Finite Group Databasebeta

← #2736291

Subgroups — #2736291

Order 512.

2230 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C2×#2440C211yesmaximal, characteristic
3#17169C212yesmaximal, complemented
4#17162C212yesmaximal, complemented
5#17155C212yesmaximal, complemented
6#17154C212yesmaximal, complemented
7#17065C211yesmaximal, characteristic, complemented
8#17063C211yesmaximal, characteristic, complemented
9#17043C211yesmaximal, characteristic, complemented
10#16962C211yesmaximal, characteristic, complemented
11#16678C211yesmaximal, characteristic, complemented
12#16560C211yesmaximal, characteristic, complemented
13#14936C211yesmaximal, characteristic
14#14934C212yesmaximal
15#14920C212yesmaximal
16#14919C212yesmaximal
17#14914C212yesmaximal
18#14843C211yesmaximal, characteristic
19#14826C211yesmaximal, characteristic
20#14663C211yesmaximal, characteristic, complemented
21#14629C211yesmaximal, characteristic, complemented
22#13901C211yesmaximal, characteristic
23C2×#1445C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27#2493—28no—
28#2440—28no—
29C2×#401C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#400C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#400C2211yescharacteristic
36C2×#398C2212yes—
37C2×#395C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#387C2211yescharacteristic
42C2×#387C2211yescharacteristic
43C2×#385C2211yescharacteristic
44C2×#385C2212yes—
45C2×#385C2211yescharacteristic
46C2×#385C2212yes—
47C2×#384C2211yescharacteristic
48C2×#383C2211yescharacteristic
49C2×#383C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×#381C2211yescharacteristic
52C2×#381C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2212yes—
58C22×#95C2212yes—
59C22×#95C2211yescharacteristic
60#1446C2212yes—
61#1446C2212yes—
62#1446C2212yes—
63#1446C2212yes—
64#1445C2212yes—
65#1445C2212yes—
66#1445C2212yes—
67#1445C2212yes—
68#1445C2212yes—
69#1445C2212yes—
70#1445C2212yes—
71#1445C2212yes—
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1445C2211yescharacteristic
78#1445C2211yescharacteristic
79#1445C2211yescharacteristic
80#1445C2211yescharacteristic
81#1444C2212yes—
82#1444C2212yes—
83#1444C2211yescharacteristic
84#1444C2211yescharacteristic
85#1443C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1443C2212yes—
89#1443C2212yes—
90#1443C2212yes—
91#1443C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1442C2212yes—
96#1442C2212yes—
97#1442C2212yes—
98#1442C2212yes—
99#1442C2212yes—
100#1442C2212yes—
101#1442C2212yes—
102#1442C2212yes—
103#1442C2212yes—
104#1442C2211yescharacteristic
105#1441C2212yes—
106#1441C2212yes—
107#1441C2212yes—
108#1441C2212yes—
109#1441C2212yes—
110#1441C2212yes—
111#1441C2212yes—
112#1441C2212yes—
113#1441C2212yes—
114#1441C2211yescharacteristic
115#1434C2211yescharacteristic
116#1434C2211yescharacteristic
117#1434C2211yescharacteristic
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2211yescharacteristic
125C23×Q8C2312yes—
126C24×C4C2311yescharacteristic
127C24×C4C2312yes—
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2312yes—
131C2×C4⋊Q8—24no—
132C2×C4⋊Q8—24no—
133C2×C4⋊Q8—42no—
134C2×C22⋊Q8—28no—
135C2×C22⋊Q8—44no—
136C2×C22⋊Q8—44no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—42no—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#401—24no—
167#400—24no—
168#400—24no—
169#400—24no—
170#400—24no—
171#400—42no—
172#400—42no—
173#398—28no—
174#395—28no—
175#389—24no—
176#389—24no—
177#387—24no—
178#387—24no—
179#387—24no—
180#385—24no—
181#385—28no—
182#385—24no—
183#385—44no—
184#384—24no—
185#383—24no—
186#383—42no—
187#381—24no—
188#381—24no—
189#381—44no—
190#380—24no—
191#380—24no—
192C4×C22⋊C4D418yes—
193C2×#95—24no—
194C2×#95—42no—
195C2×#95—44no—
196C2×#95—44no—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
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×#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
264C25C2411yescharacteristic
265C22×Q8—24no—
266C22×Q8—24no—
267C22×Q8—42no—
268C22×Q8—42no—
269C22×Q8—42no—
270C22×Q8—42no—
271C22×Q8—42no—
272C23×C4—24no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—22no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—41no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×D414yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C4⋊Q8—416no—
324C22⋊Q8—432no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—416no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
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×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4#4114yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
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#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95C2×D414yes—
463#95C2×D414yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—21no—
469C24—22no—
470C24C22×D412yes—
471C24H(5,𝔽2)14yes—
472C242−1+412yes—
473C242−1+414yes—
474C242−1+412yes—
475C24C2511yescharacteristic
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—84no—
479C2×Q8—84no—
480C2×Q8—84no—
481C2×Q8—84no—
482C2×Q8—84no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
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—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
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—21no—
584C22×C4—21no—
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—21no—
605C22×C4—44no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—82no—
624C22×C4—84no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C2×#4114yes—
639C22×C4C2×#4112yes—
640C22×C4H(5,𝔽2)12yes—
641C22×C42−1+412yes—
642C4⋊C4—28no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—84no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—48no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—48no—
666C42—28no—
667C42—44no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23#53514yes—
687C23#53614yes—
688C23#53614yes—
689C23#56318yes—
690C23#56318yes—
691C23C23×D411yescharacteristic
692C23C22×#4111yescharacteristic
693C23C2×H(5,𝔽2)12yes—
694C23C2×H(5,𝔽2)11yescharacteristic
695C23C2×2−1+412yes—
696C23C2×2−1+411yescharacteristic
697C23C2×2−1+411yescharacteristic
698C23C2×2−1+411yescharacteristic
699C23#58512yes—
700C23#58511yescharacteristic
701C23#58512yes—
702Q8—816no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—416no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
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—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—41no—
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—816no—
835C2×C4—816no—
836C2×C4—88no—
837C2×C4#54614yes—
838C22—24no—
839C22—28no—
840C22—28no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—28no—
847C22—28no—
848C22#282118yes—
849C22C2×#53511yescharacteristic
850C22C2×#53611yescharacteristic
851C22C2×#53611yescharacteristic
852C22C2×#54611yescharacteristic
853C22#348511yescharacteristic
854C22#348911yescharacteristic
855C22#349512yes—
856C22#350011yescharacteristic
857C22#351312yes—
858C22#351611yescharacteristic
859C22#352311yescharacteristic
860C22C2×#56312yes—
861C22C2×#56312yes—
862C22#353312yes—
863C22#353512yes—
864C22#353512yes—
865C22#354212yes—
866C22#355211yescharacteristic
867C22#355312yes—
868C22#356111yescharacteristic
869C22#356312yes—
870C22#356412yes—
871C22#356412yes—
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—81no—
890C4—82no—
891C4—82no—
892C4—81no—
893C4—82no—
894C2—28no—
895C2C2×#282111yescharacteristic
896C2#3783511yescharacteristic
897C2#3802711yescharacteristic
898C2#3808411yescharacteristic
899C2#4137411yescharacteristic
900C2#4140911yescharacteristic
901C2#4215011yescharacteristic
902C2#4555112yes—
903C2#4555912yes—
904C2#5236812yes—
905C2#5237712yes—
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
3. #17169C2semidirect
4. #17162C2semidirect
5. #17155C2semidirect
6. #17154C2semidirect
7. #17065C2semidirect
8. #17063C2semidirect
9. #17043C2semidirect
10. #16962C2semidirect
11. #16678C2semidirect
12. #16560C2semidirect
20. #14663C2semidirect
21. #14629C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C2×#24402
#171692
#171622
#171552
#171542
#170652
#170632
#170432
#169622
#166782
#165602
#149362
#149342
#149202
#149192
#149142
#148432
#148262
#146632
#146292
#139012
C2×#14452