Finite Group Databasebeta

← #16853971

Subgroups — #16853971

Order 3968.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#14520989C212yesmaximal, complemented
2#14520985C211yesmaximal, characteristic
3#14520983C212yesmaximal, complemented
4#14520983C212yesmaximal, complemented
5#14520972C212yesmaximal
6#14520968C212yesmaximal, complemented
7#14520910C211yesmaximal, characteristic
8#14520907C212yesmaximal
9C31×#393C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C23×Dic31C2211yescharacteristic
12C2×C22⋊C4×C31C2212yes—
13C2×C22⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31C2212yes—
15C2×C22⋊Dic31C2211yescharacteristic
16C2×C4⋊Dic31C2212yes—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×Dic31⋊C4C2212yes—
19C2×Dic31⋊C4C2212yes—
20C2×Dic31⋊C4C2212yes—
21C2×Dic31⋊C4C2212yes—
22C2×Dic31⋊C4C2212yes—
23C31×#95C2211yescharacteristic
24C31×#95C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2211yescharacteristic
31C24×C31C2311yescharacteristic
32C2×Q8×C31—41no—
33C2×Q8×C31—42no—
34C22×C4×C31C2311yescharacteristic
35C22×C4×C31C2312yes—
36C22×C4×C31C2311yescharacteristic
37C22×C4×C31C2312yes—
38C22×Dic31—41no—
39C22×Dic31—41no—
40C22×Dic31Q814yescomplemented
41C22×Dic31C2312yes—
42C22×Dic31C2312yes—
43C22×Dic31C2312yes—
44C22×Dic31C2312yes—
45C22⋊C4×C31—42no—
46C22⋊C4×C31—41no—
47C22⋊Dic31—42no—
48C22⋊Dic31—41no—
49C4⋊Dic31—41no—
50C4⋊Dic31—42no—
51Dic31⋊C4—42no—
52Dic31⋊C4—42no—
53Dic31⋊C4—42no—
54Dic31⋊C4—42no—
55Dic31⋊C4—42no—
56C23×C31—22no—
57C23×C31—21no—
58C23×C31—21no—
59C23×C31—22no—
60C23×C31C2×Q812yes—
61C23×C31C2411yescharacteristic
62Q8×C31—44no—
63C2×C4×C31—22no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31—22no—
82C2×Dic31—22no—
83C2×Dic31—22no—
84C2×Dic31—44no—
85C2×Dic31C2×Q814yes—
86#2841—311nomaximal, Sylow
87C22×C31—22no—
88C22×C31—24no—
89C22×C31—41no—
90C22×C31—42no—
91C22×C31—41no—
92C22×C31C22×Q811yescharacteristic
93C22×C31H(5,𝔽2)11yescharacteristic
94C22×C31H(5,𝔽2)12yes—
95C22×C31H(5,𝔽2)11yescharacteristic
96C22×C312−1+412yes—
97C4×C31—42no—
98C4×C31—41no—
99C4×C31—42no—
100C4×C31—41no—
101Dic31—24no—
102Dic31—42no—
103Dic31—42no—
104Dic31—42no—
105#400—312no—
106#399—311no—
107#398—312no—
108#398—312no—
109#396—312no—
110#395—312no—
111#393D3111yescharacteristic
112#381—311no—
113#380—312no—
114C2×C31—42no—
115C2×C31#54311yescharacteristic
116C2×C31#54412yes—
117C2×C31#56011yescharacteristic
118C2×C31#56212yes—
119C2×C31#56311yescharacteristic
120C22×Q8C2×D3111yescharacteristic
121C23×C4—311no—
122C2×C4⋊C4—312no—
123C2×C4⋊C4—312no—
124C2×C4⋊C4—312no—
125C2×C4⋊C4—312no—
126C2×C4⋊C4—312no—
127C2×C4⋊C4—312no—
128C2×C4⋊C4—311no—
129C2×C22⋊C4—312no—
130C2×C22⋊C4—311no—
131C2×C22⋊C4C2×D3112yes—
132C2×C22⋊C4C2×D3111yescharacteristic
133#95—312no—
134#95—312no—
135#95—312no—
136#95—312no—
137#95—312no—
138#95—311no—
139#95C2×D3111yescharacteristic
140#95C2×D3112yes—
141C31#284111yescharacteristic, complemented, Sylow
142C24C22×D3111yescharacteristic
143C2×Q8—41no—
144C2×Q8—42no—
145C22×C4—312no—
146C22×C4—314no—
147C22×C4—312no—
148C22×C4—312no—
149C22×C4—312no—
150C22×C4—1241no—
151C22×C4—1241no—
152C22×C4C22×D3111yescharacteristic
153C22×C4C22×D3112yes—
154C22×C4C22×D3111yescharacteristic
155C22×C4C22×D3112yes—
156C4⋊C4—1242no—
157C4⋊C4—1242no—
158C4⋊C4—1242no—
159C4⋊C4—1242no—
160C4⋊C4—1242no—
161C4⋊C4—1241no—
162C4⋊C4—1242no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—1242no—
166C22⋊C4—1241no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D3112yes—
172C23C23×D3111yescharacteristic
173Q8—44no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—314no—
185C2×C4—622no—
186C2×C4—622no—
187C2×C4—622no—
188C2×C4—622no—
189C2×C4—622no—
190C2×C4—622no—
191C2×C4—622no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—1244no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22#1175856111yescharacteristic
203C22#1175856112yes—
204C22C2×Q8×D3111yescharacteristic
205C22#1175856611yescharacteristic
206C22#1175856712yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—624no—
212C4—1242no—
213C4—1242no—
214C4—1242no—
215C2—42no—
216C2#1452167411yescharacteristic
217C2#1452167812yes—
218C2#1452178811yescharacteristic
219C2#1452179312yes—
220C2#1452179911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#393C2
prime radicalC24×C31C23
hypercenter#393D31
hypocenterC31#2841
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #14520989C2semidirect
3. #14520983C2semidirect
4. #14520983C2semidirect
6. #14520968C2semidirect
40. C22×Dic31Q8semidirect
141. C31#2841semidirect

Maximal subgroups

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

subgroupindex
#145209892
#145209852
#145209832
#145209722
#145209682
#145209102
#145209072
C31×#3932
#284131