Finite Group Databasebeta

← C2×#10593274 #11796039

Subgroups — C2×#10593274 #11796039

Order 1152.

354 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C22×#3792C211yesmaximal, characteristic
2C2×#64218C212yesmaximal, complemented
3#10593274C214yesmaximal, direct product factor
4C23×C3⋊Dic3C411yescharacteristic
5C2×#3792—22no—
6C2×#3792—22no—
7C2×#3792C412yes—
8C2×#3792C2212yes—
9C22×#622C411yescharacteristic
10C22×#622C2211yescharacteristic
11#64218—22no—
12#64218C2214yescomplemented
13C2×#3771—22no—
14C24×C32C811yescharacteristic
15C22×C3⋊Dic3—21no—
16C22×C3⋊Dic3—21no—
17C22×C3⋊Dic3—21no—
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3C811yescharacteristic
20C22×C3⋊Dic3C812yes—
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2×C411yescharacteristic
23#3792—24no—
24#3792—24no—
25C2×#622—21no—
26C2×#622—21no—
27C2×#622C2×C412yes—
28C2×#622C2×C411yescharacteristic
29C2×#622D412yes—
30C2×#622D412yes—
31C2×#622C2311yescharacteristic
32#3771—24no—
33C2×#349—91nomaximal, Sylow
34C23×Dic3—121no—
35C23×C32—21no—
36C23×C32—21no—
37C23×C32—42no—
38C23×C32C2×C811yescharacteristic
39C23×C32C2×C812yes—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—22no—
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3C22⋊C411yescharacteristic
47C2×C3⋊Dic3C22⋊C411yescharacteristic
48C2×C3⋊Dic3C2×C812yes—
49C2×C3⋊Dic3C2×C811yescharacteristic
50C2×C3⋊Dic3M1611yescharacteristic
51C2×C3⋊Dic3M1611yescharacteristic
52C2×C3⋊Dic3C22×C411yescharacteristic
53#622—22no—
54#622C22⋊C412yes—
55#622C2×D412yes—
56C22×M16—91no—
57C2×M32—92no—
58#349—94no—
59C24×C3—41no—
60C22×Dic3—122no—
61C22×Dic3—121no—
62C22×Dic3—121no—
63C22×Dic3—122no—
64C22×Dic3—122no—
65C22×Dic3—122no—
66C22×Dic3—122no—
67C22×Dic3—122no—
68C22×C32—22no—
69C22×C32—22no—
70C22×C32—42no—
71C22×C32—42no—
72C22×C32—42no—
73C22×C32C22⋊C811yescharacteristic
74C22×C32C22⋊C811yescharacteristic
75C22×C32C22×C811yescharacteristic
76C3⋊Dic3—22no—
77C3⋊Dic3C22⋊C811yescharacteristic
78C3⋊Dic3C22⋊C811yescharacteristic
79C3⋊Dic3C2×C22⋊C411yescharacteristic
80C3⋊Dic3C2×M1611yescharacteristic
81C23×C4—91no—
82C2×M16—92no—
83C2×M16—92no—
84C2×M16—182no—
85C2×M16—182no—
86C22×C8—91no—
87C22×C8—91no—
88M32—94no—
89M32—182no—
90C2×C16—182no—
91C23×C3—42no—
92C23×C3—42no—
93C23×C3—48no—
94C23×C3—42no—
95C23×C3—41no—
96C2×Dic3—121no—
97C2×Dic3—121no—
98C2×Dic3—121no—
99C2×Dic3—122no—
100C2×Dic3—121no—
101C2×Dic3—121no—
102C2×Dic3—121no—
103C2×Dic3—124no—
104C2×Dic3—124no—
105C2×Dic3—124no—
106C2×Dic3—124no—
107C2×Dic3—122no—
108C2×Dic3—122no—
109C2×C32—21no—
110C2×C32—21no—
111C2×C32—42no—
112C2×C32#34912yescomplemented
113C2×C32C2×C22⋊C811yescharacteristic
114C24AGL(1,𝔽9)11yescharacteristic
115C22×C4—91no—
116C22×C4—92no—
117C22×C4—92no—
118C22×C4—91no—
119C22×C4—181no—
120C22×C4—181no—
121C22×C4—181no—
122C22×C4—181no—
123M16—184no—
124M16—184no—
125C2×C8—92no—
126C2×C8—91no—
127C2×C8—92no—
128C2×C8—91no—
129C2×C8—92no—
130C2×C8—181no—
131C2×C8—181no—
132C16—184no—
133C22×C3—44no—
134C22×C3—44no—
135C22×C3—48no—
136C22×C3—48no—
137C22×C3—48no—
138C22×C3—41no—
139C22×C3—41no—
140C22×C3—41no—
141Dic3—121no—
142Dic3—121no—
143Dic3—121no—
144Dic3—121no—
145Dic3—124no—
146C32C2×#34911yescharacteristic, complemented, Sylow
147C23—21no—
148C23—21no—
149C23—42no—
150C23C2×AGL(1,𝔽9)12yes—
151C23C2×AGL(1,𝔽9)11yescharacteristic
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—92no—
159C2×C4—182no—
160C2×C4—182no—
161C2×C4—182no—
162C2×C4—182no—
163C2×C4—181no—
164C2×C4—181no—
165C8—92no—
166C8—92no—
167C8—182no—
168C2×C3—42no—
169C2×C3—42no—
170C2×C3—48no—
171C2×C3—41no—
172C2×C3—42no—
173C22—22no—
174C22—22no—
175C22—42no—
176C22—42no—
177C22—42no—
178C22C22⋊AGL(1,𝔽9)11yescharacteristic
179C22C22⋊AGL(1,𝔽9)11yescharacteristic
180C22C22×AGL(1,𝔽9)11yescharacteristic
181C4—91no—
182C4—91no—
183C4—91no—
184C4—91no—
185C4—182no—
186C3—41no—
187C2—21no—
188C2—21no—
189C2—42no—
190C2#1059327412yesdirect product factor
191C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC22C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
Fitting, prime radicalC24×C32C8
socleC22×C32C22⋊C8
cosocleC2×#622C23
hypercenterC24AGL(1,𝔽9)
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#64218C2semidirect
3. #10593274C2direct (N × H)
12. #64218C22semidirect
112. C2×C32#349semidirect
146. C32C2×#349semidirect
190. C2#10593274direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#642182
#105932742
C2×#3499