Finite Group Databasebeta

← #669481

Subgroups — #669481

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2855C211yesmaximal, characteristic, complemented
3C2×C4×#123C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5#16104C214yesmaximal, complemented
6#15354C214yesmaximal, complemented
7#15179C212yesmaximal, complemented
8#15128C212yesmaximal, complemented
9#14934C212yesmaximal, complemented
10#14720C212yesmaximal, complemented
11#14139C211yesmaximal, characteristic, complemented
12#14130C212yesmaximal, complemented
13#14017C212yesmaximal, complemented
14#14015C212yesmaximal
15#13968C212yesmaximal
16#13924C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic
18C2×#554—28no—
19C2×#554—28no—
20C2×#554—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#125C2212yes—
23C22×#123C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C4⋊C4C2212yes—
35C23×C42C2211yescharacteristic
36#2855—28no—
37C2×#395C2214yes—
38C4×#123—28no—
39C2×#391C2212yes—
40C2×#391C2212yes—
41C2×#389—28no—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2214yes—
46C2×#388C2212yes—
47C2×#387C2214yes—
48C2×#387C2212yes—
49C2×#386C2212yes—
50C2×#386C2211yescharacteristic
51C2×#385C2212yes—
52C2×#385C2211yescharacteristic
53C2×#385C2214yes—
54C2×#381C2212yes—
55C2×#381C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C22×#95C2212yes—
62#1446C2214yes—
63#1445C2214yes—
64#1444C2214yes—
65#1444C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2212yes—
72#1441C2214yes—
73#1441C2214yes—
74#1440C2214yes—
75#1439C2212yes—
76#1439C2214yes—
77#1436C2214yes—
78#1436C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99#554—2128no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×#125—28no—
104C2×#125—28no—
105C2×#125—28no—
106C2×#123—24no—
107C2×#123—24no—
108C2×#123Q818yescomplemented
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8D418yes—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×D4—28no—
125C2×C4×D4—28no—
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—28no—
129C2×C4×D4D418yes—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—28no—
137C22×C4⋊C4—28no—
138C22×C4⋊C4—48no—
139C22×C4⋊C4D418yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176#395—48no—
177#391—28no—
178#391—28no—
179#389—28no—
180#389—28no—
181#389—216no—
182#389—28no—
183#388—28no—
184#387—216no—
185#387—28no—
186#386—24no—
187#386—28no—
188#385—28no—
189#385—24no—
190#385—48no—
191#381—28no—
192#381—24no—
193#380—24no—
194#380—28no—
195C4×C4⋊C4—28no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—24no—
198C2×#95—28no—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—24no—
230C22×Q8—44no—
231C22×Q8—44no—
232C22×Q8C2×D414yes—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4C2×D414yes—
238C22×D4C2×Q814yes—
239C22×D4#4114yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—28no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—44no—
266C23×C4—42no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D418yes—
276C23×C4C2×Q814yes—
277C23×C4C2414yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2414yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C4⋊Q8—232no—
293#125—264no—
294#123—232no—
295C22⋊Q8—232no—
296C22⋊Q8—264no—
297C22⋊Q8—264no—
298C22⋊Q8—232no—
299C4×Q8—232no—
300C4×D4—264no—
301C4×D4—232no—
302C2×C4⋊C4—232no—
303C2×C4⋊C4—232no—
304C2×C4⋊C4—232no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—432no—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D418yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D418yes—
357C2×C4⋊C4C2×Q818yes—
358C2×C4⋊C4#4118yes—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4C2×D414yes—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×Q814yes—
388C2×C22⋊C4C2×Q818yes—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—416no—
404C2×C42C2×D414yes—
405#95—28no—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C22×Q812yes—
444C24C22×Q812yes—
445C24C2×#4112yes—
446C24C2×#4112yes—
447C242−1+412yes—
448C242−1+412yes—
449C24C2511yescharacteristic
450C2×Q8—216no—
451C2×Q8—28no—
452C2×Q8—216no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—48no—
456C2×Q8—84no—
457C2×Q8—84no—
458C2×Q8—88no—
459C2×Q8—88no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4C22⋊Q8116yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—216no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—28no—
533C22×C4—216no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—416no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—416no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—88no—
568C22×C4—88no—
569C22×C4—88no—
570C22×C4—88no—
571C22×C4#120116yes—
572C22×C4C22×D414yes—
573C22×C4C22×D412yes—
574C22×C4C22×D414yes—
575C22×C4C22×D412yes—
576C22×C4C22×D414yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×Q814yes—
586C22×C4C22×Q814yes—
587C22×C4C22×Q812yes—
588C22×C4C2×#4118yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4114yes—
591C22×C4H(5,𝔽2)14yes—
592C22×C42−1+414yes—
593C4⋊C4—216no—
594C4⋊C4—216no—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—216no—
598C4⋊C4—28no—
599C4⋊C4—216no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—48no—
607C4⋊C4—416no—
608C4⋊C4—416no—
609C4⋊C4—416no—
610C4⋊C4—48no—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—216no—
616C22⋊C4—28no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—44no—
620C22⋊C4—48no—
621C42—216no—
622C42—28no—
623C42—48no—
624C42—48no—
625C42—48no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23C2×#12014yes—
665C23C2×C22⋊Q814yes—
666C23C2×C22⋊Q814yes—
667C23#53614yes—
668C23#54814yes—
669C23#54814yes—
670C23D4×Q814yes—
671C23D4×Q814yes—
672C23C23×D411yescharacteristic
673C23C23×D411yescharacteristic
674C23C23×D411yescharacteristic
675C23C23×Q811yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4112yes—
678C23C2×H(5,𝔽2)12yes—
679C23C2×2−1+412yes—
680C23C2×2−1+411yescharacteristic
681C23C2×2−1+411yescharacteristic
682C23#58512yes—
683Q8—416no—
684Q8—816no—
685D4—232no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—232no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—28no—
723C2×C4—432no—
724C2×C4—416no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—416no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—416no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—816no—
774C2×C4—816no—
775C2×C4C2×#12014yes—
776C2×C4C2×#12014yes—
777C2×C4C2×C22⋊Q814yes—
778C2×C4#52514yes—
779C2×C4#53614yes—
780C2×C4#54718yes—
781C2×C4#54718yes—
782C22—28no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—24no—
793C22—28no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—42no—
802C22—44no—
803C22#240918yes—
804C22C22×#12011yescharacteristic
805C22C22×C22⋊Q811yescharacteristic
806C22C2×#52511yescharacteristic
807C22C2×#53611yescharacteristic
808C22C2×#53611yescharacteristic
809C22C2×#54712yes—
810C22C2×#54712yes—
811C22C2×#54811yescharacteristic
812C22C2×#54811yescharacteristic
813C22C2×D4×Q811yescharacteristic
814C22C2×D4×Q811yescharacteristic
815C22Q8×#4112yes—
816C22#348112yes—
817C22#348411yescharacteristic
818C22#348511yescharacteristic
819C22#348812yes—
820C22#348812yes—
821C22#350312yes—
822C22#351512yes—
823C22#351612yes—
824C22#352012yes—
825C22#355212yes—
826C22#356312yes—
827C4—24no—
828C4—24no—
829C4—44no—
830C4—42no—
831C4—44no—
832C4—48no—
833C4—44no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—44no—
838C4—42no—
839C4—82no—
840C4—84no—
841C4#240618yes—
842C2—28no—
843C2—44no—
844C2C2×#240911yescharacteristic
845C2C2×#240611yescharacteristic
846C2#3551211yescharacteristic
847C2#3627512yes—
848C2#3652811yescharacteristic
849C2#3654711yescharacteristic
850C2#3804012yes—
851C2#3912211yescharacteristic
852C2#3959211yescharacteristic
853C2#5907612yes—
854C2#5911312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2855C2semidirect
4. C22×#389C2semidirect
5. #16104C2semidirect
6. #15354C2semidirect
7. #15179C2semidirect
8. #15128C2semidirect
9. #14934C2semidirect
10. #14720C2semidirect
11. #14139C2semidirect
12. #14130C2semidirect
13. #14017C2semidirect
16. #13924C2semidirect
108. C2×#123Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#28552
C2×C4×#1232
C22×#3892
#161042
#153542
#151792
#151282
#149342
#147202
#141392
#141302
#140172
#140152
#139682
#139242
#138722