Finite Group Databasebeta

← #517603

Subgroups — #517603

Order 512.

3626 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2635C211yesmaximal, characteristic
2C2×#2364C211yesmaximal, characteristic, complemented
3C2×#2275C211yesmaximal, characteristic, complemented
4#14299C212yesmaximal, complemented
5#14216C212yesmaximal, complemented
6#14215C212yesmaximal, complemented
7#14201C212yesmaximal, complemented
8#14199C212yesmaximal, complemented
9#14187C212yesmaximal, complemented
10#14173C212yesmaximal, complemented
11#14165C211yesmaximal, characteristic, complemented
12#14146C212yesmaximal, complemented
13#14145C212yesmaximal, complemented
14#14136C211yesmaximal, characteristic, complemented
15C4×#392C212yesmaximal, complemented
16#13839C211yesmaximal, characteristic, complemented
17#13816C212yesmaximal, complemented
18#13813C212yesmaximal, complemented
19#13799C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2212yes—
25C22×#117C2211yescharacteristic
26#2635C4116yescomplemented
27C2×#400C2211yescharacteristic
28C2×#399C2211yescharacteristic
29C2×#394C2212yes—
30C2×#394C2211yescharacteristic
31C2×#392C2212yes—
32C2×#392C2211yescharacteristic
33#2364—28no—
34C2×#390C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#387C2212yes—
41C2×#387C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#381C2211yescharacteristic
47#2275—28no—
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×#376C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63#1444C2212yes—
64#1442C2212yes—
65#1441C2212yes—
66#1440C2211yescharacteristic
67#1440C2211yescharacteristic
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1438C2211yescharacteristic
76#1438C2211yescharacteristic
77#1438C2212yes—
78#1438C2212yes—
79#1438C2212yes—
80#1438C2212yes—
81#1437C2212yes—
82#1437C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97C4⋊#95C2212yes—
98C4⋊#95C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102#1434C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C4×#95C2212yes—
110C23×D4C2311yescharacteristic
111C23×D4C2312yes—
112C23×D4C2312yes—
113C23×D4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C24×C4C2312yes—
118C24×C4C2311yescharacteristic
119C2×#121—24no—
120C2×#121—24no—
121C2×#121C2×C418yescomplemented
122C2×C4×D4—28no—
123C2×C4×D4—24no—
124C2×C4×D4—28no—
125C2×C4×D4—24no—
126C2×C4×D4—28no—
127C2×C4×D4—28no—
128C2×C4×D4—28no—
129C2×C4×D4—44no—
130C2×C4×D4—44no—
131C2×C4×D4—44no—
132C2×C4×D4—44no—
133C2×C4×D4C2×C418yescomplemented
134C2×#117—24no—
135C2×#117—44no—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2312yes—
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2312yes—
177#400C2×C418yescomplemented
178#399C2×C418yescomplemented
179#394C2×C418yescomplemented
180#394C2×C4116yescomplemented
181#392C2×C418yescomplemented
182#392C2×C4116yescomplemented
183#390—44no—
184#388—28no—
185#388—28no—
186#388—44no—
187#388—44no—
188#388C2×C4116yescomplemented
189#387—28no—
190#387—44no—
191#386—28no—
192#386—28no—
193#386—28no—
194#386C2×C4116yescomplemented
195#381C2×C418yescomplemented
196C4×C4⋊C4—28no—
197C4×C4⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—28no—
202C4×C22⋊C4—28no—
203C4×C22⋊C4—28no—
204C4×C22⋊C4—24no—
205C4×C22⋊C4—44no—
206C4×C22⋊C4—44no—
207C4×C22⋊C4—44no—
208#376—24no—
209C2×#95—24no—
210C2×#95D418yescomplemented
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
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×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2312yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—22no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4C22×C414yes—
272C22×D4C22×C418yes—
273C22×D4C22×C414yes—
274C22×D4C22×C418yes—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—42no—
286C23×C4—42no—
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×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C22×C414yes—
301C23×C4C22×C414yes—
302C23×C4C2×D418yes—
303C23×C4C2×D414yes—
304C23×C4#4118yes—
305C23×C4#4114yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2412yes—
322#121—232no—
323C4×D4—264no—
324C4×D4—232no—
325C4×D4—432no—
326C4×D4—432no—
327#117—416no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
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⋊C4C22×C414yes—
350C2×C4⋊C4C22×C414yes—
351C2×C4⋊C4C22×C418yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C22×C414yes—
410C2×C22⋊C4C22×C414yes—
411C2×C22⋊C4C22×C418yes—
412C2×C22⋊C4C22×C418yes—
413C2×C22⋊C4C22×C418yes—
414C2×C22⋊C4C22×C418yes—
415C2×C22⋊C4C22×C418yes—
416C2×C22⋊C4C22×C418yes—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42C22×C414yes—
446C2×C42#4118yes—
447#95—22no—
448#95—24no—
449#95—22no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95C22×C418yes—
477#95C22×C414yes—
478#95C22×C414yes—
479#95C22×C418yes—
480#95C22×C418yes—
481#95C2×D414yes—
482#95C2×D418yes—
483#95C2×D414yes—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24C23×C414yes—
512C24C23×C412yes—
513C24C23×C412yes—
514C24C22×D412yes—
515C24C2×#4112yes—
516C24C2×#4114yes—
517C24C2511yescharacteristic
518C2×D4—216no—
519C2×D4—216no—
520C2×D4—28no—
521C2×D4—28no—
522C2×D4—216no—
523C2×D4—216no—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—48no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4—84no—
542C22×C4—21no—
543C22×C4—21no—
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—21no—
554C22×C4—22no—
555C22×C4—21no—
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—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
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—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—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—28no—
610C22×C4—216no—
611C22×C4—216no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—44no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—44no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—84no—
640C22×C4—82no—
641C22×C4—84no—
642C22×C4—82no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4—84no—
650C22×C4—84no—
651C22×C4—84no—
652C22×C4—84no—
653C22×C4C4×D4116yescomplemented
654C22×C4C23×C414yes—
655C22×C4C23×C414yes—
656C22×C4C23×C412yes—
657C22×C4C23×C414yes—
658C22×C4C23×C412yes—
659C22×C4C23×C412yes—
660C22×C4C23×C412yes—
661C22×C4C23×C412yes—
662C22×C4C22×D414yes—
663C22×C4C22×D412yes—
664C22×C4C22×D412yes—
665C22×C4C22×D414yes—
666C22×C4C2×#4114yes—
667C22×C4C2×#4114yes—
668C22×C4C2×#4112yes—
669C22×C4C2×#4112yes—
670C22×C4C2×#4114yes—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C22×C4H(5,𝔽2)14yes—
674C22×C4H(5,𝔽2)14yes—
675C4⋊C4—216no—
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—48no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—48no—
682C4⋊C4—84no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—216no—
686C22⋊C4—216no—
687C22⋊C4—28no—
688C22⋊C4—28no—
689C22⋊C4—28no—
690C22⋊C4—216no—
691C22⋊C4—216no—
692C22⋊C4—48no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—48no—
699C22⋊C4—44no—
700C22⋊C4—48no—
701C22⋊C4—44no—
702C22⋊C4—48no—
703C22⋊C4—84no—
704C22⋊C4—84no—
705C22⋊C4—84no—
706C42—28no—
707C42—216no—
708C42—48no—
709C42—48no—
710C42—48no—
711C42—84no—
712C42—84no—
713C42—84no—
714C42—84no—
715C42—84no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23C2×C4×D414yes—
792C23C4×#4114yes—
793C23C24×C411yescharacteristic
794C23C23×D411yescharacteristic
795C23C22×#4111yescharacteristic
796C23C22×#4112yes—
797C23C22×#4112yes—
798C23C2×H(5,𝔽2)12yes—
799C23C2×H(5,𝔽2)12yes—
800C23#58512yes—
801C23#58512yes—
802D4—232no—
803D4—432no—
804D4—432no—
805D4—88no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—416no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—816no—
906C2×C4—816no—
907C2×C4—88no—
908C2×C4—816no—
909C2×C4C2×C4×D414yes—
910C2×C4C2×C4×D414yes—
911C2×C4C4×#4114yes—
912C2×C4#52518yes—
913C22—24no—
914C22—24no—
915C22—28no—
916C22—24no—
917C22—24no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—82no—
939C22—82no—
940C22—82no—
941C22—82no—
942C22—82no—
943C22—82no—
944C22—82no—
945C22—82no—
946C22C22×C4×D411yescharacteristic
947C22C2×C4×#4111yescharacteristic
948C22C2×C4×#4111yescharacteristic
949C22C4×H(5,𝔽2)12yes—
950C22C4×H(5,𝔽2)12yes—
951C22C2×#52512yes—
952C22#344412yes—
953C22#348411yescharacteristic
954C22#348711yescharacteristic
955C22#349012yes—
956C22#349011yescharacteristic
957C22#349111yescharacteristic
958C22#349312yes—
959C22#349412yes—
960C22#349412yes—
961C22#349612yes—
962C22#350512yes—
963C22#350612yes—
964C22#350612yes—
965C22#350812yes—
966C22#351212yes—
967C4—28no—
968C4—24no—
969C4—24no—
970C4—24no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—44no—
976C4—42no—
977C4—44no—
978C4—42no—
979C4—44no—
980C4—44no—
981C4—82no—
982C4—82no—
983C2—44no—
984C2—44no—
985C2—84no—
986C2C4×#52511yescharacteristic
987C2#3426511yescharacteristic
988C2#3427311yescharacteristic
989C2#3427712yes—
990C2#3428012yes—
991C2#3568112yes—
992C2#3568412yes—
993C2#3575212yes—
994C2#3575512yes—
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. C2×#2364C2semidirect
3. C2×#2275C2semidirect
4. #14299C2semidirect
5. #14216C2semidirect
6. #14215C2semidirect
7. #14201C2semidirect
8. #14199C2semidirect
9. #14187C2semidirect
10. #14173C2semidirect
11. #14165C2semidirect
12. #14146C2semidirect
13. #14145C2semidirect
14. #14136C2semidirect
15. C4×#392C2semidirect
16. #13839C2semidirect
17. #13816C2semidirect
18. #13813C2semidirect
19. #13799C2semidirect
26. #2635C4semidirect
121. C2×#121C2×C4semidirect
133. C2×C4×D4C2×C4semidirect
177. #400C2×C4semidirect
178. #399C2×C4semidirect
179. #394C2×C4semidirect
180. #394C2×C4semidirect
181. #392C2×C4semidirect
182. #392C2×C4semidirect
188. #388C2×C4semidirect
194. #386C2×C4semidirect
195. #381C2×C4semidirect
210. C2×#95D4semidirect
653. C22×C4C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26352
C2×#23642
C2×#22752
#142992
#142162
#142152
#142012
#141992
#141872
#141732
#141652
#141462
#141452
#141362
C4×#3922
#138392
#138162
#138132
#137992