Finite Group Databasebeta

← #636803

Subgroups — #636803

Order 512.

4392 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#2854C211yesmaximal, characteristic, complemented
3C2×#2414C212yesmaximal, complemented
4#16654C214yesmaximal, complemented
5#16251C212yesmaximal, complemented
6#16250C212yesmaximal, complemented
7#15158C211yesmaximal, characteristic, complemented
8#15157C211yesmaximal, characteristic, complemented
9#15129C211yesmaximal, characteristic, complemented
10#15123C211yesmaximal, characteristic, complemented
11#14933C212yesmaximal, complemented
12#14930C214yesmaximal, complemented
13#14928C212yesmaximal, complemented
14#14264C212yesmaximal, complemented
15#14257C212yesmaximal, complemented
16#13871C212yesmaximal, complemented
17#13756C211yesmaximal, characteristic, complemented
18C2×#529—28no—
19C2×#529—216no—
20C22×#126C2212yes—
21C22×#125C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#123C2212yes—
24C22×#123C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×#117C2212yes—
33C22×#117C2212yes—
34C23×C42C2211yescharacteristic
35#2854—28no—
36#2414—216no—
37C2×#395C2212yes—
38C2×#394C2214yes—
39C2×#394C2212yes—
40C2×#393C2212yes—
41C2×#392C2214yes—
42C2×#392C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2214yes—
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2214yes—
53C2×#386C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58#1444C2214yes—
59#1442C2214yes—
60#1441C2214yes—
61#1441C2212yes—
62#1441C2212yes—
63#1440C2214yes—
64#1440C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1437C2214yes—
77#1436C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C4×#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2314yes—
92C23×D4C2312yes—
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97#529—2128no—
98C2×#126—28no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#125—28no—
102C2×#125—24no—
103C2×#124—28no—
104C2×#124—24no—
105C2×#123—28no—
106C2×#123—28no—
107C2×#123—28no—
108C2×#123—28no—
109C2×#123—44no—
110C2×#123—44no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—28no—
113C2×#121—28no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—28no—
117C2×#121—28no—
118C2×#121—28no—
119C2×#121—44no—
120C2×C4×Q8—24no—
121C2×C4×Q8—28no—
122C2×C4×D4—28no—
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4D4116yescomplemented
127C2×#117—28no—
128C2×#117—28no—
129C2×#117—28no—
130C2×#117—28no—
131C2×#117—28no—
132C2×#117—44no—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C42—28no—
166C22×C42D418yescomplemented
167C22×C42C2314yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173#395—44no—
174#394—216no—
175#394—44no—
176#393—44no—
177#392—216no—
178#392—44no—
179#390—216no—
180#390—24no—
181#390—24no—
182#390—28no—
183#389—24no—
184#389—24no—
185#389—28no—
186#388—216no—
187#388—28no—
188#388—28no—
189#386—28no—
190#380—24no—
191#380—28no—
192#380—28no—
193#380—44no—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C25C2412yes—
212C25C2412yes—
213C25C2411yescharacteristic
214C22×Q8—24no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—42no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—28no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—44no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4C2×D418yes—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4C2×D418yes—
266C23×C4C2×D414yes—
267C23×C4C2×D418yes—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2414yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284#126—264no—
285#125—232no—
286#124—232no—
287#123—264no—
288#123—432no—
289C22⋊Q8—232no—
290#121—232no—
291#121—432no—
292#121—416no—
293C4×Q8—232no—
294C4×D4—232no—
295C4×D4—264no—
296#117—264no—
297#117—432no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4C2×D418yes—
335C2×C4⋊C4#4118yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D418yes—
387C2×C22⋊C4C2×D418yes—
388C2×C42—232no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—28no—
396C2×C42—28no—
397C2×C42—44no—
398C2×C42C2×D414yes—
399C2×C42C2×D418yes—
400C2×C42C2×D414yes—
401C2×C42C2×D414yes—
402C2×C42C2×D414yes—
403#95—24no—
404#95—28no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—42no—
412#95—44no—
413#95—44no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—22no—
453C24—24no—
454C24C22×D414yes—
455C24C22×D412yes—
456C24C22×D414yes—
457C24C2511yescharacteristic
458C2×Q8—28no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×D4—28no—
464C2×D4—216no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—44no—
470C2×D4—416no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—416no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—88no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—88no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—216no—
540C22×C4—28no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4#120116yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D414yes—
590C22×C4C2×#4118yes—
591C22×C4C2×#4114yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C42−1+412yes—
596C4⋊C4—216no—
597C4⋊C4—216no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—48no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—88no—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—416no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—416no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C42—28no—
629C42—28no—
630C42—28no—
631C42—28no—
632C42—216no—
633C42—416no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23C2×#12014yes—
715C23C23×D411yescharacteristic
716C23C23×D412yes—
717C23C22×#4112yes—
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×2−1+411yescharacteristic
722C23#58512yes—
723C23#58511yescharacteristic
724C23#58511yescharacteristic
725C23#58512yes—
726Q8—416no—
727D4—416no—
728D4—432no—
729D4—832no—
730D4—816no—
731D4—88no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—232no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—416no—
763C2×C4—416no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—432no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4C2×#12014yes—
812C2×C4C2×#12014yes—
813C2×C4#53214yes—
814C2×C4#53514yes—
815C2×C4#53714yes—
816C2×C4#54618yes—
817C2×C4#54718yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—84no—
848C22—84no—
849C22—84no—
850C22—84no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22C22×#12011yescharacteristic
856C22C2×#53211yescharacteristic
857C22C2×#53511yescharacteristic
858C22C2×#53711yescharacteristic
859C22#344911yescharacteristic
860C22#344911yescharacteristic
861C22#344912yes—
862C22#344912yes—
863C22#344911yescharacteristic
864C22C2×#54612yes—
865C22C2×#54712yes—
866C22#348812yes—
867C22#348812yes—
868C22#351412yes—
869C22#351712yes—
870C22#352112yes—
871C22#352412yes—
872C22#354611yescharacteristic
873C22#354611yescharacteristic
874C22#354711yescharacteristic
875C22#354711yescharacteristic
876C22#356212yes—
877C22#356512yes—
878C4—24no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—44no—
883C4—48no—
884C4—44no—
885C4—42no—
886C4—44no—
887C4—82no—
888C4—84no—
889C4—82no—
890C4—82no—
891C4#243018yes—
892C2—44no—
893C2—84no—
894C2—162no—
895C2#3463211yescharacteristic
896C2C2×#243011yescharacteristic
897C2#3519111yescharacteristic
898C2#3521211yescharacteristic
899C2#3525011yescharacteristic
900C2#3755311yescharacteristic
901C2#3762111yescharacteristic
902C2#3803312yes—
903C2#3803412yes—
904C2#3804912yes—
905C2#3805012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C2×#2854C2semidirect
3. C2×#2414C2semidirect
4. #16654C2semidirect
5. #16251C2semidirect
6. #16250C2semidirect
7. #15158C2semidirect
8. #15157C2semidirect
9. #15129C2semidirect
10. #15123C2semidirect
11. #14933C2semidirect
12. #14930C2semidirect
13. #14928C2semidirect
14. #14264C2semidirect
15. #14257C2semidirect
16. #13871C2semidirect
17. #13756C2semidirect
126. C2×C4×D4D4semidirect
166. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#28542
C2×#24142
#166542
#162512
#162502
#151582
#151572
#151292
#151232
#149332
#149302
#149282
#142642
#142572
#138712
#137562