Finite Group Databasebeta

← #582929

Subgroups — #582929

Order 512.

2854 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2406C211yesmaximal, characteristic
2#14666C211yesmaximal, characteristic, complemented
3#14658C211yesmaximal, characteristic, complemented
4#14645C212yesmaximal, complemented
5#14645C212yesmaximal, complemented
6#14626C212yesmaximal, complemented
7#14554C212yesmaximal, complemented
8#14516C211yesmaximal, characteristic, complemented
9#14506C211yesmaximal, characteristic, complemented
10#14428C212yesmaximal, complemented
11#14360C212yesmaximal, complemented
12#14269C212yesmaximal, complemented
13#14143C212yesmaximal, complemented
14#14104C212yesmaximal, complemented
15#14075C212yesmaximal, complemented
16#14011C212yesmaximal, complemented
17#13937C211yesmaximal, characteristic
18#13882C212yesmaximal, complemented
19#13851C211yesmaximal, characteristic
20C23×#41C2211yescharacteristic
21C22×#123C2211yescharacteristic
22C22×#123C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24#2406C4116yescomplemented
25C2×#395C2212yes—
26C2×#394C2212yes—
27C2×#391C2212yes—
28C2×#390C2212yes—
29C2×#389C2212yes—
30C2×#388C2212yes—
31C2×#387C2212yes—
32C2×#387C2212yes—
33C2×#387C2212yes—
34C2×#386C2211yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#381C2211yescharacteristic
39C2×#380C2212yes—
40C2×#380C2211yescharacteristic
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2212yes—
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46#1446C2211yescharacteristic
47#1446C2211yescharacteristic
48#1445C2212yes—
49#1445C2212yes—
50#1445C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1441C2212yes—
58#1441C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1438C2212yes—
77#1438C2212yes—
78#1438C2211yescharacteristic
79#1438C2211yescharacteristic
80#1438C2211yescharacteristic
81#1438C2211yescharacteristic
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yes—
108C22×#41—42no—
109C22×#41—42no—
110C22×#41—44no—
111C22×#41—44no—
112C22×#41C2×C418yes—
113C23×Q8C2311yescharacteristic
114C23×D4C2311yescharacteristic
115C23×D4C2311yescharacteristic
116C23×D4C2311yescharacteristic
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C2×#123—44no—
123C2×#123—44no—
124C2×#123C2×C418yes—
125C2×#123C2×C418yes—
126C22×C4⋊C4—42no—
127C22×C4⋊C4—42no—
128C22×C4⋊C4C2×C418yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163#395C2×C4116yes—
164#394C2×C4116yes—
165#391—44no—
166#390—44no—
167#389—44no—
168#388—44no—
169#387—44no—
170#387—44no—
171#387—44no—
172#386C2×C418yes—
173#386C2×C418yes—
174#385C2×C4116yes—
175#385C2×C4116yes—
176#381C2×C418yes—
177#380—42no—
178#380—44no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4—44no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—44no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
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×#95C2311yescharacteristic
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×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—432no—
235C2×#41—432no—
236C22×Q8—24no—
237C22×Q8—41no—
238C22×Q8—42no—
239C22×Q8—41no—
240C22×Q8C22×C414yes—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—41no—
245C22×D4—41no—
246C22×D4—41no—
247C22×D4—41no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—41no—
252C22×D4—41no—
253C22×D4C22×C414yes—
254C22×D4C22×C414yes—
255C22×D4C22×C414yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—41no—
274C23×C4—41no—
275C23×C4—42no—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C22×C414yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297#123—416no—
298#123—416no—
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—416no—
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—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4C22×C418yes—
324C2×C4⋊C4C22×C418yes—
325C2×C4⋊C4C22×C418yes—
326C2×C4⋊C4C22×C418yes—
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—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
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—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
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—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C22×C414yes—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C418yes—
380C2×C22⋊C4C22×C418yes—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—41no—
413#95—42no—
414#95—41no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
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—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95C22×C418yes—
437#95C22×C418yes—
438#95C22×C418yes—
439#95C22×C418yes—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C23×C412yes—
464C24C23×C412yes—
465C24C23×C412yes—
466C24H(5,𝔽2)14yes—
467C24C2511yescharacteristic
468#41—4128no—
469C2×Q8—28no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×Q8—48no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
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—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
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—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—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—44no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4C23×C414yes—
607C22×C4C23×C414yes—
608C22×C4C23×C414yes—
609C22×C4C23×C412yes—
610C22×C4C23×C412yes—
611C22×C4C23×C414yes—
612C22×C4C23×C412yes—
613C22×C4C23×C412yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C42−1+414yes—
618C4⋊C4—216no—
619C4⋊C4—216no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—28no—
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—44no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—84no—
647C42—84no—
648C42—84no—
649C42—84no—
650C42—84no—
651C42—84no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
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—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23#51814yes—
715C23C24×C411yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+412yes—
721C23#58512yes—
722C23#58512yes—
723C23#58512yes—
724Q8—416no—
725D4—416no—
726D4—416no—
727D4—416no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
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—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—416no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
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—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
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—42no—
817C2×C4—42no—
818C2×C4—42no—
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—42no—
834C2×C4—88no—
835C2×C4#51814yes—
836C2×C4#51814yes—
837C22—24no—
838C22—28no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22C2×#51811yescharacteristic
865C22C2×#51811yescharacteristic
866C22C2×#51811yescharacteristic
867C22#342812yes—
868C22C4×2−1+412yes—
869C22#352912yes—
870C22#352911yescharacteristic
871C22#352911yescharacteristic
872C22#353212yes—
873C22#353212yes—
874C22#353312yes—
875C22#353512yes—
876C22#353912yes—
877C22#354112yes—
878C22#354112yes—
879C22#355011yescharacteristic
880C22#355111yescharacteristic
881C22#355412yes—
882C22#355912yes—
883C22#356012yes—
884C22#356212yes—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—42no—
889C4—42no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C2—44no—
902C2—82no—
903C2—82no—
904C2#3434211yescharacteristic
905C2#3435611yescharacteristic
906C2#3441311yescharacteristic
907C2#3446912yes—
908C2#3447312yes—
909C2#5232612yes—
910C2#5232912yes—
911C2#5241512yes—
912C2#5241812yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14666C2semidirect
3. #14658C2semidirect
4. #14645C2semidirect
5. #14645C2semidirect
6. #14626C2semidirect
7. #14554C2semidirect
8. #14516C2semidirect
9. #14506C2semidirect
10. #14428C2semidirect
11. #14360C2semidirect
12. #14269C2semidirect
13. #14143C2semidirect
14. #14104C2semidirect
15. #14075C2semidirect
16. #14011C2semidirect
18. #13882C2semidirect
24. #2406C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24062
#146662
#146582
#146452
#146262
#145542
#145162
#145062
#144282
#143602
#142692
#141432
#141042
#140752
#140112
#139372
#138822
#138512