Finite Group Databasebeta

← #11797372

Subgroups — #11797372

Order 1152.

341 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 102 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#10592388C211yesmaximal, characteristic
2C3×C4⋊(C3⋊C16)C212yesmaximal, complemented
3#10589108C212yesmaximal
4#10589104C211yesmaximal, characteristic, complemented
5#10589102C211yesmaximal, characteristic, complemented
6#69276—32nomaximal
7C2×#3743C411yescharacteristic
8C2×C8×C3⋊D3C2211yescharacteristic
9#64081C411yescharacteristic
10C32×C4×C8C2211yescharacteristic
11#63642C411yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13#63630C411yescharacteristic
14C2×C3×C3⋊C16C2212yes—
15C2×C3×C3⋊C16C2212yes—
16#4689—32no—
17#4689—61no—
18C3×C4⋊C16—32no—
19(C2×D3)⋊C16—32no—
20(C2×D3)⋊C16—32no—
21#4502—32no—
22Dic3×C16—32no—
23C4⋊(C3⋊C16)D312yescomplemented
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C32×C8C2×C411yescharacteristic
26C2×C32×C8C2311yescharacteristic
27C32×C42C2×C411yescharacteristic
28#3752C812yes—
29#3750C812yes—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33#3743—22no—
34C8×C3⋊D3—22no—
35C3×C3⋊C16—22no—
36C3×C3⋊C16—22no—
37#2164—91noSylow
38C2×ΓL(1,𝔽25)—32no—
39C2×ΓL(1,𝔽25)—61no—
40C2×D3×C8—32no—
41C2×D3×C8—61no—
42#872—32no—
43#872—61no—
44C2×C3×C16—32no—
45C2×C3×C16—32no—
46C3×C4×C8—21no—
47C3×C4×C8C2×D312yes—
48#815—32no—
49#815—61no—
50C8×Dic3—32no—
51C8×Dic3—61no—
52C2×C3⋊C16C2×D312yes—
53C2×C3⋊C16C2×D312yes—
54#803—32no—
55#803—61no—
56C22×C3⋊D3C2×C811yescharacteristic
57C2×C32×C4C2×C812yes—
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3C2×C812yes—
60C2×C3⋊Dic3C2×C811yescharacteristic
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63C32×C8—21no—
64C32×C8#4112yes—
65C3⋊(C3⋊C8)—21no—
66C3⋊(C3⋊C8)M1612yes—
67#405—91no—
68C4⋊C16—32no—
69C22⋊C16—92no—
70#346—91no—
71C4×C16—91no—
72C2×C4×D3—32no—
73C2×C4×D3—61no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C2×C3×C8C4×D312yes—
77C2×C3×C8C22×D312yes—
78C3×C42—21no—
79C3×C42C4×D312yes—
80(C2×D3)⋊C4—32no—
81(C2×D3)⋊C4—32no—
82(C2×D3)⋊C4—62no—
83Dic3⋊C4—32no—
84Dic3⋊C4—32no—
85Dic3⋊C4—62no—
86C4×Dic3—32no—
87C4×Dic3—61no—
88C2×C3⋊C8—32no—
89C2×C3⋊C8—32no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92ΓL(1,𝔽25)—64no—
93ΓL(1,𝔽25)—64no—
94D3×C8—64no—
95D3×C8—62no—
96D3×C8—62no—
97C3×C16—62no—
98C3×C16—62no—
99C3⋊C16—22no—
100C3⋊C16—22no—
101C22×C32C22×C811yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—22no—
104C32×C4—22no—
105C32×C4#11711yescharacteristic
106C32×C4C2×M1611yescharacteristic
107C3⋊Dic3—21no—
108C3⋊Dic3—22no—
109C2×M16—91no—
110C22×C8—91no—
111#117—91no—
112C2×C16—32no—
113C2×C16—32no—
114#97—91no—
115#97—91no—
116C4×C8—91no—
117C4×C8D3211yescharacteristic
118C22×D3—32no—
119C22×D3—61no—
120C2×C3×C4—22no—
121C2×C3×C4—21no—
122C2×C3×C4D3×C812yes—
123C2×C3×C4D3×C812yes—
124C2×C3×C4C2×C4×D312yes—
125C2×Dic3—32no—
126C2×Dic3—32no—
127C2×Dic3—32no—
128C2×Dic3—61no—
129C2×Dic3—62no—
130C4×D3—62no—
131C4×D3—62no—
132C4×D3—62no—
133C4×D3—62no—
134C3×C8—22no—
135C3×C8—22no—
136C3×C8—22no—
137C3×C8#23712yes—
138C3×C8#23912yes—
139C3⋊C8—34no—
140C3⋊C8—62no—
141C3⋊C8—62no—
142C3⋊C8—62no—
143C2×C32#43111yescharacteristic
144C2×C32#50412yes—
145C3⋊D3—41no—
146C22×C4—91no—
147M16—182no—
148C2×C8—91no—
149C2×C8—91no—
150C2×C8—182no—
151C2×C8#62411yescharacteristic
152C2×C8C2×D3211yescharacteristic
153C4⋊C4—92no—
154C22⋊C4—92no—
155C42—91no—
156C42#62411yescharacteristic
157C16—62no—
158C16—62no—
159C22×C3—21no—
160C22×C3C2×D3×C812yes—
161C2×D3—62no—
162C2×D3—62no—
163C2×D3—62no—
164C2×D3—62no—
165C2×D3—122no—
166C3×C4—22no—
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—42no—
171C3×C4#89212yes—
172C3×C4D3×M1612yes—
173Dic3—62no—
174Dic3—62no—
175Dic3—62no—
176Dic3—62no—
177Dic3—122no—
178C32#216411yescharacteristic, complemented, Sylow
179C23—91no—
180C2×C4—92no—
181C2×C4—91no—
182C2×C4—181no—
183C2×C4—181no—
184C2×C4#371012yes—
185C2×C4C2×#62411yescharacteristic
186C8—21no—
187C8—92no—
188C8—181no—
189C8#379612yes—
190C2×C3—21no—
191C2×C3—22no—
192C2×C3#483312yes—
193C2×C3#490112yes—
194C2×C3#490712yes—
195D3—122no—
196D3—122no—
197C22—181no—
198C22—182no—
199C22C2×#371011yescharacteristic
200C4—22no—
201C4—181no—
202C4—182no—
203C4#6381811yescharacteristic
204C4#6384911yescharacteristic
205C3—21no—
206C3#6927612yescomplemented
207C2—361no—
208C2#1059025611yescharacteristic
209C2#1059062412yes—
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC32×C4×C8C22
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C32×C8C23
hypercenterC4×C8D32
hypocenterC32#2164
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×C4⋊(C3⋊C16)C2semidirect
4. #10589104C2semidirect
5. #10589102C2semidirect
23. C4⋊(C3⋊C16)D3semidirect
178. C32#2164semidirect
206. C3#69276semidirect

Maximal subgroups

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

subgroupindex
#105923882
C3×C4⋊(C3⋊C16)2
#105891082
#105891042
#105891022
#692763