Finite Group Databasebeta

← #5491018

Subgroups — #5491018

Order 512.

2160 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17250C212yesmaximal, complemented
2#17196C211yesmaximal, characteristic, complemented
3#17118C211yesmaximal, characteristic, complemented
4#17083C211yesmaximal, characteristic
5#16736C212yesmaximal, complemented
6#16397C212yesmaximal, complemented
7#16301C212yesmaximal, complemented
8#16289C212yesmaximal, complemented
9#16177C211yesmaximal, characteristic, complemented
10#16084C212yesmaximal, complemented
11#16046C212yesmaximal, complemented
12#15882C212yesmaximal, complemented
13#15307C212yesmaximal, complemented
14#15295C212yesmaximal, complemented
15#15107C211yesmaximal, characteristic, complemented
16#15071C211yesmaximal, characteristic, complemented
17#14730C212yesmaximal, complemented
18#14623C212yesmaximal, complemented
19#13905C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C2×#400C2211yescharacteristic
23C2×#397C2212yes—
24C2×#396C2212yes—
25C2×#394C2211yescharacteristic
26C2×#394C2212yes—
27C2×#394C2212yes—
28C2×#394C2212yes—
29C2×#394C2212yes—
30C2×#392C2212yes—
31C2×#392C2212yes—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#387C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#382C2211yescharacteristic
40C2×#381C2212yes—
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×C4×C4⋊C4C2211yescharacteristic
44#1445C2211yescharacteristic
45#1445C2212yes—
46#1445C2212yes—
47#1445C2212yes—
48#1445C2211yescharacteristic
49#1445C2211yescharacteristic
50#1444C2211yescharacteristic
51#1444C2212yes—
52#1444C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2211yescharacteristic
59#1441C2211yescharacteristic
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1441C2212yes—
64#1441C2211yescharacteristic
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1438C2211yescharacteristic
88#1438C2212yes—
89#1438C2211yescharacteristic
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1438C2211yescharacteristic
94#1438C2212yes—
95#1437C2212yes—
96#1437C2212yes—
97#1437C2212yes—
98#1437C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1434C2211yescharacteristic
103#1434C2212yes—
104#1434C2212yes—
105#1434C2211yescharacteristic
106C22⋊#95C2212yes—
107C23×D4C2312yes—
108C23×D4C2311yescharacteristic
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2312yes—
112C2×#125—42no—
113C2×#125—44no—
114C2×C4×D4—24no—
115C2×C4×D4—42no—
116C2×C4×D4—42no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
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⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157#400—42no—
158#397—44no—
159#396—44no—
160#394—44no—
161#394—44no—
162#394—44no—
163#394—42no—
164#394—44no—
165#392—28no—
166#392—44no—
167#390—42no—
168#390—44no—
169#388—44no—
170#388—44no—
171#387—44no—
172#386—44no—
173#386—44no—
174#382—42no—
175#381—44no—
176#380—44no—
177#380—44no—
178C4×C4⋊C4—42no—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2311yescharacteristic
182C2×#95C2312yes—
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
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×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C25C2412yes—
222C25C2412yes—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—41no—
228C22×D4—41no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—41no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—41no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4#4114yes—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271#125—416no—
272C4×D4—416no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
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—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—41no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
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—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
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—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—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—42no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—22no—
398#95—22no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—41no—
410#95—41no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—41no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—41no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—41no—
430#95—42no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
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—22no—
458C24—22no—
459C24—22no—
460C24C2×#4114yes—
461C24C2511yescharacteristic
462C2×D4—44no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—48no—
471C2×D4—84no—
472C2×D4—82no—
473C2×D4—84no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—84no—
479C2×D4—82no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—84no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
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—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—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
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—21no—
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—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C42−1+412yes—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—48no—
605C4⋊C4—44no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—84no—
609C4⋊C4—82no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—84no—
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—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—
636C42—28no—
637C42—44no—
638C42—82no—
639C42—84no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
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—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—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23C22×#4111yescharacteristic
711C23C2×H(5,𝔽2)11yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)12yes—
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+411yescharacteristic
718C23#58512yes—
719C23#58512yes—
720C23#58512yes—
721D4—416no—
722D4—816no—
723D4—88no—
724D4—816no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
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—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
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—41no—
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—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—
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—816no—
832C2×C4#56214yes—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
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—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22#349011yescharacteristic
864C22#349112yes—
865C22#351312yes—
866C22#351911yescharacteristic
867C22#352011yescharacteristic
868C22C2×#56211yescharacteristic
869C22#352911yescharacteristic
870C22#353211yescharacteristic
871C22#353611yescharacteristic
872C22#353711yescharacteristic
873C22#353912yes—
874C22#353912yes—
875C22#354011yescharacteristic
876C22#354212yes—
877C22#354212yes—
878C22#354311yescharacteristic
879C22#354511yescharacteristic
880C22#354612yes—
881C22#354712yes—
882C22#355112yes—
883C22#355812yes—
884C22#356212yes—
885C22#356512yes—
886C4—24no—
887C4—42no—
888C4—44no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—81no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C2—84no—
904C2—162no—
905C2#4546111yescharacteristic
906C2#4608811yescharacteristic
907C2#4717011yescharacteristic
908C2#4983712yes—
909C2#4994612yes—
910C2#5240511yescharacteristic
911C2#5289311yescharacteristic
912C2#5306212yes—
913C2#5383211yescharacteristic
914C2#5386111yescharacteristic
915C2#5497612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#17083C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17250C2semidirect
2. #17196C2semidirect
3. #17118C2semidirect
5. #16736C2semidirect
6. #16397C2semidirect
7. #16301C2semidirect
8. #16289C2semidirect
9. #16177C2semidirect
10. #16084C2semidirect
11. #16046C2semidirect
12. #15882C2semidirect
13. #15307C2semidirect
14. #15295C2semidirect
15. #15107C2semidirect
16. #15071C2semidirect
17. #14730C2semidirect
18. #14623C2semidirect
19. #13905C2semidirect

Maximal subgroups

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

subgroupindex
#172502
#171962
#171182
#170832
#167362
#163972
#163012
#162892
#161772
#160842
#160462
#158822
#153072
#152952
#151072
#150712
#147302
#146232
#139052