Finite Group Databasebeta

← #762667

Subgroups — #762667

Order 512.

3374 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16830C211yesmaximal, characteristic, complemented
2#16718C212yesmaximal, complemented
3#16707C211yesmaximal, characteristic, complemented
4#15054C212yesmaximal, complemented
5#15016C212yesmaximal, complemented
6#14830C212yesmaximal, complemented
7#14829C212yesmaximal, complemented
8#14820C211yesmaximal, characteristic
9#14734C211yesmaximal, characteristic
10#14727C212yesmaximal
11#14248C211yesmaximal, characteristic, complemented
12#14215C211yesmaximal, characteristic, complemented
13#14040C212yesmaximal, complemented
14#13980C212yesmaximal, complemented
15#13896C212yesmaximal, complemented
16#13888C212yesmaximal, complemented
17#13883C212yesmaximal, complemented
18C4×#379C212yesmaximal
19C2×C22⋊#95C211yesmaximal, characteristic
20C25×C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C2×#399C2211yescharacteristic
24C2×#399C2211yescharacteristic
25C2×#397C2211yescharacteristic
26C2×#397C2212yes—
27C2×#397C2212yes—
28C2×#397C2211yescharacteristic
29C2×#387C2212yescomplemented
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#382C2212yescomplemented
33C2×#380C2211yescharacteristic
34C2×#380C2211yescharacteristic
35C2×#379C2212yes—
36C2×#379C2212yes—
37C2×C4×C22⋊C4C2212yes—
38C2×C4×C22⋊C4C2212yes—
39C2×C4×C22⋊C4C2212yes—
40C2×C4×C22⋊C4C2212yes—
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2212yes—
43C22×#95C2212yes—
44C22×#95C2212yes—
45#1445C2212yescomplemented
46#1445C2212yescomplemented
47#1445C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1441C2212yescomplemented
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2211yescharacteristic
70#1439C2211yescharacteristic
71#1439C2212yes—
72#1439C2212yes—
73#1439C2211yescharacteristic
74#1439C2211yescharacteristic
75#1436C2212yescomplemented
76#1436C2212yescomplemented
77#1436C2212yescomplemented
78#1436C2212yescomplemented
79#1436C2212yescomplemented
80#1436C2212yescomplemented
81C4⋊#95C2212yescomplemented
82#1434C2212yescomplemented
83#1434C2212yescomplemented
84#1434C2212yescomplemented
85#1434C2212yescomplemented
86#1434C2212yescomplemented
87#1434C2212yescomplemented
88#1434C2212yescomplemented
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2211yescharacteristic
94C22⋊#95C2212yes—
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2211yescharacteristic
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C26C2311yescharacteristic
108C24×C4—28no—
109C24×C4—24no—
110C24×C4—44no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157#399—24no—
158#399—42no—
159#397—24no—
160#397—44no—
161#397—42no—
162#397—44no—
163#387—44no—
164#385—28no—
165#385—28no—
166#382—44no—
167#380—42no—
168#380—42no—
169#379—28no—
170#379—28no—
171C4×C22⋊C4—28no—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—44no—
174C4×C22⋊C4—44no—
175C4×C22⋊C4—44no—
176C4×C22⋊C4—44no—
177C2×#95—28no—
178C2×#95—44no—
179C2×#95C2311yescharacteristic
180C2×#95C2312yes—
181C2×#95C2311yescharacteristic
182C2×#95C2312yes—
183C2×#95C2312yes—
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×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
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×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—24no—
234C25—24no—
235C25—42no—
236C25—42no—
237C25#4114yes—
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C25C2411yescharacteristic
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—41no—
270C23×C4—42no—
271C23×C4—41no—
272C23×C4—416no—
273C23×C4—432no—
274C23×C4—41no—
275C23×C4—41no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—432no—
283C23×C4—416no—
284C23×C4—416no—
285C23×C4#4118yes—
286C23×C4#4114yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2412yes—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—41no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
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—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
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—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—416no—
381C2×C22⋊C4—416no—
382C2×C22⋊C4#4118yes—
383C2×C22⋊C4#4114yes—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
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—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—22no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
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—41no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—41no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—22no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—216no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—44no—
484C24—44no—
485C24—48no—
486C24—44no—
487C24—48no—
488C24—44no—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24C2×#4114yes—
495C24C2×#4114yes—
496C24H(5,𝔽2)12yes—
497C24H(5,𝔽2)12yes—
498C24H(5,𝔽2)12yes—
499C242−1+412yes—
500C24C2511yescharacteristic
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—216no—
506C22×C4—216no—
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—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—216no—
534C22×C4—216no—
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—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—21no—
559C22×C4—21no—
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—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
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—44no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—44no—
623C22×C4—4128no—
624C22×C4—44no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—82no—
634C22×C4—82no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4—84no—
639C22×C4C2×#4114yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4114yes—
642C22×C4C2×#4114yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4114yes—
646C22×C4H(5,𝔽2)14yes—
647C4⋊C4—48no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C4⋊C4—84no—
651C4⋊C4—84no—
652C4⋊C4—84no—
653C4⋊C4—82no—
654C4⋊C4—82no—
655C22⋊C4—216no—
656C22⋊C4—44no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C42—48no—
675C42—84no—
676C42—84no—
677C42—84no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—232no—
697C23—22no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—432no—
722C23—432no—
723C23—416no—
724C23—416no—
725C23—432no—
726C23—416no—
727C23—432no—
728C23—416no—
729C23—416no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—416no—
749C23—42no—
750C23—42no—
751C23#52914yes—
752C23#52918yes—
753C23#53814yes—
754C23#53914yes—
755C23#55114yes—
756C23#55218yes—
757C23#55914yes—
758C23C22×#4111yescharacteristic
759C23C22×#4112yes—
760C23C22×#4111yescharacteristic
761C23C22×#4112yes—
762C23C22×#4111yescharacteristic
763C23C2×H(5,𝔽2)11yescharacteristic
764C23C2×H(5,𝔽2)11yescharacteristic
765C23C2×H(5,𝔽2)11yescharacteristic
766C23C2×H(5,𝔽2)12yes—
767C23C2×2−1+411yescharacteristic
768C23#58512yes—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—416no—
789C2×C4—432no—
790C2×C4—432no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
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—41no—
806C2×C4—42no—
807C2×C4—41no—
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—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—41no—
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—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—88no—
877C2×C4—88no—
878C2×C4—816no—
879C2×C4#55118yes—
880C22—24no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—28no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28no—
893C22—28no—
894C22—464no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—42no—
907C22—42no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22#251718yes—
914C22C2×#52911yescharacteristic
915C22C2×#52912yes—
916C22C2×#53811yescharacteristic
917C22C2×#53911yescharacteristic
918C22#345912yes—
919C22C2×#55111yescharacteristic
920C22C2×#55112yes—
921C22C2×#55212yes—
922C22#347512yes—
923C22#347512yes—
924C22C2×#55911yescharacteristic
925C22#348112yes—
926C22#349012yes—
927C22#349011yescharacteristic
928C22#349011yescharacteristic
929C22#349211yescharacteristic
930C22#349211yescharacteristic
931C22#349412yes—
932C22#351312yes—
933C22#351912yes—
934C22#353211yescharacteristic
935C22#353311yescharacteristic
936C22#354112yes—
937C4—28no—
938C4—44no—
939C4—42no—
940C4—44no—
941C4—44no—
942C4—42no—
943C4—81no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—82no—
948C4—82no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—81no—
953C2—28no—
954C2—44no—
955C2—44no—
956C2C2×#251711yescharacteristic
957C2#3475412yes—
958C2#3499711yescharacteristic
959C2#3499812yes—
960C2#3745711yescharacteristic
961C2#5919211yescharacteristic
962C2#5919311yescharacteristic
963C2#5920512yes—
964C2#5925212yes—
965C2#5936711yescharacteristic
966C2#5962311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16830C2semidirect
2. #16718C2semidirect
3. #16707C2semidirect
4. #15054C2semidirect
5. #15016C2semidirect
6. #14830C2semidirect
7. #14829C2semidirect
11. #14248C2semidirect
12. #14215C2semidirect
13. #14040C2semidirect
14. #13980C2semidirect
15. #13896C2semidirect
16. #13888C2semidirect
17. #13883C2semidirect
29. C2×#387C22semidirect
32. C2×#382C22semidirect
45. #1445C22semidirect
46. #1445C22semidirect
47. #1445C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
75. #1436C22semidirect
76. #1436C22semidirect
77. #1436C22semidirect
78. #1436C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. C4⋊#95C22semidirect
82. #1434C22semidirect
83. #1434C22semidirect
84. #1434C22semidirect
85. #1434C22semidirect
86. #1434C22semidirect
87. #1434C22semidirect
88. #1434C22semidirect

Maximal subgroups

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

subgroupindex
#168302
#167182
#167072
#150542
#150162
#148302
#148292
#148202
#147342
#147272
#142482
#142152
#140402
#139802
#138962
#138882
#138832
C4×#3792
C2×C22⋊#952