Finite Group Databasebeta

← #16846842

Subgroups — #16846842

Order 3968.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521611C211yesmaximal, characteristic
2C2×#11758506C212yesmaximal, complemented
3C2×#11758394C212yesmaximal, complemented
4#14520816C211yesmaximal, characteristic, complemented
5C31×#381C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31C2212yes—
8C2×C22⋊C4×C31C2211yescharacteristic
9C2×C22⋊C4×C31C2211yescharacteristic
10C2×C22⋊Dic31C2212yes—
11#11758507—22no—
12#11758506—24no—
13#11758506—24no—
14C2×(C2×D31)⋊C4—22no—
15C2×Dic31⋊C4—22no—
16#11758463—22no—
17#11758459—22no—
18C31×#95—22no—
19#11758394—24no—
20C24×C31C2311yescharacteristic
21C23×D31D412yes—
22C22×C4×C31—21no—
23C22×C4×C31—22no—
24C22×C4×C31—22no—
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31D412yes—
28C22×C4×C31D412yescomplemented
29C2×C22⋊D31—22no—
30C2×C22⋊D31—22no—
31C2×C22⋊D31—22no—
32C2×C22⋊D31—22no—
33C2×C22⋊D31—22no—
34C2×C22⋊D31—22no—
35C22×Dic31—22no—
36C22×Dic31D412yes—
37C2×D124—22no—
38C22⋊C4×C31—22no—
39C22⋊C4×C31—22no—
40C22⋊Dic31—22no—
41C22⋊Dic31D414yescomplemented
42(C2×D31)⋊C4—24no—
43(C2×D31)⋊C4—28no—
44C4⋊Dic31—22no—
45Dic31⋊C4—28no—
46C23×C31—42no—
47C23×C31C2×D411yescharacteristic
48C23×C31C2×D412yes—
49C23×C31C2×D412yes—
50C23×C31C2×D411yescharacteristic
51C23×C31#4111yescharacteristic
52C22×D31—22no—
53C22×D31—22no—
54C22×D31—22no—
55C22×D31—44no—
56C2×C4×C31—24no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—41no—
60C2×C4×C31—42no—
61C2×C4×C31—41no—
62C2×C4×C31—42no—
63C2×C4×C31—42no—
64C2×C4×C31—41no—
65C22⋊D31—42no—
66C22⋊D31—42no—
67C22⋊D31—42no—
68C22⋊D31—42no—
69C2×Dic31—22no—
70C2×Dic31—24no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—44no—
74D124—82no—
75#2022—311nomaximal, Sylow
76C22×C31—24no—
77C22×C31—22no—
78C22×C31—41no—
79C22×C31—42no—
80C22×C31—41no—
81C22×C31#12012yes—
82C22×C31#12011yescharacteristic
83C22×C31#12112yes—
84C22×C31#12111yescharacteristic
85C22×C31#12711yescharacteristic
86C2×D31—44no—
87C2×D31—42no—
88C2×D31—44no—
89C2×D31—82no—
90C4×C31—42no—
91C4×C31—42no—
92C4×C31—81no—
93Dic31—44no—
94Dic31—42no—
95#534—311no—
96C2×#123—312no—
97C2×#99—312no—
98#381D3111yescharacteristic, complemented
99#342—311no—
100C2×C31—22no—
101C2×C31—21no—
102C2×C31—22no—
103C2×C31—21no—
104C2×C31#39211yescharacteristic
105C2×C31#45812yes—
106D31—82no—
107C22×D4—312no—
108C23×C4C2×D3111yescharacteristic
109#123—622no—
110#123—624no—
111#123—624no—
112#121—622no—
113#120—622no—
114C2×C4⋊C4—622no—
115C2×C22⋊C4—312no—
116C2×C22⋊C4—622no—
117C2×C22⋊C4C2×D3111yescharacteristic
118C2×C22⋊C4C2×D3111yescharacteristic
119#99—624no—
120#95—22no—
121C31#202211yescharacteristic, complemented, Sylow
122C24—312no—
123C24C22×D3111yescharacteristic
124C2×D4—622no—
125C2×D4—622no—
126C2×D4—622no—
127C2×D4—622no—
128C2×D4—622no—
129C2×D4—622no—
130C2×D4—622no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—312no—
137C22×C4—622no—
138C22×C4D12412yescomplemented
139C22×C4C22⋊D3112yes—
140C4⋊C4—628no—
141C4⋊C4—622no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—314no—
145C22⋊C4—628no—
146C22⋊C4—624no—
147C22⋊C4—622no—
148C23—42no—
149C23—622no—
150C23—622no—
151C23—622no—
152C23—1244no—
153C23C2×D12411yescharacteristic
154C23#9249511yescharacteristic
155C23D4×D3112yes—
156C23D4×D3112yes—
157C23C2×C22⋊D3111yescharacteristic
158D4—1242no—
159D4—1242no—
160D4—1242no—
161D4—1242no—
162D4—2482no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—624no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4—622no—
176C2×C4—1244no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—1244no—
183C22—1242no—
184C22—1244no—
185C22—2482no—
186C22#1175845912yes—
187C22#1175846112yes—
188C22#1175850711yescharacteristic
189C22#1175851411yescharacteristic
190C22#1175851711yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—1244no—
195C4—1242no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—2482no—
201C2#1452095811yescharacteristic
202C2#1452123812yes—
subgroupG/H
centerC22#11758514
commutator, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#381C2
socleC22×C31#120
prime radical#14521611C2
hypercenter#381D31
hypocenterC31#2022
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11758506C2semidirect
3. C2×#11758394C2semidirect
4. #14520816C2semidirect
5. C31×#381C2semidirect
28. C22×C4×C31D4semidirect
41. C22⋊Dic31D4semidirect
98. #381D31semidirect
121. C31#2022semidirect
138. C22×C4D124semidirect

Maximal subgroups

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

subgroupindex
#145216112
C2×#117585062
C2×#117583942
#145208162
C31×#3812
#202231