Finite Group Databasebeta

← C2×#10590180 #11796031

Subgroups — C2×#10590180 #11796031

Order 1152.

534 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3743C211yesmaximal, characteristic
2C2×#63773C212yesmaximal, complemented
3#10590180C214yesmaximal, direct product factor
4C22×C4×C3⋊D3C411yescharacteristic
5C22×C32×C8C411yescharacteristic
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C2×#3743—22no—
8C2×#3743—22no—
9C2×#3743C412yes—
10C2×#3743C2212yes—
11#63773—22no—
12#63773C2214yescomplemented
13C2×#3708—22no—
14C22×ΓL(1,𝔽25)—62no—
15C23×C3⋊D3C811yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C3⋊Dic3C811yescharacteristic
18C2×C4×C3⋊D3—21no—
19C2×C4×C3⋊D3—21no—
20C2×C4×C3⋊D3—21no—
21C2×C4×C3⋊D3—21no—
22C2×C4×C3⋊D3C812yes—
23C2×C4×C3⋊D3C2×C412yes—
24C2×C32×C8—21no—
25C2×C32×C8—21no—
26C2×C32×C8C2×C412yes—
27C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)D412yes—
29C2×C3⋊(C3⋊C8)D412yes—
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31#3743—24no—
32#3743—24no—
33#3708—24no—
34C2×#349—91nomaximal, Sylow
35C22×C4×D3—62no—
36C22×C3×C8—22no—
37C22×C3⋊C8—62no—
38C2×ΓL(1,𝔽25)—64no—
39C2×ΓL(1,𝔽25)—64no—
40C2×ΓL(1,𝔽25)—68no—
41C2×ΓL(1,𝔽25)—68no—
42C23×C32C2×C811yescharacteristic
43C22×C3⋊D3—21no—
44C22×C3⋊D3—21no—
45C22×C3⋊D3—42no—
46C22×C3⋊D3C2×C812yes—
47C2×C32×C4C22⋊C411yescharacteristic
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C2×C811yescharacteristic
50C2×C32×C4M1611yescharacteristic
51C2×C32×C4M1611yescharacteristic
52C2×C32×C4C22×C411yescharacteristic
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3C2×C812yes—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58C4×C3⋊D3—22no—
59C4×C3⋊D3—22no—
60C32×C8—22no—
61C3⋊(C3⋊C8)C22⋊C412yes—
62C3⋊(C3⋊C8)C2×D412yes—
63C22×M16—91no—
64C2×M32—92no—
65#349—94no—
66C23×D3—62no—
67C22×C3×C4—22no—
68C22×Dic3—62no—
69C2×C4×D3—64no—
70C2×C4×D3—64no—
71C2×C4×D3—64no—
72C2×C4×D3—64no—
73C2×C4×D3—64no—
74C2×C4×D3—64no—
75C2×C3×C8—24no—
76C2×C3×C8—24no—
77C2×C3×C8—24no—
78C2×C3⋊C8—62no—
79C2×C3⋊C8—64no—
80C2×C3⋊C8—64no—
81C2×C3⋊C8—62no—
82ΓL(1,𝔽25)—616no—
83ΓL(1,𝔽25)—616no—
84C22×C32—22no—
85C22×C32C22⋊C811yescharacteristic
86C22×C32C22⋊C811yescharacteristic
87C22×C32C22×C811yescharacteristic
88C2×C3⋊D3—22no—
89C2×C3⋊D3—42no—
90C2×C3⋊D3—42no—
91C2×C3⋊D3—42no—
92C32×C4C22⋊C811yescharacteristic
93C32×C4C22⋊C811yescharacteristic
94C32×C4C2×C22⋊C411yescharacteristic
95C32×C4C2×M1611yescharacteristic
96C3⋊Dic3—22no—
97C23×C4—91no—
98C2×M16—92no—
99C2×M16—92no—
100C2×M16—182no—
101C2×M16—182no—
102C22×C8—91no—
103C22×C8#15711yescharacteristic
104M32—94no—
105M32—182no—
106C2×C16—182no—
107C23×C3—22no—
108C22×D3—64no—
109C22×D3—64no—
110C22×D3—64no—
111C22×D3—128no—
112C2×C3×C4—22no—
113C2×C3×C4—22no—
114C2×C3×C4—22no—
115C2×C3×C4—22no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—64no—
121C4×D3—68no—
122C4×D3—68no—
123C4×D3—68no—
124C4×D3—68no—
125C3×C8—28no—
126C3⋊C8—64no—
127C3⋊C8—64no—
128C2×C32—21no—
129C2×C32—21no—
130C2×C32#34912yescomplemented
131C2×C32C2×C22⋊C811yescharacteristic
132C3⋊D3—42no—
133C24—91no—
134C22×C4—91no—
135C22×C4—92no—
136C22×C4—92no—
137C22×C4—181no—
138C22×C4—181no—
139C22×C4—181no—
140C22×C4—181no—
141C22×C4C2×#15711yescharacteristic
142M16—184no—
143M16—184no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—91no—
147C2×C8—91no—
148C2×C8—92no—
149C2×C8—92no—
150C2×C8C2×#15712yes—
151C16—184no—
152C22×C3—28no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—22no—
156C2×D3—68no—
157C2×D3—128no—
158C2×D3—128no—
159C2×D3—128no—
160C3×C4—22no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—22no—
164Dic3—68no—
165C32C2×#34911yescharacteristic, complemented, Sylow
166C23—92no—
167C23—181no—
168C23—181no—
169C23—362no—
170C23#378711yescharacteristic
171C2×C4—92no—
172C2×C4—181no—
173C2×C4—181no—
174C2×C4—182no—
175C2×C4—182no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4#378711yescharacteristic
179C2×C4#378811yescharacteristic
180C2×C4#378811yescharacteristic
181C2×C4C22⋊#15711yescharacteristic
182C2×C4C22⋊#15711yescharacteristic
183C2×C4C22×#15711yescharacteristic
184C8—22no—
185C8—92no—
186C8—92no—
187C2×C3—24no—
188C2×C3—24no—
189C2×C3—22no—
190C2×C3—24no—
191D3—128no—
192C22—22no—
193C22—182no—
194C22—362no—
195C22—362no—
196C22—362no—
197C22#6377811yescharacteristic
198C22#6377811yescharacteristic
199C22C2×#378711yescharacteristic
200C4—182no—
201C4#6377811yescharacteristic
202C4#6377811yescharacteristic
203C4C2×#378811yescharacteristic
204C4C2×C22⋊#15711yescharacteristic
205C3—22no—
206C2—21no—
207C2—21no—
208C2—362no—
209C2#1059018012yesdirect product factor
210C2C2×#6377811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C22×C8
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C22⋊C8
prime radicalC23×C3⋊D3C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C8#157
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. #10590180C2direct (N × H)
12. #63773C22semidirect
130. C2×C32#349semidirect
165. C32C2×#349semidirect
209. C2#10590180direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#637732
#105901802
C2×#3499