Finite Group Databasebeta

← #16844840

Subgroups — #16844840

Order 3968.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521721C211yesmaximal, characteristic
2#14521422C211yesmaximal, characteristic, complemented
3#14521344C211yesmaximal, characteristic, complemented
4#14521340C211yesmaximal, characteristic, complemented
5#14520792C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic, complemented
7C31×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#92499—21no—
9C4×Q8×C31C2211yescharacteristic
10C2×#92470—22no—
11#11758472—22no—
12#11758472—21no—
13#11758451—21no—
14#11758451C2211yescharacteristic
15C4×D124—21no—
16C4×D124C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C4×C8×C31C2211yescharacteristic
20#11758423—21no—
21#11758409—21no—
22#11758405—21no—
23#11758395—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31D411yescharacteristic
26#92499—42no—
27#92499—42no—
28C2×D124—22no—
29C2×D124—21no—
30C2×D124—21no—
31C2×D124—22no—
32C2×D124D411yescharacteristic
33C2×D124D412yes—
34C2×C4×D31—22no—
35C2×C4×D31—21no—
36C2×Dic62—21no—
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31D411yescharacteristic
41C42×C31—21no—
42C42×C31C2311yescharacteristic
43(C2×D31)⋊C4—22no—
44(C2×D31)⋊C4—21no—
45C4⋊Dic31—21no—
46C4⋊Dic31—21no—
47C4⋊Dic31D411yescharacteristic
48C2×C31⋊C8—21no—
49#92470—44no—
50C22×D31—21no—
51C22×D31—22no—
52Q8×C31—21no—
53Q8×C31SD1612yescomplemented
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×Dic31—21no—
60C2×Dic31—41no—
61D124—21no—
62D124—21no—
63D124—42no—
64D124—44no—
65D124—41no—
66D124—41no—
67D124—41no—
68D124—41no—
69D124—82no—
70C4×D31—44no—
71C4×D31—41no—
72C4×D31—41no—
73Dic62—42no—
74C8×C31—22no—
75C8×C31—41no—
76C31⋊C8—41no—
77#1631—311nomaximal, Sylow
78C22×C31#12011yescharacteristic
79C2×D31—42no—
80C2×D31—41no—
81C2×D31—41no—
82C2×D31—42no—
83C2×D31—42no—
84C2×D31—41no—
85C4×C31—22no—
86C4×C31—21no—
87C4×C31—41no—
88C4×C31C2×SD1611yescharacteristic
89C4×C31#13511yescharacteristic
90C4×C31AGL(1,ℤ/8)11yescharacteristic
91C4×C31#13711yescharacteristic
92Dic31—41no—
93Dic31—81no—
94#550—311no—
95#492—311no—
96#477—311no—
97#476—311no—
98#331—311no—
99Q8⋊C8D3111yescharacteristic, complemented
100D4⋊C8—311no—
101C2×C31#45011yescharacteristic
102C2×C31#45211yescharacteristic
103C2×C31#45311yescharacteristic
104D31—81no—
105D31—82no—
106C2×#41—621no—
107C2×SD16—622no—
108C4⋊Q8—311no—
109#127—311no—
110#127—621no—
111#121—622no—
112#121—621no—
113C4×Q8C2×D3111yescharacteristic
114C4×D4—311no—
115C4×D4—621no—
116#107—621no—
117#106—621no—
118C4⋊C8—311no—
119C4⋊C8C2×D3111yescharacteristic
120#103—621no—
121#102—621no—
122C4×C8C2×D3111yescharacteristic
123C31#163111yescharacteristic, complemented, Sylow
124#41—1242no—
125#41—1242no—
126C2×Q8—621no—
127C2×Q8D12411yescharacteristic
128C2×D4—311no—
129C2×D4—312no—
130C2×D4—622no—
131C2×D4—622no—
132C2×D4—621no—
133C2×D4—621no—
134C22×C4—622no—
135C22×C4—621no—
136SD16—1244no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—621no—
140C4⋊C4—21no—
141C4⋊C4—311no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4D12411yescharacteristic
145C22⋊C4—622no—
146C22⋊C4—621no—
147C42—21no—
148C42C22×D3111yescharacteristic
149C23—621no—
150C23—622no—
151Q8—21no—
152Q8—1242no—
153Q8#9247012yescomplemented
154D4—621no—
155D4—621no—
156D4—1242no—
157D4—1244no—
158D4—1241no—
159D4—1241no—
160D4—1241no—
161D4—1241no—
162D4—2482no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—621no—
166C2×C4—1244no—
167C2×C4—1241no—
168C2×C4—1241no—
169C2×C4—1241no—
170C2×C4C2×D12411yescharacteristic
171C2×C4D4×D3111yescharacteristic
172C2×C4D4×D3111yescharacteristic
173C8—22no—
174C8—41no—
175C8—1241no—
176C22—1242no—
177C22—1241no—
178C22—1241no—
179C22—1242no—
180C22—1242no—
181C22—1241no—
182C22#1175845911yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—1241no—
187C4—2481no—
188C4C2×#9247011yescharacteristic
189C4#1175848511yescharacteristic
190C4#1175849311yescharacteristic
191C4#1175849511yescharacteristic
192C2—2481no—
193C2—2482no—
194C2#1452120211yescharacteristic
195C2#1452121411yescharacteristic
196C2#1452121811yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×Q8⋊C8C2
socleC22×C31#120
prime radical#14521721C2
hypercenterQ8⋊C8D31
hypocenterC31#1631
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #14521422C2semidirect
3. #14521344C2semidirect
4. #14521340C2semidirect
5. #14520792C2semidirect
6. #14520778C2semidirect
7. C31×Q8⋊C8C2semidirect
53. Q8×C31SD16semidirect
99. Q8⋊C8D31semidirect
123. C31#1631semidirect
153. Q8#92470semidirect

Maximal subgroups

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

subgroupindex
#145217212
#145214222
#145213442
#145213402
#145207922
#145207782
C31×Q8⋊C82
#163131