Finite Group Databasebeta

← #1739851

Subgroups — #1739851

Order 512.

2336 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17150C212yesmaximal, complemented
2#16825C211yesmaximal, characteristic, complemented
3#16476C212yesmaximal, complemented
4#16453C212yesmaximal, complemented
5#16341C212yesmaximal, complemented
6#16340C212yesmaximal, complemented
7#15934C212yesmaximal, complemented
8#15866C212yesmaximal, complemented
9#15667C212yesmaximal, complemented
10#15556C212yesmaximal, complemented
11#15272C212yesmaximal, complemented
12#15117C212yesmaximal, complemented
13#14926C211yesmaximal, characteristic, complemented
14#14722C211yesmaximal, characteristic
15#14429C212yesmaximal, complemented
16#14418C211yesmaximal, characteristic, complemented
17#14349C211yesmaximal, characteristic, complemented
18#14016C211yesmaximal, characteristic, complemented
19#13959C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C2×#400C2212yes—
24C2×#397C2212yes—
25C2×#396C2212yes—
26C2×#396C2212yes—
27C2×#394C2211yescharacteristic
28C2×#394C2212yes—
29C2×#392C2212yes—
30C2×#392C2211yescharacteristic
31C2×#390C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#387C2212yes—
36C2×#387C2212yes—
37C2×#386C2211yescharacteristic
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#383C2211yescharacteristic
43C2×#376C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1445C2212yes—
46#1445C2212yes—
47#1445C2212yes—
48#1444C2212yes—
49#1444C2212yes—
50#1443C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2211yescharacteristic
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2211yescharacteristic
78#1439C2212yes—
79#1439C2212yes—
80#1438C2212yes—
81#1438C2212yes—
82#1438C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94C4⋊#95C2212yes—
95C4⋊#95C2212yes—
96#1434C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2212yes—
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C23×D4C2311yescharacteristic
108C23×D4C2312yes—
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×#123—44no—
116C2×#123—44no—
117C2×#123—44no—
118C2×#121—24no—
119C2×#121—44no—
120C2×C4×D4—24no—
121C2×C4×D4—42no—
122C2×C4×D4—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
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⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160#400—44no—
161#397—44no—
162#396—44no—
163#396—44no—
164#394—44no—
165#394—42no—
166#392—42no—
167#392—44no—
168#390—28no—
169#388—44no—
170#388—44no—
171#388—44no—
172#387—44no—
173#387—44no—
174#386—24no—
175#386—42no—
176#386—44no—
177#386—44no—
178#385—42no—
179#383—42no—
180#376—42no—
181C2×#95—24no—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
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—
224C25C2412yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—41no—
239C22×D4—41no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—41no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—41no—
252C22×D4—42no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—41no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—41no—
269C23×C4—42no—
270C23×C4—41no—
271C23×C4—42no—
272C23×C4#4114yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289#123—432no—
290#121—416no—
291C4×D4—416no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
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—42no—
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×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
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—22no—
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—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
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—41no—
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—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—41no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4#4114yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—41no—
416#95—42no—
417#95—41no—
418#95—42no—
419#95—41no—
420#95—41no—
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—41no—
436#95—41no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24C2×#4112yes—
478C24C2×#4112yes—
479C24H(5,𝔽2)12yes—
480C242−1+412yes—
481C24C2511yescharacteristic
482C2×D4—28no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4—84no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
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—21no—
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—21no—
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—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4114yes—
628C22×C4H(5,𝔽2)12yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C4H(5,𝔽2)14yes—
631C22×C4H(5,𝔽2)12yes—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—44no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—84no—
638C4⋊C4—84no—
639C4⋊C4—84no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—44no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—82no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C22⋊C4—84no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C42—28no—
667C42—48no—
668C42—84no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23#55514yes—
750C23C22×#4111yescharacteristic
751C23C22×#4111yescharacteristic
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)11yescharacteristic
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×H(5,𝔽2)12yes—
756C23C2×H(5,𝔽2)12yes—
757C23C2×2−1+411yescharacteristic
758C23#58512yes—
759C23#58511yescharacteristic
760C23#58512yes—
761D4—416no—
762D4—816no—
763D4—88no—
764D4—816no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
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—24no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
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—42no—
806C2×C4—42no—
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—41no—
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—88no—
870C2×C4—88no—
871C2×C4—88no—
872C2×C4—88no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—44no—
889C22—81no—
890C22—81no—
891C22—82no—
892C22—81no—
893C22—81no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22#345511yescharacteristic
911C22#345911yescharacteristic
912C22C2×#55511yescharacteristic
913C22#349011yescharacteristic
914C22#349011yescharacteristic
915C22#349111yescharacteristic
916C22#349211yescharacteristic
917C22#349511yescharacteristic
918C22#350811yescharacteristic
919C22#351912yes—
920C22#352112yes—
921C22#353212yes—
922C22#353412yes—
923C22#353411yescharacteristic
924C22#353512yes—
925C22#353611yescharacteristic
926C22#353912yes—
927C22#354112yes—
928C22#354612yes—
929C22#354612yes—
930C22#354612yes—
931C22#356012yes—
932C22#356212yes—
933C4—44no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—82no—
941C4—81no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—82no—
948C4—82no—
949C2—44no—
950C2—82no—
951C2—162no—
952C2#3681211yescharacteristic
953C2#3794811yescharacteristic
954C2#3893511yescharacteristic
955C2#4065311yescharacteristic
956C2#4131412yes—
957C2#4396311yescharacteristic
958C2#4638911yescharacteristic
959C2#5012612yes—
960C2#5105511yescharacteristic
961C2#5405612yes—
962C2#5729712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14722C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17150C2semidirect
2. #16825C2semidirect
3. #16476C2semidirect
4. #16453C2semidirect
5. #16341C2semidirect
6. #16340C2semidirect
7. #15934C2semidirect
8. #15866C2semidirect
9. #15667C2semidirect
10. #15556C2semidirect
11. #15272C2semidirect
12. #15117C2semidirect
13. #14926C2semidirect
15. #14429C2semidirect
16. #14418C2semidirect
17. #14349C2semidirect
18. #14016C2semidirect
19. #13959C2semidirect

Maximal subgroups

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

subgroupindex
#171502
#168252
#164762
#164532
#163412
#163402
#159342
#158662
#156672
#155562
#152722
#151172
#149262
#147222
#144292
#144182
#143492
#140162
#139592