Finite Group Databasebeta

← #26107203

Subgroups — #26107203

Order 12032.

444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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#20245943C211yesmaximal, characteristic
2#20243136C212yesmaximal
3C2×#15688864C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#1295C211yesmaximal, characteristic
6C2×#13094016C2211yescharacteristic
7C2×#13093935C2212yes—
8#15689019C412yes—
9#15689005—22no—
10C4⋊C4×Dic47C412yes—
11#15688974—22no—
12C42×Dic47C2211yescharacteristic
13#15688877—22no—
14#15688877—22no—
15#15688864C418yescomplemented
16C2×#97×C47C2212yes—
17C47×#382C2211yescharacteristic
18C22×C47⋊C8—22no—
19#13094016—21no—
20#13094016—21no—
21#13094016C2×C414yes—
22C2×C4⋊Dic47C2×C412yes—
23C2×Dic47⋊C4—22no—
24C2×Dic47⋊C4—22no—
25C2×C4×Dic47—22no—
26C2×C4×Dic47C2×C411yescharacteristic
27C2×C4×Dic47C2×C411yescharacteristic
28C2×C4×Dic47D412yes—
29C2×C4×Dic47D412yes—
30#13093935—22no—
31#13093935C2×C414yes—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C22×C8×C47—22no—
35C2×C4⋊C4×C47C2×C412yes—
36C2×C42×C47C2311yescharacteristic
37#97×C47—22no—
38#97×C47C2×C414yes—
39#95×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C22×C411yescharacteristic
42C22×C4×C47C2×D412yes—
43C22×Dic47—22no—
44C22×Dic47C22⋊C411yescharacteristic
45C22×Dic47C22⋊C412yes—
46C22×Dic47C22⋊C411yescharacteristic
47C2×C8×C47—24no—
48C2×C8×C47—42no—
49C2×C8×C47—42no—
50C4⋊C4×C47—42no—
51C42×C47C22×C412yes—
52C42×C47#4111yescharacteristic
53C42×C47#4111yescharacteristic
54C4⋊Dic47—22no—
55C4⋊Dic47C4214yes—
56Dic47⋊C4—24no—
57Dic47⋊C4—24no—
58Dic47⋊C4—44no—
59C4×Dic47—22no—
60C4×Dic47—41no—
61C4×Dic47—42no—
62C4×Dic47—42no—
63C4×Dic47—44no—
64C2×C47⋊C8—24no—
65C2×C47⋊C8—42no—
66C2×C47⋊C8—42no—
67C23×C47C2×C22⋊C411yescharacteristic
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47C2×C4211yescharacteristic
76C2×C4×C47#11711yescharacteristic
77C2×C4×C47C4×D412yes—
78C2×C4×C47C4×D412yes—
79C2×Dic47—22no—
80C2×Dic47—24no—
81C2×Dic47—21no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47#10112yes—
89C8×C47—44no—
90C47⋊C8—44no—
91#8225—471nomaximal, Sylow
92C22×C47C4×C22⋊C411yescharacteristic
93C22×C47C2×#10111yescharacteristic
94C22×C47#41311yescharacteristic
95C22×C47#42112yes—
96C22×C47#42112yes—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47—22no—
101C4×C47—82no—
102Dic47—22no—
103Dic47—41no—
104Dic47—44no—
105Dic47—42no—
106C4×#125—471no—
107#1745—472no—
108C2×#330—472no—
109#1295—471no—
110#1295D4711yescharacteristic
111C2×C47#153411yescharacteristic
112C2×C47#153512yes—
113C2×C47#153711yescharacteristic
114C2×C47C4×#10111yescharacteristic
115C2×C47#175912yes—
116C2×#125—471no—
117C2×#97—472no—
118C2×#97C2×D4712yes—
119#389—472no—
120#387—942no—
121#382C2×D4711yescharacteristic
122C4×C4⋊C4—472no—
123C4×C4⋊C4—942no—
124C43—471no—
125#336—942no—
126#336—942no—
127#330—478no—
128C47#822511yescharacteristic, complemented, Sylow
129C22×C8—22no—
130C22×C8—942no—
131#125—474no—
132#125—941no—
133#125—941no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—942no—
136C2×C4⋊C4—942no—
137C2×C4⋊C4C4×D4712yes—
138C2×C42—471no—
139C2×C42—471no—
140C2×C42—472no—
141C2×C42—472no—
142C2×C42—942no—
143C2×C42C22×D4711yescharacteristic
144#97—22no—
145#97—474no—
146#97—942no—
147#97C4×D4714yes—
148#95—22no—
149#95—942no—
150#95—942no—
151C22×C4—22no—
152C22×C4—471no—
153C22×C4—471no—
154C22×C4—472no—
155C22×C4—942no—
156C22×C4C2×C4×D4711yescharacteristic
157C22×C4D4×D4712yes—
158C2×C8—24no—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—944no—
162C2×C8—1882no—
163C2×C8—1882no—
164C4⋊C4—42no—
165C4⋊C4—474no—
166C4⋊C4—942no—
167C4⋊C4—944no—
168C4⋊C4—944no—
169C4⋊C4—1884no—
170C42—942no—
171C42—1881no—
172C42—1882no—
173C42—1882no—
174C42—1884no—
175C42C2×C4×D4712yes—
176C42#1062535211yescharacteristic
177C42#1062535411yescharacteristic
178C23C22⋊C4×D4711yescharacteristic
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—472no—
187C2×C4—942no—
188C2×C4—944no—
189C2×C4—941no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4C42×D4711yescharacteristic
197C2×C4#1309398211yescharacteristic
198C2×C4(C22⋊D47)⋊C412yes—
199C2×C4#1309398612yes—
200C8—44no—
201C8—1884no—
202C22#1568897011yescharacteristic
203C22#101×D4711yescharacteristic
204C22#1568910411yescharacteristic
205C22#1568913812yes—
206C22#1568913812yes—
207C4—21no—
208C4—21no—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—942no—
213C4—1882no—
214C4—1881no—
215C4—1884no—
216C2#2024201311yescharacteristic
217C2#2024201612yes—
218C2#2024202411yescharacteristic
219C2#2024318311yescharacteristic
220C2#2024319712yes—
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1295D47
hypocenterC47#8225
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
15. #15688864C4semidirect
128. C47#8225semidirect

Maximal subgroups

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

subgroupindex
#202459432
#202431362
C2×#156888642
#202412692
C47×#12952
#822547