Finite Group Databasebeta

← #16844709

Subgroups — #16844709

Order 3968.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#14521644C211yesmaximal, characteristic
2#14521380C211yesmaximal, characteristic, complemented
3#14521360C211yesmaximal, characteristic
4#14520981C211yesmaximal, characteristic, complemented
5#14520785C211yesmaximal, characteristic, complemented
6#14520774C211yesmaximal, characteristic, complemented
7C31×#327C211yesmaximal, characteristic
8C31×#121C2211yescharacteristic
9#11758512—21no—
10#11758512—21no—
11D4×Dic31—21no—
12C2×C4⋊Dic31—21no—
13C2×C4⋊Dic31C2211yescharacteristic
14#11758501C2211yescharacteristic
15C2×Dic31⋊C4C2211yescharacteristic
16#11758466—21no—
17#11758456—21no—
18#11758455—21no—
19C31×C22⋊C8C2211yescharacteristic
20C31×#95C2211yescharacteristic
21#11758420—21no—
22C31⋊#95—21no—
23C22⋊(C31⋊C8)C2211yescharacteristic
24#11758405—21no—
25#11758404—21no—
26#11758395—21no—
27C2×D4×C31—21no—
28C2×D4×C31D411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C22×Dic31—21no—
32C22×Dic31—21no—
33C22×Dic31D411yescharacteristic
34C22×Dic31D411yescharacteristic
35C2×Dic62D411yescharacteristic
36C2×C8×C31—21no—
37C4⋊C4×C31D411yescharacteristic
38C22⋊C4×C31—21no—
39C22⋊Dic31—21no—
40C22⋊Dic31—21no—
41C22⋊Dic31—21no—
42C22⋊Dic31—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—42no—
47C4⋊Dic31D411yescharacteristic
48Dic31⋊C4—21no—
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52Dic31⋊C4—21no—
53C4×Dic31—21no—
54C2×C31⋊C8—21no—
55C23×C31—21no—
56C23×C31C2×D411yescharacteristic
57D4×C31—41no—
58D4×C31—41no—
59D4×C31—41no—
60C2×C4×C31—22no—
61C2×C4×C31—21no—
62C2×C4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—21no—
71C2×Dic31—21no—
72C2×Dic31—21no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77C2×Dic31—81no—
78Dic62—41no—
79C8×C31—41no—
80C31⋊C8—41no—
81#1609—311nomaximal, Sylow
82C22×C31—21no—
83C22×C31—21no—
84C22×C31—41no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31#12011yescharacteristic
88C22×C31#13511yescharacteristic
89C22×C31AGL(1,ℤ/8)11yescharacteristic
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—42no—
93C4×C31—41no—
94Dic31—41no—
95Dic31—41no—
96Dic31—41no—
97Dic31—41no—
98Dic31—81no—
99#539—311no—
100#483—311no—
101#480—311no—
102#398—311no—
103#328—311no—
104#327D3111yescharacteristic
105#324—311no—
106C2×C31—21no—
107C2×C31—21no—
108C2×C31—81no—
109C2×C31#44911yescharacteristic
110C2×C31#45611yescharacteristic
111C2×C31#45811yescharacteristic
112#126—621no—
113#125—621no—
114#123—621no—
115#123—621no—
116C22⋊Q8—311no—
117C22⋊Q8—621no—
118#121C2×D3111yescharacteristic
119C4×D4—621no—
120C2×C4⋊C4—311no—
121C2×C4⋊C4—311no—
122C2×C4⋊C4—621no—
123#107—621no—
124#106—621no—
125#103—621no—
126#102—621no—
127C22⋊C8—311no—
128C22⋊C8C2×D3111yescharacteristic
129#95—621no—
130#95C2×D3111yescharacteristic
131C31#160911yescharacteristic, complemented, Sylow
132C2×Q8—311no—
133C2×D4—21no—
134C2×D4D12411yescharacteristic
135C22×C4—21no—
136C22×C4—311no—
137C22×C4—311no—
138C22×C4—621no—
139C22×C4—621no—
140C22×C4C22×D3111yescharacteristic
141C2×C8—21no—
142C2×C8—621no—
143C4⋊C4—311no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C4⋊C4—621no—
150C4⋊C4—621no—
151C4⋊C4—621no—
152C4⋊C4—1242no—
153C4⋊C4D12411yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—621no—
156C22⋊C4—621no—
157C22⋊C4—621no—
158C22⋊C4—621no—
159C42—621no—
160C23—21no—
161C23D4×D3111yescharacteristic
162Q8—1241no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—621no—
172C2×C4—621no—
173C2×C4—621no—
174C2×C4—621no—
175C2×C4—621no—
176C2×C4—621no—
177C2×C4—1241no—
178C2×C4—1241no—
179C2×C4—1241no—
180C2×C4—1241no—
181C2×C4—2481no—
182C2×C4C2×D12411yescharacteristic
183C2×C4D4×D3111yescharacteristic
184C8—41no—
185C8—1241no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1175845911yescharacteristic
192C22#1175848811yescharacteristic
193C22#1175849311yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—1241no—
199C4—1241no—
200C4—1241no—
201C4—1241no—
202C4—2481no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1452119511yescharacteristic
207C2#1452123311yescharacteristic
208C2#1452124011yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#327C2
socleC22×C31#120
prime radicalC31×#121C22
hypercenter#327D31
hypocenterC31#1609
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14521380C2semidirect
4. #14520981C2semidirect
5. #14520785C2semidirect
6. #14520774C2semidirect
131. C31#1609semidirect

Maximal subgroups

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

subgroupindex
#145216442
#145213802
#145213602
#145209812
#145207852
#145207742
C31×#3272
#160931