Finite Group Databasebeta

← #26113980

Subgroups — #26113980

Order 12032.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252473C211yesmaximal, characteristic
2#20248600C211yesmaximal, characteristic
3#20242104C212yesmaximal
4#20241243C212yesmaximal
5C47×#1467C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689254—24no—
8#15689180—21no—
9#15689180C2212yes—
10#15689176—21no—
11#15689062—21no—
12#15689062—21no—
13#15689030C412yes—
14#15689029—21no—
15#15689029—21no—
16#15688988C412yes—
17C4×C4⋊Dic47C2211yescharacteristic
18#15688868—24no—
19C2×C4×Q8×C47C2211yescharacteristic
20C47×#432C2212yes—
21C47×#324—21no—
22C47×#324—21no—
23C22×Dic94—21no—
24#13094024—22no—
25#13094024—22no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C412yes—
29C2×C4×Dic47C2×C412yes—
30C4⋊(C47⋊C8)—22no—
31C4⋊(C47⋊C8)—22no—
32C4⋊(C47⋊C8)D414yes—
33C22⋊(C47⋊C8)—22no—
34#13093935—22no—
35#13093935—22no—
36C4×C47⋊C8—22no—
37C47⋊#95—22no—
38C47⋊#95—22no—
39C47⋊#95—22no—
40C47⋊#95—22no—
41C47⋊#95—21no—
42C22×Q8×C47C2×C411yescharacteristic
43C4×Q8×C47—22no—
44C4×Q8×C47—22no—
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—22no—
52C22⋊C8×C47—22no—
53#97×C47—22no—
54C2×Q8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47C22⋊C411yescharacteristic
61C22×C4×C47C22×C411yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×Dic47—22no—
65C22×Dic47—22no—
66C2×Dic94—44no—
67C2×Dic94—41no—
68C2×Dic94—41no—
69C2×C8×C47—42no—
70C4⋊C4×C47—22no—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C42×C47—21no—
74C42×C47—21no—
75C42×C47—21no—
76C42×C47—21no—
77C42×C47C2×D412yes—
78C42×C47#4112yes—
79C4⋊Dic47—24no—
80C4⋊Dic47—42no—
81C4⋊Dic47—42no—
82C4×Dic47—42no—
83C2×C47⋊C8—24no—
84C23×C47C2×C22⋊C411yescharacteristic
85Q8×C47—44no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47#10112yes—
100C2×C4×C47C4×D412yes—
101C2×C4×C47#12011yescharacteristic
102C2×C4×C47#12112yes—
103C2×C4×C47#12311yescharacteristic
104C2×Dic47—42no—
105C2×Dic47—44no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108C2×Dic47—42no—
109Dic94—82no—
110Dic94—82no—
111C8×C47—82no—
112C47⋊C8—44no—
113#9456—471nomaximal, Sylow
114C22×C47—21no—
115C22×C47—21no—
116C22×C47#38611yescharacteristic
117C22×C47C2×#10111yescharacteristic
118C22×C47#41311yescharacteristic
119C4×C47—21no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—22no—
123C4×C47—41no—
124C4×C47—41no—
125C4×C47—41no—
126C4×C47#45412yes—
127Dic47—82no—
128Dic47—82no—
129#2983—471no—
130#2568—471no—
131#1556—472no—
132#1467D4711yescharacteristic
133#1285—472no—
134C2×C47—21no—
135C2×C47—21no—
136C2×C47#188811yescharacteristic
137C2×C47#190111yescharacteristic
138C2×C47#190911yescharacteristic
139C2×C4⋊Q8—471no—
140C2×C4×Q8C2×D4711yescharacteristic
141#446—944no—
142#432—472no—
143#432—941no—
144#432C2×D4712yes—
145#431—941no—
146#400—941no—
147#400—941no—
148#391—472no—
149#391—941no—
150#391—941no—
151#382—472no—
152C4×C4⋊C4—471no—
153#332—944no—
154#324—21no—
155#324—21no—
156C47#945611yescharacteristic, complemented, Sylow
157C22×Q8—941no—
158C22×Q8C4×D4711yescharacteristic
159C4⋊Q8—942no—
160C4⋊Q8—942no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—472no—
164C2×C4⋊C4—941no—
165C2×C4⋊C4—941no—
166C2×C4⋊C4C4×D4711yescharacteristic
167C2×C4⋊C4C22⋊D4711yescharacteristic
168C2×C4⋊C4C22⋊D4711yescharacteristic
169C2×C42—472no—
170C2×C42D18811yescharacteristic
171C2×C42D18811yescharacteristic
172C2×C42C22×D4711yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—474no—
175C4⋊C8—942no—
176C4⋊C8—942no—
177C22⋊C8—22no—
178C22⋊C8—942no—
179#97—22no—
180#97—942no—
181#97—942no—
182C4×C8—942no—
183#95—942no—
184#95—942no—
185#95—942no—
186#95—942no—
187#95—941no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—1884no—
192C2×Q8—1881no—
193C2×Q8—1881no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4(C2×D47)⋊C411yescharacteristic
197C22×C4(C2×D47)⋊C411yescharacteristic
198C22×C4(C2×D47)⋊C411yescharacteristic
199C22×C4(C2×D47)⋊C411yescharacteristic
200C22×C4C2×C4×D4711yescharacteristic
201C22×C4C2×D18811yescharacteristic
202C22×C4C2×C22⋊D4711yescharacteristic
203C2×C8—42no—
204C2×C8—944no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—944no—
209C4⋊C4—1882no—
210C4⋊C4—1882no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—1882no—
216C42D4×D4712yes—
217C42#1062535212yes—
218C23C2×(C2×D47)⋊C411yescharacteristic
219Q8—44no—
220Q8—3762no—
221Q8—3762no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1882no—
236C2×C4—1882no—
237C2×C4—1884no—
238C2×C4—1882no—
239C2×C4—1882no—
240C2×C4#1309394212yes—
241C2×C4(C22⋊D47)⋊C412yes—
242C2×C4#1309399411yescharacteristic
243C2×C4#1309399612yes—
244C2×C4#1309400811yescharacteristic
245C8—82no—
246C8—1884no—
247C22—21no—
248C22—21no—
249C22#1568900011yescharacteristic
250C22C2×#1309394211yescharacteristic
251C22#1568910511yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—3762no—
260C4—3762no—
261C4#1568929812yes—
262C2—21no—
263C2—21no—
264C2#2024378911yescharacteristic
265C2#2024385411yescharacteristic
266C2#2024390811yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1467C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1467D47
hypocenterC47#9456
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
156. C47#9456semidirect

Maximal subgroups

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

subgroupindex
#202524732
#202486002
#202421042
#202412432
C47×#14672
#945647