Finite Group Databasebeta

← C2×#10593390 #11874932

Subgroups — C2×#10593390 #11874932

Order 1152.

586 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 135 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×#63870C212yesmaximal
2C2×C4×#622C211yesmaximal, characteristic
3C2×#63743C211yesmaximal, characteristic
4C2×#63743C211yesmaximal, characteristic
5C2×#63742C212yesmaximal
6#10593390C218yesmaximal, direct product factor
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×Dic3⋊C4—22no—
11C2×#3724C2212yes—
12C2×#3724C2212yes—
13C2×Dic3⋊Dic3—22no—
14#63870—24no—
15#63870C2218yes—
16C4×#622C2214yes—
17#63743C2214yes—
18#63743C2214yes—
19#63742C2218yes—
20C2×#889—62no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—22no—
25C22×C3×Dic3—22no—
26C2×#622Q814yes—
27C2×#622Q814yes—
28C2×#622C2312yes—
29C2×#622C2312yes—
30C4×C3⋊Dic3D412yes—
31C4×C3⋊Dic3C2312yes—
32C3×Dic3⋊C4—28no—
33#3724—22no—
34#3724—22no—
35#3724C2314yes—
36#3724C2314yes—
37Dic3⋊Dic3—28no—
38C2×#499—91nomaximal, Sylow
39C2×C3×C4⋊C4—62no—
40C2×C4⋊Dic3—62no—
41C2×Dic3⋊C4—22no—
42C2×Dic3⋊C4—62no—
43C2×Dic3⋊C4—62no—
44C2×Dic3⋊C4—62no—
45C2×C4×Dic3—62no—
46#889—68no—
47#889—68no—
48C23×C32C2×D411yescharacteristic
49C2×C32×C4—22no—
50C2×C32×C4C2×D412yes—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3C2×D412yes—
53C2×C3⋊Dic3C2×D411yescharacteristic
54C2×C3⋊Dic3C2×Q812yes—
55C2×C3⋊Dic3C2×Q812yes—
56C2×C3⋊Dic3C2411yescharacteristic
57C2×C3×Dic3—24no—
58C2×C3×Dic3—24no—
59C2×C3×Dic3—44no—
60C2×C3×Dic3—44no—
61#622C2×Q814yes—
62#622C2×Q814yes—
63C2×#125—92no—
64#499—98no—
65C2×#107—91no—
66C2×#107—91no—
67C2×#106—92no—
68C2×C4×C8—91no—
69C22×C3×C4—22no—
70C22×C3×C4—62no—
71C22×C3×C4—62no—
72C22×Dic3—22no—
73C22×Dic3—22no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C3×C4⋊C4—68no—
77C4⋊Dic3—68no—
78Dic3⋊C4—28no—
79Dic3⋊C4—64no—
80Dic3⋊C4—64no—
81Dic3⋊C4—68no—
82Dic3⋊C4—64no—
83Dic3⋊C4—64no—
84C4×Dic3—64no—
85C4×Dic3—64no—
86C22×C32C4⋊Q812yes—
87C22×C32#13512yes—
88C22×C32#13512yes—
89C22×C32C22×D411yescharacteristic
90C32×C4—22no—
91C3⋊Dic3—22no—
92C3⋊Dic3C4⋊Q812yes—
93C3⋊Dic3C22×Q811yescharacteristic
94C3⋊Dic3C22×Q811yescharacteristic
95C3×Dic3—44no—
96C3×Dic3—44no—
97C22×C8—91no—
98C22×C8—91no—
99#125—98no—
100#125—184no—
101C2×C4⋊C4—62no—
102C2×C4⋊C4—92no—
103C2×C4⋊C4—92no—
104C2×C4⋊C4—182no—
105C2×C42—91no—
106#107—94no—
107#107—94no—
108#106—98no—
109C4×C8—94no—
110C23×C3—22no—
111C2×C3×C4—24no—
112C2×C3×C4—44no—
113C2×C3×C4—64no—
114C2×C3×C4—64no—
115C2×C3×C4—124no—
116C2×C3×C4—124no—
117C2×Dic3—24no—
118C2×Dic3—24no—
119C2×Dic3—44no—
120C2×Dic3—44no—
121C2×Dic3—62no—
122C2×Dic3—64no—
123C2×Dic3—64no—
124C2×Dic3—62no—
125C2×Dic3—64no—
126C2×Dic3—124no—
127C2×C32#49914yescomplemented
128C2×C32C2×C4⋊Q811yescharacteristic
129C2×C32C2×#13511yescharacteristic
130C2×C32C2×#13511yescharacteristic
131C22×C4—62no—
132C22×C4—62no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4GO+(4,𝔽2)11yescharacteristic
136C2×C8—92no—
137C2×C8—92no—
138C2×C8—94no—
139C2×C8—94no—
140C4⋊C4—68no—
141C4⋊C4—94no—
142C4⋊C4—94no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—188no—
146C42—92no—
147C42—92no—
148C22×C3—22no—
149C22×C3—24no—
150C22×C3—24no—
151C22×C3—24no—
152C3×C4—44no—
153C3×C4—124no—
154C3×C4—124no—
155Dic3—44no—
156Dic3—44no—
157Dic3—64no—
158Dic3—62no—
159Dic3—62no—
160Dic3—124no—
161C32C2×#49911yescharacteristic, complemented, Sylow
162C23C2×GO+(4,𝔽2)11yescharacteristic
163C2×C4—22no—
164C2×C4—64no—
165C2×C4—64no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—92no—
169C2×C4—92no—
170C2×C4—92no—
171C2×C4—124no—
172C2×C4—124no—
173C2×C4—182no—
174C2×C4C2×GO+(4,𝔽2)12yes—
175C8—94no—
176C8—94no—
177C2×C3—28no—
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—22no—
181C22#6422212yes—
182C22#6422312yes—
183C22#6423712yes—
184C22C22×GO+(4,𝔽2)11yescharacteristic
185C4—22no—
186C4—91no—
187C4—91no—
188C4—92no—
189C4—124no—
190C4—124no—
191C4—182no—
192C3—22no—
193C2#1059339014yesdirect product factor
194C2C2×#6422211yescharacteristic
195C2C2×#6422311yescharacteristic
196C2C2×#6423711yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#499
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593390C2direct (N × H)
127. C2×C32#499semidirect
161. C32C2×#499semidirect
193. C2#10593390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638702
C2×C4×#6222
C2×#637432
C2×#637422
#105933902
C2×#4999