Finite Group Databasebeta

← C2×#10593387 #11858388

Subgroups — C2×#10593387 #11858388

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×#63742C214yesmaximal, complemented
4#10593387C218yesmaximal, 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#63742C22116yescomplemented
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×#106—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⋊D3SD1618yes—
43C22×C3⋊D3C2×D412yes—
44C2×C32×C4C4⋊C414yes—
45C2×C32×C4C2×D412yes—
46C2×C3⋊Dic3C22×C412yes—
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3C2×Q812yes—
49C2×C3⋊Dic3C2411yescharacteristic
50C4×C3⋊D3C4⋊C418yes—
51C4×C3⋊D3C22×C414yes—
52C4×C3⋊D3C2×Q814yes—
53C2×C3×Dic3—28no—
54C2×C3×Dic3—48no—
55#624—416no—
56#622C22×C418yescomplemented
57C23×C8—91no—
58C22×C4⋊C4—92no—
59C2×#106—98no—
60C2×#106—94no—
61C23×D3—62no—
62C22×C3×C4—22no—
63C22×C3×C4—64no—
64C22×Dic3—24no—
65C22×Dic3—62no—
66C2×C4×D3—64no—
67C2×C4×D3—64no—
68C2×C4×D3—68no—
69C2×C4×D3—68no—
70C2×C4×D3—616no—
71C2×C4×D3—1216no—
72C3×C4⋊C4—68no—
73C4⋊Dic3—28no—
74Dic3⋊C4—68no—
75Dic3⋊C4—68no—
76C22×C32C2×C4⋊C412yes—
77C22×C32C2×SD1614yes—
78C22×C32C22×D411yescharacteristic
79C2×C3⋊D3#106116yescomplemented
80C2×C3⋊D3C2×C4⋊C414yes—
81C2×C3⋊D3C2×SD1618yes—
82C32×C4C2×C4⋊C414yes—
83C3⋊Dic3C2×C4⋊C412yes—
84C3⋊Dic3C23×C411yescharacteristic
85C3⋊Dic3C22×Q811yescharacteristic
86C3×Dic3—48no—
87C23×C4—91no—
88C23×C4—182no—
89C22×C8—98no—
90C22×C8—94no—
91C22×C8—92no—
92C2×C4⋊C4—62no—
93C2×C4⋊C4—98no—
94C2×C4⋊C4—94no—
95C2×C4⋊C4—184no—
96#106—916no—
97C23×C3—22no—
98C22×D3—68no—
99C22×D3—68no—
100C22×D3—68no—
101C22×D3—64no—
102C2×C3×C4—24no—
103C2×C3×C4—28no—
104C2×C3×C4—68no—
105C2×C3×C4—128no—
106C2×Dic3—28no—
107C2×Dic3—48no—
108C2×Dic3—64no—
109C2×Dic3—62no—
110C2×Dic3—64no—
111C2×Dic3—62no—
112C4×D3—616no—
113C4×D3—68no—
114C4×D3—68no—
115C4×D3—1232no—
116C2×C32C2×#10614yescomplemented
117C2×C32C22×C4⋊C411yescharacteristic
118C2×C32C22×SD1612yes—
119C3⋊D3C2×#10618yescomplemented
120C24—91no—
121C22×C4—64no—
122C22×C4—91no—
123C22×C4—92no—
124C22×C4—92no—
125C22×C4—94no—
126C22×C4—94no—
127C22×C4—188no—
128C22×C4—368no—
129C22×C4GO+(4,𝔽2)11yescharacteristic
130C2×C8—94no—
131C2×C8—916no—
132C2×C8—98no—
133C4⋊C4—68no—
134C4⋊C4—98no—
135C4⋊C4—184no—
136C22×C3—22no—
137C22×C3—24no—
138C22×C3—24no—
139C22×C3—24no—
140C2×D3—68no—
141C2×D3—68no—
142C2×D3—632no—
143C2×D3—68no—
144C3×C4—28no—
145C3×C4—128no—
146Dic3—48no—
147Dic3—64no—
148Dic3—62no—
149Dic3—62no—
150C32C22×#10611yescharacteristic, complemented, Sylow
151C23—92no—
152C23—98no—
153C23—94no—
154C23C2×GO+(4,𝔽2)11yescharacteristic
155C2×C4—68no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—92no—
159C2×C4—92no—
160C2×C4—94no—
161C2×C4—94no—
162C2×C4—98no—
163C2×C4—128no—
164C2×C4—3616no—
165C2×C4#377314yes—
166C2×C4C2×GO+(4,𝔽2)12yes—
167C8—98no—
168C2×C3—28no—
169C2×C3—22no—
170C2×C3—22no—
171C2×C3—22no—
172D3—616no—
173C22—916no—
174C22—98no—
175C22—94no—
176C22#6422714yes—
177C22C2×#377312yes—
178C22C22×GO+(4,𝔽2)11yescharacteristic
179C4—91no—
180C4—91no—
181C4—92no—
182C4—128no—
183C4C2×#377314yes—
184C3—22no—
185C2—98no—
186C2#1059338714yesdirect product factor
187C2C2×#6422712yes—
188C2C22×#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×#106
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×#63742C2semidirect
4. #10593387C2direct (N × H)
8. C2×#3787C4semidirect
14. #63742C22semidirect
26. C2×#622C2×C4semidirect
28. #3787C2×C4semidirect
56. #622C22×C4semidirect
79. C2×C3⋊D3#106semidirect
116. C2×C32C2×#106semidirect
119. C3⋊D3C2×#106semidirect
150. C32C22×#106semidirect
186. C2#10593387direct (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×#637422
#105933872
C22×#1069