Finite Group Databasebeta

← #26137667

Subgroups — #26137667

Order 12032.

2782 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093980C212yesmaximal
2C23×Dic47⋊C4C211yesmaximal, characteristic
3Dic47⋊#95C218yesmaximal, complemented
4#20241611C211yesmaximal, characteristic
5#20241610C212yesmaximal
6C47×C22⋊#95C211yesmaximal, characteristic
7C24×Dic47C2211yescharacteristic
8C24×Dic47C2211yescharacteristic
9C2×#13093980—28no—
10C2×#13093980—28no—
11C2×#13093980C4116yescomplemented
12C22×Dic47⋊C4—28no—
13C22×Dic47⋊C4C418yescomplemented
14C22×Dic47⋊C4C2214yes—
15C22×Dic47⋊C4C2214yes—
16C22×C22⋊Dic47C2212yes—
17C22×C4×Dic47C2214yes—
18C2×C47⋊#95C2218yes—
19C2×C47⋊#95C2214yes—
20C24×C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47C2212yes—
22C2×#95×C47C2214yes—
23C23×Dic47—24no—
24C23×Dic47—44no—
25C23×Dic47C2×C414yes—
26C23×Dic47C2×C414yes—
27C23×Dic47C2×C418yes—
28C23×Dic47D418yes—
29C23×Dic47D414yes—
30C23×Dic47Q814yes—
31C23×Dic47C2314yes—
32C23×Dic47C2312yes—
33C23×Dic47C2312yes—
34#13093980—264no—
35C2×Dic47⋊C4—232no—
36C2×Dic47⋊C4—28no—
37C2×Dic47⋊C4—28no—
38C2×Dic47⋊C4—28no—
39C2×Dic47⋊C4—28no—
40C2×Dic47⋊C4C2×C4116yes—
41C2×Dic47⋊C4C2×C4116yescomplemented
42C2×C22⋊Dic47—24no—
43C2×C22⋊Dic47—24no—
44C2×C22⋊Dic47C2×C418yes—
45C2×C4×Dic47—28no—
46C2×C4×Dic47—28no—
47C2×C4×Dic47C2×C4116yescomplemented
48C47⋊#95—44no—
49C47⋊#95—48no—
50C25×C47C2311yescharacteristic
51C23×C4×C47—24no—
52C23×C4×C47—44no—
53C23×C4×C47C2×C414yes—
54C23×C4×C47C2314yes—
55C23×C4×C47C2312yes—
56C2×C22⋊C4×C47—24no—
57C2×C22⋊C4×C47—24no—
58C2×C22⋊C4×C47C2×C418yes—
59#95×C47—44no—
60C24×C47—24no—
61C24×C47—24no—
62C24×C47C22×C414yes—
63C24×C47C22×C412yes—
64C24×C47C2×D412yes—
65C24×C47C2×D414yes—
66C24×C47C2×Q812yes—
67C24×C47C2411yescharacteristic
68C22×C4×C47—28no—
69C22×C4×C47—24no—
70C22×C4×C47—24no—
71C22×C4×C47—24no—
72C22×C4×C47—24no—
73C22×C4×C47—24no—
74C22×C4×C47—28no—
75C22×C4×C47—28no—
76C22×C4×C47—48no—
77C22×C4×C47—416no—
78C22×C4×C47C22×C418yes—
79C22×C4×C47C22×C414yes—
80C22×Dic47—28no—
81C22×Dic47—24no—
82C22×Dic47—24no—
83C22×Dic47—24no—
84C22×Dic47—28no—
85C22×Dic47—28no—
86C22×Dic47—28no—
87C22×Dic47—48no—
88C22×Dic47—416no—
89C22×Dic47C42116yes—
90C22×Dic47C22⋊C4116yes—
91C22×Dic47C22⋊C4132yes—
92C22×Dic47C4⋊C4116yes—
93C22×Dic47C4⋊C4132yes—
94C22×Dic47C22×C418yes—
95C22×Dic47C22×C414yes—
96C22×Dic47C22×C414yes—
97C22×Dic47C22×C414yes—
98C22×Dic47C22×C414yes—
99C22×Dic47C2×D414yes—
100C22×Dic47C2×D414yes—
101C22×Dic47C2×D414yes—
102C22×Dic47C2×Q814yes—
103C22⋊C4×C47—216no—
104C22⋊Dic47—216no—
105Dic47⋊C4—232no—
106Dic47⋊C4—232no—
107C4×Dic47—232no—
108C23×C47—24no—
109C23×C47—24no—
110C23×C47—216no—
111C23×C47—28no—
112C23×C47—28no—
113C23×C47—28no—
114C23×C47—28no—
115C23×C47C2×C4214yes—
116C23×C47C2×C22⋊C418yes—
117C23×C47C2×C22⋊C414yes—
118C23×C47C2×C4⋊C414yes—
119C23×C47C2×C4⋊C418yes—
120C23×C47C23×C411yescharacteristic
121C23×C47C23×C412yes—
122C23×C47C22×D412yes—
123C23×C47C22×D411yescharacteristic
124C23×C47C22×Q811yescharacteristic
125C23×C47H(5,𝔽2)14yes—
126C23×C472−1+414yes—
127C2×C4×C47—28no—
128C2×C4×C47—24no—
129C2×C4×C47—24no—
130C2×C4×C47—24no—
131C2×C4×C47—216no—
132C2×C4×C47—416no—
133C2×C4×C47—44no—
134C2×C4×C47—48no—
135C2×C4×C47—44no—
136C2×C4×C47—48no—
137C2×Dic47—28no—
138C2×Dic47—24no—
139C2×Dic47—28no—
140C2×Dic47—216no—
141C2×Dic47—416no—
142C2×Dic47—44no—
143C2×Dic47—48no—
144C2×Dic47—44no—
145C2×Dic47—48no—
146C2×Dic47#95164yescomplemented
147C2×Dic47C2×C4218yes—
148C2×Dic47C2×C22⋊C418yes—
149C2×Dic47C2×C22⋊C418yes—
150C2×Dic47C2×C22⋊C418yes—
151C2×Dic47C2×C4⋊C418yes—
152C2×Dic47C2×C4⋊C418yes—
153C2×Dic47C2×C4⋊C418yes—
154#13795—471nomaximal, Sylow
155C22×C47—24no—
156C22×C47—24no—
157C22×C47—216no—
158C22×C47—28no—
159C22×C47—216no—
160C22×C47—28no—
161C22×C47C2×#9518yes—
162C22×C47C22×C4211yescharacteristic
163C22×C47C22×C22⋊C411yescharacteristic
164C22×C47C22×C22⋊C412yes—
165C22×C47C22×C4⋊C411yescharacteristic
166C22×C47C22×C4⋊C412yes—
167C22×C47#51812yes—
168C22×C47#51912yes—
169C22×C47#52018yes—
170C22×C47#53514yes—
171C22×C47#53614yes—
172C22×C47#53714yes—
173C22×C47#54414yes—
174C4×C47—44no—
175C4×C47—48no—
176Dic47—44no—
177Dic47—48no—
178Dic47C2×#95116yes—
179C22×#117—472no—
180C23×C4⋊C4—471no—
181C4⋊#95—478no—
182C22⋊#95—471no—
183C22⋊#95—472no—
184C22⋊#95D4711yescharacteristic
185C2×C47—28no—
186C2×C47C22×#9511yescharacteristic
187C2×C47#227412yes—
188C2×C47#230911yescharacteristic
189C2×C47#231011yescharacteristic
190C2×C47#231114yes—
191C2×C47#231612yes—
192C2×C47#231714yes—
193C24×C4—471no—
194C24×C4—471no—
195C24×C4C2×D4711yescharacteristic
196C2×#117—4716no—
197C2×#117—948no—
198C2×#117—948no—
199C22×C4⋊C4—478no—
200C22×C4⋊C4—474no—
201C22×C4⋊C4—474no—
202C22×C4⋊C4—948no—
203C22×C22⋊C4—472no—
204C22×C22⋊C4C2×D4712yes—
205C22×C42—474no—
206C2×#95—474no—
207C2×#95—478no—
208C2×#95C2×D4714yes—
209C47#1379511yescharacteristic, complemented, Sylow
210C25C22×D4711yescharacteristic
211C23×C4—24no—
212C23×C4—44no—
213C23×C4—474no—
214C23×C4—478no—
215C23×C4—478no—
216C23×C4—474no—
217C23×C4—474no—
218C23×C4—472no—
219C23×C4—474no—
220C23×C4—472no—
221C23×C4—474no—
222C23×C4—944no—
223C23×C4—1884no—
224C23×C4C4×D4714yes—
225C23×C4C22×D4714yes—
226C23×C4C22×D4712yes—
227#117—9464no—
228C2×C4⋊C4—4716no—
229C2×C4⋊C4—4716no—
230C2×C4⋊C4—9432no—
231C2×C4⋊C4—948no—
232C2×C4⋊C4—948no—
233C2×C4⋊C4—948no—
234C2×C4⋊C4—948no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—478no—
238C2×C22⋊C4—944no—
239C2×C22⋊C4—944no—
240C2×C22⋊C4C4×D4718yes—
241C2×C42—4716no—
242C2×C42—948no—
243C2×C42—948no—
244#95—44no—
245#95—1888no—
246#95—1884no—
247C24—24no—
248C24—24no—
249C24C2×C4×D4714yes—
250C24C2×C4×D4712yes—
251C24D4×D4712yes—
252C24D4×D4714yes—
253C24Q8×D4712yes—
254C24C23×D4711yescharacteristic
255C22×C4—28no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—28no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—48no—
264C22×C4—416no—
265C22×C4—4716no—
266C22×C4—4716no—
267C22×C4—4732no—
268C22×C4—4716no—
269C22×C4—4732no—
270C22×C4—474no—
271C22×C4—474no—
272C22×C4—474no—
273C22×C4—474no—
274C22×C4—474no—
275C22×C4—474no—
276C22×C4—474no—
277C22×C4—478no—
278C22×C4—474no—
279C22×C4—948no—
280C22×C4—944no—
281C22×C4—944no—
282C22×C4—944no—
283C22×C4—948no—
284C22×C4—948no—
285C22×C4—948no—
286C22×C4—1888no—
287C22×C4—18816no—
288C22×C4C2×C4×D4718yes—
289C22×C4C2×C4×D4714yes—
290C4⋊C4—9432no—
291C4⋊C4—9432no—
292C22⋊C4—216no—
293C22⋊C4—9416no—
294C42—9432no—
295C23—28no—
296C23—24no—
297C23—24no—
298C23—216no—
299C23—28no—
300C23—28no—
301C23—28no—
302C23C42×D4714yes—
303C23C22⋊C4×D4718yes—
304C23C22⋊C4×D4714yes—
305C23C4⋊C4×D4714yes—
306C23C4⋊C4×D4718yes—
307C23C22×C4×D4711yescharacteristic
308C23C22×C4×D4712yes—
309C23C2×D4×D4712yes—
310C23C2×D4×D4711yescharacteristic
311C23C2×Q8×D4711yescharacteristic
312C23#1309406914yes—
313C23#1309407114yes—
314C2×C4—28no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—216no—
319C2×C4—416no—
320C2×C4—44no—
321C2×C4—48no—
322C2×C4—44no—
323C2×C4—48no—
324C2×C4—4764no—
325C2×C4—478no—
326C2×C4—478no—
327C2×C4—478no—
328C2×C4—478no—
329C2×C4—478no—
330C2×C4—478no—
331C2×C4—478no—
332C2×C4—948no—
333C2×C4—944no—
334C2×C4—948no—
335C2×C4—9416no—
336C2×C4—18816no—
337C2×C4—1884no—
338C2×C4—1888no—
339C2×C4—1884no—
340C2×C4—1888no—
341C22—24no—
342C22—24no—
343C22—216no—
344C22—28no—
345C22—28no—
346C22—216no—
347C22#95×D4718yes—
348C22C2×C42×D4711yescharacteristic
349C22C2×C22⋊C4×D4711yescharacteristic
350C22C2×C22⋊C4×D4712yes—
351C22C2×C4⋊C4×D4711yescharacteristic
352C22C2×C4⋊C4×D4712yes—
353C22#1568959612yes—
354C22#1568960012yes—
355C22#1568960218yes—
356C22#1568968814yes—
357C22#1568969514yes—
358C22#1568970014yes—
359C22#1568975214yes—
360C4—44no—
361C4—48no—
362C4—4716no—
363C4—1884no—
364C4—1888no—
365C2—28no—
366C2C2×#95×D4711yescharacteristic
367C2#2024574312yes—
368C2#2024596911yescharacteristic
369C2#2024597311yescharacteristic
370C2#2024597514yes—
371C2#2024600512yes—
372C2#2024600714yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#13795
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. Dic47⋊#95C2semidirect
11. C2×#13093980C4semidirect
13. C22×Dic47⋊C4C4semidirect
41. C2×Dic47⋊C4C2×C4semidirect
47. C2×C4×Dic47C2×C4semidirect
146. C2×Dic47#95semidirect
209. C47#13795semidirect

Maximal subgroups

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

subgroupindex
C22×#130939802
C23×Dic47⋊C42
Dic47⋊#952
#202416112
#202416102
C47×C22⋊#952
#1379547