Finite Group Databasebeta

← #16844344

Subgroups — #16844344

Order 3968.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#14521598C211yesmaximal, characteristic
2#14521104C212yesmaximal, complemented
3#14520789C211yesmaximal, characteristic, complemented
4#14520788C212yesmaximal, complemented
5C31×#329C211yesmaximal, characteristic, complemented
6C2×#92499C411yescharacteristic
7C2×#92497C411yescharacteristic
8C31×#124C2211yescharacteristic
9#11758521C411yescharacteristic
10#11758517C411yescharacteristic
11#11758461—22no—
12(C22⋊D31)⋊C4—22no—
13#11758452C2211yescharacteristic
14C42×D31C2211yescharacteristic
15C31×#97C2212yes—
16(C2×D31)⋊C8—22no—
17Dic31⋊C8—22no—
18#11758391C2212yes—
19C2×Q8×C31C2×C411yescharacteristic
20C2×D4×C31C2×C411yescharacteristic
21C2×C22⋊D31—21no—
22C2×C22⋊D31—22no—
23C22×Dic31—21no—
24#92499—42no—
25#92497—42no—
26C2×D124—21no—
27C2×D124C2×C411yescharacteristic
28C2×C4×D31—21no—
29C2×C4×D31C2×C411yescharacteristic
30C2×C4×D31D412yes—
31C2×Dic62C2×C411yescharacteristic
32C2×C8×C31—22no—
33C22⋊C4×C31—22no—
34C42×C31C2311yescharacteristic
35(C2×D31)⋊C4—22no—
36Dic31⋊C4—22no—
37C4×Dic31C2×C411yescharacteristic
38C4×Dic31D412yes—
39C2×C31⋊C8—22no—
40C23×C31—21no—
41C22×D31—21no—
42C22×D31C22⋊C411yescharacteristic
43Q8×C31—41no—
44D4×C31—41no—
45C2×C4×C31—21no—
46C2×C4×C31C22×C411yescharacteristic
47C2×C4×C31C2×D412yes—
48C22⋊D31—44no—
49C22⋊D31—42no—
50C2×Dic31—21no—
51C2×Dic31—42no—
52C2×Dic31C22⋊C412yes—
53C2×Dic31C22⋊C411yescharacteristic
54D124—41no—
55D124—42no—
56C4×D31—22no—
57C4×D31—42no—
58C4×D31—42no—
59Dic62—41no—
60C8×C31—42no—
61C31⋊C8—42no—
62#1536—311nomaximal, Sylow
63C22×C31—41no—
64C22×C31—42no—
65C22×C31C2×C22⋊C411yescharacteristic
66C2×D31—21no—
67C2×D31—22no—
68C2×D31—41no—
69C2×D31—42no—
70C4×C31—21no—
71C4×C31—22no—
72C4×C31—41no—
73Dic31—22no—
74Dic31—41no—
75Dic31#10012yes—
76#532—311no—
77#432—312no—
78#329—311no—
79#329—312no—
80#329D3111yescharacteristic, complemented
81C2×C31—81no—
82C2×C31C2×#10011yescharacteristic
83C2×C31#42112yes—
84D31—41no—
85D31—81no—
86C2×#41—311no—
87C2×#41—311no—
88C4⋊Q8—311no—
89#127—311no—
90#124—311no—
91#124C2×D3111yescharacteristic
92#121—622no—
93C4×D4—622no—
94C2×C42—311no—
95C4⋊C8—622no—
96C22⋊C8—622no—
97#97—312no—
98#97C2×D3112yes—
99C31#153611yescharacteristic, complemented, Sylow
100#41—1242no—
101#41—1242no—
102C2×Q8—311no—
103C2×Q8C4×D3111yescharacteristic
104C2×D4—311no—
105C2×D4—621no—
106C2×D4—622no—
107C2×D4—621no—
108C2×D4C4×D3111yescharacteristic
109C22×C4—311no—
110C22×C4—312no—
111C22×C4—621no—
112C22×C4—621no—
113C2×C8—22no—
114C2×C8—622no—
115C4⋊C4—622no—
116C22⋊C4—22no—
117C22⋊C4—622no—
118C42—311no—
119C42—312no—
120C42C22×D3111yescharacteristic
121C23—21no—
122C23—311no—
123C23—621no—
124Q8—41no—
125Q8—1241no—
126D4—41no—
127D4—1241no—
128D4—1242no—
129D4—1244no—
130D4—1242no—
131C2×C4—21no—
132C2×C4—311no—
133C2×C4—312no—
134C2×C4—622no—
135C2×C4—621no—
136C2×C4—1242no—
137C2×C4—1242no—
138C2×C4—1242no—
139C2×C4C2×C4×D3111yescharacteristic
140C2×C4D4×D3112yes—
141C8—42no—
142C8—1242no—
143C22—41no—
144C22—42no—
145C22—621no—
146C22—622no—
147C22—1241no—
148C22—1242no—
149C22C22⋊C4×D3111yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—312no—
154C4—622no—
155C4—1241no—
156C2—81no—
157C2—1241no—
158C2—2481no—
159C2#100×D3111yescharacteristic
160C2#1452106412yes—
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#329C2
socleC22×C31C2×C22⋊C4
prime radical#14521598C2
cosocleC42×C31C23
hypercenter#329D31
hypocenterC31#1536
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14521104C2semidirect
3. #14520789C2semidirect
4. #14520788C2semidirect
5. C31×#329C2semidirect
80. #329D31semidirect
99. C31#1536semidirect

Maximal subgroups

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

subgroupindex
#145215982
#145211042
#145207892
#145207882
C31×#3292
#153631