Finite Group Databasebeta

← #16844686

Subgroups — #16844686

Order 3968.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521678C211yesmaximal, characteristic
2#14521207C211yesmaximal, characteristic
3#14521204C211yesmaximal, characteristic
4#14520970C211yesmaximal, characteristic
5#14520785C211yesmaximal, characteristic
6#14520774C211yesmaximal, characteristic
7C31×#328C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C31×C22⋊Q8C2211yescharacteristic
10#11758521—21no—
11C2×#92482—21no—
12C2×C4⋊Dic31—21no—
13#11758501C2211yescharacteristic
14C2×Dic31⋊C4C2211yescharacteristic
15C2×Dic124—21no—
16#11758466—21no—
17#11758466—21no—
18#11758465—21no—
19#11758455—21no—
20#11758454—21no—
21C31×C22⋊C8C2211yescharacteristic
22C31×#95C2211yescharacteristic
23C31⋊#95—21no—
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758404—21no—
26#11758398—21no—
27C2×Q8×C31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31D411yescharacteristic
32C22×Dic31D411yescharacteristic
33C2×Dic62—21no—
34C2×Dic62—21no—
35C2×Dic62—21no—
36C2×Dic62—42no—
37C2×Dic62D411yescharacteristic
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31D411yescharacteristic
41C22⋊C4×C31—21no—
42C22⋊Dic31—21no—
43#92482—42no—
44C4⋊Dic31—21no—
45C4⋊Dic31—42no—
46C4⋊Dic31D411yescharacteristic
47Dic31⋊C4—21no—
48Dic31⋊C4—21no—
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53Dic31⋊C4—21no—
54C4×Dic31—21no—
55C4×Dic31—21no—
56C2×C31⋊C8—21no—
57Dic124—42no—
58C23×C31C2×D411yescharacteristic
59Q8×C31—41no—
60C2×C4×C31—22no—
61C2×C4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—22no—
71C2×Dic31—21no—
72C2×Dic31—21no—
73C2×Dic31—21no—
74C2×Dic31—41no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77C2×Dic31Q1612yescomplemented
78Dic62—22no—
79Dic62—22no—
80Dic62—41no—
81Dic62—41no—
82Dic62—41no—
83Dic62—81no—
84C8×C31—41no—
85C31⋊C8—41no—
86#1605—311nomaximal, Sylow
87C22×C31—21no—
88C22×C31—21no—
89C22×C31#12011yescharacteristic
90C22×C31C2×Q1611yescharacteristic
91C22×C31#13711yescharacteristic
92C4×C31—21no—
93C4×C31—21no—
94C4×C31—42no—
95C4×C31—41no—
96C4×C31—41no—
97Dic31—22no—
98Dic31—41no—
99Dic31—42no—
100Dic31—41no—
101Dic31—41no—
102#544—311no—
103#451—311no—
104#451—311no—
105#395—311no—
106#328—311no—
107#328D3111yescharacteristic
108#324—311no—
109C2×C31—21no—
110C2×C31—21no—
111C2×C31#45111yescharacteristic
112C2×C31#45611yescharacteristic
113C2×C31B(4,𝔽2)11yescharacteristic
114C22×Q8—311no—
115C2×Q16—621no—
116C2×Q16—621no—
117C4⋊Q8—621no—
118C4⋊Q8—621no—
119#125—621no—
120#125—621no—
121C22⋊Q8—311no—
122C22⋊Q8—621no—
123C22⋊Q8C2×D3111yescharacteristic
124#117—621no—
125C2×C4⋊C4—311no—
126C2×C4⋊C4—621no—
127#103—621no—
128#103—621no—
129C22⋊C8—311no—
130C22⋊C8C2×D3111yescharacteristic
131#95—621no—
132#95C2×D3111yescharacteristic
133C31#160511yescharacteristic, complemented, Sylow
134C2×Q8—311no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8—621no—
138C2×Q8—1242no—
139C2×Q8D12411yescharacteristic
140C22×C4—21no—
141C22×C4—311no—
142C22×C4—311no—
143C22×C4—621no—
144C22×C4C22×D3111yescharacteristic
145Q16—1242no—
146Q16—1242no—
147C2×C8—21no—
148C2×C8—621no—
149C4⋊C4—21no—
150C4⋊C4—311no—
151C4⋊C4—621no—
152C4⋊C4—621no—
153C4⋊C4—621no—
154C4⋊C4—621no—
155C4⋊C4—621no—
156C4⋊C4—621no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C4⋊C4—1242no—
160C4⋊C4D12411yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—621no—
163C42—621no—
164C42—621no—
165C23D4×D3111yescharacteristic
166Q8—41no—
167Q8—622no—
168Q8—622no—
169Q8—1241no—
170Q8—1241no—
171Q8—1241no—
172Q8—2481no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—312no—
180C2×C4—621no—
181C2×C4—621no—
182C2×C4—622no—
183C2×C4—621no—
184C2×C4—621no—
185C2×C4—621no—
186C2×C4—1241no—
187C2×C4—1241no—
188C2×C4—1241no—
189C2×C4C2×D12411yescharacteristic
190C2×C4D4×D3111yescharacteristic
191C8—41no—
192C8—1241no—
193C22—21no—
194C22—21no—
195C22#1175845911yescharacteristic
196C22#1175849211yescharacteristic
197C22Q16×D3111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—622no—
204C4—1241no—
205C4—1242no—
206C4—1241no—
207C4—1241no—
208C2—21no—
209C2—21no—
210C2#1452120611yescharacteristic
211C2#1452123311yescharacteristic
212C2#1452123711yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#328D31
hypocenterC31#1605
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic31Q16semidirect
133. C31#1605semidirect

Maximal subgroups

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

subgroupindex
#145216782
#145212072
#145212042
#145209702
#145207852
#145207742
C31×#3282
#160531