Finite Group Databasebeta

← #1409147

Subgroups — #1409147

Order 512.

2386 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic
2C2×#2493C211yesmaximal, characteristic
3#17048C211yesmaximal, characteristic, complemented
4#16898C211yesmaximal, characteristic, complemented
5#16880C212yesmaximal, complemented
6#16862C212yesmaximal, complemented
7#16727C212yesmaximal, complemented
8#16710C212yesmaximal, complemented
9#16700C211yesmaximal, characteristic, complemented
10#16696C211yesmaximal, characteristic, complemented
11#15073C212yesmaximal
12#15073C211yesmaximal, characteristic
13#15021C211yesmaximal, characteristic, complemented
14#14935C212yesmaximal
15#14934C211yesmaximal, characteristic
16#14872C211yesmaximal, characteristic, complemented
17#14758C211yesmaximal, characteristic
18#14356C211yesmaximal, characteristic, complemented
19#14327C211yesmaximal, characteristic, complemented
20#13904C212yesmaximal
21#13874C212yesmaximal
22C2×#1444C211yesmaximal, characteristic
23#13814C211yesmaximal, characteristic
24C22×C22⋊Q8C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27#2503—28no—
28#2493—28no—
29C2×#401C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2212yes—
32C2×#400C2212yes—
33C2×#400C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#395C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#387C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2212yes—
43C2×#385C2211yescharacteristic
44C2×#383C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×#382C2211yescharacteristic
47C2×#381C2212yes—
48C2×#381C2211yescharacteristic
49C2×#381C2212yes—
50C2×#381C2211yescharacteristic
51C2×#381C2212yes—
52C2×#381C2212yes—
53C2×#381C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59C22×#95C2212yes—
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1446C2211yescharacteristic
63#1446C2211yescharacteristic
64#1446C2211yescharacteristic
65#1445C2212yes—
66#1445C2212yes—
67#1445C2212yes—
68#1445C2212yes—
69#1444C2211yescharacteristic
70#1444C2211yescharacteristic
71#1444C2211yescharacteristic
72#1444C2211yescharacteristic
73#1444C2212yes—
74#1444C2212yes—
75#1444C2211yescharacteristic
76#1444C2212yes—
77#1443C2212yes—
78#1443C2212yes—
79#1443C2212yes—
80#1443C2212yes—
81#1442C2211yescharacteristic
82#1442C2212yes—
83#1442C2211yescharacteristic
84#1442C2212yes—
85#1442C2211yescharacteristic
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2211yescharacteristic
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2211yescharacteristic
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1441C2211yescharacteristic
103#1441C2212yes—
104#1441C2212yes—
105#1441C2212yes—
106#1441C2212yes—
107#1441C2212yes—
108#1441C2211yescharacteristic
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2212yes—
115C4⋊#95C2212yes—
116C4⋊#95C2212yes—
117C4⋊#95C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120#1434C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C24×C4C2312yes—
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2312yes—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—44no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—28no—
135C22×C4⋊C4—44no—
136C22×C4⋊C4—44no—
137C22×C4⋊C4—44no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167#401—24no—
168#400—24no—
169#400—24no—
170#400—24no—
171#400—28no—
172#400—28no—
173#395—24no—
174#391—24no—
175#391—24no—
176#387—24no—
177#387—24no—
178#387—24no—
179#385—24no—
180#385—28no—
181#385—24no—
182#383—24no—
183#382—24no—
184#382—24no—
185#381—24no—
186#381—24no—
187#381—28no—
188#381—28no—
189#381—44no—
190#381—44no—
191#381—44no—
192#380—24no—
193#380—44no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—44no—
196C4×C22⋊C4D418yes—
197C2×#95—24no—
198C2×#95—28no—
199C2×#95—24no—
200C2×#95C2312yes—
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
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×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C25C2411yescharacteristic
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—42no—
269C22×Q8—42no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—22no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4C2×D414yes—
298C23×C4#4118yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C22⋊Q8—416no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
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—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—416no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42C2×D414yes—
401C2×C42C2×D414yes—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—22no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—22no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
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#95C2×D414yes—
464#95C2×D414yes—
465#95#4114yes—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—22no—
471C24—21no—
472C24C22×D412yes—
473C24C2×#4114yes—
474C24H(5,𝔽2)14yes—
475C24H(5,𝔽2)12yes—
476C242−1+412yes—
477C24C2511yescharacteristic
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—84no—
482C2×Q8—84no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—28no—
490C22×C4—216no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—28no—
524C22×C4—216no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
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—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—82no—
628C22×C4—84no—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4114yes—
638C22×C4C2×#4114yes—
639C22×C42−1+412yes—
640C22×C42−1+412yes—
641C22×C42−1+414yes—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—48no—
653C4⋊C4—44no—
654C4⋊C4—48no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—82no—
658C4⋊C4—82no—
659C4⋊C4—82no—
660C4⋊C4—84no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—44no—
664C22⋊C4—48no—
665C22⋊C4—44no—
666C22⋊C4—48no—
667C42—28no—
668C42—44no—
669C42—84no—
670C42—84no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23#53214yes—
690C23#53514yes—
691C23#53714yes—
692C23#53818yes—
693C23#54218yes—
694C23C23×D411yescharacteristic
695C23C22×#4112yes—
696C23C22×#4111yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×2−1+411yescharacteristic
700C23C2×2−1+411yescharacteristic
701C23C2×2−1+412yes—
702C23C2×2−1+411yescharacteristic
703C23#58512yes—
704C23#58511yescharacteristic
705Q8—88no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—432no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
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—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—88no—
837C2×C4—816no—
838C2×C4—88no—
839C2×C4#54714yes—
840C2×C4#55218yes—
841C22—24no—
842C22—28no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—28no—
848C22—28no—
849C22—28no—
850C22—24no—
851C22#266218yes—
852C22C2×#53211yescharacteristic
853C22C2×#53511yescharacteristic
854C22C2×#53711yescharacteristic
855C22C2×#53812yes—
856C22C2×#54212yes—
857C22C2×#54711yescharacteristic
858C22C2×#55212yes—
859C22#348511yescharacteristic
860C22#348911yescharacteristic
861C22#349112yes—
862C22#349512yes—
863C22#349911yescharacteristic
864C22#350912yes—
865C22#351312yes—
866C22#351311yescharacteristic
867C22#352311yescharacteristic
868C22#353512yes—
869C22#353512yes—
870C22#353512yes—
871C22#354412yes—
872C22#354411yescharacteristic
873C22#356311yescharacteristic
874C22#356312yes—
875C4—24no—
876C4—28no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—44no—
882C4—42no—
883C4—42no—
884C4—82no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—81no—
890C4—82no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—82no—
896C4—81no—
897C2—28no—
898C2C2×#266211yescharacteristic
899C2#3606111yescharacteristic
900C2#3618111yescharacteristic
901C2#3803911yescharacteristic
902C2#3804311yescharacteristic
903C2#3806512yes—
904C2#3806912yes—
905C2#4137311yescharacteristic
906C2#4139312yes—
907C2#4229711yescharacteristic
908C2#4231912yes—
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. #17048C2semidirect
4. #16898C2semidirect
5. #16880C2semidirect
6. #16862C2semidirect
7. #16727C2semidirect
8. #16710C2semidirect
9. #16700C2semidirect
10. #16696C2semidirect
13. #15021C2semidirect
16. #14872C2semidirect
18. #14356C2semidirect
19. #14327C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24932
#170482
#168982
#168802
#168622
#167272
#167102
#167002
#166962
#150732
#150212
#149352
#149342
#148722
#147582
#143562
#143272
#139042
#138742
C2×#14442
#138142