Finite Group Databasebeta

← #5511043

Subgroups — #5511043

Order 512.

2344 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2821C211yesmaximal, characteristic, complemented
2C2×#2840C211yesmaximal, characteristic
3#17198C211yesmaximal, characteristic, complemented
4#17152C212yesmaximal, complemented
5#17100C212yesmaximal, complemented
6#17023C212yesmaximal, complemented
7#16803C212yesmaximal, complemented
8#16788C212yesmaximal, complemented
9#16375C212yesmaximal, complemented
10#15986C211yesmaximal, characteristic
11#15931C212yesmaximal, complemented
12#15910C211yesmaximal, characteristic, complemented
13#15467C211yesmaximal, characteristic
14#15322C212yesmaximal, complemented
15#15297C212yesmaximal
16#15284C212yesmaximal
17#15004C212yesmaximal, complemented
18#14956C212yesmaximal, complemented
19#14232C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic, complemented
21C22×#126C2211yescharacteristic
22#2840—28no—
23#2821—28no—
24C2×#400C2212yescomplemented
25C2×#399C2212yes—
26C2×#398C2212yescomplemented
27C2×#397C2212yes—
28C2×#396C2212yes—
29C2×#395C2211yescharacteristic, complemented
30C2×#395C2211yescharacteristic, complemented
31C2×#395C2211yescharacteristic, complemented
32C2×#393C2212yes—
33C2×#393C2211yescharacteristic
34C2×#393C2211yescharacteristic
35C2×#393C2212yes—
36C2×#393C2212yes—
37C2×#393C2212yes—
38C2×#393C2212yes—
39C2×#393C2212yes—
40C2×#393C2211yescharacteristic
41C2×#391C2211yescharacteristic, complemented
42C2×#391C2212yescomplemented
43C2×#391C2212yescomplemented
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#383C2211yescharacteristic, complemented
48C2×#379C2211yescharacteristic
49C2×#379C2212yes—
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C2×#379C2211yescharacteristic
53#1446C2212yescomplemented
54#1446C2212yescomplemented
55#1446C2212yescomplemented
56#1446C2212yescomplemented
57#1446C2212yescomplemented
58#1445C2211yescharacteristic, complemented
59#1445C2212yescomplemented
60#1445C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2211yescharacteristic
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2211yescharacteristic
83#1440C2211yescharacteristic
84#1440C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1437C2211yescharacteristic
97#1437C2212yes—
98#1437C2212yes—
99#1437C2212yes—
100#1437C2212yes—
101#1437C2212yes—
102#1436C2212yescomplemented
103#1436C2211yescharacteristic, complemented
104#1436C2212yescomplemented
105#1434C2212yescomplemented
106#1434C2212yescomplemented
107#1434C2212yescomplemented
108C4×#95C2212yescomplemented
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×Q8C2312yes—
113C23×Q8C2311yescharacteristic
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×#126—24no—
118C2×#126—42no—
119C2×#126—42no—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157#400—28no—
158#399—28no—
159#398—28no—
160#397—28no—
161#396—44no—
162#395—24no—
163#395—24no—
164#395—42no—
165#393—28no—
166#393—24no—
167#393—24no—
168#393—28no—
169#393—28no—
170#393—28no—
171#393—28no—
172#393—44no—
173#393D418yes—
174#391—44no—
175#391—44no—
176#391—42no—
177#388—44no—
178#388—44no—
179#388—44no—
180#383—24no—
181#379—24no—
182#379—28no—
183#379—42no—
184#379—42no—
185#379—44no—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
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×#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×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C25—22no—
232C25—24no—
233C25—42no—
234C25—42no—
235C25—42no—
236C25—42no—
237C25—41no—
238C25—41no—
239C25—42no—
240C25C2411yescharacteristic
241C25C2412yes—
242C22×Q8—22no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—41no—
246C22×Q8—41no—
247C22×Q8—41no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×Q8—42no—
255C22×Q8—41no—
256C22×Q8—42no—
257C22×Q8—42no—
258C22×Q8—42no—
259C22×Q8—42no—
260C22×Q8—42no—
261C22×Q8—42no—
262C22×Q8—41no—
263C22×Q8C2×D414yes—
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C4⋊Q8—416no—
282#126—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
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×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
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—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
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—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—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—41no—
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⋊C4C2×D414yes—
378C2×C22⋊C4C2×D418yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—42no—
385C2×C42—41no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—22no—
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—42no—
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—41no—
431#95—42no—
432#95—42no—
433#95C2×D414yes—
434#95C2×D418yes—
435C24—28no—
436C24—22no—
437C24—21no—
438C24—21no—
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—22no—
458C24—48no—
459C24—44no—
460C24—44no—
461C24—82no—
462C24—84no—
463C24—82no—
464C24—84no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24—84no—
471C24—82no—
472C24—84no—
473C24—84no—
474C24—82no—
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—
486C2×Q8—82no—
487C2×Q8—84no—
488C2×Q8—84no—
489C2×Q8—84no—
490C2×Q8—84no—
491C2×Q8—84no—
492C2×Q8—82no—
493C2×Q8—82no—
494C2×Q8—82no—
495C2×Q8—84no—
496C2×Q8—84no—
497C2×Q8—82no—
498C2×Q8—82no—
499C2×Q8—84no—
500C2×Q8—84no—
501C2×Q8—84no—
502C2×Q8—84no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
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—22no—
526C22×C4—22no—
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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
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—21no—
554C22×C4—21no—
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—21no—
565C22×C4—21no—
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×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C22⋊C4—48no—
620C22⋊C4—44no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—82no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C42—28no—
644C42—84no—
645C42—84no—
646C42—82no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—42no—
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—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—42no—
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—42no—
703C23—88no—
704C23—816no—
705C23—88no—
706C23—816no—
707C23—816no—
708C23—88no—
709C23—816no—
710C23—816no—
711C23—816no—
712C23C23×D411yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×2−1+412yes—
717C23#58512yes—
718C23#58512yes—
719C23#58512yes—
720C23#58512yes—
721Q8—88no—
722Q8—88no—
723Q8—88no—
724Q8—816no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
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—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
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—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
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—41no—
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—41no—
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—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—
832C22—42no—
833C22—44no—
834C22—42no—
835C22—44no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—832no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22#348411yescharacteristic
858C22#348611yescharacteristic
859C22#349612yes—
860C22#350011yescharacteristic
861C22#350012yes—
862C22#352912yes—
863C22#353512yes—
864C22#353512yes—
865C22#354011yescharacteristic
866C22#354011yescharacteristic
867C22#354011yescharacteristic
868C22#354512yes—
869C22#354512yes—
870C22#354911yescharacteristic
871C22#355812yes—
872C22#356112yes—
873C22#356112yes—
874C22#356412yes—
875C22#356412yes—
876C22#356812yes—
877C22#356812yes—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—44no—
882C4—44no—
883C4—42no—
884C4—44no—
885C4—81no—
886C4—82no—
887C4—81no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C2—82no—
896C2—84no—
897C2#4623712yes—
898C2#4635711yescharacteristic
899C2#4785512yes—
900C2#4956211yescharacteristic
901C2#5174911yescharacteristic
902C2#5264712yes—
903C2#5293012yes—
904C2#5467012yes—
905C2#5742412yes—
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. C2×#2821C2semidirect
3. #17198C2semidirect
4. #17152C2semidirect
5. #17100C2semidirect
6. #17023C2semidirect
7. #16803C2semidirect
8. #16788C2semidirect
9. #16375C2semidirect
11. #15931C2semidirect
12. #15910C2semidirect
14. #15322C2semidirect
17. #15004C2semidirect
18. #14956C2semidirect
19. #14232C2semidirect
20. C22×C4⋊Q8C22semidirect
24. C2×#400C22semidirect
26. C2×#398C22semidirect
29. C2×#395C22semidirect
30. C2×#395C22semidirect
31. C2×#395C22semidirect
41. C2×#391C22semidirect
42. C2×#391C22semidirect
43. C2×#391C22semidirect
47. C2×#383C22semidirect
53. #1446C22semidirect
54. #1446C22semidirect
55. #1446C22semidirect
56. #1446C22semidirect
57. #1446C22semidirect
58. #1445C22semidirect
59. #1445C22semidirect
60. #1445C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1434C22semidirect
106. #1434C22semidirect
107. #1434C22semidirect
108. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28212
C2×#28402
#171982
#171522
#171002
#170232
#168032
#167882
#163752
#159862
#159312
#159102
#154672
#153222
#152972
#152842
#150042
#149562
#142322