Finite Group Databasebeta

← #16844839

Subgroups — #16844839

Order 3968.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521719C211yesmaximal, characteristic
2#14521421C211yesmaximal, characteristic, complemented
3#14521345C211yesmaximal, characteristic, complemented
4#14521340C211yesmaximal, characteristic, complemented
5#14520779C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic, complemented
7C31×#331C211yesmaximal, characteristic, complemented
8C2×#92497—21no—
9C31×#127C2211yescharacteristic
10#11758517—21no—
11#11758516—22no—
12#11758515—21no—
13D4×Dic31—21no—
14C2×#92480—22no—
15C4×D124C2211yescharacteristic
16#11758446C2211yescharacteristic
17C4×Dic62C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20#11758409—21no—
21#11758406—21no—
22#11758405—21no—
23#11758404—21no—
24C4×C31⋊C8C2211yescharacteristic
25C2×D4×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31D412yes—
28C2×C22⋊D31—22no—
29C2×C22⋊D31—22no—
30C22×Dic31—22no—
31#92497—42no—
32#92497—42no—
33C2×D124D411yescharacteristic
34C2×C4×D31—21no—
35C2×Dic62—21no—
36C2×Dic62D411yescharacteristic
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C42×C31C2311yescharacteristic
40C22⋊Dic31—22no—
41#92480—44no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31D411yescharacteristic
46C4⋊Dic31D411yescharacteristic
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C2×C31⋊C8—21no—
50C23×C31—22no—
51C22×D31—21no—
52D4×C31—42no—
53D4×C31—41no—
54D4×C31—41no—
55D4×C31—41no—
56D4×C31—41no—
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C22⋊D31—44no—
61C22⋊D31—82no—
62C2×Dic31—21no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—44no—
66C2×Dic31—41no—
67D124—21no—
68D124—21no—
69C4×D31—41no—
70C4×D31—41no—
71Dic62—21no—
72Dic62—42no—
73Dic62SD1612yescomplemented
74C8×C31—41no—
75C8×C31—41no—
76C31⋊C8—22no—
77#1631—311nomaximal, Sylow
78C22×C31—42no—
79C22×C31—42no—
80C22×C31—42no—
81C22×C31#12011yescharacteristic
82C2×D31—41no—
83C2×D31—41no—
84C2×D31—41no—
85C4×C31—21no—
86C4×C31C2×SD1611yescharacteristic
87C4×C31#13511yescharacteristic
88C4×C31AGL(1,ℤ/8)11yescharacteristic
89C4×C31#13711yescharacteristic
90Dic31—22no—
91Dic31—41no—
92Dic31—41no—
93Dic31—81no—
94#550—311no—
95#492—311no—
96#477—311no—
97#476—311no—
98#331D3111yescharacteristic, complemented
99Q8⋊C8—311no—
100D4⋊C8—311no—
101C2×C31—82no—
102C2×C31#45011yescharacteristic
103C2×C31#45211yescharacteristic
104C2×C31#45311yescharacteristic
105D31—81no—
106C2×#41—621no—
107C2×SD16—622no—
108C4⋊Q8—311no—
109#127—621no—
110#127C2×D3111yescharacteristic
111#121—621no—
112#121—622no—
113C4×Q8—311no—
114C4×D4—311no—
115C4×D4—621no—
116#107—621no—
117#106—621no—
118C4⋊C8C2×D3111yescharacteristic
119C4⋊C8C2×D3111yescharacteristic
120#103—621no—
121#102—621no—
122C4×C8—311no—
123C31#163111yescharacteristic, complemented, Sylow
124#41—1242no—
125#41—1242no—
126C2×Q8—311no—
127C2×Q8—621no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—311no—
131C2×D4—622no—
132C2×D4—622no—
133C2×D4D12412yes—
134C22×C4—622no—
135C22×C4—621no—
136SD16—1244no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—621no—
140C4⋊C4—311no—
141C4⋊C4—311no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C22⋊C4—622no—
146C22⋊C4—621no—
147C42—621no—
148C42C22×D3111yescharacteristic
149C23—22no—
150C23—621no—
151Q8—312no—
152Q8—621no—
153Q8—1242no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—621no—
160D4—621no—
161D4—1244no—
162D4—2482no—
163C2×C4—621no—
164C2×C4—621no—
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—41no—
174C8—41no—
175C8—622no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1241no—
180C22—1241no—
181C22—1241no—
182C22#1175845911yescharacteristic
183C4—21no—
184C4—622no—
185C4—1241no—
186C4—1241no—
187C4—2481no—
188C4#1175848811yescharacteristic
189C4#1175848911yescharacteristic
190C4SD16×D3111yescharacteristic
191C4#1175849211yescharacteristic
192C2—82no—
193C2—2481no—
194C2#1452120111yescharacteristic
195C2#1452121211yescharacteristic
196C2#1452121911yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#331C2
socleC22×C31#120
prime radical#14521719C2
hypercenter#331D31
hypocenterC31#1631
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14521421C2semidirect
3. #14521345C2semidirect
4. #14521340C2semidirect
5. #14520779C2semidirect
6. #14520776C2semidirect
7. C31×#331C2semidirect
73. Dic62SD16semidirect
98. #331D31semidirect
123. C31#1631semidirect

Maximal subgroups

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

subgroupindex
#145217192
#145214212
#145213452
#145213402
#145207792
#145207762
C31×#3312
#163131