Finite Group Databasebeta

← #917707

Subgroups — #917707

Order 512.

2822 conjugacy classes of subgroups.

The subgroup lattice has 957 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C22×#395C211yesmaximal, characteristic
3#17155C212yesmaximal, complemented
4#17099C212yesmaximal, complemented
5#16833C212yesmaximal, complemented
6#16663C212yesmaximal, complemented
7#16524C212yesmaximal, complemented
8#16293C212yesmaximal, complemented
9#15856C212yesmaximal, complemented
10#15437C212yesmaximal, complemented
11#15015C211yesmaximal, characteristic
12#14919C211yesmaximal, characteristic
13#14919C211yesmaximal, characteristic
14#14874C211yesmaximal, characteristic
15#14786C211yesmaximal, characteristic
16#14728C211yesmaximal, characteristic
17#14342C211yesmaximal, characteristic
18#14263C211yesmaximal, characteristic
19#14044C211yesmaximal, characteristic
20#14039C211yesmaximal, characteristic
21#13922C211yesmaximal, characteristic
22#13881C211yesmaximal, characteristic
23#13874C211yesmaximal, characteristic
24C24×Q8C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2493—28no—
29C2×#401C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#398C2212yes—
34C2×#398C2212yes—
35C2×#395—28no—
36C2×#395C2212yes—
37C2×#395C2212yes—
38C2×#395C2212yes—
39C2×#395C2212yes—
40C2×#395C2212yes—
41C2×#395C2212yes—
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2211yescharacteristic
47C2×#387C2212yes—
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#383C2211yescharacteristic
55C2×#382C2212yes—
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67#1446C2212yes—
68#1446C2212yes—
69#1446C2212yes—
70#1446C2212yes—
71#1445C2212yes—
72#1445C2212yes—
73#1445C2212yes—
74#1445C2212yes—
75#1445C2212yes—
76#1445C2212yes—
77#1445C2212yes—
78#1445C2212yes—
79#1444C2212yes—
80#1444C2212yes—
81#1444C2212yes—
82#1444C2212yes—
83#1443C2212yes—
84#1443C2212yes—
85#1443C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1443C2212yes—
89#1443C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1442C2212yes—
96#1442C2212yes—
97#1442C2212yes—
98#1442C2212yes—
99#1442C2212yes—
100#1442C2212yes—
101#1441C2212yes—
102#1441C2212yes—
103#1441C2212yes—
104#1441C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108C4⋊#95C2212yes—
109C4⋊#95C2212yes—
110#1434C2212yes—
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C23×Q8—24no—
126C23×Q8—24no—
127C23×Q8—42no—
128C23×Q8—44no—
129C23×Q8—44no—
130C23×Q8C2312yes—
131C23×Q8C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—44no—
144C22×C4⋊C4—44no—
145C22×C4⋊C4—42no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174#401—24no—
175#400—24no—
176#400—24no—
177#400—24no—
178#398—44no—
179#398—44no—
180#395—28no—
181#395—28no—
182#395—28no—
183#395—28no—
184#395—44no—
185#395—44no—
186#391—44no—
187#391—44no—
188#387—24no—
189#387—24no—
190#387—24no—
191#387—44no—
192#385—24no—
193#385—24no—
194#385—24no—
195#385—24no—
196#385—42no—
197#385—42no—
198#383—24no—
199#382—44no—
200#381—24no—
201#381—24no—
202#381—24no—
203#381—42no—
204#380—24no—
205#380—42no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—24no—
208C2×#95—24no—
209C2×#95—24no—
210C2×#95D418yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C25C2411yescharacteristic
274C22×Q8—24no—
275C22×Q8—24no—
276C22×Q8—24no—
277C22×Q8—24no—
278C22×Q8—24no—
279C22×Q8—24no—
280C22×Q8—24no—
281C22×Q8—24no—
282C22×Q8—42no—
283C22×Q8—42no—
284C22×Q8—42no—
285C22×Q8—42no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8—416no—
289C22×Q8—416no—
290C22×Q8—416no—
291C22×Q8—432no—
292C22×Q8—432no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—24no—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4—24no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—42no—
324C23×C4—42no—
325C23×C4—42no—
326C23×C4C2×D414yes—
327C23×C4C2×D414yes—
328C23×C4C2×D414yes—
329C23×C4#4114yes—
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2412yes—
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336C23×C4C2411yescharacteristic
337C23×C4C2412yes—
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2411yescharacteristic
351C23×C4C2411yescharacteristic
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4—416no—
387C2×C4⋊C4—416no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4#4114yes—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—42no—
430C2×C42—42no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95—42no—
481#95—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—42no—
487#95—42no—
488#95—42no—
489#95C2×D414yes—
490#95C2×D414yes—
491#95C2×D414yes—
492#95C2×D414yes—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24C22×D412yes—
498C24C2×#4112yes—
499C24C2×#4112yes—
500C24H(5,𝔽2)12yes—
501C242−1+412yes—
502C242−1+412yes—
503C242−1+412yes—
504C24C2511yescharacteristic
505C2×Q8—216no—
506C2×Q8—48no—
507C2×Q8—48no—
508C2×Q8—48no—
509C2×Q8—48no—
510C2×Q8—48no—
511C2×Q8—48no—
512C2×Q8—48no—
513C2×Q8—48no—
514C2×Q8—48no—
515C2×Q8—48no—
516C2×Q8—48no—
517C2×Q8—4128no—
518C2×Q8—48no—
519C2×Q8—48no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—48no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—48no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—84no—
674C22×C4—84no—
675C22×C4C22×D412yes—
676C22×C4C22×D412yes—
677C22×C4C22×D412yes—
678C22×C4C22×D412yes—
679C22×C4C22×D412yes—
680C22×C4C22×D412yes—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C22×C4H(5,𝔽2)14yes—
684C22×C4H(5,𝔽2)14yes—
685C22×C42−1+414yes—
686C22×C42−1+414yes—
687C4⋊C4—48no—
688C4⋊C4—48no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—44no—
694C4⋊C4—48no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—82no—
698C4⋊C4—84no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C4⋊C4—84no—
702C4⋊C4—84no—
703C4⋊C4—84no—
704C22⋊C4—28no—
705C22⋊C4—44no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C42—48no—
713C42—44no—
714C42—82no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23#53614yes—
732C23#54114yes—
733C23#54214yes—
734C23#54614yes—
735C23#54714yes—
736C23#55214yes—
737C23#56314yes—
738C23C23×D411yescharacteristic
739C23C22×#4111yescharacteristic
740C23C22×#4111yescharacteristic
741C23C2×H(5,𝔽2)12yes—
742C23C2×H(5,𝔽2)11yescharacteristic
743C23C2×H(5,𝔽2)12yes—
744C23C2×2−1+411yescharacteristic
745C23C2×2−1+411yescharacteristic
746C23C2×2−1+412yes—
747C23C2×2−1+411yescharacteristic
748C23C2×2−1+412yes—
749Q8—432no—
750Q8—432no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—416no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—416no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—88no—
886C2×C4#53514yes—
887C2×C4#53614yes—
888C22—24no—
889C22—24no—
890C22—28no—
891C22—28no—
892C22—28no—
893C22—24no—
894C22—28no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22#269818yes—
899C22C2×#53511yescharacteristic
900C22C2×#53611yescharacteristic
901C22C2×#53611yescharacteristic
902C22C2×#54111yescharacteristic
903C22C2×#54211yescharacteristic
904C22C2×#54611yescharacteristic
905C22C2×#54711yescharacteristic
906C22C2×#55211yescharacteristic
907C22#348411yescharacteristic
908C22#348611yescharacteristic
909C22#349012yes—
910C22#350912yes—
911C22#352012yes—
912C22#352012yes—
913C22C2×#56311yescharacteristic
914C22#353212yes—
915C22#353812yes—
916C22#353812yes—
917C22#354412yes—
918C22#355212yes—
919C22#355212yes—
920C22#355212yes—
921C22#355212yes—
922C4—24no—
923C4—24no—
924C4—44no—
925C4—44no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—44no—
931C4—44no—
932C4—81no—
933C4—81no—
934C4—82no—
935C4—81no—
936C4—81no—
937C4—82no—
938C4—82no—
939C4—81no—
940C4—81no—
941C4—82no—
942C4—81no—
943C4—81no—
944C2—28no—
945C2#3723311yescharacteristic
946C2#3761511yescharacteristic
947C2#3783311yescharacteristic
948C2#3803711yescharacteristic
949C2#3891711yescharacteristic
950C2#3946511yescharacteristic
951C2#4054712yes—
952C2#4083812yes—
953C2#4308212yes—
954C2C2×#269811yescharacteristic
955C2#5232212yes—
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
3. #17155C2semidirect
4. #17099C2semidirect
5. #16833C2semidirect
6. #16663C2semidirect
7. #16524C2semidirect
8. #16293C2semidirect
9. #15856C2semidirect
10. #15437C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C22×#3952
#171552
#170992
#168332
#166632
#165242
#162932
#158562
#154372
#150152
#149192
#148742
#147862
#147282
#143422
#142632
#140442
#140392
#139222
#138812
#138742