Finite Group Databasebeta

← #5082802

Subgroups — #5082802

Order 512.

2312 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2736C211yesmaximal, characteristic
2C2×#2637C211yesmaximal, characteristic, complemented
3#17229C211yesmaximal, characteristic, complemented
4#17217C212yesmaximal, complemented
5#17165C212yesmaximal, complemented
6#16342C212yesmaximal, complemented
7#16331C212yesmaximal, complemented
8#16298C212yesmaximal
9#15986C211yesmaximal, characteristic
10#15928C211yesmaximal, characteristic, complemented
11#15765C212yesmaximal, complemented
12#15572C212yesmaximal, complemented
13#15480C211yesmaximal, characteristic
14#15402C212yesmaximal, complemented
15#15389C212yesmaximal, complemented
16#15350C212yesmaximal, complemented
17#15284C212yesmaximal
18#14875C212yesmaximal, complemented
19#14649C211yesmaximal, characteristic, complemented
20C22×#126C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic, complemented
22#2736—28no—
23#2637—28no—
24C2×#400C2211yescharacteristic, complemented
25C2×#399C2212yes—
26C2×#399C2212yes—
27C2×#398C2212yescomplemented
28C2×#398C2211yescharacteristic, complemented
29C2×#397C2212yes—
30C2×#397C2211yescharacteristic
31C2×#397C2211yescharacteristic
32C2×#397C2212yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#395C2211yescharacteristic, complemented
36C2×#393C2212yes—
37C2×#393C2211yescharacteristic
38C2×#389C2212yescomplemented
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#387C2212yescomplemented
45C2×#387C2212yescomplemented
46C2×#384C2211yescharacteristic, complemented
47C2×#382C2211yescharacteristic, complemented
48C2×#379C2211yescharacteristic
49C2×#379C2212yes—
50C2×#379C2211yescharacteristic
51C2×#379C2211yescharacteristic
52C2×#379C2212yes—
53#1446C2212yescomplemented
54#1445C2211yescharacteristic, complemented
55#1445C2212yescomplemented
56#1445C2212yescomplemented
57#1444C2212yescomplemented
58#1444C2212yescomplemented
59#1444C2212yescomplemented
60#1444C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2211yescharacteristic
76#1440C2212yes—
77#1440C2211yescharacteristic
78#1440C2211yescharacteristic
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1437C2212yes—
99#1437C2212yes—
100#1437C2211yescharacteristic
101#1437C2212yes—
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2211yescharacteristic, complemented
107#1436C2212yescomplemented
108#1434C2212yescomplemented
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C2×#126—24no—
112C2×#126—42no—
113C2×#126—42no—
114C2×C4×Q8—24no—
115C2×C4×Q8—42no—
116C2×C4×Q8—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161#400—42no—
162#399—44no—
163#399—44no—
164#398—24no—
165#398—28no—
166#397—24no—
167#397—24no—
168#397—28no—
169#397—44no—
170#396—28no—
171#396—44no—
172#395—24no—
173#393—28no—
174#393D418yes—
175#389—44no—
176#388—28no—
177#388—28no—
178#388—28no—
179#388—28no—
180#388—44no—
181#387—28no—
182#387—44no—
183#384—42no—
184#382—24no—
185#379—28no—
186#379—24no—
187#379—42no—
188#379—42no—
189#379—44no—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
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×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C25—22no—
232C25—24no—
233C25—42no—
234C25—42no—
235C25—42no—
236C25—42no—
237C25—41no—
238C25—42no—
239C25—41no—
240C25C2411yescharacteristic
241C25C2412yes—
242C22×Q8—41no—
243C22×Q8—41no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8C2×D414yes—
247C23×C4C2411yescharacteristic
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264#126—416no—
265C4×Q8—416no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
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—41no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
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—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—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
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—42no—
358C2×C22⋊C4—42no—
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—41no—
367C2×C22⋊C4—41no—
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—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D418yes—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—41no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394#95—24no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
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—41no—
432#95—42no—
433#95C2×D414yes—
434#95C2×D418yes—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—48no—
458C24—44no—
459C24—44no—
460C24—48no—
461C24—44no—
462C24—82no—
463C24—84no—
464C24—82no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24—84no—
471C24—82no—
472C24—84no—
473C24—82no—
474C24—84no—
475C24—84no—
476C24—84no—
477C24—84no—
478C24C22×D412yes—
479C242−1+414yes—
480C24C2511yescharacteristic
481C2×Q8—44no—
482C2×Q8—48no—
483C2×Q8—44no—
484C2×Q8—48no—
485C2×Q8—44no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
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—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—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—22no—
534C22×C4—22no—
535C22×C4—21no—
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—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
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×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D414yes—
589C22×C4C22×D414yes—
590C22×C4H(5,𝔽2)14yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C4H(5,𝔽2)12yes—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—82no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C4⋊C4—84no—
605C4⋊C4—84no—
606C4⋊C4—84no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
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—82no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C42—28no—
634C42—48no—
635C42—44no—
636C42—84no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—88no—
694C23—816no—
695C23—816no—
696C23—816no—
697C23—816no—
698C23—88no—
699C23—88no—
700C23—816no—
701C23—816no—
702C23C23×D411yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×H(5,𝔽2)12yes—
706C23C2×2−1+412yes—
707C23#58512yes—
708C23#58512yes—
709C23#58512yes—
710C23#58512yes—
711Q8—416no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
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—41no—
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—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—41no—
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—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—44no—
831C22—832no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22#348411yescharacteristic
845C22#348512yes—
846C22#348711yescharacteristic
847C22#348912yes—
848C22#349811yescharacteristic
849C22#352911yescharacteristic
850C22#353312yes—
851C22#353412yes—
852C22#353512yes—
853C22#353811yescharacteristic
854C22#354011yescharacteristic
855C22#354012yes—
856C22#354011yescharacteristic
857C22#354112yes—
858C22#354612yes—
859C22#356012yes—
860C22#356112yes—
861C22#356412yes—
862C22#356412yes—
863C22#356612yes—
864C22#356612yes—
865C4—44no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—44no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—81no—
879C4—82no—
880C4—81no—
881C4—82no—
882C2—84no—
883C2—82no—
884C2#4544211yescharacteristic
885C2#4642511yescharacteristic
886C2#4769012yes—
887C2#5152812yes—
888C2#5153011yescharacteristic
889C2#5293212yes—
890C2#5408612yes—
891C2#5667012yes—
892C2#5816512yes—
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
2. C2×#2637C2semidirect
3. #17229C2semidirect
4. #17217C2semidirect
5. #17165C2semidirect
6. #16342C2semidirect
7. #16331C2semidirect
10. #15928C2semidirect
11. #15765C2semidirect
12. #15572C2semidirect
14. #15402C2semidirect
15. #15389C2semidirect
16. #15350C2semidirect
18. #14875C2semidirect
19. #14649C2semidirect
21. C22×C4×Q8C22semidirect
24. C2×#400C22semidirect
27. C2×#398C22semidirect
28. C2×#398C22semidirect
35. C2×#395C22semidirect
38. C2×#389C22semidirect
44. C2×#387C22semidirect
45. C2×#387C22semidirect
46. C2×#384C22semidirect
47. C2×#382C22semidirect
53. #1446C22semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#27362
C2×#26372
#172292
#172172
#171652
#163422
#163312
#162982
#159862
#159282
#157652
#155722
#154802
#154022
#153892
#153502
#152842
#148752
#146492