Finite Group Databasebeta

← #794483

Subgroups — #794483

Order 512.

2676 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2353C211yesmaximal, characteristic
2C2×#2344C211yesmaximal, characteristic, complemented
3#16991C211yesmaximal, characteristic, complemented
4#16676C211yesmaximal, characteristic, complemented
5#16114C212yesmaximal, complemented
6#16030C212yesmaximal, complemented
7#16027C212yesmaximal, complemented
8#15990C212yesmaximal, complemented
9#15213C211yesmaximal, characteristic, complemented
10#15121C211yesmaximal, characteristic, complemented
11#15110C211yesmaximal, characteristic, complemented
12#15069C211yesmaximal, characteristic
13#15045C211yesmaximal, characteristic, complemented
14#15015C211yesmaximal, characteristic, complemented
15#14836C211yesmaximal, characteristic
16#14240C211yesmaximal, characteristic, complemented
17#14164C211yesmaximal, characteristic, complemented
18#14135C212yesmaximal
19#13968C212yesmaximal
20#13901C211yesmaximal, characteristic, complemented
21#13878C212yesmaximal, complemented
22#13874C212yesmaximal, complemented
23C2×#1442C211yesmaximal, characteristic, complemented
24C22×#123C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×#117C2212yes—
27C23×C4⋊C4C2211yescharacteristic
28C2×#399C2211yescharacteristic
29#2353—28no—
30#2344—28no—
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#388C2211yescharacteristic
34C2×#388C2211yescharacteristic
35C2×#387C2212yes—
36C2×#387C2212yes—
37C2×#387C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#386C2211yescharacteristic
40C2×#386C2211yescharacteristic
41C2×#386C2212yes—
42C2×#383C2211yescharacteristic
43C2×#383C2211yescharacteristic
44C2×#381C2212yes—
45C2×#381C2211yescharacteristic
46C2×#381C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×#376C2211yescharacteristic
56C22×#95C2212yes—
57C22×#95C2212yes—
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1445C2211yescharacteristic
61#1445C2211yescharacteristic
62#1445C2211yescharacteristic
63#1445C2212yes—
64#1444C2211yescharacteristic
65#1444C2212yes—
66#1444C2212yes—
67#1444C2211yescharacteristic
68#1444C2211yescharacteristic
69#1444C2212yes—
70#1443C2212yes—
71#1443C2212yes—
72#1443C2212yes—
73#1443C2212yes—
74#1443C2212yes—
75#1443C2212yes—
76#1442C2211yescharacteristic
77#1442C2211yescharacteristic
78#1442C2211yescharacteristic
79#1442C2211yescharacteristic
80#1442C2211yescharacteristic
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2211yescharacteristic
88#1441C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105#1436C2212yes—
106#1436C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1434C2211yescharacteristic
114#1434C2212yes—
115#1434C2212yes—
116#1434C2211yescharacteristic
117#1434C2211yescharacteristic
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C23×D4C2311yescharacteristic
126C24×C4C2312yes—
127C24×C4C2311yescharacteristic
128C24×C4C2312yes—
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C2×#123—28no—
133C2×#123—28no—
134C2×#123—44no—
135C2×C4×D4—24no—
136C2×C4×D4—24no—
137C2×C4×D4—24no—
138C2×#117—28no—
139C2×#117—44no—
140C2×#117—44no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—28no—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#399—24no—
179#389—24no—
180#389—24no—
181#388—24no—
182#388—24no—
183#387—24no—
184#387—28no—
185#387—28no—
186#387—24no—
187#386—24no—
188#386—24no—
189#386—44no—
190#383—24no—
191#383—24no—
192#381—28no—
193#381—24no—
194#381—44no—
195#380—24no—
196#380—24no—
197#380—44no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4—24no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4D418yes—
203#376—24no—
204C2×#95—24no—
205C2×#95—28no—
206C2×#95—28no—
207C2×#95—24no—
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
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×#95C2312yes—
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C25C2411yescharacteristic
266C25C2411yescharacteristic
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—24no—
270C22×D4—24no—
271C22×D4#4114yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—41no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4C2×D414yes—
304C23×C4#4118yes—
305C23×C4#4114yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2412yes—
320C23×C4C2411yescharacteristic
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327#123—432no—
328C4×D4—232no—
329#117—432no—
330C2×C4⋊C4—232no—
331C2×C4⋊C4—22no—
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—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
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—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—41no—
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⋊C4C2×D414yes—
405C2×C22⋊C4C2×D414yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—41no—
422C2×C42—42no—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—22no—
441#95—22no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—22no—
455#95—24no—
456#95—22no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
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#95—42no—
477#95—42no—
478#95—42no—
479#95C2×D414yes—
480#95C2×D414yes—
481#95#4114yes—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24C22×D412yes—
499C24C2×#4112yes—
500C24C2×#4112yes—
501C24C2×#4114yes—
502C24C2×#4112yes—
503C24H(5,𝔽2)14yes—
504C24C2511yescharacteristic
505C2×D4—28no—
506C2×D4—216no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—48no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
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—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
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—21no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
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—21no—
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—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—44no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—48no—
640C22×C4—82no—
641C22×C4—84no—
642C22×C4—82no—
643C22×C4—82no—
644C22×C4—84no—
645C22×C4—82no—
646C22×C4—82no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4—84no—
650C22×C4—84no—
651C22×C4—84no—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C22×D412yes—
658C22×C4C2×#4112yes—
659C22×C4C2×#4112yes—
660C22×C4C2×#4114yes—
661C22×C4C2×#4114yes—
662C22×C4C2×#4114yes—
663C22×C4C2×#4112yes—
664C22×C4C2×#4112yes—
665C22×C42−1+412yes—
666C22×C42−1+412yes—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—216no—
670C4⋊C4—28no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—44no—
677C4⋊C4—82no—
678C4⋊C4—84no—
679C4⋊C4—82no—
680C4⋊C4—84no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—44no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—82no—
692C22⋊C4—84no—
693C22⋊C4—82no—
694C22⋊C4—84no—
695C42—28no—
696C42—28no—
697C42—44no—
698C42—44no—
699C42—48no—
700C42—48no—
701C42—82no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—24no—
722C23—22no—
723C23—22no—
724C23—24no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23#52514yes—
744C23#52514yes—
745C23#53514yes—
746C23#55118yes—
747C23#55318yes—
748C23C23×D411yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4112yes—
751C23C22×#4111yescharacteristic
752C23C22×#4111yescharacteristic
753C23C2×H(5,𝔽2)12yes—
754C23C2×2−1+411yescharacteristic
755C23C2×2−1+411yescharacteristic
756C23#58512yes—
757C23#58511yescharacteristic
758C23#58512yes—
759D4—416no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—416no—
797C2×C4—432no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
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—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
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—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
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—41no—
863C2×C4—41no—
864C2×C4—42no—
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—88no—
885C2×C4—88no—
886C2×C4—816no—
887C2×C4—88no—
888C2×C4#54714yes—
889C22—24no—
890C22—28no—
891C22—28no—
892C22—24no—
893C22—28no—
894C22—28no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—44no—
902C22—42no—
903C22—44no—
904C22—82no—
905C22—82no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22#259818yes—
911C22C2×#52511yescharacteristic
912C22C2×#52511yescharacteristic
913C22C2×#53511yescharacteristic
914C22C2×#54711yescharacteristic
915C22C2×#55112yes—
916C22C2×#55312yes—
917C22#347511yescharacteristic
918C22#347512yes—
919C22#348211yescharacteristic
920C22#348511yescharacteristic
921C22#348911yescharacteristic
922C22#349112yes—
923C22#349412yes—
924C22#349512yes—
925C22#349512yes—
926C22#350011yescharacteristic
927C22#350911yescharacteristic
928C22#351012yes—
929C22#351511yescharacteristic
930C22#352112yes—
931C22#355912yes—
932C22#355912yes—
933C22#356012yes—
934C4—24no—
935C4—42no—
936C4—44no—
937C4—44no—
938C4—42no—
939C4—44no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—81no—
952C4—82no—
953C4—81no—
954C4—81no—
955C2—28no—
956C2—82no—
957C2C2×#259811yescharacteristic
958C2#3601011yescharacteristic
959C2#3607911yescharacteristic
960C2#3634111yescharacteristic
961C2#3637511yescharacteristic
962C2#3786411yescharacteristic
963C2#4141311yescharacteristic
964C2#4446212yes—
965C2#4447412yes—
966C2#5926612yes—
967C2#5930012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2344C2semidirect
3. #16991C2semidirect
4. #16676C2semidirect
5. #16114C2semidirect
6. #16030C2semidirect
7. #16027C2semidirect
8. #15990C2semidirect
9. #15213C2semidirect
10. #15121C2semidirect
11. #15110C2semidirect
13. #15045C2semidirect
14. #15015C2semidirect
16. #14240C2semidirect
17. #14164C2semidirect
20. #13901C2semidirect
21. #13878C2semidirect
22. #13874C2semidirect
23. C2×#1442C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23532
C2×#23442
#169912
#166762
#161142
#160302
#160272
#159902
#152132
#151212
#151102
#150692
#150452
#150152
#148362
#142402
#141642
#141352
#139682
#139012
#138782
#138742
C2×#14422