Finite Group Databasebeta

← #26119309

Subgroups — #26119309

Order 12032.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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#20248630C211yesmaximal, characteristic
2#20244335C212yesmaximal
3#20244189C211yesmaximal, characteristic
4#20241227C212yesmaximal
5C47×#1296C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13093947—22no—
8C2×C4×C47⋊C8C2211yescharacteristic
9#15689062—22no—
10#15689022—22no—
11#15688988—22no—
12C4×C4⋊Dic47C2212yes—
13#15688886—22no—
14#15688886—22no—
15C2×C4⋊C8×C47C2212yes—
16C47×#384C2211yescharacteristic
17C22×Dic94—21no—
18C22×C47⋊C8—21no—
19#13094024—22no—
20#13094024—21no—
21#13094024Q812yes—
22C2×C4⋊Dic47—22no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47D412yes—
25C2×C4⋊Dic47D412yes—
26C2×C4×Dic47—22no—
27#13093947—44no—
28C4×C47⋊C8—22no—
29C47⋊#95—22no—
30C47⋊#95—24no—
31C47⋊#95—22no—
32C22×C8×C47—22no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47D412yes—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47C2×D411yescharacteristic
40C22×C4×C47C2×D412yes—
41C22×Dic47—22no—
42C22×Dic47—22no—
43C22×Dic47—41no—
44C2×Dic94—22no—
45C2×Dic94—42no—
46C2×Dic94—42no—
47C2×Dic94—41no—
48C2×C8×C47—42no—
49C2×C8×C47—42no—
50C2×C8×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—42no—
53C4⋊C4×C47—42no—
54C42×C47C2×Q811yescharacteristic
55C42×C47#4112yes—
56C42×C47#4111yescharacteristic
57C4⋊Dic47—24no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47—42no—
63C4⋊Dic47—82no—
64C4×Dic47—42no—
65C4×Dic47—42no—
66C2×C47⋊C8—22no—
67C2×C47⋊C8—41no—
68C2×C47⋊C8—41no—
69C23×C47#12011yescharacteristic
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—44no—
73C2×C4×C47—42no—
74C2×C4×C47C22⋊Q812yes—
75C2×C4×C47C22⋊Q811yescharacteristic
76C2×C4×C47#12412yes—
77C2×C4×C47#12411yescharacteristic
78C2×C4×C47#13512yes—
79C2×C4×C47#13512yes—
80C2×C4×C47#13712yes—
81C2×C4×C47#13712yes—
82C2×Dic47—42no—
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—81no—
90C2×Dic47—81no—
91Dic94—44no—
92Dic94—82no—
93C8×C47—82no—
94C47⋊C8—42no—
95#10352—471nomaximal, Sylow
96C22×C47#39311yescharacteristic
97C22×C47#45212yes—
98C22×C47#45212yes—
99C22×C47#45311yescharacteristic
100C22×C47#45411yescharacteristic
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—82no—
104C4×C47#47912yes—
105C4×C47#47912yes—
106C4×C47#48812yes—
107C4×C47#49112yes—
108Dic47—82no—
109Dic47—82no—
110Dic47—82no—
111#2571—471no—
112#1987—472no—
113#1956—471no—
114#1296D4711yescharacteristic
115#1279—472no—
116C2×C47#163011yescharacteristic
117C2×C47#163411yescharacteristic
118C2×C47#163812yes—
119C2×C47#202612yes—
120C2×C47#202711yescharacteristic
121C2×C4⋊Q8—471no—
122C2×C4⋊C8C2×D4712yes—
123C2×#103—942no—
124C2×C4×C8—471no—
125#400—942no—
126#389—942no—
127#384C2×D4711yescharacteristic
128#382—942no—
129C4×C4⋊C4—472no—
130#340—942no—
131#340—942no—
132C47#1035211yescharacteristic, complemented, Sylow
133C22×Q8—941no—
134C22×C8—22no—
135C22×C8—941no—
136C4⋊Q8—472no—
137C4⋊Q8—942no—
138C4⋊Q8—941no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—942no—
143C2×C4⋊C4—942no—
144C2×C4⋊C4D18812yes—
145C2×C42—942no—
146C2×C42C22×D4711yescharacteristic
147C4⋊C8—22no—
148C4⋊C8—22no—
149#103—1884no—
150C4×C8—942no—
151#95—942no—
152#95—944no—
153#95—942no—
154C2×Q8—942no—
155C2×Q8—1882no—
156C2×Q8—1882no—
157C2×Q8—1881no—
158C22×C4—22no—
159C22×C4—942no—
160C22×C4—942no—
161C22×C4—1881no—
162C22×C4C2×D18811yescharacteristic
163C22×C4D4×D4712yes—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—942no—
168C2×C8—1881no—
169C2×C8—1881no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—944no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—3762no—
179C4⋊C4—1882no—
180C42—1882no—
181C42—1882no—
182C42#1062535012yes—
183C42#1062535211yescharacteristic
184C42Q8×D4711yescharacteristic
185C23#1309399411yescharacteristic
186Q8—3762no—
187Q8—1884no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—44no—
191C2×C4—42no—
192C2×C4—3761no—
193C2×C4—3761no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4#1309400212yes—
202C2×C4#1309400411yescharacteristic
203C2×C4#1309401012yes—
204C2×C4#1309401211yescharacteristic
205C2×C4#1309404312yes—
206C2×C4#1309404512yes—
207C2×C4#1309405312yes—
208C2×C4#1309405612yes—
209C8—82no—
210C8—1882no—
211C22#1568903611yescharacteristic
212C22#1568928612yes—
213C22#1568928812yes—
214C22#1568929311yescharacteristic
215C22#1568929811yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—3762no—
220C4—3762no—
221C4—3762no—
222C4#1568942912yes—
223C4#1568943312yes—
224C4#1568947612yes—
225C4#1568949012yes—
226C2#2024251011yescharacteristic
227C2#2024253411yescharacteristic
228C2#2024256112yes—
229C2#2024453812yes—
230C2#2024454511yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socle, prime radicalC23×C47#120
hypercenter#1296D47
hypocenterC47#10352
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
132. C47#10352semidirect

Maximal subgroups

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

subgroupindex
#202486302
#202443352
#202441892
#202412272
C47×#12962
#1035247