Finite Group Databasebeta

← #744395

Subgroups — #744395

Order 512.

2166 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2343C211yesmaximal, characteristic
2C2×#2330C211yesmaximal, characteristic, complemented
3#17065C211yesmaximal, characteristic, complemented
4#16985C211yesmaximal, characteristic, complemented
5#16983C211yesmaximal, characteristic, complemented
6#16605C211yesmaximal, characteristic, complemented
7#16044C212yesmaximal
8#16042C212yesmaximal, complemented
9#16040C212yesmaximal, complemented
10#15305C212yesmaximal
11#15195C211yesmaximal, characteristic
12#15165C211yesmaximal, characteristic
13#15045C211yesmaximal, characteristic
14#14940C212yesmaximal, complemented
15#14916C211yesmaximal, characteristic
16#14769C212yesmaximal
17#14298C211yesmaximal, characteristic, complemented
18#14212C212yesmaximal, complemented
19#13980C212yesmaximal
20#13955C211yesmaximal, characteristic, complemented
21#13952C211yesmaximal, characteristic, complemented
22#13938C211yesmaximal, characteristic
23#13852C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C2×#398C2212yes—
27C2×#396C2212yes—
28#2343—28no—
29#2330—28no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#387C2212yes—
35C2×#387C2212yes—
36C2×#387C2211yescharacteristic
37C2×#387C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#387C2211yescharacteristic
40C2×#385C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2212yes—
43C2×#384C2211yescharacteristic
44C2×#383C2211yescharacteristic
45C2×#383C2211yescharacteristic
46C2×#382C2211yescharacteristic
47C2×#381C2211yescharacteristic
48C2×#380C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×#376C2211yescharacteristic
57C22×#95C2211yescharacteristic
58#1445C2212yes—
59#1445C2212yes—
60#1445C2212yes—
61#1444C2211yescharacteristic
62#1444C2211yescharacteristic
63#1444C2212yes—
64#1444C2212yes—
65#1443C2212yes—
66#1442C2211yescharacteristic
67#1442C2211yescharacteristic
68#1442C2211yescharacteristic
69#1442C2212yes—
70#1442C2212yes—
71#1442C2211yescharacteristic
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2211yescharacteristic
78#1442C2212yes—
79#1442C2211yescharacteristic
80#1442C2212yes—
81#1441C2211yescharacteristic
82#1441C2211yescharacteristic
83#1441C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1441C2211yescharacteristic
88#1441C2212yes—
89#1441C2211yescharacteristic
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2211yescharacteristic
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1437C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2212yes—
113C4⋊#95C2212yes—
114C4⋊#95C2212yes—
115#1434C2211yescharacteristic
116#1434C2211yescharacteristic
117#1434C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120#1434C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2212yes—
125C24×C4C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2311yescharacteristic
128C2×#125—28no—
129C2×#125—24no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117Q818yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#398—28no—
172#396—44no—
173#389—24no—
174#389—24no—
175#389—28no—
176#389—28no—
177#387—24no—
178#387—24no—
179#387—28no—
180#387—28no—
181#387—24no—
182#387—24no—
183#385—28no—
184#385—24no—
185#385—24no—
186#384—24no—
187#383—24no—
188#383—24no—
189#382—24no—
190#381—24no—
191#380—44no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4—24no—
195C4×C4⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—44no—
199#376D418yes—
200C2×#95—24no—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2311yescharacteristic
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×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
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×#95C2311yescharacteristic
256C2×#95C2311yescharacteristic
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C25C2411yescharacteristic
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—41no—
270C23×C4—41no—
271C23×C4—42no—
272C23×C4—41no—
273C23×C4—41no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4C2×Q814yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#125—232no—
300#117—232no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
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—42no—
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⋊C4C2×Q814yes—
354C2×C4⋊C4C2×Q814yes—
355C2×C4⋊C4#4118yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4C2×Q814yes—
379C2×C22⋊C4C2×Q814yes—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42C2×D414yes—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400C2×C42C2×Q814yes—
401C2×C42C2×Q814yes—
402C2×C42#4114yes—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
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#95C2×D414yes—
458#95C2×D414yes—
459#95C2×D414yes—
460#95C2×D414yes—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24C22×Q812yes—
470C24H(5,𝔽2)12yes—
471C242−1+412yes—
472C24C2511yescharacteristic
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
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—21no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
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—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
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—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
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—21no—
585C22×C4—22no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—82no—
597C22×C4—84no—
598C22×C4—82no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×Q812yes—
609C22×C4C22×Q812yes—
610C22×C4C22×Q812yes—
611C22×C4C22×Q812yes—
612C22×C4C22×Q812yes—
613C22×C4C22×Q812yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4114yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—216no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—216no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—84no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4—84no—
635C4⋊C4—84no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4—84no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—84no—
649C42—28no—
650C42—28no—
651C42—44no—
652C42—84no—
653C42—84no—
654C42—84no—
655C42—82no—
656C42—82no—
657C42C22⋊Q8116yes—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23#54414yes—
681C23C23×D411yescharacteristic
682C23C23×Q811yescharacteristic
683C23C22×#4111yescharacteristic
684C23C22×#4112yes—
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×2−1+411yescharacteristic
687C23#58512yes—
688C23#58511yescharacteristic
689C23#58511yescharacteristic
690C23#58512yes—
691C23#58512yes—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
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—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—416no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
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—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
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—42no—
807C2×C4—42no—
808C2×C4—42no—
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—42no—
818C2×C4—42no—
819C2×C4—88no—
820C2×C4—88no—
821C2×C4C2×C22⋊Q814yes—
822C2×C4C2×C22⋊Q814yes—
823C2×C4C2×C22⋊Q814yes—
824C2×C4#52514yes—
825C22—28no—
826C22—24no—
827C22—44no—
828C22—42no—
829C22—42no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22C22×C22⋊Q811yescharacteristic
837C22C2×#52511yescharacteristic
838C22#344911yescharacteristic
839C22C2×#54411yescharacteristic
840C22#345811yescharacteristic
841C22Q8×#4112yes—
842C22#348012yes—
843C22#348811yescharacteristic
844C22#348911yescharacteristic
845C22#349312yes—
846C22#349411yescharacteristic
847C22#349512yes—
848C22#349511yescharacteristic
849C22#350011yescharacteristic
850C22#350011yescharacteristic
851C22#350412yes—
852C22#351212yes—
853C22#351312yes—
854C22#352112yes—
855C22#353312yes—
856C22#356412yes—
857C22#356612yes—
858C22#356712yes—
859C4—24no—
860C4—24no—
861C4—24no—
862C4—24no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—44no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—82no—
881C2—44no—
882C2#3495211yescharacteristic
883C2#3525311yescharacteristic
884C2#3562011yescharacteristic
885C2#3597911yescharacteristic
886C2#3608011yescharacteristic
887C2#3844912yes—
888C2#3997112yes—
889C2#4194411yescharacteristic
890C2#4230411yescharacteristic
891C2#4440212yes—
892C2#4472812yes—
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×#2330C2semidirect
3. #17065C2semidirect
4. #16985C2semidirect
5. #16983C2semidirect
6. #16605C2semidirect
8. #16042C2semidirect
9. #16040C2semidirect
14. #14940C2semidirect
17. #14298C2semidirect
18. #14212C2semidirect
20. #13955C2semidirect
21. #13952C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23432
C2×#23302
#170652
#169852
#169832
#166052
#160442
#160422
#160402
#153052
#151952
#151652
#150452
#149402
#149162
#147692
#142982
#142122
#139802
#139552
#139522
#139382
#138522