Finite Group Databasebeta

← #16844914

Subgroups — #16844914

Order 3968.

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

normal subgroups only

This group has 250 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#14521396C211yesmaximal, characteristic, complemented
3#14521334C211yesmaximal, characteristic, complemented
4#14521255C211yesmaximal, characteristic, complemented
5#14520792C211yesmaximal, characteristic, complemented
6#14520778C211yesmaximal, characteristic, complemented
7C31×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#92499—21no—
9C4×Q8×C31C2211yescharacteristic
10C2×#92470—21no—
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—22no—
22#11758404—21no—
23#11758396—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—42no—
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—41no—
74Dic62—41no—
75C8×C31—41no—
76C8×C31—41no—
77C31⋊C8—41no—
78#1642—311nomaximal, Sylow
79C22×C31#12011yescharacteristic
80C2×D31—41no—
81C2×D31—42no—
82C2×D31—42no—
83C2×D31—41no—
84C2×D31—42no—
85C2×D31—41no—
86C4×C31—22no—
87C4×C31—21no—
88C4×C31—41no—
89C4×C31C2×SD1611yescharacteristic
90C4×C31#13511yescharacteristic
91C4×C31AGL(1,ℤ/8)11yescharacteristic
92C4×C31AGL(1,ℤ/8)11yescharacteristic
93Dic31—41no—
94Dic31—81no—
95#550—311no—
96#486—311no—
97#475—311no—
98#461—311no—
99#331—311no—
100Q8⋊C8D3111yescharacteristic, complemented
101D4⋊C8—311no—
102C2×C31#44911yescharacteristic
103C2×C31#45011yescharacteristic
104C2×C31#45511yescharacteristic
105D31—81no—
106D31—82no—
107C2×#41—621no—
108C2×SD16—621no—
109C4⋊Q8—311no—
110#127—311no—
111#127—621no—
112#121—622no—
113#121—621no—
114C4×Q8C2×D3111yescharacteristic
115C4×D4—311no—
116C4×D4—621no—
117#106—621no—
118C4⋊C8—311no—
119C4⋊C8C2×D3111yescharacteristic
120#103—621no—
121#103—621no—
122#102—622no—
123C4×C8C2×D3111yescharacteristic
124C31#164211yescharacteristic, complemented, Sylow
125#41—1242no—
126#41—1242no—
127C2×Q8—621no—
128C2×Q8D12411yescharacteristic
129C2×D4—311no—
130C2×D4—312no—
131C2×D4—622no—
132C2×D4—622no—
133C2×D4—621no—
134C2×D4—621no—
135C22×C4—622no—
136C22×C4—621no—
137SD16—1242no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—621no—
141C4⋊C4—21no—
142C4⋊C4—311no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4D12411yescharacteristic
146C22⋊C4—622no—
147C22⋊C4—621no—
148C42—21no—
149C42C22×D3111yescharacteristic
150C23—621no—
151C23—622no—
152Q8—21no—
153Q8—1241no—
154Q8—1241no—
155Q8#9247012yescomplemented
156D4—621no—
157D4—621no—
158D4—1242no—
159D4—1244no—
160D4—1241no—
161D4—1241no—
162D4—1241no—
163D4—1241no—
164D4—2482no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—621no—
168C2×C4—1244no—
169C2×C4—1241no—
170C2×C4—1241no—
171C2×C4—1241no—
172C2×C4C2×D12411yescharacteristic
173C2×C4D4×D3111yescharacteristic
174C2×C4D4×D3111yescharacteristic
175C8—41no—
176C8—41no—
177C8—1241no—
178C22—1241no—
179C22—1242no—
180C22—1242no—
181C22—1241no—
182C22—1242no—
183C22—1241no—
184C22#1175845911yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—1241no—
189C4—2481no—
190C4C2×#9247011yescharacteristic
191C4#1175848511yescharacteristic
192C4#1175849111yescharacteristic
193C4#1175849611yescharacteristic
194C2—2481no—
195C2—2482no—
196C2#1452119711yescharacteristic
197C2#1452120211yescharacteristic
198C2#1452122811yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×Q8⋊C8C2
socleC22×C31#120
prime radical#14521721C2
hypercenterQ8⋊C8D31
hypocenterC31#1642
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. #14521396C2semidirect
3. #14521334C2semidirect
4. #14521255C2semidirect
5. #14520792C2semidirect
6. #14520778C2semidirect
7. C31×Q8⋊C8C2semidirect
53. Q8×C31SD16semidirect
100. Q8⋊C8D31semidirect
124. C31#1642semidirect
155. Q8#92470semidirect

Maximal subgroups

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

subgroupindex
#145217212
#145213962
#145213342
#145212552
#145207922
#145207782
C31×Q8⋊C82
#164231