Finite Group Databasebeta

← #16847384

Subgroups — #16847384

Order 3968.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521619C211yesmaximal, characteristic
2#14521021C212yesmaximal
3#14520844C211yesmaximal, characteristic, complemented
4#14520843C212yesmaximal, complemented
5C31×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D31C411yescharacteristic, complemented
7C2×#92497C2211yescharacteristic
8C31×#124C2211yescharacteristic
9#11758521C411yescharacteristic, complemented
10#11758513C2211yescharacteristic
11#11758460—22no—
12#11758455—22no—
13#11758454—22no—
14#11758449C411yescharacteristic, complemented
15#11758446C411yescharacteristic, complemented
16C31×#99C2212yes—
17#11758422C2212yes—
18#11758394—22no—
19C2×Q8×C31C2×C411yescharacteristic
20C2×D4×C31C2311yescharacteristic
21C2×C22⋊D31D412yes—
22C22×Dic31D412yes—
23Q8×D31—42no—
24#92497—42no—
25C2×C4×D31—21no—
26C2×C4×D31C2×C411yescharacteristic
27C2×Dic62—21no—
28C2×Dic62C2×C411yescharacteristic
29C2×Dic62C2×C411yescharacteristic
30C22⋊C4×C31—22no—
31C22⋊C4×C31—22no—
32C42×C31C2×C411yescharacteristic
33C22⋊Dic31—22no—
34C22⋊Dic31—22no—
35(C2×D31)⋊C4—21no—
36C4⋊Dic31—22no—
37Dic31⋊C4—21no—
38Dic31⋊C4—22no—
39Dic31⋊C4—42no—
40C4×Dic31—42no—
41C4×Dic31C2×C411yescharacteristic
42C23×C31C2×D412yes—
43C22×D31C22⋊C411yescharacteristic
44Q8×C31—41no—
45D4×C31—41no—
46C2×C4×C31—21no—
47C2×C4×C31—21no—
48C2×C4×C31—42no—
49C2×C4×C31C22×C411yescharacteristic
50C22⋊D31—42no—
51C2×Dic31—22no—
52C2×Dic31—22no—
53C2×Dic31—21no—
54C2×Dic31—21no—
55C2×Dic31—42no—
56C2×Dic31C22⋊C412yes—
57C2×Dic31C22⋊C411yescharacteristic
58C4×D31—22no—
59C4×D31—42no—
60Dic62—41no—
61Dic62—42no—
62Dic62—41no—
63#2129—311nomaximal, Sylow
64C22×C31—22no—
65C22×C31—42no—
66C22×C31C2×C22⋊C411yescharacteristic
67C2×D31—21no—
68C2×D31—41no—
69C4×C31—21no—
70C4×C31—41no—
71C4×C31—41no—
72C4×C31—82no—
73Dic31—22no—
74Dic31—41no—
75Dic31—41no—
76Dic31—82no—
77Dic31#9912yes—
78#536—311no—
79#410—312no—
80#354—311no—
81#354—312no—
82#354D3111yescharacteristic, complemented
83C2×C31—21no—
84C2×C31—42no—
85C2×C31C2×#9911yescharacteristic
86D31—41no—
87C2×#41—311no—
88C22×Q8—311no—
89C4⋊Q8—311no—
90C4⋊Q8—311no—
91#124—311no—
92#124C2×D3111yescharacteristic
93#123—622no—
94C22⋊Q8—622no—
95#117—311no—
96#117—622no—
97#99—312no—
98#99—622no—
99#99C2×D3112yes—
100C31#212911yescharacteristic, complemented, Sylow
101#41—1242no—
102C2×Q8—311no—
103C2×Q8—311no—
104C2×Q8—621no—
105C2×Q8—1242no—
106C2×Q8C4×D3111yescharacteristic
107C2×D4—312no—
108C2×D4C22×D3111yescharacteristic
109C22×C4—312no—
110C22×C4—311no—
111C22×C4—621no—
112C4⋊C4—621no—
113C4⋊C4—622no—
114C4⋊C4—622no—
115C4⋊C4—1242no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—621no—
119C22⋊C4—622no—
120C22⋊C4—622no—
121C42—311no—
122C42—1242no—
123C42C4×D3111yescharacteristic
124C23—311no—
125C23D4×D3112yes—
126Q8—41no—
127Q8—1241no—
128Q8—1241no—
129Q8—1242no—
130D4—41no—
131D4—1242no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—311no—
136C2×C4—312no—
137C2×C4—622no—
138C2×C4—622no—
139C2×C4—622no—
140C2×C4—621no—
141C2×C4—621no—
142C2×C4—1242no—
143C2×C4—1242no—
144C2×C4C2×C4×D3111yescharacteristic
145C22—22no—
146C22—42no—
147C22—621no—
148C22—1241no—
149C22C22⋊C4×D3111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—312no—
155C4—622no—
156C4—1241no—
157C4—1241no—
158C4—2482no—
159C2—21no—
160C2—42no—
161C2—1241no—
162C2#99×D3111yescharacteristic
subgroupG/H
centerC2#99×D31
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#354C2
socleC2×C31C2×#99
prime radicalC2×#92497C22
cosocleC2×D4×C31C23
hypercenter#354D31
hypocenterC31#2129
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #14520844C2semidirect
4. #14520843C2semidirect
5. C31×#354C2semidirect
6. C2×Q8×D31C4semidirect
9. #11758521C4semidirect
14. #11758449C4semidirect
15. #11758446C4semidirect
82. #354D31semidirect
100. C31#2129semidirect

Maximal subgroups

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

subgroupindex
#145216192
#145210212
#145208442
#145208432
C31×#3542
#212931