Finite Group Databasebeta

← #16844713

Subgroups — #16844713

Order 3968.

254 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521630C211yesmaximal, characteristic
2#14521362C212yesmaximal, complemented
3#14520782C212yesmaximal, complemented
4#14520775C211yesmaximal, characteristic, complemented
5C31×#398C211yesmaximal, characteristic, complemented
6C2×#92495—21no—
7C2×C4⋊C4×C31—21no—
8C2×C4⋊C4×C31C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10#11758507—21no—
11#11758507C2212yes—
12#11758474—22no—
13#11758472—22no—
14C31×#95—21no—
15C31×#95C2211yescharacteristic
16C22⋊(C31⋊C8)C2212yes—
17#11758397—22no—
18#11758395—22no—
19C22×C4×C31—21no—
20C22×C4×C31—21no—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C2×C22⋊D31—22no—
25#92495—42no—
26#92495—42no—
27C2×D124—21no—
28C2×D124—21no—
29C2×D124D412yes—
30C2×C4×D31—22no—
31C2×Dic62—21no—
32C4⋊C4×C31—22no—
33C4⋊C4×C31—22no—
34C4⋊C4×C31—42no—
35(C2×D31)⋊C4—22no—
36(C2×D31)⋊C4—22no—
37C4⋊Dic31—21no—
38C4⋊Dic31D412yes—
39C2×C31⋊C8—22no—
40C23×C31C2×D411yescharacteristic
41C22×D31—22no—
42C2×C4×C31—21no—
43C2×C4×C31—21no—
44C2×C4×C31—22no—
45C2×C4×C31—21no—
46C2×C4×C31—41no—
47C2×C4×C31—41no—
48C2×C4×C31—41no—
49C2×C4×C31—41no—
50C2×C4×C31—41no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31D812yes—
54C2×C4×C31C2×D412yes—
55C22⋊D31—42no—
56C22⋊D31—42no—
57C2×Dic31—22no—
58D124—42no—
59D124—42no—
60D124—81no—
61C4×D31—44no—
62Dic62—42no—
63C31⋊C8—42no—
64#1610—311nomaximal, Sylow
65C22×C31—21no—
66C22×C31—21no—
67C22×C31#12011yescharacteristic
68C22×C31C2×D811yescharacteristic
69C22×C31AGL(1,ℤ/8)11yescharacteristic
70C2×D31—42no—
71C2×D31—42no—
72C2×D31—42no—
73C4×C31—22no—
74C4×C31—22no—
75C4×C31—42no—
76C4×C31—41no—
77C4×C31—81no—
78Dic31—42no—
79#537—311no—
80#480—312no—
81#398D3111yescharacteristic, complemented
82#327—312no—
83#324—311no—
84C2×C31—21no—
85C2×C31—21no—
86C2×C31#44711yescharacteristic
87C2×C31#45611yescharacteristic
88C2×C31#45811yescharacteristic
89D31—82no—
90C2×#41—621no—
91C22⋊Q8—622no—
92#121—312no—
93#121—622no—
94#121—621no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D3111yescharacteristic
97C2×C4⋊C4C2×D3111yescharacteristic
98#107—622no—
99#102—622no—
100C22⋊C8—312no—
101#95—21no—
102#95C2×D3111yescharacteristic
103C31#161011yescharacteristic, complemented, Sylow
104#41—1242no—
105#41—1242no—
106C2×Q8—621no—
107C2×D4—312no—
108C2×D4—621no—
109C2×D4—621no—
110C2×D4—622no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—622no—
114C22×C4C22⋊D3111yescharacteristic
115C22×C4C22⋊D3111yescharacteristic
116C22×C4C22×D3111yescharacteristic
117C2×C8—622no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—312no—
122C4⋊C4—621no—
123C22⋊C4—622no—
124C22⋊C4—622no—
125C23—622no—
126C23C2×C22⋊D3111yescharacteristic
127Q8—1242no—
128D4—1242no—
129D4—1242no—
130D4—1242no—
131D4—1242no—
132D4—2481no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—622no—
145C2×C4—1244no—
146C2×C4#9247912yes—
147C2×C4D4×D3112yes—
148C8—1242no—
149C22—21no—
150C22—21no—
151C22—1242no—
152C22—1242no—
153C22—1242no—
154C22C2×#9247911yescharacteristic
155C22#1175851411yescharacteristic
156C22#1175852611yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—1242no—
163C2—21no—
164C2—21no—
165C2—2482no—
166C2#1452118211yescharacteristic
167C2#1452123111yescharacteristic
168C2#1452123811yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#398C2
socleC22×C31#120
prime radical#14521630C2
hypercenter#398D31
hypocenterC31#1610
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #14521362C2semidirect
3. #14520782C2semidirect
4. #14520775C2semidirect
5. C31×#398C2semidirect
81. #398D31semidirect
103. C31#1610semidirect

Maximal subgroups

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

subgroupindex
#145216302
#145213622
#145207822
#145207752
C31×#3982
#161031