Finite Group Databasebeta

← #5638

Subgroups — #5638

Order 192.

218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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×C22⋊Q8C211yesmaximal, characteristic, complemented
2#946C211yesmaximal, characteristic, complemented
3#946C211yesmaximal, characteristic, complemented
4#929C211yesmaximal, characteristic, complemented
5C4×#67C211yesmaximal, characteristic, complemented
6#898C211yesmaximal, characteristic, complemented
7#894C211yesmaximal, characteristic, complemented
8#893C211yesmaximal, characteristic, complemented
9D3×C4⋊C4C211yesmaximal, characteristic, complemented
10#889C211yesmaximal, characteristic, complemented
11#889C211yesmaximal, characteristic, complemented
12#884C211yesmaximal, characteristic
13#883C211yesmaximal, characteristic, complemented
14#883C211yesmaximal, characteristic, complemented
15#879C211yesmaximal, characteristic, complemented
16#539—31nomaximal, Sylow
17C2×C3×Q8C2211yescharacteristic
18C22×C3×C4C2211yescharacteristic
19C2×#67C2211yescharacteristic
20C2×#67C2211yescharacteristic
21C2×D12C2211yescharacteristic
22C2×C4×D3C2211yescharacteristic
23C2×C4×D3C2211yescharacteristic
24C2×C4×D3C2211yescharacteristic
25C2×C4×D3C2211yescharacteristic
26C3×C4⋊C4C2211yescharacteristic
27C3×C4⋊C4C2211yescharacteristic
28C3×C4⋊C4C2211yescharacteristic
29C3×C22⋊C4C2211yescharacteristic
30C3×C22⋊C4C2211yescharacteristic
31#217C2211yescharacteristic
32#217C2211yescharacteristic
33(C2×D3)⋊C4C2211yescharacteristic
34(C2×D3)⋊C4C2211yescharacteristic
35(C2×D3)⋊C4C2211yescharacteristic
36(C2×D3)⋊C4C2211yescharacteristic
37(C2×D3)⋊C4C2211yescharacteristic
38(C2×D3)⋊C4C2211yescharacteristic
39C4⋊Dic3C2211yescharacteristic
40C4⋊Dic3C2211yescharacteristic
41C4⋊Dic3C2211yescharacteristic
42Dic3⋊C4C2211yescharacteristic
43Dic3⋊C4C2211yescharacteristic
44Dic3⋊C4C2211yescharacteristic
45Dic3⋊C4C2211yescharacteristic
46Dic3⋊C4C2211yescharacteristic
47Dic3⋊C4C2211yescharacteristic
48Dic3⋊C4C2211yescharacteristic
49Dic3⋊C4C2211yescharacteristic
50C4×Dic3C2211yescharacteristic
51C4×Dic3C2211yescharacteristic
52#126—31no—
53#126—31no—
54#125—31no—
55#125—31no—
56#123—31no—
57#123—31no—
58#123—31no—
59#123—31no—
60C22⋊Q8—31no—
61C22⋊Q8—31no—
62C22⋊Q8D311yescharacteristic, complemented
63#121—31no—
64C4×D4—31no—
65C4×D4—31no—
66C2×C4⋊C4—31no—
67C23×C3C2311yescharacteristic
68C22×D3C2311yescharacteristic
69C22×D3C2311yescharacteristic
70C3×Q8—41no—
71C2×C3×C4—41no—
72C2×C3×C4C2311yescharacteristic
73C2×C3×C4C2311yescharacteristic
74C2×C3×C4C2311yescharacteristic
75C2×C3×C4C2311yescharacteristic
76C2×C3×C4C2311yescharacteristic
77C2×C3×C4C2311yescharacteristic
78#67—22no—
79#67—41no—
80C2×Dic3C2311yescharacteristic
81C2×Dic3C2311yescharacteristic
82C2×Dic3C2311yescharacteristic
83C2×Dic3C2311yescharacteristic
84C2×Dic3C2311yescharacteristic
85C2×Dic3C2311yescharacteristic
86D12—22no—
87C4×D3—22no—
88C4×D3—41no—
89C4×D3—41no—
90C4×D3—41no—
91C2×Q8C2×D311yescharacteristic
92C2×D4—31no—
93C2×D4—31no—
94C2×D4—31no—
95C22×C4—31no—
96C22×C4—31no—
97C22×C4—31no—
98C22×C4—31no—
99C22×C4C2×D311yescharacteristic
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⋊C4—31no—
109C4⋊C4—31no—
110C4⋊C4—31no—
111C4⋊C4C2×D311yescharacteristic
112C4⋊C4C2×D311yescharacteristic
113C4⋊C4C2×D311yescharacteristic
114C22⋊C4—31no—
115C22⋊C4—31no—
116C22⋊C4—31no—
117C22⋊C4—31no—
118C22⋊C4—31no—
119C22⋊C4—31no—
120C22⋊C4—31no—
121C22⋊C4—31no—
122C22⋊C4C2×D311yescharacteristic
123C22⋊C4C2×D311yescharacteristic
124C42—31no—
125C42—31no—
126C22×C3—21no—
127C22×C3—21no—
128C22×C3—21no—
129C22×C3C2411yescharacteristic
130C2×D3—21no—
131C2×D3—21no—
132C2×D3—21no—
133C2×D3—21no—
134C2×D3—21no—
135C2×D3#4112yes—
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142Dic3—21no—
143Dic3—21no—
144Dic3—21no—
145Dic3—21no—
146Dic3—21no—
147Dic3—21no—
148C23—31no—
149C23—31no—
150C23C22×D311yescharacteristic
151Q8—41no—
152D4—62no—
153D4—62no—
154D4—121no—
155C2×C4—31no—
156C2×C4—31no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—31no—
160C2×C4—31no—
161C2×C4—41no—
162C2×C4—62no—
163C2×C4—121no—
164C2×C4—121no—
165C2×C4—121no—
166C2×C4C22×D311yescharacteristic
167C2×C4C22×D311yescharacteristic
168C2×C4C22×D311yescharacteristic
169C2×C4C22×D311yescharacteristic
170C2×C4C22×D311yescharacteristic
171C2×C4C22×D311yescharacteristic
172C2×C3—41no—
173C2×C3C2×#4111yescharacteristic
174C2×C3H(5,𝔽2)11yescharacteristic
175C2×C32−1+411yescharacteristic
176D3—22no—
177D3—41no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—32no—
182C22—61no—
183C22—61no—
184C22—61no—
185C22—61no—
186C22—61no—
187C22C23×D311yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—61no—
195C4—61no—
196C4—61no—
197C4—61no—
198C4—61no—
199C4—61no—
200C3#53911yescharacteristic, complemented, Sylow
201C2—41no—
202C2—62no—
203C2—121no—
204C2#100411yescharacteristic
205C2#100711yescharacteristic
206C2D3×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3
commutator, socle, cosocleC22×C3C24
FittingC3×C22⋊Q8C2
prime radical#884C2
hypercenterC22⋊Q8D3
hypocenterC3#539
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×C22⋊Q8C2semidirect
2. #946C2semidirect
3. #946C2semidirect
4. #929C2semidirect
5. C4×#67C2semidirect
6. #898C2semidirect
7. #894C2semidirect
8. #893C2semidirect
9. D3×C4⋊C4C2semidirect
10. #889C2semidirect
11. #889C2semidirect
13. #883C2semidirect
14. #883C2semidirect
15. #879C2semidirect
62. C22⋊Q8D3semidirect
200. C3#539semidirect

Maximal subgroups

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

subgroupindex
C3×C22⋊Q82
#9462
#9292
C4×#672
#8982
#8942
#8932
D3×C4⋊C42
#8892
#8842
#8832
#8792
#5393