Finite Group Databasebeta

← #5653

Subgroups — #5653

Order 192.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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×D3×D4C211yesmaximal, characteristic, complemented
2C22×D12C211yesmaximal, characteristic, complemented
3C3×#123C211yesmaximal, characteristic, complemented
4#937C211yesmaximal, characteristic, complemented
5#929C211yesmaximal, characteristic, complemented
6#895C212yesmaximal, complemented
7#894C212yesmaximal, complemented
8#884C212yesmaximal, complemented
9#882C212yesmaximal, complemented
10#882C211yesmaximal, characteristic, complemented
11D3×C22⋊C4C211yesmaximal, characteristic, complemented
12#534—31nomaximal, Sylow
13C23×D3C2211yescharacteristic
14C23×D3C2211yescharacteristic, complemented
15C23×D3C2211yescharacteristic, complemented
16C2×C3×D4C2211yescharacteristic
17C22×C3×C4C2211yescharacteristic, complemented
18C2×#67C2211yescharacteristic
19C2×#67C2211yescharacteristic, complemented
20C2×#67C2212yescomplemented
21D3×D4—24no—
22C2×D12—24no—
23C2×D12C2212yes—
24C2×D12C2212yescomplemented
25C2×D12C2211yescharacteristic, complemented
26C2×D12C2212yescomplemented
27C2×C4×D3C2211yescharacteristic, complemented
28C2×C4×D3C2212yescomplemented
29C3×C4⋊C4C2212yescomplemented
30C3×C22⋊C4C2211yescharacteristic, complemented
31C3×C22⋊C4C2212yescomplemented
32#217C2211yescharacteristic, complemented
33(C2×D3)⋊C4C2212yescomplemented
34(C2×D3)⋊C4C2212yescomplemented
35(C2×D3)⋊C4C2212yescomplemented
36(C2×D3)⋊C4C2212yescomplemented
37Dic3⋊C4C2212yescomplemented
38C22×D4—31no—
39C22×D4—31no—
40#123—31no—
41#123—32no—
42#123D311yescharacteristic, complemented
43#121—32no—
44#121—32no—
45#120—31no—
46#120—32no—
47#120—31no—
48C2×C22⋊C4—31no—
49C23×C3C2311yescharacteristic
50C23×C3C2311yescharacteristic
51C22×D3—22no—
52C22×D3—22no—
53C22×D3—42no—
54C22×D3—42no—
55C22×D3—42no—
56C22×D3D414yescomplemented
57C22×D3C2312yes—
58C22×D3C2311yescharacteristic
59C22×D3C2311yescharacteristic
60C22×D3C2311yescharacteristic
61C3×D4—22no—
62C2×C3×C4—22no—
63C2×C3×C4C2312yes—
64C2×C3×C4C2312yes—
65C2×C3×C4C2311yescharacteristic
66#67—22no—
67#67—22no—
68#67—42no—
69C2×Dic3C2311yescharacteristic
70C2×Dic3C2312yes—
71D12—24no—
72D12—24no—
73D12—22no—
74D12—42no—
75C4×D3—22no—
76C4×D3—42no—
77C24—31no—
78C24—31no—
79C24—31no—
80C2×D4—31no—
81C2×D4—31no—
82C2×D4—32no—
83C2×D4—32no—
84C2×D4—31no—
85C2×D4—32no—
86C2×D4—32no—
87C2×D4—64no—
88C2×D4—64no—
89C2×D4C2×D311yescharacteristic
90C22×C4—31no—
91C22×C4—32no—
92C22×C4C2×D311yescharacteristic, complemented
93C4⋊C4—32no—
94C4⋊C4C2×D312yescomplemented
95C22⋊C4—31no—
96C22⋊C4—32no—
97C22⋊C4—32no—
98C22⋊C4—32no—
99C22⋊C4—32no—
100C22⋊C4C2×D311yescharacteristic, complemented
101C22⋊C4C2×D312yescomplemented
102C22×C3—22no—
103C22×C3—21no—
104C22×C3—22no—
105C22×C3C2×D412yes—
106C22×C3C2411yescharacteristic
107C2×D3—22no—
108C2×D3—22no—
109C2×D3—22no—
110C2×D3—21no—
111C2×D3—22no—
112C2×D3—22no—
113C2×D3—22no—
114C2×D3—44no—
115C2×D3—44no—
116C2×D3—44no—
117C2×D3C2×D412yes—
118C2×D3C2×D412yes—
119C3×C4—21no—
120C3×C4—22no—
121C3×C4—22no—
122Dic3—21no—
123Dic3—22no—
124C23—31no—
125C23—31no—
126C23—34no—
127C23—31no—
128C23—32no—
129C23—62no—
130C23—62no—
131C23—122no—
132C23—122no—
133C23—122no—
134C23C22×D311yescharacteristic
135C23C22×D311yescharacteristic
136D4—22no—
137D4—64no—
138D4—64no—
139D4—62no—
140D4—62no—
141D4—62no—
142D4—122no—
143D4—122no—
144C2×C4—22no—
145C2×C4—32no—
146C2×C4—31no—
147C2×C4—62no—
148C2×C4—122no—
149C2×C4C22×D312yes—
150C2×C4C22×D311yescharacteristic
151C2×C4C22×D312yes—
152C2×C3—22no—
153C2×C3—41no—
154C2×C3C22×D411yescharacteristic
155C2×C3H(5,𝔽2)12yes—
156D3—22no—
157D3—22no—
158D3—42no—
159D3—41no—
160C22—22no—
161C22—21no—
162C22—22no—
163C22—32no—
164C22—32no—
165C22—62no—
166C22—62no—
167C22—62no—
168C22—61no—
169C22—62no—
170C22—62no—
171C22—62no—
172C22—124no—
173C22—124no—
174C22—124no—
175C22D3×D412yes—
176C22C23×D311yescharacteristic
177C4—22no—
178C4—21no—
179C4—22no—
180C4—61no—
181C4—62no—
182C3#53411yescharacteristic, complemented, Sylow
183C2—22no—
184C2—41no—
185C2—62no—
186C2—62no—
187C2—122no—
188C2—121no—
189C2C2×D3×D411yescharacteristic
190C2#100912yes—
subgroupG/H
center, FrattiniC22C23×D3
commutator, socle, cosocleC22×C3C24
FittingC3×#123C2
hypercenter#123D3
hypocenterC3#534
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×D3×D4C2semidirect
2. C22×D12C2semidirect
3. C3×#123C2semidirect
4. #937C2semidirect
5. #929C2semidirect
6. #895C2semidirect
7. #894C2semidirect
8. #884C2semidirect
9. #882C2semidirect
10. #882C2semidirect
11. D3×C22⋊C4C2semidirect
14. C23×D3C22semidirect
15. C23×D3C22semidirect
17. C22×C3×C4C22semidirect
19. C2×#67C22semidirect
20. C2×#67C22semidirect
24. C2×D12C22semidirect
25. C2×D12C22semidirect
26. C2×D12C22semidirect
27. C2×C4×D3C22semidirect
28. C2×C4×D3C22semidirect
29. C3×C4⋊C4C22semidirect
30. C3×C22⋊C4C22semidirect
31. C3×C22⋊C4C22semidirect
32. #217C22semidirect
33. (C2×D3)⋊C4C22semidirect
34. (C2×D3)⋊C4C22semidirect
35. (C2×D3)⋊C4C22semidirect
36. (C2×D3)⋊C4C22semidirect
37. Dic3⋊C4C22semidirect
42. #123D3semidirect
56. C22×D3D4semidirect
92. C22×C4C2×D3semidirect
94. C4⋊C4C2×D3semidirect
100. C22⋊C4C2×D3semidirect
101. C22⋊C4C2×D3semidirect
182. C3#534semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D42
C22×D122
C3×#1232
#9372
#9292
#8952
#8942
#8842
#8822
D3×C22⋊C42
#5343