Finite Group Databasebeta

← C2×#88935 #11724321

Subgroups — C2×#88935 #11724321

Order 864.

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

normal subgroups only

This group has 324 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×#6295C211yesmaximal, characteristic, complemented
2C2×C3×#625C211yesmaximal, characteristic, complemented
3C2×C3⋊#622C211yesmaximal, characteristic, complemented
4#88935C214yesmaximal, direct product factor
5C2×#3774—31nomaximal
6C22×C3×C3⋊D3—21no—
7C22×C32×D3—21no—
8C2×C3×C3⋊Dic3C2211yescharacteristic
9#6295—21no—
10#6295C2212yescomplemented
11C3×#625—21no—
12C3×#625C2212yescomplemented
13C3⋊#622C2212yescomplemented
14C2×C3×#67—61no—
15C2×#626—61no—
16C2×#625—31no—
17C2×#625D311yescharacteristic, complemented
18C2×#622—31no—
19#3774—34no—
20C22×C33D411yescharacteristic
21C2×C3×C3⋊D3—22no—
22C2×C3×C3⋊D3—42no—
23C2×C32×D3—22no—
24C2×C32×D3—42no—
25C3×C3⋊Dic3D411yescharacteristic
26C3×C3⋊Dic3C2311yescharacteristic
27C2×#213—91nomaximal
28C23×C32—61no—
29C22×C3⋊D3—21no—
30C22×C3×D3—21no—
31C22×C3×D3—21no—
32C22×C3×D3—41no—
33C22×C3×D3—61no—
34C22×C3×D3—61no—
35C22×C3×D3—121no—
36C2×C3⋊Dic3C2×D311yescharacteristic
37C3×#67—62no—
38C3×#67—62no—
39C2×C3×Dic3—61no—
40C2×C3×Dic3—61no—
41#626—62no—
42#626—62no—
43#625—21no—
44#625—32no—
45#625—61no—
46#625C2×D312yescomplemented
47#622—32no—
48C2×C33D812yescomplemented
49C2×C33C2×D411yescharacteristic
50C3×C3⋊D3—42no—
51C32×D3—42no—
52C2×C3×D4—91no—
53C2×#67—61no—
54C2×#67—181no—
55C2×D12—91no—
56#213—94no—
57C2×C3⋊C8—91no—
58C22×C32—21no—
59C22×C32—21no—
60C22×C32—41no—
61C22×C32—41no—
62C22×C32—62no—
63C22×C32—122no—
64C22×C32#6711yescharacteristic
65C2×C3⋊D3—22no—
66C2×C3⋊D3—42no—
67C2×C3×D3—22no—
68C2×C3×D3—22no—
69C2×C3×D3—42no—
70C2×C3×D3—42no—
71C2×C3×D3—44no—
72C2×C3×D3—42no—
73C2×C3×D3—62no—
74C2×C3×D3—62no—
75C2×C3×D3—122no—
76C2×C3×D3—122no—
77C2×C3×D3—124no—
78C2×C3×D3—122no—
79C3⋊Dic3#6711yescharacteristic
80C3⋊Dic3C22×D311yescharacteristic
81C3×Dic3—61no—
82C3×Dic3—61no—
83C3×Dic3—61no—
84C3×Dic3—61no—
85C2×D8—271noSylow
86C33C2×D811yescharacteristic, complemented, Sylow
87C23×C3—61no—
88C23×C3—61no—
89C23×C3—121no—
90C23×C3—181no—
91C22×D3—21no—
92C22×D3—61no—
93C22×D3—61no—
94C22×D3—121no—
95C3×D4—92no—
96C3×D4—181no—
97C2×C3×C4—91no—
98#67—62no—
99#67—62no—
100#67—182no—
101#67—182no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104D12—92no—
105D12—181no—
106C3⋊C8—92no—
107C2×C32—21no—
108C2×C32—21no—
109C2×C32—22no—
110C2×C32—22no—
111C2×C32—42no—
112C2×C32—42no—
113C2×C32—41no—
114C2×C32—41no—
115C2×C32—122no—
116C2×C32#21312yescomplemented
117C2×C32C2×#6711yescharacteristic
118C3⋊D3—42no—
119C3×D3—42no—
120C3×D3—44no—
121C3×D3—42no—
122C3×D3—122no—
123C3×D3—124no—
124C3×D3—122no—
125C2×D4—91no—
126C2×D4—271no—
127D8—274no—
128C2×C8—271no—
129C22×C3—21no—
130C22×C3—21no—
131C22×C3—41no—
132C22×C3—41no—
133C22×C3—62no—
134C22×C3—62no—
135C22×C3—122no—
136C22×C3—122no—
137C22×C3—124no—
138C22×C3—122no—
139C22×C3—182no—
140C22×C3—362no—
141C22×C3GO+(4,𝔽2)11yescharacteristic
142C2×D3—22no—
143C2×D3—42no—
144C2×D3—62no—
145C2×D3—62no—
146C2×D3—122no—
147C2×D3—122no—
148C2×D3—124no—
149C2×D3—122no—
150C3×C4—91no—
151C3×C4—91no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—61no—
156C32—21no—
157C32—21no—
158C32—41no—
159C32—41no—
160C32C2×#21311yescharacteristic, complemented
161C23—61no—
162C23—181no—
163D4—92no—
164D4—181no—
165D4—272no—
166D4—541no—
167C2×C4—91no—
168C8—272no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—22no—
172C2×C3—22no—
173C2×C3—41no—
174C2×C3—41no—
175C2×C3—42no—
176C2×C3—42no—
177C2×C3—122no—
178C2×C3—124no—
179C2×C3—122no—
180C2×C3—362no—
181C2×C3#377412yescomplemented
182C2×C3C2×GO+(4,𝔽2)11yescharacteristic
183D3—42no—
184D3—122no—
185D3—124no—
186D3—122no—
187C22—62no—
188C22—122no—
189C22—182no—
190C22—362no—
191C22D32⋊D311yescharacteristic
192C4—91no—
193C4—91no—
194C3—21no—
195C3—21no—
196C3—41no—
197C3—41no—
198C3C2×#377411yescharacteristic, complemented
199C2—122no—
200C2—362no—
201C2#8893512yesdirect product factor
202C2C2×D32⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22D32⋊D3
commutator, cosocleC3×C3⋊Dic3C23
FrattiniC2C2×D32⋊D3
Fitting, socleC22×C33D4
hypocenterC33C2×D8
LCSG ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#6295C2semidirect
2. C2×C3×#625C2semidirect
3. C2×C3⋊#622C2semidirect
4. #88935C2direct (N × H)
10. #6295C22semidirect
12. C3×#625C22semidirect
13. C3⋊#622C22semidirect
17. C2×#625D3semidirect
46. #625C2×D3semidirect
48. C2×C33D8semidirect
86. C33C2×D8semidirect
116. C2×C32#213semidirect
160. C32C2×#213semidirect
181. C2×C3#3774semidirect
198. C3C2×#3774semidirect
201. C2#88935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#62952
C2×C3×#6252
C2×C3⋊#6222
#889352
C2×#37743
C2×#2139