Finite Group Databasebeta

← #5531

Subgroups — #5531

Order 192.

214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C3×#117C211yesmaximal, characteristic, complemented
2#929C211yesmaximal, characteristic
3C2×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#898C211yesmaximal, characteristic, complemented
5#896C211yesmaximal, characteristic, complemented
6#889C211yesmaximal, characteristic, complemented
7#889C211yesmaximal, characteristic, complemented
8#886C211yesmaximal, characteristic
9#67⋊C4C211yesmaximal, characteristic
10#878C211yesmaximal, characteristic, complemented
11#877C211yesmaximal, characteristic, complemented
12#876C211yesmaximal, characteristic, complemented
13#872C211yesmaximal, characteristic, complemented
14#870C211yesmaximal, characteristic, complemented
15C4×Dic6C211yesmaximal, characteristic, complemented
16#552—31nomaximal, Sylow
17C22×C3×C4C2211yescharacteristic
18C2×#67C2211yescharacteristic
19C22×Dic3C2211yescharacteristic
20C22×Dic3C2211yescharacteristic
21C2×C4×D3C2211yescharacteristic
22C2×Dic6C2211yescharacteristic
23C3×C4⋊C4C2211yescharacteristic
24C3×C4⋊C4C2211yescharacteristic
25C3×C22⋊C4C2211yescharacteristic
26C3×C22⋊C4C2211yescharacteristic
27C3×C42C2211yescharacteristic
28C3×C42C2211yescharacteristic
29#217C2211yescharacteristic
30(C2×D3)⋊C4C2211yescharacteristic
31(C2×D3)⋊C4C2211yescharacteristic
32(C2×D3)⋊C4C2211yescharacteristic
33(C2×D3)⋊C4C2211yescharacteristic
34(C2×D3)⋊C4C2211yescharacteristic
35C4⋊Dic3C2211yescharacteristic
36C4⋊Dic3C2211yescharacteristic
37C4⋊Dic3C2211yescharacteristic
38Dic3⋊C4C2211yescharacteristic
39Dic3⋊C4C2211yescharacteristic
40Dic3⋊C4C2211yescharacteristic
41Dic3⋊C4C2211yescharacteristic
42Dic3⋊C4C2211yescharacteristic
43Dic3⋊C4C2211yescharacteristic
44Dic3⋊C4C2211yescharacteristic
45Dic3⋊C4C2211yescharacteristic
46Dic3⋊C4C2211yescharacteristic
47Dic3⋊C4C2211yescharacteristic
48Dic3⋊C4C2211yescharacteristic
49C4×Dic3C2211yescharacteristic
50C4×Dic3C2211yescharacteristic
51C4×Dic3C2211yescharacteristic
52#126—31no—
53#126—31no—
54#125—31no—
55#125—31no—
56#125—31no—
57#123—31no—
58#123—31no—
59C22⋊Q8—31no—
60C22⋊Q8—31no—
61C4×Q8—31no—
62C4×D4—31no—
63#117—31no—
64#117—31no—
65#117D311yescharacteristic, complemented
66C2×C4⋊C4—31no—
67C23×C3C2311yescharacteristic
68C22×D3C2311yescharacteristic
69C2×C3×C4—22no—
70C2×C3×C4C2311yescharacteristic
71C2×C3×C4C2311yescharacteristic
72C2×C3×C4C2311yescharacteristic
73C2×C3×C4C2311yescharacteristic
74C2×C3×C4C2311yescharacteristic
75C2×C3×C4C2311yescharacteristic
76#67—22no—
77C2×Dic3—22no—
78C2×Dic3—22no—
79C2×Dic3C2311yescharacteristic
80C2×Dic3C2311yescharacteristic
81C2×Dic3C2311yescharacteristic
82C2×Dic3C2311yescharacteristic
83C2×Dic3C2311yescharacteristic
84C2×Dic3C2311yescharacteristic
85C2×Dic3C2311yescharacteristic
86C4×D3—22no—
87Dic6—22no—
88C2×Q8—31no—
89C2×D4—31no—
90C22×C4—31no—
91C22×C4—31no—
92C22×C4—31no—
93C22×C4C2×D311yescharacteristic
94C4⋊C4—31no—
95C4⋊C4—31no—
96C4⋊C4—31no—
97C4⋊C4—31no—
98C4⋊C4—31no—
99C4⋊C4—31no—
100C4⋊C4—31no—
101C4⋊C4—31no—
102C4⋊C4—31no—
103C4⋊C4—31no—
104C4⋊C4—31no—
105C4⋊C4—31no—
106C4⋊C4—31no—
107C4⋊C4—31no—
108C4⋊C4C2×D311yescharacteristic
109C4⋊C4C2×D311yescharacteristic
110C22⋊C4—31no—
111C22⋊C4—31no—
112C22⋊C4—31no—
113C22⋊C4—31no—
114C22⋊C4—31no—
115C22⋊C4—31no—
116C22⋊C4C2×D311yescharacteristic
117C22⋊C4C2×D311yescharacteristic
118C42—31no—
119C42—31no—
120C42—31no—
121C42C2×D311yescharacteristic
122C42C2×D311yescharacteristic
123C22×C3—21no—
124C22×C3—21no—
125C22×C3#4112yes—
126C22×C3C2411yescharacteristic
127C2×D3—21no—
128C2×D3—21no—
129C2×D3—21no—
130C3×C4—21no—
131C3×C4—21no—
132C3×C4—21no—
133C3×C4—21no—
134C3×C4—21no—
135C3×C4—21no—
136Dic3—21no—
137Dic3—21no—
138Dic3—21no—
139Dic3—21no—
140Dic3—21no—
141Dic3—21no—
142Dic3#4112yes—
143C23—31no—
144C23C22×D311yescharacteristic
145Q8—62no—
146D4—62no—
147C2×C4—22no—
148C2×C4—31no—
149C2×C4—31no—
150C2×C4—31no—
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—31no—
154C2×C4—31no—
155C2×C4—62no—
156C2×C4—62no—
157C2×C4—62no—
158C2×C4C22×D311yescharacteristic
159C2×C4C22×D311yescharacteristic
160C2×C4C22×D311yescharacteristic
161C2×C4C22×D311yescharacteristic
162C2×C4C22×D311yescharacteristic
163C2×C4C22×D311yescharacteristic
164C2×C3—22no—
165C2×C3C2×#4111yescharacteristic
166C2×C3C2×#4111yescharacteristic
167C2×C32−1+411yescharacteristic
168D3—41no—
169C22—21no—
170C22—21no—
171C22—61no—
172C22—61no—
173C22—61no—
174C22#23512yes—
175C22C23×D311yescharacteristic
176C4—21no—
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—32no—
183C4—61no—
184C4—61no—
185C4—61no—
186C4—61no—
187C4—61no—
188C4—61no—
189C3#55211yescharacteristic, complemented, Sylow
190C2—22no—
191C2—121no—
192C2C2×#23511yescharacteristic
193C2D3×#4111yescharacteristic
194C2#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3
commutator, socle, cosocleC22×C3C24
FittingC3×#117C2
prime radicalC2×#67C22
hypercenter#117D3
hypocenterC3#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#117C2semidirect
3. C2×Dic3⋊C4C2semidirect
4. #898C2semidirect
5. #896C2semidirect
6. #889C2semidirect
7. #889C2semidirect
10. #878C2semidirect
11. #877C2semidirect
12. #876C2semidirect
13. #872C2semidirect
14. #870C2semidirect
15. C4×Dic6C2semidirect
65. #117D3semidirect
189. C3#552semidirect

Maximal subgroups

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

subgroupindex
C3×#1172
#9292
C2×Dic3⋊C42
#8982
#8962
#8892
#8862
#67⋊C42
#8782
#8772
#8762
#8722
#8702
C4×Dic62
#5523