Finite Group Databasebeta

← #649127

Subgroups — #649127

Order 512.

3390 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2442C211yesmaximal, characteristic
3C2×Q8×C22⋊C4C211yesmaximal, characteristic
4C22×#391C211yesmaximal, characteristic
5#15509C214yesmaximal, complemented
6#15337C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#14766C214yesmaximal
12#14686C211yesmaximal, characteristic
13#14028C214yesmaximal
14#13978C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13942C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic
18#13881C211yesmaximal, characteristic
19C4×#385C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2565—28no—
27#2442—28no—
28C2×#400C2212yes—
29C2×#398C2214yes—
30C2×#398C2212yes—
31Q8×C22⋊C4—28no—
32C2×#391—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2214yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#387C2214yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2214yes—
60C2×#380C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2214yes—
67#1446C2214yes—
68#1445C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1436C2212yes—
81#1436C2214yes—
82#1436C2214yes—
83#1436C2212yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2214yes—
89#1434C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8Q818yes—
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C23×Q8C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C2×#125—24no—
110C2×#125—24no—
111C2×#125—42no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C2×C4×Q8—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C42—24no—
144C22×C42—24no—
145C22×C42—42no—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#400—28no—
156#398—216no—
157#398—28no—
158#391—24no—
159#391—24no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—28no—
166#391—28no—
167#391—216no—
168#391—42no—
169#391—42no—
170#391D418yes—
171#389—24no—
172#389—24no—
173#387—216no—
174#385—28no—
175#385—28no—
176#384—24no—
177#384—42no—
178#382—24no—
179#382—24no—
180#382—42no—
181#380—24no—
182#380—24no—
183#380—216no—
184#380—28no—
185#380—28no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—42no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4D418yes—
191C2×#95—216no—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2311yescharacteristic
223C2×#95C2314yes—
224C2×#95C2311yescharacteristic
225C25C2411yescharacteristic
226C22×Q8—232no—
227C22×Q8—232no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—24no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—42no—
243C22×Q8—42no—
244C22×Q8—416no—
245C22×Q8—416no—
246C22×Q8—416no—
247C22×Q8—416no—
248C22×Q8—416no—
249C22×Q8C2×D414yes—
250C22×Q8C2×Q814yes—
251C22×Q8C2×Q818yes—
252C22×Q8C2×Q814yes—
253C22×Q8#4114yes—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—28no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—44no—
275C23×C4C2×D414yes—
276C23×C4C2×Q818yes—
277C23×C4C2×Q814yes—
278C23×C4#4118yes—
279C23×C4#4114yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298#125—416no—
299C4×Q8—416no—
300C4×Q8—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4C2×D414yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4C2×D414yes—
361C2×C22⋊C4C2×D414yes—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—416no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42C2×D414yes—
388C2×C42C2×D414yes—
389C2×C42C2×D414yes—
390#95—28no—
391#95—28no—
392#95—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—24no—
405#95—28no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—24no—
413#95—42no—
414#95—44no—
415#95—44no—
416#95—42no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95C2×D4116yes—
421#95C2×D414yes—
422#95C2×D414yes—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24C22×D412yes—
430C24C22×Q812yes—
431C24C2×#4112yes—
432C24C2×#4114yes—
433C242−1+414yes—
434C24C2511yescharacteristic
435C2×Q8—28no—
436C2×Q8—216no—
437C2×Q8—216no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—48no—
447C2×Q8—48no—
448C2×Q8—48no—
449C2×Q8—48no—
450C2×Q8—48no—
451C2×Q8—4128no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8C22⋊Q8116yes—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—416no—
562C22×C4—48no—
563C22×C4—84no—
564C22×C4—88no—
565C22×C4C22⋊Q8116yes—
566C22×C4C22×D412yes—
567C22×C4C22×D414yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D414yes—
572C22×C4C22×D412yes—
573C22×C4C22×D414yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×Q814yes—
577C22×C4C22×Q812yes—
578C22×C4C22×Q814yes—
579C22×C4C22×Q812yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4H(5,𝔽2)12yes—
588C22×C42−1+414yes—
589C4⋊C4—28no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—88no—
604C4⋊C4—84no—
605C4⋊C4—84no—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C42—28no—
612C42—28no—
613C42—28no—
614C42—48no—
615C42—48no—
616C42—48no—
617C42—44no—
618C42—44no—
619C42—44no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23C2×C22⋊Q814yes—
639C23#53214yes—
640C23#53614yes—
641C23#55218yes—
642C23#55718yes—
643C23C23×D411yescharacteristic
644C23C23×D411yescharacteristic
645C23C23×Q811yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C22×#4112yes—
649C23C2×H(5,𝔽2)11yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×2−1+412yes—
652C23C2×2−1+412yes—
653C23#58512yes—
654Q8—232no—
655Q8—432no—
656Q8—416no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—232no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—816no—
757C2×C4C2×C22⋊Q818yes—
758C2×C4C2×C22⋊Q814yes—
759C2×C4C2×C22⋊Q814yes—
760C2×C4C2×C22⋊Q814yes—
761C2×C4#54314yes—
762C2×C4D4214yes—
763C2×C4#54614yes—
764C2×C4#54614yes—
765C2×C4#54818yes—
766C2×C4#55114yes—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—24no—
772C22—24no—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—28no—
777C22#256518yescomplemented
778C22C22×C22⋊Q811yescharacteristic
779C22C22×C22⋊Q811yescharacteristic
780C22C2×#53211yescharacteristic
781C22C2×#53611yescharacteristic
782C22C2×#54311yescharacteristic
783C22C2×D4211yescharacteristic
784C22C2×#54611yescharacteristic
785C22C2×#54611yescharacteristic
786C22C2×#54812yes—
787C22C2×#55111yescharacteristic
788C22C2×#55212yes—
789C22C2×#55712yes—
790C22#348012yes—
791C22#348912yes—
792C22#349512yes—
793C22#349911yescharacteristic
794C22#350011yescharacteristic
795C22#350212yes—
796C22#350512yes—
797C22#351112yes—
798C22#352312yes—
799C22#353812yes—
800C22#356112yes—
801C4—24no—
802C4—28no—
803C4—28no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—44no—
808C4—44no—
809C4—44no—
810C4—42no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4#243718yes—
819C2—28no—
820C2C2×#243711yescharacteristic
821C2C2×#256511yescharacteristic
822C2#3566811yescharacteristic
823C2#3612211yescharacteristic
824C2#3639611yescharacteristic
825C2#3657712yes—
826C2#3767611yescharacteristic
827C2#3808111yescharacteristic
828C2#3975212yes—
829C2#5901412yes—
830C2#5927112yes—
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×#2565C2semidirect
5. #15509C2semidirect
6. #15337C2semidirect
7. #15240C2semidirect
8. #15238C2semidirect
9. #15237C2semidirect
10. #15184C2semidirect
14. #13978C2semidirect
15. #13976C2semidirect
16. #13942C2semidirect
777. C22#2565semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#24422
C2×Q8×C22⋊C42
C22×#3912
#155092
#153372
#152402
#152382
#152372
#151842
#147662
#146862
#140282
#139782
#139762
#139422
#139222
#138812
C4×#3852