Finite Group Databasebeta

← #679600

Subgroups — #679600

Order 512.

2434 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2345C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic
3#16101C212yesmaximal, complemented
4#16023C212yesmaximal, complemented
5#16019C212yesmaximal, complemented
6#15895C212yesmaximal, complemented
7#15019C211yesmaximal, characteristic
8#15019C211yesmaximal, characteristic
9#15015C211yesmaximal, characteristic
10#15003C212yesmaximal, complemented
11#14990C212yesmaximal, complemented
12#14822C211yesmaximal, characteristic
13#14685C211yesmaximal, characteristic
14#14180C212yesmaximal, complemented
15#14149C211yesmaximal, characteristic
16#14126C212yesmaximal, complemented
17#14040C211yesmaximal, characteristic
18#14039C211yesmaximal, characteristic
19#13992C211yesmaximal, characteristic
20#13992C211yesmaximal, characteristic
21#13966C211yesmaximal, characteristic
22#13923C211yesmaximal, characteristic
23C4×#381C211yesmaximal, characteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27C2×#400C2212yes—
28#2345—28no—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#387—28no—
32C2×#387C2212yes—
33C2×#387C2212yes—
34C2×#387C2212yes—
35C2×#387C2211yescharacteristic
36C2×#387C2211yescharacteristic
37C2×#387C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#385C2211yescharacteristic
42C2×#385C2211yescharacteristic
43C2×#381C2211yescharacteristic
44C2×#381C2211yescharacteristic
45C2×#381C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1445C2212yes—
62#1445C2212yes—
63#1445C2212yes—
64#1445C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1443C2212yes—
68#1443C2212yes—
69#1443C2212yes—
70#1443C2212yes—
71#1443C2212yes—
72#1443C2212yes—
73#1443C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99C4⋊#95C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104#1434C2212yes—
105#1434C2212yes—
106#1434C2212yes—
107#1434C2212yes—
108#1434C2212yes—
109C22⋊#95C2211yescharacteristic
110C22⋊#95C2211yescharacteristic
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C4×#95C2212yes—
124C4×#95C2212yes—
125C24×C4C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—24no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4D418yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C42—24no—
161C22×C42—24no—
162C22×C42—24no—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#400—28no—
173#389—24no—
174#389—24no—
175#387—24no—
176#387—24no—
177#387—24no—
178#387—24no—
179#387—28no—
180#387—28no—
181#387—28no—
182#387—28no—
183#387—28no—
184#385—24no—
185#385—24no—
186#381—24no—
187#381—24no—
188#381—24no—
189#381—24no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C2×#95—24no—
201C2×#95—24no—
202C2×#95—24no—
203C2×#95—24no—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
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—
264C25C2411yescharacteristic
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4#4114yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C2×C4⋊C4—232no—
325C2×C4⋊C4—232no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4#4118yes—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4#4114yes—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—42no—
404C2×C42—416no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24C22×D412yes—
476C24C2×#4112yes—
477C24C2×#4112yes—
478C24C2×#4112yes—
479C24C2×#4112yes—
480C242−1+412yes—
481C242−1+412yes—
482C24C2511yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
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—28no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
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—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4#123116yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C2×#4114yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4114yes—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—216no—
652C4⋊C4—48no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—84no—
658C4⋊C4—82no—
659C4⋊C4—82no—
660C4⋊C4—84no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C42—44no—
670C42—48no—
671C42—48no—
672C42—44no—
673C42—82no—
674C42—82no—
675C42—84no—
676C42—82no—
677C42—82no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23C2×#12314yes—
695C23#52914yes—
696C23#54114yes—
697C23#54814yes—
698C23#54814yes—
699C23#55214yes—
700C23#55614yes—
701C23C23×D411yescharacteristic
702C23C22×#4111yescharacteristic
703C23C22×#4111yescharacteristic
704C23C22×#4112yes—
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C2×2−1+411yescharacteristic
708C23C2×2−1+411yescharacteristic
709C23#58512yes—
710C23#58512yes—
711C23#58512yes—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—416no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—416no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
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—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—88no—
841C2×C4—88no—
842C2×C4C2×#12314yes—
843C2×C4C2×#12314yes—
844C2×C4#52514yes—
845C22—24no—
846C22—28no—
847C22—24no—
848C22—24no—
849C22—28no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—28no—
854C22—28no—
855C22#242118yes—
856C22C22×#12311yescharacteristic
857C22C2×#52511yescharacteristic
858C22C2×#52911yescharacteristic
859C22#344911yescharacteristic
860C22C2×#54111yescharacteristic
861C22C2×#54811yescharacteristic
862C22C2×#54811yescharacteristic
863C22C2×#55211yescharacteristic
864C22C2×#55611yescharacteristic
865C22#347512yes—
866C22#347512yes—
867C22#347512yes—
868C22#348012yes—
869C22#348511yescharacteristic
870C22#348511yescharacteristic
871C22#349112yes—
872C22#349112yes—
873C22#349512yes—
874C22#351212yes—
875C22#351612yes—
876C22#352112yes—
877C22#355312yes—
878C22#356412yes—
879C4—24no—
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—44no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—42no—
889C4—44no—
890C4—81no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—82no—
900C4—82no—
901C2—28no—
902C2C2×#242111yescharacteristic
903C2#3480911yescharacteristic
904C2#3544811yescharacteristic
905C2#3634512yes—
906C2#3651611yescharacteristic
907C2#3658211yescharacteristic
908C2#3839512yes—
909C2#3911711yescharacteristic
910C2#3971711yescharacteristic
911C2#5924112yes—
912C2#5932712yes—
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. #16101C2semidirect
4. #16023C2semidirect
5. #16019C2semidirect
6. #15895C2semidirect
10. #15003C2semidirect
11. #14990C2semidirect
14. #14180C2semidirect
16. #14126C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23452
C22×#3872
#161012
#160232
#160192
#158952
#150192
#150152
#150032
#149902
#148222
#146852
#141802
#141492
#141262
#140402
#140392
#139922
#139662
#139232
C4×#3812