Finite Group Databasebeta

← #873712

Subgroups — #873712

Order 512.

2846 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2429C211yesmaximal, characteristic
4C2×#2423C211yesmaximal, characteristic
5#16521C214yesmaximal
6#15520C214yesmaximal, complemented
7#15460C214yesmaximal, complemented
8#15199C211yesmaximal, characteristic, complemented
9#15196C211yesmaximal, characteristic, complemented
10#15188C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic
12#15180C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic
14#14702C211yesmaximal, characteristic
15#14408C214yesmaximal
16#14024C211yesmaximal, characteristic, complemented
17#13976C211yesmaximal, characteristic, complemented
18#13926C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2857—28no—
30#2546—28no—
31#2429—28no—
32#2423—28no—
33C2×#399C2212yes—
34C2×#398C2212yes—
35C2×#398C2214yes—
36C2×#398C2212yes—
37C2×#396C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#389C2214yes—
49C2×#389C2214yes—
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2212yes—
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#387C2212yes—
56C2×#385C2212yes—
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#380C2214yes—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2212yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—42no—
104C2×C4⋊Q8—42no—
105C2×C4⋊Q8—42no—
106C2×C4⋊Q8—42no—
107C2×C4⋊Q8—42no—
108C2×C4⋊Q8D418yes—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C4×Q8—24no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—42no—
123C2×C4×Q8—42no—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C42—24no—
154C22×C42—42no—
155C22×C42—42no—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165#399—28no—
166#398—216no—
167#398—28no—
168#398—28no—
169#396—28no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—42no—
178#391—42no—
179#391—42no—
180#389—216no—
181#389—216no—
182#389—24no—
183#389—24no—
184#389—28no—
185#388—28no—
186#388—28no—
187#387—28no—
188#385Q8116yescomplemented
189#384—24no—
190#384—24no—
191#384—42no—
192#380—24no—
193#380—216no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—42no—
196C4×C22⋊C4—42no—
197C4×C22⋊C4D418yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C25C2411yescharacteristic
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8C2×D414yes—
247C22×Q8C2×D414yes—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4C2×D414yes—
261C23×C4C2×Q818yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C4⋊Q8—416no—
281C4⋊Q8—416no—
282C4⋊Q8—416no—
283C22⋊Q8—416no—
284C22⋊Q8—416no—
285C22⋊Q8—416no—
286C4×Q8—416no—
287C4×Q8—416no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D4116yes—
347C2×C4⋊C4C2×Q818yes—
348C2×C4⋊C4C2×Q818yes—
349C2×C4⋊C4#4114yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4C2×D414yes—
365C2×C22⋊C4C2×D414yes—
366C2×C22⋊C4C2×Q818yes—
367C2×C22⋊C4C2×Q818yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—416no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396#95—24no—
397#95—24no—
398#95—28no—
399#95—28no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—28no—
407#95—24no—
408#95—28no—
409#95—24no—
410#95—28no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95C2×D414yes—
421#95C2×D414yes—
422#95C2×Q818yes—
423#95C2×Q818yes—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24C22×D412yes—
434C24C22×Q814yes—
435C24C2511yescharacteristic
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4C22×D412yes—
557C22×C4C22×D414yes—
558C22×C4C22×D412yes—
559C22×C4C22×D414yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D414yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×Q814yes—
567C22×C4C22×Q814yes—
568C22×C4C22×Q814yes—
569C22×C4C22×Q814yes—
570C22×C4C22×Q814yes—
571C22×C4C22×Q814yes—
572C22×C4C2×#4114yes—
573C22×C4C2×#4112yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C4H(5,𝔽2)12yes—
577C22×C42−1+414yes—
578C22×C42−1+412yes—
579C4⋊C4—28no—
580C4⋊C4—216no—
581C4⋊C4—416no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—416no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—416no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—84no—
599C4⋊C4—84no—
600C4⋊C4—88no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—84no—
607C22⋊C4C4⋊Q8116yescomplemented
608C42—28no—
609C42—28no—
610C42—28no—
611C42—48no—
612C42—48no—
613C42—48no—
614C42—44no—
615C42—44no—
616C42—44no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23C2×C4⋊Q814yes—
640C23C23×D411yescharacteristic
641C23C23×D411yescharacteristic
642C23C23×Q812yes—
643C23C22×#4111yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)11yescharacteristic
646C23C2×H(5,𝔽2)11yescharacteristic
647C23C2×2−1+411yescharacteristic
648C23C2×2−1+412yes—
649C23#58512yes—
650C23#58512yes—
651Q8—416no—
652Q8—416no—
653Q8—88no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—28no—
694C2×C4—432no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4C2×C4⋊Q814yes—
755C2×C4C2×C4⋊Q814yes—
756C2×C4#53414yes—
757C2×C4#53714yes—
758C2×C4#54014yes—
759C2×C4D4214yes—
760C2×C4#54614yes—
761C2×C4#54714yes—
762C2×C4D4×Q818yes—
763C2×C4#56214yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—42no—
774C22—44no—
775C22C22×C4⋊Q811yescharacteristic
776C22C2×#53411yescharacteristic
777C22C2×#53711yescharacteristic
778C22#344911yescharacteristic
779C22C2×#54011yescharacteristic
780C22C2×D4211yescharacteristic
781C22C2×#54611yescharacteristic
782C22C2×#54711yescharacteristic
783C22C2×D4×Q812yes—
784C22Q8×#4112yes—
785C22#348712yes—
786C22#349911yescharacteristic
787C22#350011yescharacteristic
788C22#350112yes—
789C22#350112yes—
790C22#350212yes—
791C22#350312yes—
792C22#351512yes—
793C22C2×#56211yescharacteristic
794C22#354112yes—
795C22#354112yes—
796C22#355512yes—
797C22#356212yes—
798C4—24no—
799C4—28no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—44no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4#267118yes—
816C2—44no—
817C2#3517311yescharacteristic
818C2D4×C4⋊Q811yescharacteristic
819C2#3627611yescharacteristic
820C2#3738911yescharacteristic
821C2#3768311yescharacteristic
822C2#3808811yescharacteristic
823C2#3959512yes—
824C2#3965612yes—
825C2#4550012yes—
826C2C2×#267111yescharacteristic
827C2#5906712yes—
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
2. C2×#2546C2semidirect
6. #15520C2semidirect
7. #15460C2semidirect
8. #15199C2semidirect
9. #15196C2semidirect
10. #15188C2semidirect
12. #15180C2semidirect
16. #14024C2semidirect
17. #13976C2semidirect
18. #13926C2semidirect
188. #385Q8semidirect
607. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25462
C2×#24292
C2×#24232
#165212
#155202
#154602
#151992
#151962
#151882
#151822
#151802
#151782
#147022
#144082
#140242
#139762
#139262
C4×#3852