Finite Group Databasebeta

← #27087021

Subgroups — #27087021

Order 12032.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic, complemented
2#20254202C214yesmaximal, complemented
3#20254194C212yesmaximal, complemented
4#20254185C212yesmaximal, complemented
5#20254153C214yesmaximal, complemented
6#20254145C212yesmaximal, complemented
7#20254136C212yesmaximal, complemented
8#20253324C212yesmaximal, complemented
9#20253311C212yesmaximal, complemented
10#20253003C214yesmaximal, complemented
11#20252638C212yesmaximal, complemented
12#20252615C212yesmaximal, complemented
13C2×#15689087C211yesmaximal, characteristic, complemented
14C22×#121×C47C211yesmaximal, characteristic, complemented
15C22×#10625350C2211yescharacteristic, complemented
16C2×#13094050C2214yescomplemented
17C22×#10625329C2212yescomplemented
18#15689634—21no—
19#15689634—21no—
20#15689634—21no—
21#15689634—21no—
22#15689634C2212yes—
23#15689634C2212yescomplemented
24#15689634C2212yescomplemented
25#15689634C2212yescomplemented
26C2×#13094007—21no—
27C2×#13094003C2211yescharacteristic, complemented
28C2×#13094003C2211yescharacteristic, complemented
29C2×#13093998C2211yescharacteristic, complemented
30C2×#13093998C2211yescharacteristic, complemented
31C2×#13093993—21no—
32C2×C4×C22⋊D47—21no—
33C2×C4×C22⋊D47—21no—
34C2×#13093983C2211yescharacteristic, complemented
35#15689458C2214yescomplemented
36#15689453C2214yescomplemented
37#15689444C2218yescomplemented
38#15689441C2214yescomplemented
39#15689439C2214yescomplemented
40#15689436C2214yescomplemented
41#15689434C2214yescomplemented
42#15689374C2218yescomplemented
43#15689367C2218yescomplemented
44#15689357C2218yescomplemented
45#15689350C2218yescomplemented
46#15689274C2214yescomplemented
47#15689274C2214yescomplemented
48#15689266C2218yescomplemented
49#15689261C2214yescomplemented
50#15689257C2214yescomplemented
51#15689257C2214yescomplemented
52#15689256C2214yescomplemented
53#15689163C2214yescomplemented
54#15689128C2214yescomplemented
55#15689122C2214yescomplemented
56#15689087C2212yescomplemented
57#15689087C2212yescomplemented
58#15689087C2212yescomplemented
59#15689087C2212yescomplemented
60C2×C22⋊(C47⋊C8)C2212yescomplemented
61C2×C22⋊(C47⋊C8)C2212yescomplemented
62C23×D4×C47—21no—
63C23×D4×C47C2211yescharacteristic, complemented
64C24×C4×C47C2211yescharacteristic
65C2×#121×C47—21no—
66C2×#121×C47—21no—
67C2×#121×C47—21no—
68C2×#121×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47—21no—
71C2×#121×C47C2212yes—
72C2×#121×C47C2212yes—
73C2×#121×C47C2212yes—
74C2×#121×C47C2212yescomplemented
75C2×#121×C47C2212yescomplemented
76C2×#121×C47C2212yescomplemented
77C22×C4⋊C4×C47C2211yescharacteristic, complemented
78C22×C22⋊C4×C47—21no—
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—44no—
82C2×#10625350C2312yes—
83C2×#10625350C2312yescomplemented
84C22×Dic94C2311yescharacteristic, complemented
85C22×D188C2311yescharacteristic, complemented
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C4×D47—21no—
90#13094050—48no—
91C2×#10625335C2318yescomplemented
92C2×#10625334C2318yescomplemented
93C2×#10625329—44no—
94C2×#10625329C2314yes—
95C2×#10625329C2314yescomplemented
96C22×C47⋊C8C2314yescomplemented
97#13094007—22no—
98#13094007—22no—
99#13094007—22no—
100#13094007—22no—
101#13094003—21no—
102#13094003—21no—
103#13094003—21no—
104#13094003—21no—
105#13094003C2312yes—
106#13094003C2312yes—
107#13094003C2312yescomplemented
108#13094003C2312yescomplemented
109#13093998—21no—
110#13093998—21no—
111#13093998—21no—
112#13093998—21no—
113#13093998C2312yes—
114#13093998C2312yes—
115#13093998C2312yescomplemented
116#13093998C2312yescomplemented
117#13093993—22no—
118#13093993—22no—
119#13093993—22no—
120#13093993—22no—
121C4×C22⋊D47—22no—
122C4×C22⋊D47—22no—
123C4×C22⋊D47—22no—
124C4×C22⋊D47—22no—
125C4×C22⋊D47—22no—
126C4×C22⋊D47—22no—
127C4×C22⋊D47—22no—
128C4×C22⋊D47—22no—
129#13093983—21no—
130#13093983—21no—
131#13093983C2312yes—
132#13093983C2312yescomplemented
133C2×C4⋊Dic47C2311yescharacteristic, complemented
134C2×C4⋊Dic47C2311yescharacteristic, complemented
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×C22⋊Dic47—21no—
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×C4×Dic47—21no—
143#13093957C2318yescomplemented
144#13093955C2318yescomplemented
145#13093947C2318yescomplemented
146#13093945C2318yescomplemented
147#13093945C2318yescomplemented
148#13093944C2318yescomplemented
149C22⋊(C47⋊C8)C2314yes—
150C22⋊(C47⋊C8)C2314yes—
151C22⋊(C47⋊C8)C2314yescomplemented
152C22⋊(C47⋊C8)C2314yescomplemented
153C25×C47—21no—
154C25×C47D411yescharacteristic
155C22×D4×C47—22no—
156C22×D4×C47—22no—
157C22×D4×C47—22no—
158C22×D4×C47—22no—
159C22×D4×C47—22no—
160C22×D4×C47—22no—
161C22×D4×C47—21no—
162C22×D4×C47—21no—
163C22×D4×C47—21no—
164C22×D4×C47—44no—
165C22×D4×C47—48no—
166C22×D4×C47C2312yes—
167C22×D4×C47C2312yes—
168C22×D4×C47C2312yes—
169C23×C4×C47—21no—
170C23×C4×C47—44no—
171C23×C4×C47D411yescharacteristic
172C23×C4×C47D411yescharacteristic
173C23×C4×C47D411yescharacteristic
174C23×C4×C47D411yescharacteristic
175C23×C4×C47D411yescharacteristic
176C23×C4×C47D411yescharacteristic
177C23×C4×C47D411yescharacteristic
178C23×C4×C47C2311yescharacteristic
179C23×C4×C47C2311yescharacteristic
180C23×C4×C47C2311yescharacteristic
181C23×C4×C47C2311yescharacteristic
182C23×C4×C47C2311yescharacteristic
183C23×C4×C47C2311yescharacteristic
184C23×C4×C47C2311yescharacteristic
185#121×C47—22no—
186#121×C47—22no—
187#121×C47—22no—
188#121×C47—22no—
189#121×C47—22no—
190#121×C47—22no—
191#121×C47—22no—
192#121×C47—22no—
193#121×C47—22no—
194#121×C47—22no—
195#121×C47—22no—
196#121×C47—22no—
197#121×C47C2314yes—
198#121×C47C2314yes—
199#121×C47C2314yes—
200#121×C47C2314yes—
201C2×C4⋊C4×C47—21no—
202C2×C4⋊C4×C47—21no—
203C2×C4⋊C4×C47—21no—
204C2×C4⋊C4×C47C2312yes—
205C2×C4⋊C4×C47C2312yes—
206C2×C4⋊C4×C47C2312yes—
207C2×C22⋊C4×C47—22no—
208C2×C22⋊C4×C47—22no—
209C2×C22⋊C4×C47—22no—
210C2×C22⋊C4×C47—22no—
211C2×C22⋊C4×C47—22no—
212C2×C22⋊C4×C47—22no—
213C24×C47—24no—
214C24×C47—22no—
215C24×C47—22no—
216C24×C47—22no—
217C24×C47—42no—
218C24×C47—42no—
219C24×C47—44no—
220C24×C47—44no—
221C24×C47—44no—
222C24×C47C2×D411yescharacteristic
223C24×C47C2×D411yescharacteristic
224C24×C47C2×D411yescharacteristic
225C24×C47C2×D411yescharacteristic
226C24×C47C2×D411yescharacteristic
227C24×C47C2×D411yescharacteristic
228C24×C47C2×D411yescharacteristic
229C23×D47—21no—
230C2×D4×C47—24no—
231C2×D4×C47—24no—
232C2×D4×C47—24no—
233C2×D4×C47—24no—
234C2×D4×C47—22no—
235C2×D4×C47—22no—
236C2×D4×C47—22no—
237C2×D4×C47—28no—
238C2×D4×C47—44no—
239C2×D4×C47—44no—
240C2×D4×C47—44no—
241C2×D4×C47—44no—
242C2×D4×C47—44no—
243C2×D4×C47—48no—
244C2×D4×C47—48no—
245C2×D4×C47—48no—
246C2×D4×C47—48no—
247C2×D4×C47—48no—
248C2×D4×C47—48no—
249C2×D4×C47C2414yes—
250C22×C4×C47—24no—
251C22×C4×C47—24no—
252C22×C4×C47—24no—
253C22×C4×C47—22no—
254C22×C4×C47—22no—
255C22×C4×C47—22no—
256C22×C4×C47—42no—
257C22×C4×C47—42no—
258C22×C4×C47—42no—
259C22×C4×C47—42no—
260C22×C4×C47—42no—
261C22×C4×C47—42no—
262C22×C4×C47—42no—
263C22×C4×C47—42no—
264C22×C4×C47—42no—
265C22×C4×C47—42no—
266C22×C4×C47—42no—
267C22×C4×C47—44no—
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D411yescharacteristic
271C22×C4×C47C2×D411yescharacteristic
272C22×C4×C47C2×D411yescharacteristic
273C22×C4×C47C2×D411yescharacteristic
274C22×C4×C47C2×D411yescharacteristic
275C22×C4×C47C2×D411yescharacteristic
276C22×C4×C47C2×D411yescharacteristic
277C22×C4×C47C2×D411yescharacteristic
278C22×C4×C47C2×D411yescharacteristic
279C22×C4×C47C2×D411yescharacteristic
280C22×C4×C47C2×D411yescharacteristic
281C22×C4×C47C2×D411yescharacteristic
282C22×C4×C47C2×D411yescharacteristic
283C22×C4×C47C2×D411yescharacteristic
284C22×C4×C47C2×D411yescharacteristic
285C22×C4×C47C2×D411yescharacteristic
286C22×C4×C47C2×D411yescharacteristic
287C22×C4×C47C2×D411yescharacteristic
288C22×C4×C47C2×D411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C22×C4×C47C2411yescharacteristic
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C2×C22⋊D47—22no—
297C2×C22⋊D47—22no—
298C2×C22⋊D47—22no—
299C2×C22⋊D47—22no—
300C2×C22⋊D47—22no—
301C2×C22⋊D47—22no—
302C2×C22⋊D47—44no—
303C2×C22⋊D47—44no—
304C2×C22⋊D47—44no—
305C22×Dic47—21no—
306C22×Dic47—21no—
307C22×Dic47—21no—
308#10625350—28no—
309#10625350—44no—
310#10625350—44no—
311#10625350—44no—
312C2×D188—21no—
313C2×D188—42no—
314C2×D188C2412yes—
315C2×C4×D47—22no—
316C2×C4×D47—22no—
317C2×C4×D47—44no—
318C2×Dic94—21no—
319C2×Dic94—42no—
320C2×Dic94C2412yes—
321C4⋊C4×C47—22no—
322C4⋊C4×C47—22no—
323C4⋊C4×C47—22no—
324C4⋊C4×C47C2414yes—
325C22⋊C4×C47—24no—
326C22⋊C4×C47—24no—
327C22⋊C4×C47—24no—
328C22⋊C4×C47—24no—
329C22⋊Dic47—22no—
330C22⋊Dic47—22no—
331C22⋊Dic47—22no—
332C22⋊Dic47—22no—
333C22⋊Dic47—22no—
334C22⋊Dic47—22no—
335#10625335—48no—
336#10625334—48no—
337(C2×D47)⋊C4—22no—
338(C2×D47)⋊C4—22no—
339(C2×D47)⋊C4—22no—
340(C2×D47)⋊C4—22no—
341C4⋊Dic47—21no—
342C4⋊Dic47—21no—
343C4⋊Dic47C2412yes—
344C4⋊Dic47C2412yes—
345Dic47⋊C4—22no—
346Dic47⋊C4—22no—
347Dic47⋊C4—22no—
348Dic47⋊C4—22no—
349C4×Dic47—22no—
350C4×Dic47—22no—
351#10625329—28no—
352#10625329—44no—
353C2×C47⋊C8—44no—
354C2×C47⋊C8C2418yes—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—22no—
361C23×C47—22no—
362C23×C47—22no—
363C23×C47—22no—
364C23×C47—22no—
365C23×C47—22no—
366C23×C47—22no—
367C23×C47—24no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—416no—
377C23×C47—44no—
378C23×C47—44no—
379C23×C47—44no—
380C23×C47—44no—
381C23×C47—44no—
382C23×C47—44no—
383C23×C47—44no—
384C23×C47—44no—
385C23×C47—44no—
386C23×C47—816no—
387C23×C47AGL(1,ℤ/8)14yescomplemented
388C23×C47C22×D411yescharacteristic
389C23×C47C22×D411yescharacteristic
390C23×C47C22×D411yescharacteristic
391C23×C47C22×D411yescharacteristic
392C23×C47C22×D411yescharacteristic
393C23×C47C22×D411yescharacteristic
394C23×C47C22×D411yescharacteristic
395C22×D47—22no—
396C22×D47—42no—
397C22×D47—42no—
398C22×D47—42no—
399D4×C47—28no—
400D4×C47—44no—
401D4×C47—44no—
402D4×C47—48no—
403D4×C47—48no—
404D4×C47—48no—
405D4×C47—48no—
406D4×C47—44no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—22no—
411C2×C4×C47—22no—
412C2×C4×C47—22no—
413C2×C4×C47—22no—
414C2×C4×C47—22no—
415C2×C4×C47—22no—
416C2×C4×C47—22no—
417C2×C4×C47—22no—
418C2×C4×C47—22no—
419C2×C4×C47—22no—
420C2×C4×C47—22no—
421C2×C4×C47—22no—
422C2×C4×C47—24no—
423C2×C4×C47—41no—
424C2×C4×C47—41no—
425C2×C4×C47—41no—
426C2×C4×C47—41no—
427C2×C4×C47—41no—
428C2×C4×C47—41no—
429C2×C4×C47—41no—
430C2×C4×C47—41no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—41no—
435C2×C4×C47—44no—
436C2×C4×C47—44no—
437C2×C4×C47—44no—
438C2×C4×C47C22×D411yescharacteristic
439C2×C4×C47C22×D411yescharacteristic
440C2×C4×C47C22×D411yescharacteristic
441C2×C4×C47C22×D411yescharacteristic
442C2×C4×C47C22×D411yescharacteristic
443C2×C4×C47C22×D411yescharacteristic
444C2×C4×C47C22×D411yescharacteristic
445C2×C4×C47H(5,𝔽2)14yes—
446C2×C4×C47C2511yescharacteristic
447C22⋊D47—44no—
448C22⋊D47—44no—
449C22⋊D47—44no—
450C22⋊D47—44no—
451C22⋊D47—44no—
452C22⋊D47—44no—
453C2×Dic47—22no—
454C2×Dic47—22no—
455C2×Dic47—22no—
456C2×Dic47—42no—
457C2×Dic47—42no—
458C2×Dic47—42no—
459D188—24no—
460D188—42no—
461C4×D47—44no—
462C4×D47—44no—
463Dic94—24no—
464Dic94—42no—
465C47⋊C8—28no—
466#60750—471nomaximal, Sylow
467C22×C47—28no—
468C22×C47—21no—
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—21no—
474C22×C47—21no—
475C22×C47—21no—
476C22×C47—21no—
477C22×C47—21no—
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—21no—
481C22×C47—21no—
482C22×C47—21no—
483C22×C47—21no—
484C22×C47—44no—
485C22×C47—44no—
486C22×C47—44no—
487C22×C47—44no—
488C22×C47—44no—
489C22×C47—44no—
490C22×C47—44no—
491C22×C47—44no—
492C22×C47—44no—
493C22×C47—88no—
494C22×C47—88no—
495C22×C47—88no—
496C22×C47#53412yes—
497C22×C47C2×AGL(1,ℤ/8)12yes—
498C22×C47C2×AGL(1,ℤ/8)12yes—
499C22×C47C2×AGL(1,ℤ/8)12yes—
500C22×C47#57512yes—
501C22×C47C23×D411yescharacteristic
502C2×D47—42no—
503C2×D47—42no—
504C2×D47—42no—
505C2×D47—84no—
506C4×C47—21no—
507C4×C47—21no—
508C4×C47—21no—
509C4×C47—21no—
510C4×C47—21no—
511C4×C47—21no—
512C4×C47—44no—
513C4×C47#53412yes—
514C4×C47C2×H(5,𝔽2)12yes—
515Dic47—42no—
516Dic47—42no—
517Dic47—42no—
518C2×#525—471no—
519C22×#121D4711yescharacteristic, complemented
520#3194—474no—
521#3193—472no—
522#3192—472no—
523#3188—474no—
524#3187—472no—
525#3186—472no—
526#3094—472no—
527#3092—472no—
528#3055—474no—
529#3006—472no—
530#3003—472no—
531C2×#407—471no—
532C2×C47—22no—
533C2×C47—22no—
534C2×C47—22no—
535C2×C47—22no—
536C2×C47—22no—
537C2×C47—41no—
538C2×C47—41no—
539C2×C47—84no—
540C2×C47C2×#53411yescharacteristic
541C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C47C2×#57511yescharacteristic
543D47—82no—
544C22×#41—471no—
545C23×D4—21no—
546C23×D4C2×D4711yescharacteristic, complemented
547C24×C4C2×D4711yescharacteristic
548C2×AGL(1,ℤ/8)—474no—
549C22×M16—472no—
550#525—472no—
551#525—472no—
552#525—472no—
553#525—472no—
554#525—941no—
555#525—941no—
556#525—941no—
557#525—941no—
558C2×#123—941no—
559C2×C22⋊Q8—471no—
560C2×C22⋊Q8—471no—
561C2×#121—21no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—471no—
568C2×#121—471no—
569C2×#121C2×D4712yes—
570C2×#121C2×D4712yes—
571C2×#121C2×D4712yes—
572C2×#121C2×D4712yescomplemented
573C2×#121C2×D4712yescomplemented
574C2×#121C2×D4712yescomplemented
575C2×#120—941no—
576C2×C4×D4—941no—
577C2×C4×D4—941no—
578C2×#117—471no—
579C22×C4⋊C4C2×D4711yescharacteristic, complemented
580C22×C22⋊C4—21no—
581#484—474no—
582#483—474no—
583#482—478no—
584#481—474no—
585#481—474no—
586#480—474no—
587#480—474no—
588#469—478no—
589#468—478no—
590#466—478no—
591#465—478no—
592#450—474no—
593#450—474no—
594#449—478no—
595#448—474no—
596#447—474no—
597#447—474no—
598#447—474no—
599#428—474no—
600#418—474no—
601#417—474no—
602#407—472no—
603#407—472no—
604#407—472no—
605#407—472no—
606C2×C22⋊C8—472no—
607C2×C22⋊C8—472no—
608C47#6075011yescharacteristic, complemented, Sylow
609C25—21no—
610C25C22⋊D4711yescharacteristic
611C2×#41—472no—
612C2×#41—472no—
613C2×#41—941no—
614C2×#41—941no—
615C2×#41—1884no—
616C22×Q8—471no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—471no—
629C22×D4—941no—
630C22×D4—941no—
631C22×D4—941no—
632C22×D4C22×D4712yes—
633C22×D4C22×D4712yes—
634C22×D4C22×D4712yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—941no—
638C23×C4C22⋊D4711yescharacteristic
639C23×C4C22⋊D4711yescharacteristic
640C23×C4C22⋊D4711yescharacteristic
641C23×C4C22⋊D4711yescharacteristic
642C23×C4C22⋊D4711yescharacteristic
643C23×C4C22⋊D4711yescharacteristic
644C23×C4C22⋊D4711yescharacteristic
645C23×C4C22×D4711yescharacteristic
646C23×C4C22×D4711yescharacteristic
647C23×C4C22×D4711yescharacteristic
648C23×C4C22×D4711yescharacteristic
649C23×C4C22×D4711yescharacteristic
650C23×C4C22×D4711yescharacteristic
651C23×C4C22×D4711yescharacteristic
652AGL(1,ℤ/8)—1888no—
653C2×SD16—478no—
654C2×D8—478no—
655C2×M16—474no—
656C2×M16—474no—
657C2×M16—1884no—
658C22×C8—474no—
659#123—942no—
660#123—942no—
661#123—942no—
662#123—942no—
663C22⋊Q8—472no—
664C22⋊Q8—472no—
665C22⋊Q8—472no—
666C22⋊Q8—472no—
667C22⋊Q8—941no—
668C22⋊Q8—941no—
669C22⋊Q8—941no—
670C22⋊Q8—941no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—472no—
684#121—472no—
685#121—472no—
686#121—472no—
687#121—941no—
688#121—941no—
689#121—941no—
690#121—941no—
691#121C22×D4714yes—
692#121C22×D4714yes—
693#121C22×D4714yes—
694#121C22×D4714yes—
695#120—942no—
696#120—942no—
697#120—942no—
698#120—942no—
699C4×D4—942no—
700C4×D4—942no—
701C4×D4—942no—
702C4×D4—942no—
703C4×D4—942no—
704C4×D4—942no—
705C4×D4—942no—
706C4×D4—942no—
707#117—472no—
708#117—472no—
709#117—941no—
710#117—941no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—471no—
715C2×C4⋊C4—471no—
716C2×C4⋊C4—941no—
717C2×C4⋊C4—941no—
718C2×C4⋊C4C22×D4712yes—
719C2×C4⋊C4C22×D4712yes—
720C2×C4⋊C4C22×D4712yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—941no—
728C2×C22⋊C4—941no—
729C2×C22⋊C4—941no—
730C2×C22⋊C4—941no—
731C2×C22⋊C4—941no—
732C2×C42—941no—
733#107—478no—
734#106—478no—
735#103—478no—
736#102—478no—
737#102—478no—
738#102—478no—
739C22⋊C8—474no—
740C22⋊C8—474no—
741C22⋊C8—474no—
742C22⋊C8—474no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—941no—
753C24C2×C22⋊D4711yescharacteristic
754C24C2×C22⋊D4711yescharacteristic
755C24C2×C22⋊D4711yescharacteristic
756C24C2×C22⋊D4711yescharacteristic
757C24C2×C22⋊D4711yescharacteristic
758C24C2×C22⋊D4711yescharacteristic
759C24C2×C22⋊D4711yescharacteristic
760#41—948no—
761#41—1884no—
762#41—1884no—
763#41—1884no—
764C2×Q8—472no—
765C2×Q8—941no—
766C2×Q8—1882no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—472no—
787C2×D4—942no—
788C2×D4—942no—
789C2×D4—942no—
790C2×D4—942no—
791C2×D4—942no—
792C2×D4—942no—
793C2×D4—941no—
794C2×D4—1882no—
795C2×D4—1884no—
796C2×D4—1884no—
797C2×D4—1884no—
798C2×D4C23×D4714yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—941no—
818C22×C4—941no—
819C22×C4—941no—
820C22×C4—942no—
821C22×C4—942no—
822C22×C4—1884no—
823C22×C4C2×C22⋊D4711yescharacteristic
824C22×C4C2×C22⋊D4711yescharacteristic
825C22×C4C2×C22⋊D4711yescharacteristic
826C22×C4C2×C22⋊D4711yescharacteristic
827C22×C4C2×C22⋊D4711yescharacteristic
828C22×C4C2×C22⋊D4711yescharacteristic
829C22×C4C2×C22⋊D4711yescharacteristic
830C22×C4C2×C22⋊D4711yescharacteristic
831C22×C4C2×C22⋊D4711yescharacteristic
832C22×C4C2×C22⋊D4711yescharacteristic
833C22×C4C2×C22⋊D4711yescharacteristic
834C22×C4C2×C22⋊D4711yescharacteristic
835C22×C4C2×C22⋊D4711yescharacteristic
836C22×C4C2×C22⋊D4711yescharacteristic
837C22×C4C2×C22⋊D4711yescharacteristic
838C22×C4C2×C22⋊D4711yescharacteristic
839C22×C4C2×C22⋊D4711yescharacteristic
840C22×C4C2×C22⋊D4711yescharacteristic
841C22×C4C2×C22⋊D4711yescharacteristic
842C22×C4C2×C22⋊D4711yescharacteristic
843C22×C4C2×C22⋊D4711yescharacteristic
844C22×C4C23×D4711yescharacteristic
845C22×C4C23×D4711yescharacteristic
846C22×C4C23×D4711yescharacteristic
847C22×C4C23×D4711yescharacteristic
848C22×C4C23×D4711yescharacteristic
849C22×C4C23×D4711yescharacteristic
850C22×C4C23×D4711yescharacteristic
851SD16—1888no—
852D8—1888no—
853M16—948no—
854M16—1884no—
855C2×C8—478no—
856C2×C8—1884no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—472no—
861C4⋊C4—472no—
862C4⋊C4—942no—
863C4⋊C4—942no—
864C4⋊C4—942no—
865C4⋊C4—942no—
866C4⋊C4—941no—
867C4⋊C4—941no—
868C4⋊C4C23×D4714yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—942no—
874C22⋊C4—942no—
875C22⋊C4—942no—
876C22⋊C4—942no—
877C22⋊C4—942no—
878C22⋊C4—942no—
879C22⋊C4—942no—
880C22⋊C4—942no—
881C22⋊C4—942no—
882C22⋊C4—942no—
883C42—942no—
884C42—942no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—942no—
918C23—1882no—
919C23—1882no—
920C23—1882no—
921C23#1309405014yescomplemented
922C23C22×C22⋊D4711yescharacteristic
923C23C22×C22⋊D4711yescharacteristic
924C23C22×C22⋊D4711yescharacteristic
925C23C22×C22⋊D4711yescharacteristic
926C23C22×C22⋊D4711yescharacteristic
927C23C22×C22⋊D4711yescharacteristic
928C23C22×C22⋊D4711yescharacteristic
929Q8—944no—
930Q8—1882no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—944no—
940D4—1882no—
941D4—1884no—
942D4—1884no—
943D4—1884no—
944D4—1884no—
945D4—1884no—
946D4—1884no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—942no—
979C2×C4—942no—
980C2×C4—942no—
981C2×C4—1884no—
982C2×C4—1882no—
983C2×C4—1882no—
984C2×C4—1882no—
985C2×C4—1884no—
986C2×C4C22×C22⋊D4711yescharacteristic
987C2×C4C22×C22⋊D4711yescharacteristic
988C2×C4C22×C22⋊D4711yescharacteristic
989C2×C4C22×C22⋊D4711yescharacteristic
990C2×C4C22×C22⋊D4711yescharacteristic
991C2×C4C22×C22⋊D4711yescharacteristic
992C2×C4C22×C22⋊D4711yescharacteristic
993C2×C4#1309406914yes—
994C2×C4C24×D4711yescharacteristic
995C8—948no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—3764no—
1026C22—1882no—
1027C22—1882no—
1028C22—1882no—
1029C22#1568968212yes—
1030C22C2×#1309405012yes—
1031C22C2×#1309405012yes—
1032C22C2×#1309405012yes—
1033C22#1568992112yes—
1034C22C23×C22⋊D4711yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—1882no—
1043C4—1882no—
1044C4—1882no—
1045C4#1568968212yes—
1046C4C2×#1309406912yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—3762no—
1056C2C2×#1568968211yescharacteristic
1057C2C22×#1309405011yescharacteristic
1058C2C2×#1568992111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×#121×C47C2
socleC22×C47C23×D4
hypercenterC22×#121D47
hypocenterC47#60750
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#15689634C2semidirect
2. #20254202C2semidirect
3. #20254194C2semidirect
4. #20254185C2semidirect
5. #20254153C2semidirect
6. #20254145C2semidirect
7. #20254136C2semidirect
8. #20253324C2semidirect
9. #20253311C2semidirect
10. #20253003C2semidirect
11. #20252638C2semidirect
12. #20252615C2semidirect
13. C2×#15689087C2semidirect
14. C22×#121×C47C2semidirect
15. C22×#10625350C22semidirect
16. C2×#13094050C22semidirect
17. C22×#10625329C22semidirect
23. #15689634C22semidirect
24. #15689634C22semidirect
25. #15689634C22semidirect
27. C2×#13094003C22semidirect
28. C2×#13094003C22semidirect
29. C2×#13093998C22semidirect
30. C2×#13093998C22semidirect
34. C2×#13093983C22semidirect
35. #15689458C22semidirect
36. #15689453C22semidirect
37. #15689444C22semidirect
38. #15689441C22semidirect
39. #15689439C22semidirect
40. #15689436C22semidirect
41. #15689434C22semidirect
42. #15689374C22semidirect
43. #15689367C22semidirect
44. #15689357C22semidirect
45. #15689350C22semidirect
46. #15689274C22semidirect
47. #15689274C22semidirect
48. #15689266C22semidirect
49. #15689261C22semidirect
50. #15689257C22semidirect
51. #15689257C22semidirect
52. #15689256C22semidirect
53. #15689163C22semidirect
54. #15689128C22semidirect
55. #15689122C22semidirect
56. #15689087C22semidirect
57. #15689087C22semidirect
58. #15689087C22semidirect
59. #15689087C22semidirect
60. C2×C22⋊(C47⋊C8)C22semidirect
61. C2×C22⋊(C47⋊C8)C22semidirect
63. C23×D4×C47C22semidirect
74. C2×#121×C47C22semidirect
75. C2×#121×C47C22semidirect
76. C2×#121×C47C22semidirect
77. C22×C4⋊C4×C47C22semidirect
83. C2×#10625350C23semidirect
84. C22×Dic94C23semidirect
85. C22×D188C23semidirect
91. C2×#10625335C23semidirect
92. C2×#10625334C23semidirect
95. C2×#10625329C23semidirect
96. C22×C47⋊C8C23semidirect
107. #13094003C23semidirect
108. #13094003C23semidirect
115. #13093998C23semidirect
116. #13093998C23semidirect
132. #13093983C23semidirect
133. C2×C4⋊Dic47C23semidirect
134. C2×C4⋊Dic47C23semidirect
143. #13093957C23semidirect
144. #13093955C23semidirect
145. #13093947C23semidirect
146. #13093945C23semidirect
147. #13093945C23semidirect
148. #13093944C23semidirect
151. C22⋊(C47⋊C8)C23semidirect
152. C22⋊(C47⋊C8)C23semidirect
387. C23×C47AGL(1,ℤ/8)semidirect
519. C22×#121D47semidirect
546. C23×D4C2×D47semidirect
572. C2×#121C2×D47semidirect
573. C2×#121C2×D47semidirect
574. C2×#121C2×D47semidirect
579. C22×C4⋊C4C2×D47semidirect
608. C47#60750semidirect
921. C23#13094050semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202542022
#202541942
#202541852
#202541532
#202541452
#202541362
#202533242
#202533112
#202530032
#202526382
#202526152
C2×#156890872
C22×#121×C472
#6075047