Finite Group Databasebeta

← C2×#88938 #11724329

Subgroups — C2×#88938 #11724329

Order 864.

228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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×#6296C211yesmaximal, characteristic
2C2×C3×#627C211yesmaximal, characteristic
3C2×C3⋊#622C211yesmaximal, characteristic
4#88938C214yesmaximal, direct product factor
5C2×#3776—31nomaximal
6C2×C3×C3⋊Dic3—21no—
7C2×C3×C3⋊Dic3C2211yescharacteristic
8C2×C32×Dic3—21no—
9#6296—21no—
10#6296C2212yes—
11C3×#627—21no—
12C3×#627C2212yes—
13C3⋊#622C2212yes—
14C2×C3×Dic6—61no—
15C2×#627—31no—
16C2×#627—61no—
17C2×#627D311yescharacteristic
18C2×#622—31no—
19#3776—34no—
20C22×C33D411yescharacteristic
21C3×C3⋊Dic3—22no—
22C3×C3⋊Dic3D411yescharacteristic
23C3×C3⋊Dic3C2311yescharacteristic
24C32×Dic3—22no—
25C2×#216—91nomaximal
26C2×C32×C4—61no—
27C2×C3⋊Dic3—21no—
28C2×C3⋊Dic3C2×D311yescharacteristic
29C2×C3×Dic3—21no—
30C2×C3×Dic3—21no—
31C2×C3×Dic3—41no—
32C2×C3×Dic3—61no—
33C2×C3×Dic3—61no—
34C2×C3×Dic3—61no—
35C2×C3×Dic3—61no—
36C2×C3×Dic3—121no—
37C3×Dic6—62no—
38C3×Dic6—62no—
39#627—21no—
40#627—32no—
41#627—62no—
42#627—62no—
43#627—61no—
44#627C2×D312yes—
45#622—32no—
46C2×C33Q1612yescomplemented
47C2×C33C2×D411yescharacteristic
48C2×C3×Q8—91no—
49C2×Dic6—61no—
50C2×Dic6—91no—
51C2×Dic6—181no—
52#216—94no—
53C2×C3⋊C8—91no—
54C22×C32—21no—
55C22×C32—21no—
56C22×C32—41no—
57C22×C32—41no—
58C22×C32#6711yescharacteristic
59C32×C4—62no—
60C3⋊Dic3—22no—
61C3⋊Dic3#6711yescharacteristic
62C3⋊Dic3C22×D311yescharacteristic
63C3×Dic3—22no—
64C3×Dic3—22no—
65C3×Dic3—42no—
66C3×Dic3—61no—
67C3×Dic3—61no—
68C3×Dic3—61no—
69C3×Dic3—61no—
70C3×Dic3—62no—
71C3×Dic3—62no—
72C3×Dic3—122no—
73C2×Q16—271noSylow
74C33C2×Q1611yescharacteristic, complemented, Sylow
75C3×Q8—92no—
76C3×Q8—181no—
77C2×C3×C4—61no—
78C2×C3×C4—61no—
79C2×C3×C4—91no—
80C2×C3×C4—121no—
81C2×C3×C4—181no—
82C2×Dic3—21no—
83C2×Dic3—61no—
84C2×Dic3—61no—
85C2×Dic3—61no—
86C2×Dic3—61no—
87C2×Dic3—121no—
88Dic6—62no—
89Dic6—62no—
90Dic6—92no—
91Dic6—182no—
92Dic6—181no—
93Dic6—182no—
94C3⋊C8—92no—
95C2×C32—21no—
96C2×C32—21no—
97C2×C32—22no—
98C2×C32—22no—
99C2×C32—42no—
100C2×C32—42no—
101C2×C32—41no—
102C2×C32—41no—
103C2×C32#21612yescomplemented
104C2×C32C2×#6711yescharacteristic
105C2×Q8—91no—
106C2×Q8—271no—
107Q16—274no—
108C2×C8—271no—
109C22×C3—21no—
110C22×C3—21no—
111C22×C3—41no—
112C22×C3—41no—
113C22×C3GO+(4,𝔽2)11yescharacteristic
114C3×C4—62no—
115C3×C4—62no—
116C3×C4—91no—
117C3×C4—91no—
118C3×C4—122no—
119C3×C4—182no—
120Dic3—22no—
121Dic3—61no—
122Dic3—61no—
123Dic3—61no—
124Dic3—61no—
125Dic3—62no—
126Dic3—62no—
127Dic3—122no—
128C32—21no—
129C32—21no—
130C32—41no—
131C32—41no—
132C32C2×#21611yescharacteristic, complemented
133Q8—92no—
134Q8—181no—
135Q8—272no—
136Q8—541no—
137C2×C4—61no—
138C2×C4—91no—
139C2×C4—181no—
140C8—272no—
141C2×C3—21no—
142C2×C3—21no—
143C2×C3—22no—
144C2×C3—22no—
145C2×C3—41no—
146C2×C3—41no—
147C2×C3—42no—
148C2×C3—42no—
149C2×C3#377612yescomplemented
150C2×C3C2×GO+(4,𝔽2)11yescharacteristic
151C22D32⋊D311yescharacteristic
152C4—62no—
153C4—91no—
154C4—91no—
155C4—182no—
156C3—21no—
157C3—21no—
158C3—41no—
159C3—41no—
160C3C2×#377611yescharacteristic, complemented
161C2#8893812yesdirect product factor
162C2C2×D32⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22D32⋊D3
commutator, cosocleC3×C3⋊Dic3C23
FrattiniC2C2×D32⋊D3
Fitting, socle, prime radicalC22×C33D4
hypocenterC33C2×Q16
LCSG ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
4. #88938C2direct (N × H)
46. C2×C33Q16semidirect
74. C33C2×Q16semidirect
103. C2×C32#216semidirect
132. C32C2×#216semidirect
149. C2×C3#3776semidirect
160. C3C2×#3776semidirect
161. C2#88938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#62962
C2×C3×#6272
C2×C3⋊#6222
#889382
C2×#37763
C2×#2169