Finite Group Databasebeta

← #26105590

Subgroups — #26105590

Order 12032.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#20251376C211yesmaximal, characteristic
2#20244952C212yesmaximal
3#20244926C211yesmaximal, characteristic
4#20241212C212yesmaximal
5C47×#1272C211yesmaximal, characteristic
6C2×#13093957—21no—
7C2×#13093948—21no—
8#15689062—21no—
9#15689055—22no—
10#15689030—21no—
11#15689021C2212yes—
12#15689010—22no—
13#15688993C2211yescharacteristic
14#15688886—22no—
15#15688886—22no—
16#15688878C2211yescharacteristic
17C47×#391C2211yescharacteristic
18C47×#336C2212yes—
19C22×C47⋊C8—21no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—22no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47—21no—
24C2×C4⋊Dic47D412yes—
25C2×C4⋊Dic47D412yes—
26C2×Dic47⋊C4—22no—
27C2×C4×Dic47—21no—
28#13093957—42no—
29#13093948—42no—
30C47⋊#95—21no—
31C47⋊#95—22no—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C22×Q8×C47D411yescharacteristic
35C22×C8×C47—22no—
36C2×C4⋊C4×C47D411yescharacteristic
37C2×C42×C47C2311yescharacteristic
38#95×C47—22no—
39C2×Q8×C47—21no—
40C2×Q8×C47—41no—
41C2×Q8×C47—41no—
42C2×Q8×C47Q1612yes—
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2×D411yescharacteristic
46C22×C4×C47C2×D412yes—
47C22×Dic47—22no—
48C22×Dic47—22no—
49C22×Dic47—41no—
50C2×C8×C47—42no—
51C2×C8×C47—42no—
52C2×C8×C47—42no—
53C4⋊C4×C47—41no—
54C42×C47—41no—
55C4⋊Dic47—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—42no—
58C4⋊Dic47—41no—
59C4⋊Dic47—41no—
60C4⋊Dic47—44no—
61C4⋊Dic47—81no—
62C4⋊Dic47—81no—
63Dic47⋊C4—42no—
64Dic47⋊C4—42no—
65C4×Dic47—81no—
66C2×C47⋊C8—22no—
67C2×C47⋊C8—41no—
68C2×C47⋊C8—41no—
69C23×C47#12011yescharacteristic
70Q8×C47—42no—
71Q8×C47—81no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47—42no—
81C2×C4×C47C2×Q1611yescharacteristic
82C2×C4×C47#13512yes—
83C2×C4×C47#13712yes—
84C2×C4×C47#13711yescharacteristic
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—42no—
91C2×Dic47—81no—
92C2×Dic47—82no—
93C8×C47—82no—
94C47⋊C8—42no—
95#7831—471nomaximal, Sylow
96C22×C47#45111yescharacteristic
97C22×C47#45212yes—
98C22×C47#45311yescharacteristic
99C22×C47#45412yes—
100C22×C47#45811yescharacteristic
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—22no—
104C4×C47—22no—
105C4×C47—42no—
106C4×C47—81no—
107Dic47—82no—
108Dic47—82no—
109Dic47—161no—
110#2809—471no—
111#2100—472no—
112#2095—471no—
113#1272D4711yescharacteristic
114#1271—472no—
115C2×C47#161411yescharacteristic
116C2×C47#161512yes—
117C2×C47#163411yescharacteristic
118C2×C47#163612yes—
119C2×C47#165711yescharacteristic
120C2×#107—941no—
121C2×#103—941no—
122#400—941no—
123#398—942no—
124#391—941no—
125#391C2×D4711yescharacteristic
126#389—472no—
127#387—942no—
128#384—471no—
129#340—942no—
130#340—942no—
131#336—471no—
132#336C2×D4712yes—
133C47#783111yescharacteristic, complemented, Sylow
134C22×Q8D18811yescharacteristic
135C22×C8—22no—
136C22×C8—941no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—941no—
140C2×C4⋊C4—941no—
141C2×C4⋊C4—942no—
142C2×C4⋊C4—941no—
143C2×C4⋊C4—942no—
144C2×C4⋊C4D18811yescharacteristic
145C2×C42—941no—
146C2×C42C22×D4711yescharacteristic
147#107—1882no—
148#103—1882no—
149#95—22no—
150#95—941no—
151#95—942no—
152#95—942no—
153#95—942no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Dic18812yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—942no—
161C22×C4—942no—
162C22×C4—1881no—
163C22×C4C2×D18811yescharacteristic
164C22×C4D4×D4712yes—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—942no—
169C2×C8—1881no—
170C2×C8—1881no—
171C4⋊C4—41no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—3761no—
175C4⋊C4—3761no—
176C4⋊C4—1881no—
177C4⋊C4—1881no—
178C4⋊C4—1884no—
179C4⋊C4—1882no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C42—41no—
183C42—3761no—
184C23#1309399411yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—3761no—
197C2×C4—3762no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1882no—
204C2×C4C2×Dic18811yescharacteristic
205C2×C4#1309404512yes—
206C2×C4#1309405612yes—
207C2×C4#1309405711yescharacteristic
208C8—82no—
209C8—1882no—
210C22#1568928111yescharacteristic
211C22#1568928812yes—
212C22#1568929311yescharacteristic
213C22#1568929712yes—
214C22#1568931411yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—3762no—
222C4—3762no—
223C4—7521no—
224C2#2024241511yescharacteristic
225C2#2024242212yes—
226C2#2024253411yescharacteristic
227C2#2024254912yes—
228C2#2024268711yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1272C2
socle, prime radicalC23×C47#120
hypercenter#1272D47
hypocenterC47#7831
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
133. C47#7831semidirect

Maximal subgroups

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

subgroupindex
#202513762
#202449522
#202449262
#202412122
C47×#12722
#783147