Finite Group Databasebeta

← #26127798

Subgroups — #26127798

Order 12032.

268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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#20254047C211yesmaximal, characteristic
2#20245204C211yesmaximal, characteristic
3#20241450C212yesmaximal, complemented
4#20241426C212yesmaximal, complemented
5C47×#2153C211yesmaximal, characteristic
6#15689735C412yes—
7#15689525C2211yescharacteristic
8#15689503C2211yescharacteristic
9#15689492C412yes—
10#15689381—21no—
11#15689364—21no—
12#15689231—21no—
13C4×Dic188—21no—
14#15688944C2212yes—
15#15688905—21no—
16#15688901—21no—
17C2×M32×C47—21no—
18C47×#405C2211yescharacteristic
19C47×#364—21no—
20C47×#364C2212yes—
21C2×Dic188—21no—
22C2×Dic188—21no—
23#13094024C2×C412yes—
24#13094017—42no—
25#13094016C2×C412yes—
26#13094014—42no—
27#13094003—22no—
28C4×Dic94—22no—
29#13093964—22no—
30#13093958—21no—
31#13093956—21no—
32#13093949—22no—
33#13093949—22no—
34C2×M16×C47D411yescharacteristic
35C22×C8×C47D411yescharacteristic
36#117×C47C2×C411yescharacteristic
37M32×C47—22no—
38M32×C47—41no—
39C2×C16×C47—41no—
40#97×C47C2×C411yescharacteristic
41#97×C47D411yescharacteristic
42C4×C8×C47D411yescharacteristic
43C4×C8×C47C2311yescharacteristic
44C22×C4×C47C22⋊C411yescharacteristic
45C2×Dic94—22no—
46M16×C47—22no—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47C22⋊C411yescharacteristic
50C2×C8×C47C22⋊C411yescharacteristic
51C2×C8×C47C2×D411yescharacteristic
52C2×C8×C47C2×D411yescharacteristic
53C4⋊C4×C47—21no—
54C22⋊C4×C47—21no—
55C42×C47C22⋊C411yescharacteristic
56C42×C47C22×C411yescharacteristic
57C22⋊Dic47—42no—
58C4⋊Dic47—22no—
59C4⋊Dic47—42no—
60Dic47⋊C4—42no—
61Dic47⋊C4—42no—
62Dic47⋊C4—42no—
63C4×Dic47—42no—
64Dic188—42no—
65Dic188—41no—
66Dic188—41no—
67C16×C47—42no—
68C47⋊C16—42no—
69C23×C47#10011yescharacteristic
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47#10011yescharacteristic
75C2×C4×C47C2×C22⋊C411yescharacteristic
76C2×Dic47—42no—
77C2×Dic47—42no—
78Dic94—42no—
79Dic94—42no—
80C8×C47—21no—
81C8×C47—21no—
82C8×C47#13512yes—
83C8×C47AGL(1,ℤ/8)11yescharacteristic
84C8×C47#13711yescharacteristic
85#11990—471nomaximal, Sylow
86C22×C47—21no—
87C22×C47—41no—
88C22×C47C2×#10011yescharacteristic
89C4×C47—21no—
90C4×C47—41no—
91C4×C47—41no—
92C4×C47#41611yescharacteristic
93C4×C47#41711yescharacteristic
94Dic47—82no—
95Dic47—82no—
96#3177—471no—
97#2166—471no—
98#2153D4711yescharacteristic
99#1366—472no—
100#1358—472no—
101C2×C47—21no—
102C2×C47—41no—
103C2×C47#155111yescharacteristic
104#541—472no—
105C2×M32—21no—
106#499—471no—
107#494—471no—
108#491—472no—
109#470—941no—
110#467—941no—
111#441—941no—
112C4×Q16—941no—
113#405C2×D4711yescharacteristic
114#364—21no—
115#364—472no—
116#364C2×D4712yes—
117#349—941no—
118#347—941no—
119C47#1199011yescharacteristic, complemented, Sylow
120C2×Q16—941no—
121C2×Q16—941no—
122C2×M16D18811yescharacteristic
123C22×C8C22⋊D4711yescharacteristic
124C4⋊Q8—472no—
125#126—1882no—
126#125—472no—
127#125—1882no—
128C22⋊Q8—942no—
129C4×Q8—942no—
130#117C4×D4711yescharacteristic
131M32—22no—
132M32—41no—
133M32—942no—
134C2×C16—41no—
135#107—941no—
136#106—941no—
137#103—942no—
138#103—942no—
139#97C4×D4711yescharacteristic
140#97D18811yescharacteristic
141C4×C8C22⋊D4711yescharacteristic
142C4×C8C22×D4711yescharacteristic
143C2×Q8—942no—
144C22×C4(C2×D47)⋊C411yescharacteristic
145Q16—1882no—
146Q16—1881no—
147Q16—1881no—
148M16—22no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8(C2×D47)⋊C411yescharacteristic
152C2×C8(C2×D47)⋊C411yescharacteristic
153C2×C8C2×D18811yescharacteristic
154C2×C8C2×C22⋊D4711yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—942no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C22⋊C4—21no—
162C22⋊C4—1882no—
163C42—1882no—
164C42(C2×D47)⋊C411yescharacteristic
165C42C2×C4×D4711yescharacteristic
166C16—42no—
167C16—1882no—
168C23#1309394011yescharacteristic
169Q8—1882no—
170Q8—1882no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—1882no—
176C2×C4—1882no—
177C2×C4#1309394011yescharacteristic
178C2×C4C2×(C2×D47)⋊C411yescharacteristic
179C8—21no—
180C8—21no—
181C8#1309404612yes—
182C8#1309405011yescharacteristic
183C8#1309405511yescharacteristic
184C22—21no—
185C22—41no—
186C22C2×#1309394011yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—3762no—
191C4—3762no—
192C4#1568912011yescharacteristic
193C4#1568912211yescharacteristic
194C2—21no—
195C2—41no—
196C2#2024208111yescharacteristic
subgroupG/H
centerC2#20242081
commutatorC42×C47C22×C4
FrattiniC4×C8C22×D47
FittingC47×#2153C2
socleC2×C47#1551
prime radicalC23×C47#100
cosocleC4×C8×C47C23
hypercenter#2153D47
hypocenterC47#11990
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
3. #20241450C2semidirect
4. #20241426C2semidirect
119. C47#11990semidirect

Maximal subgroups

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

subgroupindex
#202540472
#202452042
#202414502
#202414262
C47×#21532
#1199047