Finite Group Databasebeta

← #16845047

Subgroups — #16845047

Order 3968.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521803C211yesmaximal, characteristic
2#14521459C211yesmaximal, characteristic, complemented
3#14521418C211yesmaximal, characteristic, complemented
4#14521409C211yesmaximal, characteristic
5#14520790C211yesmaximal, characteristic, complemented
6#14520788C211yesmaximal, characteristic
7C31×#330C211yesmaximal, characteristic, complemented
8C31×#125C2211yescharacteristic
9#11758475—21no—
10#11758475—21no—
11#11758474—21no—
12#11758473—21no—
13#11758471—21no—
14#11758465—21no—
15#11758452C2211yescharacteristic
16#11758447C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×#97C2211yescharacteristic
19C31×#97C2211yescharacteristic
20#11758409—21no—
21#11758404—21no—
22#11758404—21no—
23#11758404—21no—
24#11758396—21no—
25#11758395—21no—
26#11758391C2211yescharacteristic
27C2×D124D411yescharacteristic
28C2×C4×D31—21no—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62D411yescharacteristic
32C2×C8×C31—21no—
33C2×C8×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31D411yescharacteristic
37C4⋊C4×C31D411yescharacteristic
38C42×C31C2311yescharacteristic
39(C2×D31)⋊C4—21no—
40(C2×D31)⋊C4—21no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43(C2×D31)⋊C4—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31D411yescharacteristic
48C4⋊Dic31D411yescharacteristic
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52C4×Dic31—21no—
53C2×C31⋊C8—21no—
54C22×D31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×Dic31—21no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31—41no—
64D124—41no—
65C4×D31—81no—
66Dic62—41no—
67Dic62—42no—
68Dic62—81no—
69C8×C31—41no—
70C8×C31—41no—
71C31⋊C8—22no—
72#1664—311nomaximal, Sylow
73C22×C31#12011yescharacteristic
74C2×D31—41no—
75C2×D31—41no—
76C2×D31—41no—
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31—41no—
81C4×C31—41no—
82Dic31—41no—
83Dic31—41no—
84Dic31—41no—
85Dic31—81no—
86#563—311no—
87#501—311no—
88#491—311no—
89#489—311no—
90#330—311no—
91#330D3111yescharacteristic, complemented
92#329—311no—
93C2×C31#45411yescharacteristic
94C2×C31#45511yescharacteristic
95C2×C31#45611yescharacteristic
96D31—81no—
97C4⋊Q8—311no—
98C4⋊Q8—621no—
99#126—621no—
100#126—621no—
101#125—311no—
102#125C2×D3111yescharacteristic
103#124—311no—
104#123—621no—
105C22⋊Q8—621no—
106C22⋊Q8—621no—
107#107—621no—
108#106—621no—
109#103—621no—
110#103—621no—
111#103—621no—
112#102—621no—
113#97—311no—
114#97C2×D3111yescharacteristic
115#97C2×D3111yescharacteristic
116C31#166411yescharacteristic, complemented, Sylow
117C2×Q8—311no—
118C2×Q8—621no—
119C2×Q8—621no—
120C2×D4—311no—
121C22×C4—621no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—621no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—311no—
128C4⋊C4—311no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C4⋊C4—621no—
132C4⋊C4—621no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C4⋊C4D12411yescharacteristic
136C4⋊C4D12411yescharacteristic
137C22⋊C4—621no—
138C22⋊C4—621no—
139C22⋊C4—621no—
140C22⋊C4—621no—
141C22⋊C4—621no—
142C42—621no—
143C42C22×D3111yescharacteristic
144C23—621no—
145Q8—1241no—
146Q8—1242no—
147Q8—2481no—
148D4—1241no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—621no—
152C2×C4—621no—
153C2×C4—621no—
154C2×C4—1241no—
155C2×C4—2481no—
156C2×C4C2×D12411yescharacteristic
157C2×C4D4×D3111yescharacteristic
158C2×C4D4×D3111yescharacteristic
159C8—41no—
160C8—41no—
161C8—622no—
162C22—1241no—
163C22—1241no—
164C22—1241no—
165C22#1175845911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—1241no—
172C4—1241no—
173C4—1241no—
174C4—2481no—
175C2—2481no—
176C2#1452122311yescharacteristic
177C2#1452122811yescharacteristic
178C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#330D31
hypocenterC31#1664
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14521459C2semidirect
3. #14521418C2semidirect
5. #14520790C2semidirect
7. C31×#330C2semidirect
91. #330D31semidirect
116. C31#1664semidirect

Maximal subgroups

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

subgroupindex
#145218032
#145214592
#145214182
#145214092
#145207902
#145207882
C31×#3302
#166431