Finite Group Databasebeta

← #14521731

Subgroups — #14521731

Order 1984.

214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C31×#125C211yesmaximal, characteristic, complemented
2#11758475C211yesmaximal, characteristic, complemented
3#11758475C211yesmaximal, characteristic, complemented
4#11758473C211yesmaximal, characteristic, complemented
5#11758473C211yesmaximal, characteristic, complemented
6#11758471C211yesmaximal, characteristic
7#11758471C211yesmaximal, characteristic
8#11758470C211yesmaximal, characteristic
9#11758469C211yesmaximal, characteristic, complemented
10C4⋊C4×D31C211yesmaximal, characteristic, complemented
11#11758466C211yesmaximal, characteristic, complemented
12#11758466C211yesmaximal, characteristic, complemented
13#11758464C211yesmaximal, characteristic, complemented
14#11758449C211yesmaximal, characteristic, complemented
15#11758449C211yesmaximal, characteristic, complemented
16C2×D124C2211yescharacteristic
17C2×C4×D31C2211yescharacteristic
18C2×C4×D31C2211yescharacteristic
19C2×C4×D31C2211yescharacteristic
20C2×C4×D31C2211yescharacteristic
21C2×Dic62C2211yescharacteristic
22C4⋊C4×C31C2211yescharacteristic
23C4⋊C4×C31C2211yescharacteristic
24C4⋊C4×C31C2211yescharacteristic
25C4⋊C4×C31C2211yescharacteristic
26C4⋊C4×C31C2211yescharacteristic
27C4⋊C4×C31C2211yescharacteristic
28C42×C31C2211yescharacteristic
29(C2×D31)⋊C4C2211yescharacteristic
30(C2×D31)⋊C4C2211yescharacteristic
31(C2×D31)⋊C4C2211yescharacteristic
32(C2×D31)⋊C4C2211yescharacteristic
33(C2×D31)⋊C4C2211yescharacteristic
34(C2×D31)⋊C4C2211yescharacteristic
35(C2×D31)⋊C4C2211yescharacteristic
36(C2×D31)⋊C4C2211yescharacteristic
37C4⋊Dic31C2211yescharacteristic
38C4⋊Dic31C2211yescharacteristic
39Dic31⋊C4C2211yescharacteristic
40Dic31⋊C4C2211yescharacteristic
41Dic31⋊C4C2211yescharacteristic
42Dic31⋊C4C2211yescharacteristic
43Dic31⋊C4C2211yescharacteristic
44Dic31⋊C4C2211yescharacteristic
45Dic31⋊C4C2211yescharacteristic
46Dic31⋊C4C2211yescharacteristic
47C4×Dic31C2211yescharacteristic
48C4×Dic31C2211yescharacteristic
49C4×Dic31C2211yescharacteristic
50C4×Dic31C2211yescharacteristic
51C22×D31C2311yescharacteristic
52C22×D31C2311yescharacteristic
53C2×C4×C31C2311yescharacteristic
54C2×C4×C31C2311yescharacteristic
55C2×C4×C31C2311yescharacteristic
56C2×C4×C31C2311yescharacteristic
57C2×C4×C31C2311yescharacteristic
58C2×C4×C31C2311yescharacteristic
59C2×C4×C31C2311yescharacteristic
60C2×Dic31C2311yescharacteristic
61C2×Dic31C2311yescharacteristic
62C2×Dic31C2311yescharacteristic
63C2×Dic31C2311yescharacteristic
64C2×Dic31C2311yescharacteristic
65C2×Dic31C2311yescharacteristic
66D124—22no—
67C4×D31—22no—
68C4×D31—22no—
69C4×D31—22no—
70C4×D31—22no—
71Dic62—22no—
72C22×C31C2411yescharacteristic
73C2×D31—21no—
74C2×D31—21no—
75C2×D31—21no—
76C2×D31—21no—
77C2×D31—21no—
78C2×D31#4112yes—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31—21no—
85C4×C31—21no—
86Dic31—21no—
87Dic31—21no—
88Dic31—21no—
89Dic31—21no—
90Dic31—21no—
91Dic31#4112yes—
92#552—311nomaximal, Sylow
93C2×C31C2×#4111yescharacteristic
94C2×C31C2×#4111yescharacteristic
95C2×C312−1+411yescharacteristic
96D31—22no—
97D31—41no—
98#126—311no—
99#126—311no—
100#125—311no—
101#125—311no—
102#125D3111yescharacteristic, complemented
103#123—311no—
104#123—311no—
105C22⋊Q8—311no—
106C22⋊Q8—311no—
107C4×Q8—311no—
108C4×D4—311no—
109#117—311no—
110#117—311no—
111#117—311no—
112C2×C4⋊C4—311no—
113C31#55211yescharacteristic, complemented, Sylow
114C2×Q8—311no—
115C2×D4—311no—
116C22×C4—311no—
117C22×C4—311no—
118C22×C4—311no—
119C22×C4—311no—
120C4⋊C4—311no—
121C4⋊C4—311no—
122C4⋊C4—311no—
123C4⋊C4—311no—
124C4⋊C4—311no—
125C4⋊C4—311no—
126C4⋊C4—311no—
127C4⋊C4—311no—
128C4⋊C4—311no—
129C4⋊C4—311no—
130C4⋊C4C2×D3111yescharacteristic
131C4⋊C4C2×D3111yescharacteristic
132C4⋊C4C2×D3111yescharacteristic
133C4⋊C4C2×D3111yescharacteristic
134C4⋊C4C2×D3111yescharacteristic
135C4⋊C4C2×D3111yescharacteristic
136C22⋊C4—311no—
137C22⋊C4—311no—
138C22⋊C4—311no—
139C22⋊C4—311no—
140C22⋊C4—311no—
141C22⋊C4—311no—
142C22⋊C4—311no—
143C22⋊C4—311no—
144C42—311no—
145C42—311no—
146C42—311no—
147C42—311no—
148C42C2×D3111yescharacteristic
149C23—311no—
150C23—311no—
151Q8—622no—
152D4—622no—
153C2×C4—311no—
154C2×C4—311no—
155C2×C4—311no—
156C2×C4—311no—
157C2×C4—311no—
158C2×C4—311no—
159C2×C4—622no—
160C2×C4—622no—
161C2×C4—622no—
162C2×C4—622no—
163C2×C4C22×D3111yescharacteristic
164C2×C4C22×D3111yescharacteristic
165C2×C4C22×D3111yescharacteristic
166C2×C4C22×D3111yescharacteristic
167C2×C4C22×D3111yescharacteristic
168C2×C4C22×D3111yescharacteristic
169C2×C4C22×D3111yescharacteristic
170C22—312no—
171C22—621no—
172C22—621no—
173C22—621no—
174C22—621no—
175C22—621no—
176C22C23×D3111yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—312no—
185C4—621no—
186C4—621no—
187C4—621no—
188C4—621no—
189C4—621no—
190C2—622no—
191C2—1241no—
192C2#1175856411yescharacteristic
193C2#41×D3111yescharacteristic
194C2#41×D3111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×#125C2
prime radicalC2×D124C22
hypercenter#125D31
hypocenterC31#552
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C31×#125C2semidirect
2. #11758475C2semidirect
3. #11758475C2semidirect
4. #11758473C2semidirect
5. #11758473C2semidirect
9. #11758469C2semidirect
10. C4⋊C4×D31C2semidirect
11. #11758466C2semidirect
12. #11758466C2semidirect
13. #11758464C2semidirect
14. #11758449C2semidirect
15. #11758449C2semidirect
102. #125D31semidirect
113. C31#552semidirect

Maximal subgroups

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

subgroupindex
C31×#1252
#117584752
#117584732
#117584712
#117584702
#117584692
C4⋊C4×D312
#117584662
#117584642
#117584492
#55231