Finite Group Databasebeta

← #582873

Subgroups — #582873

Order 512.

2960 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic
2#14671C212yesmaximal, complemented
3#14642C212yesmaximal, complemented
4#14636C211yesmaximal, characteristic, complemented
5#14628C212yesmaximal, complemented
6#14627C211yesmaximal, characteristic, complemented
7#14581C211yesmaximal, characteristic, complemented
8#14551C211yesmaximal, characteristic, complemented
9#14484C212yesmaximal, complemented
10#14442C212yesmaximal, complemented
11#14434C212yesmaximal, complemented
12#14265C212yesmaximal, complemented
13#14127C212yesmaximal
14#14043C212yesmaximal, complemented
15#13991C212yesmaximal
16#13972C212yesmaximal, complemented
17#13962C212yesmaximal, complemented
18#13869C211yesmaximal, characteristic
19C2×#1439C211yesmaximal, characteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2482C4116yescomplemented
26C2×#399C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#397C2211yescharacteristic
30C2×#389C2212yescomplemented
31C2×#389C2212yescomplemented
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#381C2212yes—
43C2×#381C2211yescharacteristic
44C2×#379C2211yescharacteristic
45C2×#379C2212yes—
46C2×C4×C22⋊C4C2212yes—
47C22×#95C2212yes—
48C22×#95C2211yescharacteristic
49#1445C2212yescomplemented
50#1445C2212yescomplemented
51#1444C2212yescomplemented
52#1444C2212yescomplemented
53#1443C2212yescomplemented
54#1443C2212yescomplemented
55#1443C2212yescomplemented
56#1443C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1439C2211yescharacteristic
74#1439C2212yes—
75#1439C2211yescharacteristic
76#1439C2211yescharacteristic
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1436C2212yescomplemented
90#1436C2212yescomplemented
91C4⋊#95C2212yescomplemented
92C4⋊#95C2212yescomplemented
93#1434C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2212yescomplemented
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2212yes—
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×#117—42no—
116C2×#117—42no—
117C2×#117C2×C418yescomplemented
118C22×C4⋊C4—44no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4—44no—
134C22×C22⋊C4—44no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—44no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—44no—
140C22×C22⋊C4C2×C418yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164#399C2×C418yescomplemented
165#399C2×C418yescomplemented
166#397C2×C418yescomplemented
167#397C2×C418yescomplemented
168#389—44no—
169#389—44no—
170#388—44no—
171#388—44no—
172#388C2×C4116yescomplemented
173#388C2×C4116yescomplemented
174#385—44no—
175#385—44no—
176#385—44no—
177#385—44no—
178#385—44no—
179#385C2×C4116yescomplemented
180#381—44no—
181#381C2×C418yescomplemented
182#379—42no—
183#379C2×C4116yes—
184C4×C22⋊C4—44no—
185C2×#95—42no—
186C2×#95—44no—
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×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—24no—
235C25—22no—
236C25—24no—
237C25—42no—
238C25—41no—
239C25—41no—
240C25—42no—
241C25C22×C414yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C25C2411yescharacteristic
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—41no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—41no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—41no—
274C23×C4—42no—
275C23×C4—41no—
276C23×C4—42no—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295#117—416no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—416no—
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⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C22×C414yes—
331C2×C4⋊C4C22×C414yes—
332C2×C4⋊C4C22×C418yes—
333C2×C4⋊C4C22×C418yes—
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—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—41no—
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—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—416no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4C22×C418yes—
388C2×C22⋊C4C22×C418yes—
389C2×C22⋊C4C22×C418yes—
390C2×C22⋊C4C22×C414yes—
391C2×C22⋊C4C22×C414yes—
392C2×C22⋊C4C22×C414yes—
393C2×C22⋊C4C22×C414yes—
394C2×C22⋊C4C22×C418yes—
395C2×C22⋊C4C22×C418yes—
396C2×C22⋊C4C22×C418yes—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C22×C418yes—
406#95—24no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—41no—
412#95—42no—
413#95—41no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
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#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#95C22×C418yes—
446#95C22×C414yes—
447#95C22×C414yes—
448#95C22×C418yes—
449#95C22×C418yes—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—28no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—22no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—28no—
476C24—216no—
477C24—44no—
478C24—48no—
479C24—48no—
480C24—44no—
481C24—44no—
482C24—48no—
483C24—44no—
484C24—44no—
485C24—48no—
486C24—48no—
487C24—44no—
488C24—48no—
489C24—44no—
490C24—82no—
491C24—82no—
492C24—84no—
493C24—84no—
494C24—84no—
495C24—84no—
496C24—84no—
497C24C23×C412yes—
498C24C23×C412yes—
499C24C23×C412yes—
500C24H(5,𝔽2)12yes—
501C24H(5,𝔽2)12yes—
502C24H(5,𝔽2)12yes—
503C24H(5,𝔽2)14yes—
504C242−1+412yes—
505C242−1+414yes—
506C24C2511yescharacteristic
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—216no—
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—21no—
519C22×C4—21no—
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—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
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—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—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—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—82no—
626C22×C4—84no—
627C22×C4—84no—
628C22×C4—82no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—82no—
633C22×C4—82no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4C23×C414yes—
637C22×C4C23×C414yes—
638C22×C4C23×C412yes—
639C22×C4C23×C414yes—
640C22×C4C23×C412yes—
641C22×C4C23×C412yes—
642C22×C4C23×C412yes—
643C22×C4C23×C414yes—
644C22×C4H(5,𝔽2)14yes—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—84no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C22⋊C4—216no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—82no—
676C22⋊C4—82no—
677C22⋊C4—84no—
678C42—48no—
679C42—84no—
680C42—84no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—24no—
716C23—416no—
717C23—432no—
718C23—41no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—416no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—41no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—88no—
748C23—816no—
749C23—88no—
750C23—88no—
751C23—816no—
752C23—816no—
753C23—88no—
754C23—88no—
755C23#51814yes—
756C23#52014yes—
757C23#52018yes—
758C23#56014yes—
759C23#56218yes—
760C23#56314yes—
761C23C24×C411yescharacteristic
762C23C2×H(5,𝔽2)11yescharacteristic
763C23C2×H(5,𝔽2)11yescharacteristic
764C23C2×H(5,𝔽2)12yes—
765C23C2×H(5,𝔽2)11yescharacteristic
766C23C2×H(5,𝔽2)12yes—
767C23C2×2−1+412yes—
768C23C2×2−1+411yescharacteristic
769C23#58511yescharacteristic
770C23#58511yescharacteristic
771C23#58512yes—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—416no—
796C2×C4—416no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
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—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
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—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
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—42no—
863C2×C4—42no—
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—816no—
879C2×C4—816no—
880C2×C4—88no—
881C2×C4—88no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—24no—
886C22—28no—
887C22—28no—
888C22—28no—
889C22—28no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—28no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—44no—
907C22—44no—
908C22—832no—
909C22—81no—
910C22—81no—
911C22—82no—
912C22—82no—
913C22—81no—
914C22—81no—
915C22#237618yes—
916C22C2×#51811yescharacteristic
917C22C2×#52012yes—
918C22C2×#52011yescharacteristic
919C22#342811yescharacteristic
920C22C4×H(5,𝔽2)12yes—
921C22C2×#56011yescharacteristic
922C22C2×#56212yes—
923C22C2×#56311yescharacteristic
924C22#353211yescharacteristic
925C22#353212yes—
926C22#353311yescharacteristic
927C22#353312yes—
928C22#353411yescharacteristic
929C22#353411yescharacteristic
930C22#353412yes—
931C22#353511yescharacteristic
932C22#353512yes—
933C22#353512yes—
934C22#353511yescharacteristic
935C22#353812yes—
936C22#354212yes—
937C22#356112yes—
938C22#356412yes—
939C4—42no—
940C4—42no—
941C4—44no—
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—44no—
947C4—44no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—82no—
955C2—28no—
956C2—44no—
957C2—82no—
958C2C2×#237611yescharacteristic
959C2#3438611yescharacteristic
960C2#3440611yescharacteristic
961C2#3445712yes—
962C2#3445812yes—
963C2#5237312yes—
964C2#5237412yes—
965C2#5239611yescharacteristic
966C2#5239711yescharacteristic
967C2#5251111yescharacteristic
968C2#5274211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14671C2semidirect
3. #14642C2semidirect
4. #14636C2semidirect
5. #14628C2semidirect
6. #14627C2semidirect
7. #14581C2semidirect
8. #14551C2semidirect
9. #14484C2semidirect
10. #14442C2semidirect
11. #14434C2semidirect
12. #14265C2semidirect
14. #14043C2semidirect
16. #13972C2semidirect
17. #13962C2semidirect
25. #2482C4semidirect
30. C2×#389C22semidirect
31. C2×#389C22semidirect
49. #1445C22semidirect
50. #1445C22semidirect
51. #1444C22semidirect
52. #1444C22semidirect
53. #1443C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1443C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. C4⋊#95C22semidirect
92. C4⋊#95C22semidirect
93. #1434C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
117. C2×#117C2×C4semidirect
164. #399C2×C4semidirect
165. #399C2×C4semidirect
166. #397C2×C4semidirect
167. #397C2×C4semidirect
172. #388C2×C4semidirect
173. #388C2×C4semidirect
179. #385C2×C4semidirect
181. #381C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
#146712
#146422
#146362
#146282
#146272
#145812
#145512
#144842
#144422
#144342
#142652
#141272
#140432
#139912
#139722
#139622
#138692
C2×#14392