Finite Group Databasebeta

← #3872830

Subgroups — #3872830

Order 512.

2594 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2566C212yesmaximal, complemented
2#16987C211yesmaximal, characteristic, complemented
3#16319C212yesmaximal, complemented
4#16305C211yesmaximal, characteristic, complemented
5#15850C212yesmaximal, complemented
6#15846C212yesmaximal, complemented
7#15508C212yesmaximal, complemented
8#15440C212yesmaximal, complemented
9#15335C212yesmaximal, complemented
10#15330C212yesmaximal, complemented
11#15165C211yesmaximal, characteristic, complemented
12#14792C212yesmaximal, complemented
13#14521C211yesmaximal, characteristic
14#14405C212yesmaximal, complemented
15#14228C211yesmaximal, characteristic
16#14171C211yesmaximal, characteristic
17#14040C211yesmaximal, characteristic, complemented
18#13985C212yesmaximal, complemented
19#13975C212yesmaximal, complemented
20C22×#125C2212yes—
21C22×C4×D4C2212yes—
22#2566—216no—
23C2×#400C2212yes—
24C2×#399C2212yes—
25C2×#398C2212yes—
26C2×#396C2212yes—
27C2×#396C2212yes—
28C2×#396C2212yes—
29C2×#396C2212yes—
30C2×#392C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#390C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2211yescharacteristic
47C2×#384C2212yes—
48C2×#382C2212yes—
49C2×#380C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C22⋊C4C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1445C2212yes—
54#1444C2211yescharacteristic
55#1444C2212yes—
56#1444C2212yes—
57#1444C2212yes—
58#1444C2212yes—
59#1444C2211yescharacteristic
60#1444C2212yes—
61#1444C2212yes—
62#1443C2212yes—
63#1442C2211yescharacteristic
64#1442C2212yes—
65#1442C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1439C2211yescharacteristic
72#1439C2211yescharacteristic
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1438C2212yes—
86#1438C2211yescharacteristic
87#1438C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2211yescharacteristic
99#1434C2212yes—
100#1434C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2211yescharacteristic
107C4×#95C2211yescharacteristic
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C2×#125—28no—
115C2×#125—44no—
116C2×#125—44no—
117C2×C4×D4—28no—
118C2×C4×D4—44no—
119C2×C4×D4—44no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#400—44no—
163#399—44no—
164#398—44no—
165#396—28no—
166#396—28no—
167#396—28no—
168#396—28no—
169#392Q818yes—
170#390—28no—
171#390—28no—
172#390—42no—
173#389—42no—
174#388—28no—
175#388—44no—
176#387—28no—
177#386—28no—
178#386—44no—
179#386—44no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—44no—
184#385—44no—
185#385D418yescomplemented
186#384—28no—
187#382—28no—
188#380—44no—
189C4×C4⋊C4—28no—
190C4×C22⋊C4—42no—
191C2×#95—42no—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—41no—
241C22×D4—42no—
242C22×D4—41no—
243C22×D4C2×Q818yes—
244C22×D4C2×Q814yes—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—41no—
255C23×C4—42no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—42no—
260C23×C4—41no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4C2×D414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284#125—432no—
285C4×D4—432no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4C2×D418yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×Q818yes—
393C2×C22⋊C4C2×Q814yes—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
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—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—41no—
427#95—41no—
428#95—42no—
429#95—42no—
430#95—41no—
431#95—42no—
432#95—41no—
433#95—41no—
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#95C2×D418yes—
444#95C2×Q814yes—
445#95#4118yes—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24C22×D412yes—
469C24C22×Q814yes—
470C24C22×Q812yes—
471C242−1+412yes—
472C24C2511yescharacteristic
473C2×D4—216no—
474C2×D4—216no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—82no—
483C2×D4—82no—
484C2×D4—84no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
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—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
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—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—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—44no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—82no—
590C22×C4—82no—
591C22×C4—84no—
592C22×C4—82no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4C22×D412yes—
602C22×C4C22×D414yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×Q812yes—
606C22×C4C22×Q812yes—
607C22×C4C22×Q814yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)14yes—
613C22×C4H(5,𝔽2)14yes—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—82no—
629C4⋊C4—84no—
630C4⋊C4—82no—
631C4⋊C4—84no—
632C22⋊C4—216no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C22⋊C4—82no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C42—216no—
652C42—48no—
653C42—48no—
654C42—82no—
655C42—82no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23D4×Q814yes—
714C23C23×D411yescharacteristic
715C23C23×Q811yescharacteristic
716C23C22×#4112yes—
717C23C2×H(5,𝔽2)12yes—
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+411yescharacteristic
721C23#58511yescharacteristic
722C23#58511yescharacteristic
723C23#58512yes—
724C23#58511yescharacteristic
725D4—432no—
726D4—88no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
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—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
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—88no—
834C2×C4—88no—
835C2×C4—88no—
836C2×C4—816no—
837C2×C4#55418yes—
838C22—28no—
839C22—24no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22#344911yescharacteristic
865C22C2×D4×Q811yescharacteristic
866C22D4×#4112yes—
867C22C2×#55412yes—
868C22#348111yescharacteristic
869C22#348412yes—
870C22#349412yes—
871C22#349611yescharacteristic
872C22#350112yes—
873C22#350111yescharacteristic
874C22#350411yescharacteristic
875C22#351212yes—
876C22#351712yes—
877C22#352012yes—
878C22#353311yescharacteristic
879C22#353512yes—
880C22#353511yescharacteristic
881C22#354311yescharacteristic
882C22#354612yes—
883C22#354911yescharacteristic
884C22#356012yes—
885C22#356212yes—
886C22#356411yescharacteristic
887C4—28no—
888C4—44no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—82no—
899C4—82no—
900C4—81no—
901C4—82no—
902C4—82no—
903C4—82no—
904C2—44no—
905C2—84no—
906C2#3837312yes—
907C2#3961011yescharacteristic
908C2#4483511yescharacteristic
909C2#4494212yes—
910C2#4641411yescharacteristic
911C2#4883811yescharacteristic
912C2#4989512yes—
913C2#5592611yescharacteristic
914C2#5915012yes—
915C2#5946611yescharacteristic
916C2#5984711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
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×#2566C2semidirect
2. #16987C2semidirect
3. #16319C2semidirect
4. #16305C2semidirect
5. #15850C2semidirect
6. #15846C2semidirect
7. #15508C2semidirect
8. #15440C2semidirect
9. #15335C2semidirect
10. #15330C2semidirect
11. #15165C2semidirect
12. #14792C2semidirect
14. #14405C2semidirect
17. #14040C2semidirect
18. #13985C2semidirect
19. #13975C2semidirect
185. #385D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25662
#169872
#163192
#163052
#158502
#158462
#155082
#154402
#153352
#153302
#151652
#147922
#145212
#144052
#142282
#141712
#140402
#139852
#139752