Finite Group Databasebeta

← C2×#10593396 #11858409

Subgroups — C2×#10593396 #11858409

Order 1152.

1018 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 247 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×#3787C211yesmaximal, characteristic
2C2×#63900C212yesmaximal
3C2×#63743C214yesmaximal, complemented
4#10593396C218yesmaximal, direct product factor
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—22no—
7C22×#622C2212yes—
8C2×#3787C418yescomplemented
9C2×#3787C2214yes—
10C2×C3×C4⋊Dic3—22no—
11C2×#3724C2214yes—
12#63900—24no—
13#63900C2218yes—
14#63743C22116yescomplemented
15C2×D3×C4⋊C4—62no—
16C23×C3⋊D3D411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2311yescharacteristic
19C2×C4×C3⋊D3C2×C414yes—
20C2×C4×C3⋊D3D412yes—
21C2×C4×C3⋊D3Q814yes—
22C2×C4×C3⋊D3C2312yes—
23C22×C3×Dic3—24no—
24C2×#624—28no—
25C2×#624—48no—
26C2×#622C2×C418yescomplemented
27C2×#622C2314yes—
28#3787C2×C4116yescomplemented
29C3×C4⋊Dic3—28no—
30#3724—24no—
31#3724C2318yes—
32C22×#107—91nomaximal, Sylow
33C22×C4×D3—62no—
34C22×C4×D3—64no—
35C2×C3×C4⋊C4—62no—
36C2×C4⋊Dic3—22no—
37C2×Dic3⋊C4—64no—
38D3×C4⋊C4—68no—
39D3×C4⋊C4—68no—
40C23×C32C2×D411yescharacteristic
41C22×C3⋊D3C4⋊C414yes—
42C22×C3⋊D3D814yes—
43C22×C3⋊D3Q1614yes—
44C22×C3⋊D3C2×D412yes—
45C2×C32×C4C4⋊C414yes—
46C2×C32×C4C2×D412yes—
47C2×C3⋊Dic3C22×C412yes—
48C2×C3⋊Dic3C2×D411yescharacteristic
49C2×C3⋊Dic3C2×Q812yes—
50C2×C3⋊Dic3C2411yescharacteristic
51C4×C3⋊D3C4⋊C418yes—
52C4×C3⋊D3C22×C414yes—
53C4×C3⋊D3C2×Q814yes—
54C2×C3×Dic3—28no—
55C2×C3×Dic3—48no—
56#624—416no—
57#622C22×C418yescomplemented
58C23×C8—91no—
59C22×C4⋊C4—92no—
60C2×#107—98no—
61C2×#107—94no—
62C23×D3—62no—
63C22×C3×C4—22no—
64C22×C3×C4—64no—
65C22×Dic3—24no—
66C22×Dic3—62no—
67C2×C4×D3—64no—
68C2×C4×D3—64no—
69C2×C4×D3—68no—
70C2×C4×D3—68no—
71C2×C4×D3—616no—
72C2×C4×D3—1216no—
73C3×C4⋊C4—68no—
74C4⋊Dic3—28no—
75Dic3⋊C4—68no—
76Dic3⋊C4—68no—
77C22×C32C2×C4⋊C412yes—
78C22×C32C2×D812yes—
79C22×C32C2×Q1612yes—
80C22×C32C22×D411yescharacteristic
81C2×C3⋊D3#107116yescomplemented
82C2×C3⋊D3C2×C4⋊C414yes—
83C2×C3⋊D3C2×D814yes—
84C2×C3⋊D3C2×Q1614yes—
85C32×C4C2×C4⋊C414yes—
86C3⋊Dic3C2×C4⋊C412yes—
87C3⋊Dic3C23×C411yescharacteristic
88C3⋊Dic3C22×Q811yescharacteristic
89C3×Dic3—48no—
90C23×C4—91no—
91C23×C4—182no—
92C22×C8—98no—
93C22×C8—94no—
94C22×C8—92no—
95C2×C4⋊C4—62no—
96C2×C4⋊C4—98no—
97C2×C4⋊C4—94no—
98C2×C4⋊C4—184no—
99#107—916no—
100C23×C3—22no—
101C22×D3—68no—
102C22×D3—68no—
103C22×D3—68no—
104C22×D3—64no—
105C2×C3×C4—24no—
106C2×C3×C4—28no—
107C2×C3×C4—68no—
108C2×C3×C4—128no—
109C2×Dic3—28no—
110C2×Dic3—48no—
111C2×Dic3—64no—
112C2×Dic3—62no—
113C2×Dic3—64no—
114C2×Dic3—62no—
115C4×D3—616no—
116C4×D3—68no—
117C4×D3—68no—
118C4×D3—1232no—
119C2×C32C2×#10714yescomplemented
120C2×C32C22×C4⋊C411yescharacteristic
121C2×C32C22×D811yescharacteristic
122C2×C32C22×Q1611yescharacteristic
123C3⋊D3C2×#10718yescomplemented
124C24—91no—
125C22×C4—64no—
126C22×C4—91no—
127C22×C4—92no—
128C22×C4—92no—
129C22×C4—94no—
130C22×C4—94no—
131C22×C4—188no—
132C22×C4—368no—
133C22×C4GO+(4,𝔽2)11yescharacteristic
134C2×C8—94no—
135C2×C8—916no—
136C2×C8—98no—
137C4⋊C4—68no—
138C4⋊C4—98no—
139C4⋊C4—184no—
140C22×C3—22no—
141C22×C3—24no—
142C22×C3—24no—
143C22×C3—24no—
144C2×D3—68no—
145C2×D3—68no—
146C2×D3—632no—
147C2×D3—68no—
148C3×C4—28no—
149C3×C4—128no—
150Dic3—48no—
151Dic3—64no—
152Dic3—62no—
153Dic3—62no—
154C32C22×#10711yescharacteristic, complemented, Sylow
155C23—92no—
156C23—94no—
157C23—94no—
158C23—94no—
159C23C2×GO+(4,𝔽2)11yescharacteristic
160C2×C4—68no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—92no—
164C2×C4—92no—
165C2×C4—94no—
166C2×C4—94no—
167C2×C4—98no—
168C2×C4—128no—
169C2×C4—3616no—
170C2×C4#377314yes—
171C2×C4C2×GO+(4,𝔽2)12yes—
172C8—98no—
173C2×C3—28no—
174C2×C3—22no—
175C2×C3—22no—
176C2×C3—22no—
177D3—616no—
178C22—916no—
179C22—94no—
180C22—94no—
181C22—94no—
182C22#6422512yes—
183C22#6422812yes—
184C22C2×#377312yes—
185C22C22×GO+(4,𝔽2)11yescharacteristic
186C4—91no—
187C4—91no—
188C4—92no—
189C4—128no—
190C4C2×#377314yes—
191C3—22no—
192C2—98no—
193C2#1059339614yesdirect product factor
194C2C2×#6422511yescharacteristic
195C2C2×#6422811yescharacteristic
196C2C22×#377311yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×#107
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63743C2semidirect
4. #10593396C2direct (N × H)
8. C2×#3787C4semidirect
14. #63743C22semidirect
26. C2×#622C2×C4semidirect
28. #3787C2×C4semidirect
57. #622C22×C4semidirect
81. C2×C3⋊D3#107semidirect
119. C2×C32C2×#107semidirect
123. C3⋊D3C2×#107semidirect
154. C32C22×#107semidirect
193. C2#10593396direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#639002
C2×#637432
#105933962
C22×#1079