Finite Group Databasebeta

← #16844680

Subgroups — #16844680

Order 3968.

282 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521187C212yesmaximal, complemented
2#14520969C211yesmaximal, characteristic, complemented
3#14520783C212yesmaximal, complemented
4#14520775C211yesmaximal, characteristic, complemented
5C31×#537C211yesmaximal, characteristic
6C2×#41×C31—21no—
7C22×Dic62C2211yescharacteristic
8C31×C22⋊Q8—22no—
9C31×#121—22no—
10C31×#121—21no—
11C31×#121C2212yes—
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×#92480—22no—
14C2×Dic31⋊C4—21no—
15C31⋊#95—21no—
16C31⋊#95C2211yescharacteristic
17C22⋊(C31⋊C8)C2212yes—
18#11758398—22no—
19#41×C31—42no—
20#41×C31—42no—
21C2×Q8×C31—21no—
22C2×D4×C31—21no—
23C2×D4×C31—22no—
24C2×D4×C31—21no—
25C2×D4×C31D412yes—
26C22×C4×C31—22no—
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31—21no—
32C2×Dic62—22no—
33C2×Dic62—42no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—22no—
36C4⋊C4×C31D412yes—
37C22⋊C4×C31—22no—
38C22⋊C4×C31—22no—
39#92480—44no—
40Dic31⋊C4—42no—
41C2×C31⋊C8—22no—
42C23×C31—22no—
43C23×C31C2×D411yescharacteristic
44Q8×C31—42no—
45D4×C31—42no—
46D4×C31—42no—
47D4×C31—42no—
48D4×C31—42no—
49D4×C31—81no—
50C2×C4×C31—21no—
51C2×C4×C31—21no—
52C2×C4×C31—21no—
53C2×C4×C31—22no—
54C2×C4×C31—41no—
55C2×C4×C31—44no—
56C2×C4×C31—41no—
57C2×C4×C31SD1612yescomplemented
58C2×C4×C31C2×D412yes—
59C2×Dic31—22no—
60C2×Dic31—22no—
61C2×Dic31—41no—
62C2×Dic31—41no—
63C2×Dic31—41no—
64C2×Dic31—41no—
65Dic62—24no—
66Dic62—42no—
67C31⋊C8—42no—
68#1604—311nomaximal, Sylow
69C22×C31—21no—
70C22×C31—21no—
71C22×C31—42no—
72C22×C31—42no—
73C22×C31—42no—
74C22×C31#12011yescharacteristic
75C22×C31C2×SD1611yescharacteristic
76C22×C31AGL(1,ℤ/8)11yescharacteristic
77C4×C31—22no—
78C4×C31—22no—
79C4×C31—42no—
80C4×C31—41no—
81Dic31—42no—
82Dic31—42no—
83#537D3111yescharacteristic
84#448—312no—
85#395—311no—
86#327—312no—
87#324—311no—
88C2×C31—21no—
89C2×C31—21no—
90C2×C31—82no—
91C2×C31#45011yescharacteristic
92C2×C31#45611yescharacteristic
93C2×C31B(4,𝔽2)11yescharacteristic
94C2×#41—21no—
95C22×Q8—311no—
96C2×SD16—622no—
97C22⋊Q8—22no—
98#121—22no—
99#121—21no—
100#121C2×D3112yes—
101C2×C4⋊C4—621no—
102C2×C4⋊C4C2×D3111yescharacteristic
103#103—622no—
104C22⋊C8—312no—
105#95—311no—
106#95—621no—
107C31#160411yescharacteristic, complemented, Sylow
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—622no—
112C2×Q8—1242no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D3112yes—
117C22×C4—22no—
118C22×C4—621no—
119C22×C4—621no—
120C22×C4C22⋊D3111yescharacteristic
121C22×C4C22⋊D3111yescharacteristic
122C22×C4C22×D3111yescharacteristic
123SD16—1244no—
124C2×C8—622no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—1242no—
128C4⋊C4C22⋊D3112yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D3111yescharacteristic
133Q8—42no—
134Q8—624no—
135Q8—1242no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—622no—
149C2×C4—622no—
150C2×C4—1241no—
151C2×C4—1241no—
152C2×C4—1241no—
153C2×C4—1241no—
154C2×C4#9248012yescomplemented
155C2×C4C2×C22⋊D3112yes—
156C8—1242no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1175850911yescharacteristic
163C22C2×#9248011yescharacteristic
164C22#1175853011yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—41no—
169C4—1242no—
170C4—1242no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1452120011yescharacteristic
175C2#1452123211yescharacteristic
176C2#1452123611yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#537C2
socleC22×C31#120
hypercenter#537D31
hypocenterC31#1604
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14521187C2semidirect
2. #14520969C2semidirect
3. #14520783C2semidirect
4. #14520775C2semidirect
57. C2×C4×C31SD16semidirect
107. C31#1604semidirect
154. C2×C4#92480semidirect

Maximal subgroups

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

subgroupindex
#145211872
#145209692
#145207832
#145207752
C31×#5372
#160431