Finite Group Databasebeta

← #16844745

Subgroups — #16844745

Order 3968.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#14521648C211yesmaximal, characteristic
2#14521382C211yesmaximal, characteristic, complemented
3#14521368C211yesmaximal, characteristic
4#14520989C211yesmaximal, characteristic, complemented
5#14520782C211yesmaximal, characteristic
6#14520774C211yesmaximal, characteristic, complemented
7C31×#328C211yesmaximal, characteristic, complemented
8C31×C22⋊Q8C2211yescharacteristic
9#11758523—21no—
10#11758507C2211yescharacteristic
11C2×C4⋊Dic31C2211yescharacteristic
12C2×Dic31⋊C4C2211yescharacteristic
13#11758475—21no—
14#11758471—21no—
15#11758467—21no—
16#11758463—21no—
17(C22⋊D31)⋊C4—21no—
18C31×C22⋊C8C2211yescharacteristic
19C31×#95C2211yescharacteristic
20#11758423—21no—
21C31⋊#95—21no—
22C31⋊#95—21no—
23C22⋊(C31⋊C8)C2211yescharacteristic
24#11758409—21no—
25#11758405—21no—
26#11758395—21no—
27C2×Q8×C31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32C22×Dic31D411yescharacteristic
33C22×Dic31D411yescharacteristic
34C2×D124D411yescharacteristic
35C2×C4×D31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31D411yescharacteristic
39C22⋊C4×C31—21no—
40(C2×D31)⋊C4—21no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43(C2×D31)⋊C4—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31—21no—
48C4⋊Dic31D411yescharacteristic
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52C4×Dic31—21no—
53C2×C31⋊C8—21no—
54C23×C31C2×D411yescharacteristic
55C22×D31—21no—
56Q8×C31—41no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C22⋊D31—41no—
66C22⋊D31—41no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—21no—
72C2×Dic31—41no—
73C2×Dic31—42no—
74C2×Dic31—41no—
75D124—41no—
76C4×D31—81no—
77C8×C31—41no—
78C31⋊C8—41no—
79#1615—311nomaximal, Sylow
80C22×C31—21no—
81C22×C31—21no—
82C22×C31#12011yescharacteristic
83C22×C31#13511yescharacteristic
84C22×C31#13711yescharacteristic
85C2×D31—41no—
86C2×D31—41no—
87C2×D31—41no—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31—41no—
91C4×C31—41no—
92C4×C31—81no—
93Dic31—41no—
94Dic31—41no—
95Dic31—41no—
96Dic31—81no—
97#539—311no—
98#484—311no—
99#481—311no—
100#400—311no—
101#328D3111yescharacteristic, complemented
102#327—311no—
103#324—311no—
104C2×C31—21no—
105C2×C31—21no—
106C2×C31#45211yescharacteristic
107C2×C31#45411yescharacteristic
108C2×C31#45811yescharacteristic
109D31—81no—
110#126—621no—
111#125—621no—
112#123—621no—
113#123—621no—
114C22⋊Q8—621no—
115C22⋊Q8C2×D3111yescharacteristic
116#121—311no—
117C4×D4—621no—
118C2×C4⋊C4—311no—
119C2×C4⋊C4—311no—
120#107—621no—
121#106—621no—
122#103—621no—
123#102—621no—
124C22⋊C8—311no—
125C22⋊C8C2×D3111yescharacteristic
126#95—621no—
127#95—621no—
128#95C2×D3111yescharacteristic
129C31#161511yescharacteristic, complemented, Sylow
130C2×Q8D12411yescharacteristic
131C2×D4—311no—
132C2×D4—621no—
133C22×C4—21no—
134C22×C4—311no—
135C22×C4—311no—
136C22×C4—621no—
137C22×C4—621no—
138C22×C4C22×D3111yescharacteristic
139C2×C8—21no—
140C2×C8—621no—
141C4⋊C4—21no—
142C4⋊C4—311no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C4⋊C4—621no—
150C4⋊C4D12411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—621no—
153C22⋊C4—621no—
154C22⋊C4—621no—
155C22⋊C4—621no—
156C42—621no—
157C23—621no—
158C23D4×D3111yescharacteristic
159Q8—41no—
160D4—1241no—
161D4—1241no—
162D4—1241no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—621no—
170C2×C4—621no—
171C2×C4—621no—
172C2×C4—621no—
173C2×C4—621no—
174C2×C4—1241no—
175C2×C4—1242no—
176C2×C4—1241no—
177C2×C4—2481no—
178C2×C4C2×D12411yescharacteristic
179C2×C4D4×D3111yescharacteristic
180C8—41no—
181C8—1241no—
182C22—21no—
183C22—21no—
184C22—1241no—
185C22—1241no—
186C22—1241no—
187C22#1175845911yescharacteristic
188C22#1175849311yescharacteristic
189C22#1175849511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—1241no—
196C4—1241no—
197C4—1241no—
198C4—2481no—
199C2—21no—
200C2—21no—
201C2—2481no—
202C2#1452121411yescharacteristic
203C2#1452122311yescharacteristic
204C2#1452124011yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31#120
prime radical#11758507C22
hypercenter#328D31
hypocenterC31#1615
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
2. #14521382C2semidirect
4. #14520989C2semidirect
6. #14520774C2semidirect
7. C31×#328C2semidirect
101. #328D31semidirect
129. C31#1615semidirect

Maximal subgroups

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

subgroupindex
#145216482
#145213822
#145213682
#145209892
#145207822
#145207742
C31×#3282
#161531