Finite Group Databasebeta

← #759755

Subgroups — #759755

Order 512.

3198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2552C211yesmaximal, characteristic, complemented
2C2×#2442C212yesmaximal
3C22×#384C211yesmaximal, characteristic
4#16523C214yesmaximal, complemented
5#15228C212yesmaximal, complemented
6#15146C212yesmaximal, complemented
7#15145C212yesmaximal, complemented
8#15137C212yesmaximal, complemented
9#14728C214yesmaximal
10#14151C211yesmaximal, characteristic, complemented
11#14130C212yesmaximal
12#13911C211yesmaximal, characteristic, complemented
13#13910C211yesmaximal, characteristic, complemented
14#13907C212yesmaximal
15#13880C212yesmaximal
16C4×#380C211yesmaximal, characteristic
17C4×#380C211yesmaximal, characteristic
18C22×#125C2212yes—
19C23×C4⋊C4C2212yes—
20C23×C4⋊C4C2212yes—
21C23×C4⋊C4C2212yes—
22C23×C42C2211yescharacteristic
23#2552—28no—
24#2442—216no—
25C2×#400C2214yes—
26C2×#398C2214yes—
27C2×#398C2214yes—
28C2×#398C2214yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#385C2214yes—
36C2×#385C2214yes—
37C2×#384—28no—
38C2×#384C2212yes—
39C2×#384C2212yes—
40C2×#384C2212yes—
41C2×#384C2211yescharacteristic
42C2×#384C2212yes—
43C2×#384C2212yes—
44C2×#384C2211yescharacteristic
45C2×#382C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2214yes—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57#1444C2214yes—
58#1444C2214yes—
59#1444C2214yes—
60#1444C2214yes—
61#1444C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69C4⋊#95C2211yescharacteristic
70C4⋊#95C2212yes—
71C4⋊#95C2211yescharacteristic
72C4⋊#95C2212yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79#1434C2212yes—
80#1434C2212yes—
81C22⋊#95C2214yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C4×#95C2212yes—
86C24×C4C2311yescharacteristic
87C24×C4C2314yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×#125—28no—
91C2×#125—28no—
92C2×#125—44no—
93C22×C4⋊C4—28no—
94C22×C4⋊C4—28no—
95C22×C4⋊C4—28no—
96C22×C4⋊C4—28no—
97C22×C4⋊C4—28no—
98C22×C4⋊C4—44no—
99C22×C4⋊C4—44no—
100C22×C4⋊C4—44no—
101C22×C4⋊C4—44no—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C42—24no—
130C22×C42—24no—
131C22×C42Q818yes—
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2312yes—
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140#400—216no—
141#398—216no—
142#398—216no—
143#398—48no—
144#389—28no—
145#389—28no—
146#389—28no—
147#389—28no—
148#389—44no—
149#389—44no—
150#385—216no—
151#385—48no—
152#384—28no—
153#384—28no—
154#384—28no—
155#384—28no—
156#384—24no—
157#384—44no—
158#384D418yes—
159#382—28no—
160#380—24no—
161#380—24no—
162#380—216no—
163#380D418yes—
164#380Q818yes—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—24no—
167C4×C4⋊C4—24no—
168C4×C4⋊C4—24no—
169C4×C22⋊C4—28no—
170C4×C22⋊C4—28no—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C25C2411yescharacteristic
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—28no—
213C23×C4—28no—
214C23×C4—28no—
215C23×C4—28no—
216C23×C4—44no—
217C23×C4—44no—
218C23×C4—44no—
219C23×C4C2×D414yes—
220C23×C4C2×Q814yes—
221C23×C4C2×Q814yes—
222C23×C4C2×Q814yes—
223C23×C4C2×Q814yes—
224C23×C4#4114yes—
225C23×C4#4114yes—
226C23×C4C2412yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2414yes—
231C23×C4C2412yes—
232C23×C4C2412yes—
233C23×C4C2414yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2411yescharacteristic
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242#125—432no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—28no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—28no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—432no—
288C2×C4⋊C4—432no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—432no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D418yes—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4C2×D418yes—
313C2×C4⋊C4C2×Q814yes—
314C2×C4⋊C4C2×Q814yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4C2×D418yes—
326C2×C22⋊C4C2×Q818yes—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—232no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42C2×D414yes—
347C2×C42C2×Q814yes—
348C2×C42C2×Q814yes—
349C2×C42C2×Q814yes—
350C2×C42C2×Q814yes—
351C2×C42#4114yes—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—28no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95C2×D418yes—
377#95C2×Q818yes—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24C22×D412yes—
387C24C22×Q812yes—
388C24C22×Q812yes—
389C24C2×#4112yes—
390C24C2×#4112yes—
391C24H(5,𝔽2)12yes—
392C242−1+412yes—
393C24C2511yescharacteristic
394C22×C4—28no—
395C22×C4—28no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—28no—
425C22×C4—28no—
426C22×C4—28no—
427C22×C4—28no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—416no—
495C22×C4—416no—
496C22×C4—416no—
497C22×C4—416no—
498C22×C4—88no—
499C22×C4—88no—
500C22×C4—88no—
501C22×C4#125116yescomplemented
502C22×C4C4⋊Q8116yes—
503C22×C4C22×D414yes—
504C22×C4C22×D414yes—
505C22×C4C22×D418yes—
506C22×C4C22×D412yes—
507C22×C4C22×D412yes—
508C22×C4C22×D412yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×Q814yes—
512C22×C4C22×Q814yes—
513C22×C4C22×Q812yes—
514C22×C4C22×Q812yes—
515C22×C4C22×Q812yes—
516C22×C4C22×Q812yes—
517C22×C4C22×Q812yes—
518C22×C4C22×Q812yes—
519C22×C4C22×Q812yes—
520C22×C4C22×Q812yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C4H(5,𝔽2)12yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C42−1+412yes—
532C22×C42−1+412yes—
533C22×C42−1+412yes—
534C4⋊C4—216no—
535C4⋊C4—28no—
536C4⋊C4—216no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—48no—
541C4⋊C4—416no—
542C4⋊C4—416no—
543C4⋊C4—416no—
544C4⋊C4—416no—
545C4⋊C4—416no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—88no—
554C4⋊C4—88no—
555C4⋊C4—88no—
556C4⋊C4—88no—
557C22⋊C4—216no—
558C22⋊C4—216no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C42—28no—
562C42—28no—
563C42—28no—
564C42—48no—
565C42—48no—
566C42—48no—
567C42—48no—
568C42C22⋊Q8116yes—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23C2×#12514yes—
598C23C2×C4⋊Q814yes—
599C23#54414yes—
600C23#54714yes—
601C23#55014yes—
602C23#55414yes—
603C23#55714yes—
604C23C23×D411yescharacteristic
605C23C23×D411yescharacteristic
606C23C23×Q811yescharacteristic
607C23C23×Q811yescharacteristic
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C22×#4111yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×H(5,𝔽2)11yescharacteristic
613C23C2×H(5,𝔽2)11yescharacteristic
614C23C2×H(5,𝔽2)11yescharacteristic
615C23C2×2−1+411yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C2×C4—232no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
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—232no—
645C2×C4—232no—
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—28no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—832no—
717C2×C4C2×C22⋊Q814yes—
718C2×C4C2×C22⋊Q814yes—
719C2×C4C2×C22⋊Q814yes—
720C2×C4C2×#12514yes—
721C2×C4C2×#12514yes—
722C2×C4C2×C4⋊Q814yes—
723C2×C4C2×C4⋊Q814yes—
724C2×C4#54414yes—
725C2×C4#54414yes—
726C2×C4#54414yes—
727C2×C4D4214yes—
728C2×C4#54614yes—
729C2×C4#54714yes—
730C2×C4#54814yes—
731C2×C4D4×Q814yes—
732C2×C4#55214yes—
733C2×C4#55314yes—
734C2×C4#55414yes—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22#255218yescomplemented
750C22C22×C22⋊Q811yescharacteristic
751C22C22×#12511yescharacteristic
752C22C22×C4⋊Q811yescharacteristic
753C22C2×#54411yescharacteristic
754C22C2×#54411yescharacteristic
755C22C2×#54411yescharacteristic
756C22C2×#54411yescharacteristic
757C22C2×D4211yescharacteristic
758C22C2×#54611yescharacteristic
759C22C2×#54711yescharacteristic
760C22C2×#54711yescharacteristic
761C22C2×#54811yescharacteristic
762C22C2×D4×Q811yescharacteristic
763C22C2×#55011yescharacteristic
764C22C2×#55211yescharacteristic
765C22C2×#55311yescharacteristic
766C22C2×#55411yescharacteristic
767C22C2×#55411yescharacteristic
768C22C2×#55711yescharacteristic
769C22#348411yescharacteristic
770C22#348611yescharacteristic
771C22#349211yescharacteristic
772C22#349211yescharacteristic
773C22#349811yescharacteristic
774C22#349911yescharacteristic
775C22#350311yescharacteristic
776C22#350311yescharacteristic
777C22#350811yescharacteristic
778C22#350911yescharacteristic
779C22#351111yescharacteristic
780C22#351111yescharacteristic
781C22#354311yescharacteristic
782C22#354411yescharacteristic
783C22#355211yescharacteristic
784C22#355211yescharacteristic
785C4—24no—
786C4—24no—
787C4—24no—
788C4—24no—
789C4—44no—
790C4—44no—
791C4—44no—
792C4—48no—
793C4—44no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—84no—
798C4—82no—
799C4#244018yes—
800C4#244218yescomplemented
801C2—28no—
802C2C2×#244011yescharacteristic
803C2C2×#244211yescharacteristic
804C2C2×#255211yescharacteristic
805C2#3522411yescharacteristic
806C2#3527511yescharacteristic
807C2#3528611yescharacteristic
808C2#3762311yescharacteristic
809C2#5912411yescharacteristic
810C2#5912511yescharacteristic
811C2#5913611yescharacteristic
812C2#5914411yescharacteristic
813C2#5930411yescharacteristic
814C2#5930511yescharacteristic
815C2#5931211yescharacteristic
816C2#5932111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2552C2semidirect
4. #16523C2semidirect
5. #15228C2semidirect
6. #15146C2semidirect
7. #15145C2semidirect
8. #15137C2semidirect
10. #14151C2semidirect
12. #13911C2semidirect
13. #13910C2semidirect
501. C22×C4#125semidirect
749. C22#2552semidirect
800. C4#2442semidirect

Maximal subgroups

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

subgroupindex
C2×#25522
C2×#24422
C22×#3842
#165232
#152282
#151462
#151452
#151372
#147282
#141512
#141302
#139112
#139102
#139072
#138802
C4×#3802