Finite Group Databasebeta

← C2×#10590201 #11796030

Subgroups — C2×#10590201 #11796030

Order 1152.

534 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3748C211yesmaximal, characteristic
2C2×#63773C212yesmaximal, complemented
3#10590201C214yesmaximal, direct product factor
4C23×C32×C4C411yescharacteristic
5C2×#3748—22no—
6C2×#3748—22no—
7C2×#3748C412yes—
8C2×#3748C2212yes—
9C22×C3⋊(C3⋊C8)C411yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11#63773—22no—
12#63773C2214yescomplemented
13C2×#3708—22no—
14C22×#208—62no—
15C24×C32C811yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—21no—
19C22×C32×C4—21no—
20C22×C32×C4C811yescharacteristic
21C22×C32×C4C812yes—
22C22×C32×C4C2×C412yes—
23C22×C32×C4C2×C411yescharacteristic
24#3748—24no—
25#3748—24no—
26C2×C3⋊(C3⋊C8)—21no—
27C2×C3⋊(C3⋊C8)—21no—
28C2×C3⋊(C3⋊C8)C2×C412yes—
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)D412yes—
31C2×C3⋊(C3⋊C8)D412yes—
32C2×C3⋊(C3⋊C8)C2311yescharacteristic
33#3708—24no—
34C2×#349—91nomaximal, Sylow
35C23×C3×C4—22no—
36C2×#208—64no—
37C2×#208—64no—
38C2×#208—68no—
39C2×#208—68no—
40C22×C3⋊C8—62no—
41C22×C3⋊C8—62no—
42C23×C32—21no—
43C23×C32—21no—
44C23×C32—42no—
45C23×C32C2×C811yescharacteristic
46C23×C32C2×C812yes—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4—22no—
50C2×C32×C4—22no—
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4C22⋊C411yescharacteristic
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C2×C812yes—
56C2×C32×C4C2×C811yescharacteristic
57C2×C32×C4M1611yescharacteristic
58C2×C32×C4M1611yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C3⋊(C3⋊C8)—22no—
61C3⋊(C3⋊C8)C22⋊C412yes—
62C3⋊(C3⋊C8)C2×D412yes—
63C22×M16—91no—
64C2×M32—92no—
65#349—94no—
66C24×C3—22no—
67C22×C3×C4—24no—
68C22×C3×C4—24no—
69C22×C3×C4—24no—
70C22×C3×C4—24no—
71C22×C3×C4—22no—
72C22×C3×C4—24no—
73C22×C3×C4—24no—
74C22×C3×C4—22no—
75#208—616no—
76#208—616no—
77C2×C3⋊C8—62no—
78C2×C3⋊C8—64no—
79C2×C3⋊C8—64no—
80C2×C3⋊C8—64no—
81C2×C3⋊C8—62no—
82C2×C3⋊C8—64no—
83C2×C3⋊C8—64no—
84C22×C32—22no—
85C22×C32—22no—
86C22×C32—42no—
87C22×C32—42no—
88C22×C32—42no—
89C22×C32C22⋊C811yescharacteristic
90C22×C32C22⋊C811yescharacteristic
91C22×C32C22×C811yescharacteristic
92C32×C4—22no—
93C32×C4C22⋊C811yescharacteristic
94C32×C4C22⋊C811yescharacteristic
95C32×C4C2×C22⋊C411yescharacteristic
96C32×C4C2×M1611yescharacteristic
97C23×C4#15711yescharacteristic
98C2×M16—92no—
99C2×M16—92no—
100C2×M16—182no—
101C2×M16—182no—
102C22×C8—91no—
103C22×C8—91no—
104M32—94no—
105M32—182no—
106C2×C16—182no—
107C23×C3—24no—
108C23×C3—24no—
109C23×C3—22no—
110C23×C3—24no—
111C23×C3—48no—
112C2×C3×C4—28no—
113C2×C3×C4—24no—
114C2×C3×C4—24no—
115C2×C3×C4—28no—
116C2×C3×C4—28no—
117C2×C3×C4—28no—
118C2×C3×C4—22no—
119C2×C3×C4—24no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C3⋊C8—64no—
126C3⋊C8—64no—
127C3⋊C8—68no—
128C2×C32—21no—
129C2×C32—21no—
130C2×C32—42no—
131C2×C32#34912yescomplemented
132C2×C32C2×C22⋊C811yescharacteristic
133C24#62211yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4#62211yescharacteristic
139C22×C4#62212yes—
140C22×C4C2×#15712yes—
141C22×C4C2×#15711yescharacteristic
142M16—184no—
143M16—184no—
144C2×C8—91no—
145C2×C8—91no—
146C2×C8—92no—
147C2×C8—92no—
148C2×C8—92no—
149C2×C8—181no—
150C2×C8—181no—
151C16—184no—
152C22×C3—28no—
153C22×C3—28no—
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—22no—
157C22×C3—48no—
158C22×C3—48no—
159C22×C3—48no—
160C3×C4—28no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—22no—
164C3×C4—22no—
165C32C2×#34911yescharacteristic, complemented, Sylow
166C23—21no—
167C23—21no—
168C23—42no—
169C23C2×#62211yescharacteristic
170C23C2×#62212yes—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4C2×#62212yes—
178C2×C4C2×#62211yescharacteristic
179C2×C4#379211yescharacteristic
180C2×C4#379211yescharacteristic
181C2×C4C22⋊#15711yescharacteristic
182C2×C4C22⋊#15711yescharacteristic
183C2×C4C22×#15711yescharacteristic
184C8—92no—
185C8—92no—
186C8—182no—
187C2×C3—24no—
188C2×C3—24no—
189C2×C3—22no—
190C2×C3—24no—
191C2×C3—48no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C22⋊#62211yescharacteristic
198C22C22⋊#62211yescharacteristic
199C22C22×#62211yescharacteristic
200C4—22no—
201C4C22⋊#62211yescharacteristic
202C4C22⋊#62211yescharacteristic
203C4C2×#379211yescharacteristic
204C4C2×C22⋊#15711yescharacteristic
205C3—22no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2#1059020112yesdirect product factor
210C2C2×C22⋊#62211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C22×C8
FrattiniC2×C4C22×#157
FittingC23×C32×C4C4
socleC22×C32C22⋊C8
prime radicalC24×C32C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC23×C4#157
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. #10590201C2direct (N × H)
12. #63773C22semidirect
131. C2×C32#349semidirect
165. C32C2×#349semidirect
209. C2#10590201direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37482
C2×#637732
#105902012
C2×#3499