Finite Group Databasebeta

← C2×#88937 #11724327

Subgroups — C2×#88937 #11724327

Order 864.

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

normal subgroups only

This group has 276 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, complemented
2C2×C3×#625C211yesmaximal, characteristic
3C2×C3⋊#622C211yesmaximal, characteristic, complemented
4#88937C214yesmaximal, direct product factor
5C2×#3775—31nomaximal
6C22×C32×D3—21no—
7C2×C3×C3⋊Dic3—21no—
8C2×C3×C3⋊Dic3C2211yescharacteristic
9#6296—21no—
10#6296C2212yescomplemented
11C3×#625—21no—
12C3×#625C2212yes—
13C3⋊#622C2212yescomplemented
14C2×C3×#67—61no—
15C2×#627—31no—
16C2×#627—61no—
17C2×#625D311yescharacteristic
18C2×#622—31no—
19#3775—34no—
20C22×C33D411yescharacteristic
21C2×C32×D3—22no—
22C2×C32×D3—42no—
23C3×C3⋊Dic3—22no—
24C3×C3⋊Dic3D411yescharacteristic
25C3×C3⋊Dic3C2311yescharacteristic
26C2×#214—91nomaximal
27C23×C32—61no—
28C22×C3×D3—21no—
29C22×C3×D3—21no—
30C22×C3×D3—41no—
31C2×C3⋊Dic3—21no—
32C2×C3⋊Dic3C2×D311yescharacteristic
33C3×#67—62no—
34C3×#67—62no—
35C2×C3×Dic3—61no—
36C2×C3×Dic3—61no—
37C2×C3×Dic3—61no—
38C2×C3×Dic3—61no—
39C2×C3×Dic3—121no—
40#627—32no—
41#627—62no—
42#627—62no—
43#627—61no—
44#625—21no—
45#625C2×D312yes—
46#622—32no—
47C2×C33SD1612yescomplemented
48C2×C33C2×D411yescharacteristic
49C32×D3—42no—
50C2×C3×D4—91no—
51C2×#67—61no—
52C2×Dic6—91no—
53C2×Dic6—181no—
54#214—94no—
55C2×C3⋊C8—91no—
56C22×C32—21no—
57C22×C32—21no—
58C22×C32—41no—
59C22×C32—41no—
60C22×C32—62no—
61C22×C32—122no—
62C22×C32#6711yescharacteristic
63C2×C3×D3—22no—
64C2×C3×D3—22no—
65C2×C3×D3—42no—
66C2×C3×D3—42no—
67C2×C3×D3—44no—
68C2×C3×D3—42no—
69C3⋊Dic3—22no—
70C3⋊Dic3#6711yescharacteristic
71C3⋊Dic3C22×D311yescharacteristic
72C3×Dic3—61no—
73C3×Dic3—61no—
74C3×Dic3—61no—
75C3×Dic3—61no—
76C3×Dic3—62no—
77C3×Dic3—62no—
78C3×Dic3—122no—
79C2×SD16—271noSylow
80C33C2×SD1611yescharacteristic, complemented, Sylow
81C23×C3—61no—
82C23×C3—61no—
83C23×C3—121no—
84C22×D3—21no—
85C3×D4—92no—
86C3×D4—181no—
87C2×C3×C4—91no—
88C2×C3×C4—181no—
89#67—62no—
90#67—62no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93C2×Dic3—61no—
94C2×Dic3—61no—
95C2×Dic3—121no—
96Dic6—92no—
97Dic6—182no—
98Dic6—181no—
99Dic6—182no—
100C3⋊C8—92no—
101C2×C32—21no—
102C2×C32—21no—
103C2×C32—22no—
104C2×C32—22no—
105C2×C32—42no—
106C2×C32—42no—
107C2×C32—41no—
108C2×C32—41no—
109C2×C32—122no—
110C2×C32#21412yescomplemented
111C2×C32C2×#6711yescharacteristic
112C3×D3—42no—
113C3×D3—44no—
114C3×D3—42no—
115C2×Q8—271no—
116C2×D4—91no—
117SD16—274no—
118C2×C8—271no—
119C22×C3—21no—
120C22×C3—21no—
121C22×C3—41no—
122C22×C3—41no—
123C22×C3—62no—
124C22×C3—62no—
125C22×C3—122no—
126C22×C3—122no—
127C22×C3—124no—
128C22×C3—122no—
129C22×C3GO+(4,𝔽2)11yescharacteristic
130C2×D3—22no—
131C2×D3—42no—
132C3×C4—91no—
133C3×C4—91no—
134C3×C4—182no—
135Dic3—61no—
136Dic3—61no—
137Dic3—61no—
138Dic3—61no—
139Dic3—62no—
140Dic3—62no—
141Dic3—122no—
142C32—21no—
143C32—21no—
144C32—41no—
145C32—41no—
146C32C2×#21411yescharacteristic, complemented
147C23—61no—
148Q8—272no—
149Q8—541no—
150D4—92no—
151D4—181no—
152C2×C4—91no—
153C2×C4—181no—
154C8—272no—
155C2×C3—21no—
156C2×C3—21no—
157C2×C3—22no—
158C2×C3—22no—
159C2×C3—41no—
160C2×C3—41no—
161C2×C3—42no—
162C2×C3—42no—
163C2×C3—122no—
164C2×C3—124no—
165C2×C3—122no—
166C2×C3#377512yescomplemented
167C2×C3C2×GO+(4,𝔽2)11yescharacteristic
168D3—42no—
169C22—62no—
170C22—122no—
171C22D32⋊D311yescharacteristic
172C4—91no—
173C4—91no—
174C4—182no—
175C3—21no—
176C3—21no—
177C3—41no—
178C3—41no—
179C3C2×#377511yescharacteristic, complemented
180C2—122no—
181C2#8893712yesdirect product factor
182C2C2×D32⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22D32⋊D3
commutator, cosocleC3×C3⋊Dic3C23
FrattiniC2C2×D32⋊D3
Fitting, socleC22×C33D4
prime radicalC2×C3×#625C2
hypocenterC33C2×SD16
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×#6296C2semidirect
3. C2×C3⋊#622C2semidirect
4. #88937C2direct (N × H)
10. #6296C22semidirect
13. C3⋊#622C22semidirect
47. C2×C33SD16semidirect
80. C33C2×SD16semidirect
110. C2×C32#214semidirect
146. C32C2×#214semidirect
166. C2×C3#3775semidirect
179. C3C2×#3775semidirect
181. C2#88937direct (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×#6252
C2×C3⋊#6222
#889372
C2×#37753
C2×#2149