Finite Group Databasebeta

← #538849

Subgroups — #538849

Order 512.

2658 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2536C211yesmaximal, characteristic
2#14593C212yesmaximal, complemented
3#14590C211yesmaximal, characteristic, complemented
4#14535C211yesmaximal, characteristic
5#14517C212yesmaximal
6#14423C212yesmaximal, complemented
7#14238C211yesmaximal, characteristic, complemented
8#14224C211yesmaximal, characteristic
9#14149C212yesmaximal, complemented
10#14106C212yesmaximal, complemented
11#14099C212yesmaximal, complemented
12#14066C212yesmaximal, complemented
13#14052C212yesmaximal, complemented
14#13986C212yesmaximal, complemented
15#13942C211yesmaximal, characteristic, complemented
16#13850C211yesmaximal, characteristic, complemented
17#13823C212yesmaximal, complemented
18#13813C212yesmaximal
19#13789C212yesmaximal, complemented
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#2536C4116yescomplemented
24C2×#398C2211yescharacteristic
25C2×#398C2211yescharacteristic
26C2×#394C2211yescharacteristic
27C2×#394C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#387C2212yes—
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#382C2211yescharacteristic
41C2×#382C2211yescharacteristic
42C2×#380C2212yes—
43C2×C4×C4⋊C4C2212yes—
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yes—
50C2×#376C2211yescharacteristic
51C22×#95C2212yes—
52#1446C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1443C2212yes—
56#1443C2212yes—
57#1443C2212yes—
58#1442C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1441C2211yescharacteristic
62#1441C2211yescharacteristic
63#1441C2211yescharacteristic
64#1441C2211yescharacteristic
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1437C2212yes—
73#1437C2212yes—
74#1437C2212yes—
75#1437C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92C4⋊#95C2212yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95#1434C2212yes—
96#1434C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C4×#95C2212yes—
108C23×Q8C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×C22⋊Q8—44no—
114C2×C22⋊Q8—44no—
115C2×C22⋊Q8C2×C4116yescomplemented
116C2×C4×Q8—42no—
117C2×C4×Q8—42no—
118C2×C4×Q8C2×C418yescomplemented
119C2×C4×D4—42no—
120C2×C4×D4—42no—
121C2×C4×D4C2×C418yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊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×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158#398C2×C418yescomplemented
159#398C2×C418yescomplemented
160#394C2×C418yes—
161#394C2×C418yes—
162#391—42no—
163#391—42no—
164#388—28no—
165#388—28no—
166#388C2×C4116yescomplemented
167#388C2×C4116yescomplemented
168#387—44no—
169#386—28no—
170#386—28no—
171#385—28no—
172#385—28no—
173#385—44no—
174#382—42no—
175#382C2×C418yescomplemented
176#380C2×C4116yescomplemented
177C4×C4⋊C4—42no—
178C4×C4⋊C4—44no—
179C4×C4⋊C4—42no—
180C4×C22⋊C4—44no—
181C4×C22⋊C4—44no—
182C4×C22⋊C4—44no—
183C4×C22⋊C4—44no—
184#376—42no—
185C2×#95—44no—
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×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
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×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C25C2412yes—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—41no—
238C22×Q8—41no—
239C22×Q8C22×C414yes—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—41no—
243C22×D4—41no—
244C22×D4C22×C414yes—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4C22×C418yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C22⋊Q8—432no—
285C4×Q8—416no—
286C4×D4—416no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
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—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4C22×C418yes—
321C2×C4⋊C4C22×C414yes—
322C2×C4⋊C4C22×C414yes—
323C2×C4⋊C4C22×C414yes—
324C2×C4⋊C4C22×C414yes—
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—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
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⋊C4C22×C418yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C22×C418yes—
356C2×C22⋊C4C22×C418yes—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4#4118yes—
359C2×C22⋊C4#4118yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—41no—
382C2×C42—41no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—41no—
386C2×C42—41no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42C22×C414yes—
391C2×C42C22×C414yes—
392C2×C42C22×C414yes—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—41no—
420#95—42no—
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—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95C22×C418yes—
435#95C22×C418yes—
436#95C22×C418yes—
437#95C22×C414yes—
438#95C22×C414yes—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24C23×C414yes—
452C24C2×#4114yes—
453C24C2×#4114yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×D4—216no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C2×D4—44no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
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—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
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—216no—
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—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4C23×C414yes—
586C22×C4C23×C414yes—
587C22×C4C23×C412yes—
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C23×C414yes—
591C22×C4C23×C412yes—
592C22×C4C23×C412yes—
593C22×C4C23×C412yes—
594C22×C4C23×C412yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4114yes—
598C22×C4C2×#4114yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C42−1+414yes—
605C22×C42−1+412yes—
606C4⋊C4—216no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—82no—
618C4⋊C4—82no—
619C4⋊C4—84no—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—84no—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—48no—
635C42—48no—
636C42—82no—
637C42—82no—
638C42—84no—
639C42—84no—
640C42—84no—
641C42—84no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23C4×#4118yes—
677C23C24×C411yescharacteristic
678C23C22×#4112yes—
679C23C22×#4112yes—
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×2−1+411yescharacteristic
686C23C2×2−1+412yes—
687C23#58512yes—
688Q8—416no—
689D4—416no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
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—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
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—816no—
806C2×C4—816no—
807C2×C4—816no—
808C2×C4#51814yes—
809C2×C4#51814yes—
810C2×C4#52014yes—
811C22—28no—
812C22—28no—
813C22—28no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22C2×C4×#4112yes—
827C22C2×#51811yescharacteristic
828C22C2×#51811yescharacteristic
829C22C2×#52011yescharacteristic
830C22C4×2−1+412yes—
831C22#348111yescharacteristic
832C22#348111yescharacteristic
833C22#348112yes—
834C22#350512yes—
835C22#350512yes—
836C22#350912yes—
837C22#351112yes—
838C22#351412yes—
839C22#351512yes—
840C22#352012yes—
841C22#352012yes—
842C22#353512yes—
843C22#353611yescharacteristic
844C22#353611yescharacteristic
845C22#353711yescharacteristic
846C22#353711yescharacteristic
847C22#354411yescharacteristic
848C22#354511yescharacteristic
849C4—24no—
850C4—24no—
851C4—24no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—44no—
857C4—44no—
858C4—44no—
859C4—44no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—82no—
865C4—82no—
866C4—82no—
867C2—48no—
868C2#3415211yescharacteristic
869C2#3431412yes—
870C2#3432712yes—
871C2#3437911yescharacteristic
872C2#3440911yescharacteristic
873C2#4379011yescharacteristic
874C2#4379111yescharacteristic
875C2#4380012yes—
876C2#4388012yes—
877C2#4486011yescharacteristic
878C2#4486211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14593C2semidirect
3. #14590C2semidirect
6. #14423C2semidirect
7. #14238C2semidirect
9. #14149C2semidirect
10. #14106C2semidirect
11. #14099C2semidirect
12. #14066C2semidirect
13. #14052C2semidirect
14. #13986C2semidirect
15. #13942C2semidirect
16. #13850C2semidirect
17. #13823C2semidirect
19. #13789C2semidirect
23. #2536C4semidirect
115. C2×C22⋊Q8C2×C4semidirect
118. C2×C4×Q8C2×C4semidirect
158. #398C2×C4semidirect
159. #398C2×C4semidirect
166. #388C2×C4semidirect
167. #388C2×C4semidirect
175. #382C2×C4semidirect
176. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25362
#145932
#145902
#145352
#145172
#144232
#142382
#142242
#141492
#141062
#140992
#140662
#140522
#139862
#139422
#138502
#138232
#138132
#137892