Finite Group Databasebeta

← #16846843

Subgroups — #16846843

Order 3968.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11758463C212yesmaximal, complemented
3C2×#11758394C212yesmaximal, complemented
4#14520910C211yesmaximal, characteristic, complemented
5C31×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D31C2212yes—
7C23×Dic31C2211yescharacteristic
8C2×C22⋊C4×C31C2211yescharacteristic
9C2×C22⋊C4×C31C2212yes—
10C2×C22⋊Dic31C2211yescharacteristic
11#11758507—22no—
12C2×(C2×D31)⋊C4—22no—
13C2×C4⋊Dic31—22no—
14#11758463—22no—
15#11758463—24no—
16#11758463—24no—
17#11758459—22no—
18C31⋊#95—22no—
19#11758394—24no—
20C24×C31C2311yescharacteristic
21C23×D31D412yes—
22C22×C4×C31—22no—
23C22×C4×C31D412yes—
24C2×C22⋊D31—22no—
25C2×C22⋊D31—22no—
26C2×C22⋊D31—22no—
27C2×C22⋊D31—22no—
28C2×C22⋊D31—22no—
29C2×C22⋊D31—22no—
30C22×Dic31—21no—
31C22×Dic31—22no—
32C22×Dic31—22no—
33C22×Dic31—21no—
34C22×Dic31—21no—
35C22×Dic31D412yes—
36C22×Dic31D412yescomplemented
37C2×D124—22no—
38C22⋊C4×C31—22no—
39C22⋊C4×C31—22no—
40C22⋊C4×C31D414yescomplemented
41C22⋊Dic31—22no—
42(C2×D31)⋊C4—24no—
43(C2×D31)⋊C4—28no—
44C4⋊Dic31—28no—
45C4⋊Dic31—22no—
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—44no—
59C2×C4×C31—42no—
60C22⋊D31—42no—
61C22⋊D31—42no—
62C22⋊D31—42no—
63C22⋊D31—42no—
64C2×Dic31—22no—
65C2×Dic31—24no—
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—41no—
70C2×Dic31—42no—
71C2×Dic31—41no—
72C2×Dic31—42no—
73C2×Dic31—41no—
74D124—82no—
75#2022—311nomaximal, Sylow
76C22×C31—22no—
77C22×C31—24no—
78C22×C31—42no—
79C22×C31—41no—
80C22×C31—41no—
81C22×C31#12012yes—
82C22×C31#12011yescharacteristic
83C22×C31#12111yescharacteristic
84C22×C31#12112yes—
85C22×C31#12711yescharacteristic
86C2×D31—44no—
87C2×D31—42no—
88C2×D31—44no—
89C2×D31—82no—
90C4×C31—44no—
91C4×C31—42no—
92Dic31—42no—
93Dic31—42no—
94Dic31—81no—
95#534—311no—
96C2×#123—312no—
97C2×#99—312no—
98#381—311no—
99#342D3111yescharacteristic, complemented
100C2×C31—21no—
101C2×C31—22no—
102C2×C31—22no—
103C2×C31—21no—
104C2×C31#39211yescharacteristic
105C2×C31#45812yes—
106D31—82no—
107C22×D4—312no—
108C23×C4—311no—
109#123—624no—
110#123—622no—
111#123—624no—
112#121—622no—
113#120—622no—
114C2×C4⋊C4—622no—
115C2×C22⋊C4—311no—
116C2×C22⋊C4—622no—
117C2×C22⋊C4C2×D3111yescharacteristic
118C2×C22⋊C4C2×D3112yes—
119#99—624no—
120#95—622no—
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—22no—
132C22×C4—312no—
133C22×C4—312no—
134C22×C4—621no—
135C22×C4—622no—
136C22×C4—622no—
137C22×C4—621no—
138C22×C4—621no—
139C22×C4D12412yes—
140C4⋊C4—628no—
141C4⋊C4—622no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—628no—
145C22⋊C4—624no—
146C22⋊C4—622no—
147C22⋊C4D12414yescomplemented
148C23—42no—
149C23—622no—
150C23—622no—
151C23—622no—
152C23—1244no—
153C23C2×D12411yescharacteristic
154C23C2×D12412yes—
155C23D4×D3112yes—
156C23D4×D3111yescharacteristic
157C23#9249911yescharacteristic
158D4—1242no—
159D4—1242no—
160D4—1242no—
161D4—1242no—
162D4—2482no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—624no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—622no—
172C2×C4—1241no—
173C2×C4—1241no—
174C2×C4—1242no—
175C2×C4—1242no—
176C2×C4—1241no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—1244no—
183C22—1242no—
184C22—1244no—
185C22—2482no—
186C22#1175845111yescharacteristic
187C22#1175845912yes—
188C22#1175845911yescharacteristic
189C22#1175847211yescharacteristic
190C22#1175847212yes—
191C4—44no—
192C4—42no—
193C4—1242no—
194C4—1242no—
195C4—2481no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—2482no—
201C2#1452095911yescharacteristic
202C2#1452124012yes—
subgroupG/H
centerC22#11758459
commutator, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31#120
prime radical#14521611C2
hypercenter#342D31
hypocenterC31#2022
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#11758463C2semidirect
3. C2×#11758394C2semidirect
4. #14520910C2semidirect
5. C31×#342C2semidirect
36. C22×Dic31D4semidirect
40. C22⋊C4×C31D4semidirect
99. #342D31semidirect
121. C31#2022semidirect
147. C22⋊C4D124semidirect

Maximal subgroups

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

subgroupindex
#145216112
C2×#117584632
C2×#117583942
#145209102
C31×#3422
#202231