C4#55111yescharacteristic
791C2×C4#55311yescharacteristic
792C2×C4#55311yescharacteristic
793C2×C4#55311yescharacteristic
794C2×C4#55311yescharacteristic
795C2×C4#55411yescharacteristic
796C2×C4#55411yescharacteristic
797C2×C4#55411yescharacteristic
798C2×C4#55411yescharacteristic
799C8—42no—
800C8—42no—
801C8—42no—
802C8—42no—
803C8—81no—
804C8—81no—
805C8—81no—
806C8—81no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22#228311yescharacteristic
823C22C2×#38711yescharacteristic
824C22#231211yescharacteristic
825C22#234211yescharacteristic
826C22#234211yescharacteristic
827C22#234511yescharacteristic
828C22#234511yescharacteristic
829C22#292211yescharacteristic
830C22#292211yescharacteristic
831C22#292311yescharacteristic
832C22#292311yescharacteristic
833C22#292411yescharacteristic
834C22#292411yescharacteristic
835C22#292411yescharacteristic
836C22#292411yescharacteristic
837C22#292511yescharacteristic
838C22#292511yescharacteristic
839C22#292511yescharacteristic
840C22#292511yescharacteristic
841C22#293111yescharacteristic
842C22#293211yescharacteristic
843C22#293511yescharacteristic
844C22#293511yescharacteristic
845C22#296011yescharacteristic
846C22#296111yescharacteristic
847C22#296211yescharacteristic
848C22#296211yescharacteristic
849C22#297611yescharacteristic
850C22#297611yescharacteristic
851C22#297611yescharacteristic
852C22#297611yescharacteristic
853C22#297711yescharacteristic
854C22#297711yescharacteristic
855C22#297811yescharacteristic
856C22#297811yescharacteristic
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4#244411yescharacteristic
871C4#244411yescharacteristic
872C4#245011yescharacteristic
873C4#245011yescharacteristic
874C4#250511yescharacteristic
875C4#250511yescharacteristic
876C4#251011yescharacteristic
877C4#251011yescharacteristic
878C2—44no—
879C2#1388311yescharacteristic
880C2#2078011yescharacteristic
881C2#2078111yescharacteristic
882C2#2102511yescharacteristic
883C2#2102611yescharacteristic
884C2#2190811yescharacteristic
885C2#2191011yescharacteristic
886C2#2256011yescharacteristic
887C2#2256011yescharacteristic
888C2#2256111yescharacteristic
889C2#2256111yescharacteristic
890C2#2263011yescharacteristic
891C2#2263011yescharacteristic
892C2#2263111yescharacteristic
893C2#2263111yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11298C2semidirect
5. #11298C2semidirect
6. #11255C2semidirect
7. #11255C2semidirect
8. #10877C2semidirect
9. #10876C2semidirect
10. #10798C2semidirect
11. #10797C2semidirect

Maximal subgroups

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

subgroupindex
C2×#17982
C2×#17502
#137562
#112982
#112552
#108772
#108762
#107982
#107972
#107132
#107122