Finite Group Databasebeta

← #16845036

Subgroups — #16845036

Order 3968.

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

normal subgroups only

This group has 196 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#14521793C211yesmaximal, characteristic
2#14521418C211yesmaximal, characteristic, complemented
3#14521409C211yesmaximal, characteristic, complemented
4#14521408C211yesmaximal, characteristic, complemented
5#14520790C211yesmaximal, characteristic, complemented
6#14520788C211yesmaximal, characteristic, complemented
7C31×#329C211yesmaximal, characteristic, complemented
8C31×#124C2211yescharacteristic
9#11758523—21no—
10#11758516—21no—
11#11758463—21no—
12#11758461—21no—
13#11758460—21no—
14#11758455—21no—
15#11758452C2211yescharacteristic
16#11758447C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×#97C2211yescharacteristic
19C31×#97C2211yescharacteristic
20#11758423—21no—
21#11758420—21no—
22#11758409—21no—
23#11758404—21no—
24#11758404—21no—
25#11758404—21no—
26#11758391C2211yescharacteristic
27C2×Q8×C31D411yescharacteristic
28C2×D4×C31D411yescharacteristic
29C2×C22⋊D31—21no—
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32C2×D124D411yescharacteristic
33C2×C4×D31—21no—
34C2×Dic62—21no—
35C2×Dic62D411yescharacteristic
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C22⋊C4×C31—21no—
39C22⋊C4×C31—21no—
40C42×C31C2311yescharacteristic
41C22⋊Dic31—21no—
42(C2×D31)⋊C4—21no—
43(C2×D31)⋊C4—21no—
44(C2×D31)⋊C4—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31—21no—
48C4⋊Dic31D411yescharacteristic
49C4⋊Dic31D411yescharacteristic
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53C2×C31⋊C8—21no—
54C23×C31—21no—
55C22×D31—21no—
56Q8×C31—41no—
57D4×C31—41no—
58C2×C4×C31—21no—
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C22⋊D31—81no—
63C22⋊D31—81no—
64C2×Dic31—21no—
65C2×Dic31—21no—
66C2×Dic31—21no—
67C2×Dic31—41no—
68C2×Dic31—81no—
69D124—41no—
70C4×D31—81no—
71Dic62—41no—
72Dic62—42no—
73C8×C31—41no—
74C8×C31—41no—
75C31⋊C8—41no—
76#1662—311nomaximal, Sylow
77C22×C31—41no—
78C22×C31—41no—
79C22×C31—41no—
80C22×C31#12011yescharacteristic
81C2×D31—41no—
82C2×D31—41no—
83C2×D31—41no—
84C4×C31—21no—
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—41no—
88Dic31—41no—
89Dic31—41no—
90Dic31—41no—
91Dic31—81no—
92#562—311no—
93#491—311no—
94#489—311no—
95#489—311no—
96#330—311no—
97#329—311no—
98#329D3111yescharacteristic, complemented
99C2×C31—81no—
100C2×C31#45411yescharacteristic
101C2×C31#45511yescharacteristic
102C2×C31#45511yescharacteristic
103D31—81no—
104C4⋊Q8—311no—
105#125—311no—
106#124—311no—
107#124C2×D3111yescharacteristic
108#123—621no—
109#123—621no—
110C22⋊Q8—621no—
111C22⋊Q8—621no—
112#121—621no—
113#121—621no—
114#103—621no—
115#103—621no—
116#103—621no—
117#103—621no—
118#102—621no—
119#102—621no—
120#97—311no—
121#97C2×D3111yescharacteristic
122#97C2×D3111yescharacteristic
123C31#166211yescharacteristic, complemented, Sylow
124C2×Q8—311no—
125C2×Q8—621no—
126C2×Q8D12411yescharacteristic
127C2×D4—311no—
128C2×D4—621no—
129C2×D4—621no—
130C2×D4D12411yescharacteristic
131C22×C4—621no—
132C22×C4—621no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—621no—
136C4⋊C4—311no—
137C4⋊C4—311no—
138C4⋊C4—621no—
139C4⋊C4—621no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—621no—
147C22⋊C4—621no—
148C22⋊C4—621no—
149C22⋊C4—621no—
150C42C22×D3111yescharacteristic
151C23—21no—
152C23—621no—
153Q8—41no—
154Q8—1241no—
155Q8—1242no—
156D4—41no—
157D4—1241no—
158D4—2481no—
159D4—2481no—
160C2×C4—21no—
161C2×C4—621no—
162C2×C4—621no—
163C2×C4—621no—
164C2×C4—1241no—
165C2×C4—2481no—
166C2×C4—2481no—
167C2×C4C2×D12411yescharacteristic
168C2×C4D4×D3111yescharacteristic
169C2×C4D4×D3111yescharacteristic
170C8—41no—
171C8—41no—
172C8—1241no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1241no—
177C22—1241no—
178C22—1241no—
179C22#1175845911yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—1241no—
185C4—1241no—
186C4—1241no—
187C4—2481no—
188C2—81no—
189C2—2481no—
190C2#1452122311yescharacteristic
191C2#1452122811yescharacteristic
192C2#1452122911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#329C2
socleC22×C31#120
prime radical#14521793C2
hypercenter#329D31
hypocenterC31#1662
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14521418C2semidirect
3. #14521409C2semidirect
4. #14521408C2semidirect
5. #14520790C2semidirect
6. #14520788C2semidirect
7. C31×#329C2semidirect
98. #329D31semidirect
123. C31#1662semidirect

Maximal subgroups

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

subgroupindex
#145217932
#145214182
#145214092
#145214082
#145207902
#145207882
C31×#3292
#166231