Finite Group Databasebeta

← C2×#10590067 #11797108

Subgroups — C2×#10590067 #11797108

Order 1152.

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

normal subgroups only

This group has 270 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
1C2×#63773C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3C2×#63574C211yesmaximal, characteristic
4#10590067C214yesmaximal, direct product factor
5C22×C3⋊(C3⋊C8)C2211yescharacteristic
6C2×C3×C4⋊Dic3—21no—
7C2×C3×#208—21no—
8#63773C412yescomplemented
9#63773C2212yes—
10C2×#3708C412yescomplemented
11#63578—21no—
12#63578C2212yes—
13#63574—21no—
14#63574C2212yes—
15C2×#822—61no—
16C2×#808—61no—
17C22×C32×C4D411yescharacteristic
18C22×C3×Dic3—41no—
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)Q811yescharacteristic
23C2×C3⋊(C3⋊C8)Q811yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×C4⋊Dic3—22no—
26C3×C4⋊Dic3—41no—
27C3×#208—22no—
28C3×#208—41no—
29C2×C3×C3⋊C8—41no—
30#3708C2×C414yescomplemented
31C2×#365—91nomaximal, Sylow
32C2×C3×M16—61no—
33C2×C3×C4⋊C4—61no—
34C2×C4⋊Dic3—21no—
35C2×#208—21no—
36C22×C3⋊C8—61no—
37C22×C3⋊C8—61no—
38#822—62no—
39#822—62no—
40#808—62no—
41#808—62no—
42C23×C32SD1611yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4SD1611yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4SD1611yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C2×C3×Dic3—42no—
50C2×C3×Dic3—82no—
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C3⋊(C3⋊C8)C22×C411yescharacteristic
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3×C3⋊C8—42no—
56C2×M32—91no—
57C2×#108—91no—
58C2×#106—91no—
59#365—94no—
60C22×C3×C4—21no—
61C22×C3×C4—21no—
62C22×C3×C4—121no—
63C22×Dic3—41no—
64C3×M16—62no—
65C3×M16—121no—
66C2×C3×C8—121no—
67C3×C4⋊C4—62no—
68C3×C4⋊C4—121no—
69C4⋊Dic3—22no—
70C4⋊Dic3—41no—
71#208—22no—
72#208—41no—
73C2×C3⋊C8—41no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85C2×C3⋊C8—61no—
86C22×C32—22no—
87C22×C32#10611yescharacteristic
88C22×C32#10611yescharacteristic
89C22×C32C2×SD1611yescharacteristic
90C32×C4#10611yescharacteristic
91C32×C4#10611yescharacteristic
92C32×C4C2×C4⋊C411yescharacteristic
93C32×C4C2×SD1611yescharacteristic
94C3×Dic3—82no—
95C2×M16—61no—
96C22×C8—91no—
97C2×C4⋊C4—61no—
98M32—92no—
99M32—92no—
100C2×C16—92no—
101#108—92no—
102#108—181no—
103#106—92no—
104#106—181no—
105C23×C3—21no—
106C23×C3—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—122no—
120C2×C3×C4—242no—
121C2×Dic3—42no—
122C2×Dic3—82no—
123C3×C8—122no—
124C3⋊C8—42no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C3⋊C8—61no—
132C3⋊C8—61no—
133C2×C32—21no—
134C2×C32—21no—
135C2×C32#36512yescomplemented
136C2×C32C2×#10611yescharacteristic
137C22×C4—121no—
138C22×C4GO+(4,𝔽2)11yescharacteristic
139M16—62no—
140M16—121no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—91no—
146C2×C8—91no—
147C2×C8—121no—
148C4⋊C4—62no—
149C4⋊C4—121no—
150C16—94no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—21no—
159C22×C3—42no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—21no—
168C3×C4—242no—
169Dic3—82no—
170C32C2×#36511yescharacteristic, complemented, Sylow
171C23#377511yescharacteristic
172C2×C4—122no—
173C2×C4—242no—
174C2×C4#377311yescharacteristic
175C2×C4#377311yescharacteristic
176C2×C4#377511yescharacteristic
177C2×C4#377511yescharacteristic
178C2×C4#377511yescharacteristic
179C2×C4C2×GO+(4,𝔽2)11yescharacteristic
180C8—91no—
181C8—91no—
182C8—91no—
183C8—91no—
184C8—122no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—22no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—41no—
193C2×C3—41no—
194C22—22no—
195C22#6374211yescharacteristic
196C22#6374211yescharacteristic
197C22C2×#377511yescharacteristic
198C4—242no—
199C4#6374211yescharacteristic
200C4#6374211yescharacteristic
201C4C2×#377311yescharacteristic
202C4C2×#377511yescharacteristic
203C3—21no—
204C3—21no—
205C2—21no—
206C2—21no—
207C2#1059006712yesdirect product factor
208C2C2×#6374211yescharacteristic
subgroupG/H
centerC22#63742
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#106
prime radicalC23×C32SD16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#365
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590067C2direct (N × H)
8. #63773C4semidirect
10. C2×#3708C4semidirect
30. #3708C2×C4semidirect
135. C2×C32#365semidirect
170. C32C2×#365semidirect
207. C2#10590067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#637732
C2×#635782
C2×#635742
#105900672
C2×#3659