Finite Group Databasebeta

← #545252

Subgroups — #545252

Order 512.

2804 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2635C211yesmaximal, characteristic
2#14621C212yesmaximal, complemented
3#14617C211yesmaximal, characteristic, complemented
4#14614C211yesmaximal, characteristic, complemented
5#14612C211yesmaximal, characteristic, complemented
6#14571C211yesmaximal, characteristic, complemented
7#14563C212yesmaximal, complemented
8#14539C212yesmaximal, complemented
9#14317C212yesmaximal, complemented
10#14299C212yesmaximal, complemented
11#14187C212yesmaximal, complemented
12#14145C212yesmaximal, complemented
13#14103C212yesmaximal, complemented
14#14100C212yesmaximal, complemented
15#14077C212yesmaximal, complemented
16#14066C212yesmaximal, complemented
17#13847C211yesmaximal, characteristic, complemented
18#13813C212yesmaximal, complemented
19#13784C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23#2635C4116yescomplemented
24C2×#400C2211yescharacteristic
25C2×#399C2211yescharacteristic
26C2×#394C2211yescharacteristic
27C2×#394C2212yes—
28C2×#392C2211yescharacteristic
29C2×#392C2212yes—
30C2×#390C2212yes—
31C2×#389C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#381C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2211yescharacteristic
48C2×C4×C22⋊C4C2212yes—
49C2×#376C2211yescharacteristic
50C22×#95C2211yescharacteristic
51#1445C2211yescharacteristic
52#1445C2211yescharacteristic
53#1445C2212yes—
54#1443C2212yes—
55#1443C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2212yes—
59#1441C2212yes—
60#1440C2212yes—
61#1440C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1438C2212yes—
71#1438C2212yes—
72#1438C2212yes—
73#1438C2211yescharacteristic
74#1438C2211yescharacteristic
75#1438C2212yes—
76#1438C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1437C2212yes—
82#1437C2212yes—
83#1437C2211yescharacteristic
84#1437C2211yescharacteristic
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2211yescharacteristic
89#1436C2211yescharacteristic
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1434C2212yes—
96#1434C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yes—
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C23×D4C2312yes—
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C2×#121—42no—
117C2×#121—42no—
118C2×#121C2×C418yescomplemented
119C2×C4×D4—28no—
120C2×C4×D4—44no—
121C2×C4×D4—42no—
122C2×C4×D4—42no—
123C2×C4×D4—44no—
124C2×C4×D4C2×C418yescomplemented
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊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⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#400C2×C418yescomplemented
163#399C2×C418yescomplemented
164#394C2×C418yescomplemented
165#394C2×C4116yescomplemented
166#392C2×C418yes—
167#392C2×C4116yescomplemented
168#390—44no—
169#389—44no—
170#388—44no—
171#388—44no—
172#388—44no—
173#388—44no—
174#388C2×C4116yescomplemented
175#386—28no—
176#386—28no—
177#386—44no—
178#386—44no—
179#386C2×C4116yescomplemented
180#381C2×C418yescomplemented
181C4×C4⋊C4—42no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—44no—
184C4×C22⋊C4—44no—
185C4×C22⋊C4—44no—
186C4×C22⋊C4—44no—
187#376—42no—
188C2×#95—42no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
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×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C25C2411yescharacteristic
232C25C2412yes—
233C25C2411yescharacteristic
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—41no—
238C22×D4—41no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—41no—
247C22×D4—41no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4C22×C414yes—
255C22×D4C22×C418yes—
256C22×D4C22×C414yes—
257C22×D4C22×C418yes—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4C22×C414yes—
280C23×C4C22×C414yes—
281C23×C4#4118yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298#121—416no—
299C4×D4—416no—
300C4×D4—432no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
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⋊C4C22×C414yes—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C22×C418yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
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—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4C22×C418yes—
381C2×C22⋊C4C22×C414yes—
382C2×C22⋊C4C22×C414yes—
383C2×C22⋊C4C22×C418yes—
384C2×C22⋊C4C22×C418yes—
385C2×C22⋊C4C22×C418yes—
386C2×C22⋊C4C22×C418yes—
387C2×C22⋊C4C22×C418yes—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—41no—
403C2×C42—41no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42C22×C414yes—
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—41no—
421#95—41no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—41no—
431#95—42no—
432#95—41no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—41no—
438#95—41no—
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#95C22×C418yes—
448#95C22×C414yes—
449#95C22×C414yes—
450#95C22×C418yes—
451#95C22×C418yes—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24C23×C414yes—
482C24C23×C412yes—
483C24C23×C412yes—
484C24C2×#4114yes—
485C24C2511yescharacteristic
486C2×D4—216no—
487C2×D4—28no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—82no—
507C2×D4—82no—
508C2×D4—84no—
509C2×D4—84no—
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—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
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—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
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—22no—
570C22×C4—28no—
571C22×C4—28no—
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—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—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4C23×C414yes—
623C22×C4C23×C412yes—
624C22×C4C23×C414yes—
625C22×C4C23×C412yes—
626C22×C4C23×C414yes—
627C22×C4C23×C412yes—
628C22×C4C23×C412yes—
629C22×C4C23×C412yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C4H(5,𝔽2)14yes—
633C22×C4H(5,𝔽2)14yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C4H(5,𝔽2)12yes—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C22⋊C4—216no—
644C22⋊C4—216no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C22⋊C4—84no—
664C22⋊C4—84no—
665C42—28no—
666C42—48no—
667C42—48no—
668C42—84no—
669C42—84no—
670C42—82no—
671C42—82no—
672C42—84no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23C4×#4114yes—
750C23C24×C411yescharacteristic
751C23C22×#4112yes—
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)11yescharacteristic
754C23C2×H(5,𝔽2)12yes—
755C23C2×H(5,𝔽2)12yes—
756C23#58512yes—
757C23#58512yes—
758C23#58512yes—
759D4—416no—
760D4—432no—
761D4—88no—
762D4—816no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
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—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
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—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—41no—
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—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
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—88no—
865C2×C4—88no—
866C2×C4—816no—
867C2×C4—816no—
868C2×C4#51814yes—
869C22—24no—
870C22—28no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—42no—
879C22—44no—
880C22—42no—
881C22—44no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22C2×C4×#4111yescharacteristic
903C22C2×#51811yescharacteristic
904C22#342811yescharacteristic
905C22C4×H(5,𝔽2)12yes—
906C22C4×H(5,𝔽2)12yes—
907C22#345912yes—
908C22#346012yes—
909C22#349012yes—
910C22#349312yes—
911C22#350512yes—
912C22#350612yes—
913C22#353412yes—
914C22#353412yes—
915C22#353912yes—
916C22#354212yes—
917C22#354311yescharacteristic
918C22#354511yescharacteristic
919C22#354911yescharacteristic
920C22#355111yescharacteristic
921C22#356212yes—
922C22#356612yes—
923C4—24no—
924C4—42no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4—44no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—44no—
933C4—44no—
934C4—44no—
935C4—82no—
936C4—82no—
937C4—82no—
938C4—82no—
939C2—44no—
940C2—82no—
941C2—84no—
942C2#3408211yescharacteristic
943C2#3427712yes—
944C2#3440811yescharacteristic
945C2#3441511yescharacteristic
946C2#3444212yes—
947C2#4104812yes—
948C2#4105112yes—
949C2#4113112yes—
950C2#4172312yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2635C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14621C2semidirect
3. #14617C2semidirect
4. #14614C2semidirect
5. #14612C2semidirect
6. #14571C2semidirect
7. #14563C2semidirect
8. #14539C2semidirect
9. #14317C2semidirect
10. #14299C2semidirect
11. #14187C2semidirect
12. #14145C2semidirect
13. #14103C2semidirect
14. #14100C2semidirect
15. #14077C2semidirect
16. #14066C2semidirect
17. #13847C2semidirect
18. #13813C2semidirect
19. #13784C2semidirect
23. #2635C4semidirect
118. C2×#121C2×C4semidirect
124. C2×C4×D4C2×C4semidirect
162. #400C2×C4semidirect
163. #399C2×C4semidirect
164. #394C2×C4semidirect
165. #394C2×C4semidirect
167. #392C2×C4semidirect
174. #388C2×C4semidirect
179. #386C2×C4semidirect
180. #381C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26352
#146212
#146172
#146142
#146122
#145712
#145632
#145392
#143172
#142992
#141872
#141452
#141032
#141002
#140772
#140662
#138472
#138132
#137842