Finite Group Databasebeta

← #16844342

Subgroups — #16844342

Order 3968.

200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521106C211yesmaximal, characteristic, complemented
2#14521106C211yesmaximal, characteristic, complemented
3#14520791C212yesmaximal, complemented
4#14520789C212yesmaximal, complemented
5C31×#529C211yesmaximal, characteristic
6C31×#126—21no—
7C31×#125C2211yescharacteristic
8C31×#124C2211yescharacteristic
9C31×#123—21no—
10C31×C22⋊Q8C411yescharacteristic
11C31×#121C411yescharacteristic
12C4×Q8×C31C411yescharacteristic
13C4×D4×C31—21no—
14C4×D4×C31C411yescharacteristic
15C31×#117—21no—
16C2×C42×C31C2211yescharacteristic
17C22⋊(C31⋊C8)—21no—
18C22⋊(C31⋊C8)—21no—
19C4⋊(C31⋊C8)—21no—
20C4⋊(C31⋊C8)—21no—
21#11758391C2212yes—
22#11758391C2212yes—
23C2×Q8×C31C2×C411yescharacteristic
24C2×D4×C31—21no—
25C2×D4×C31C2×C411yescharacteristic
26C22×C4×C31—21no—
27C22×C4×C31C2×C411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C4⋊C4×C31—21no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31C2×C411yescharacteristic
35C4⋊C4×C31C2×C411yescharacteristic
36C22⋊C4×C31—21no—
37C22⋊C4×C31—21no—
38C22⋊C4×C31—21no—
39C22⋊C4×C31—21no—
40C22⋊C4×C31—21no—
41C42×C31—21no—
42C42×C31C2×C411yescharacteristic
43C42×C31D411yescharacteristic
44C42×C31D411yescharacteristic
45C42×C31C2311yescharacteristic
46C2×C31⋊C8—22no—
47C2×C31⋊C8—22no—
48C23×C31—21no—
49C23×C31C22⋊C411yescharacteristic
50Q8×C31—41no—
51D4×C31—41no—
52D4×C31—42no—
53C2×C4×C31—21no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—41no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31—42no—
60C2×C4×C31C22⋊C411yescharacteristic
61C2×C4×C31C22⋊C411yescharacteristic
62C2×C4×C31C22⋊C411yescharacteristic
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C31⋊C8—42no—
67C31⋊C8—42no—
68#1535—311nomaximal, Sylow
69C22×C31—21no—
70C22×C31—21no—
71C22×C31—21no—
72C22×C31—41no—
73C22×C31—41no—
74C22×C31—41no—
75C22×C31C2×C22⋊C411yescharacteristic
76C4×C31—21no—
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—41no—
83C4×C31—41no—
84C4×C31—41no—
85#529D3111yescharacteristic
86#432—311no—
87#432—311no—
88#330—312no—
89#329—312no—
90C2×C31—41no—
91C2×C31—81no—
92C2×C31#41311yescharacteristic
93C2×C31#42111yescharacteristic
94C2×C31#42111yescharacteristic
95#126—21no—
96#125C2×D3111yescharacteristic
97#124C2×D3111yescharacteristic
98#123—21no—
99C22⋊Q8Dic3111yescharacteristic
100#121Dic3111yescharacteristic
101C4×Q8Dic3111yescharacteristic
102C4×D4—21no—
103C4×D4Dic3111yescharacteristic
104#117—21no—
105C2×C42C2×D3111yescharacteristic
106C4⋊C8—621no—
107C4⋊C8—621no—
108C22⋊C8—621no—
109C22⋊C8—621no—
110#97—312no—
111#97—312no—
112C31#153511yescharacteristic, complemented, Sylow
113C2×Q8C2×Dic3111yescharacteristic
114C2×D4—21no—
115C2×D4C2×Dic3111yescharacteristic
116C22×C4—21no—
117C22×C4C2×Dic3111yescharacteristic
118C22×C4C22⋊D3111yescharacteristic
119C22×C4C22⋊D3111yescharacteristic
120C2×C8—622no—
121C2×C8—622no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4C2×Dic3111yescharacteristic
127C4⋊C4C2×Dic3111yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C42—21no—
134C42C2×Dic3111yescharacteristic
135C42C22⋊D3111yescharacteristic
136C42C22⋊D3111yescharacteristic
137C42C22×D3111yescharacteristic
138C23—21no—
139C23C22⋊Dic3111yescharacteristic
140Q8—41no—
141D4—41no—
142D4—42no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4C22⋊Dic3111yescharacteristic
151C2×C4C22⋊Dic3111yescharacteristic
152C2×C4C22⋊Dic3111yescharacteristic
153C2×C4C22×Dic3111yescharacteristic
154C2×C4C2×C22⋊D3111yescharacteristic
155C2×C4C2×C22⋊D3111yescharacteristic
156C8—1242no—
157C8—1242no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊Dic3111yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—41no—
174C2—41no—
175C2—81no—
176C2#1452103311yescharacteristic
177C2#1452106611yescharacteristic
178C2#1452106611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#529C2
socleC22×C31C2×C22⋊C4
prime radicalC31×#121C4
cosocleC42×C31C23
hypercenter#529D31
hypocenterC31#1535
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14521106C2semidirect
2. #14521106C2semidirect
3. #14520791C2semidirect
4. #14520789C2semidirect
112. C31#1535semidirect

Maximal subgroups

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

subgroupindex
#145211062
#145207912
#145207892
C31×#5292
#153531