Finite Group Databasebeta

← #16844877

Subgroups — #16844877

Order 3968.

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

normal subgroups only

This group has 228 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#14521714C211yesmaximal, characteristic
2#14521401C211yesmaximal, characteristic, complemented
3#14521345C211yesmaximal, characteristic, complemented
4#14521340C211yesmaximal, characteristic
5#14520779C211yesmaximal, characteristic, complemented
6#14520776C211yesmaximal, characteristic
7C31×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D31—21no—
9C31×C4⋊Q8C2211yescharacteristic
10#11758523—21no—
11#11758473—22no—
12#11758470—21no—
13#11758465—21no—
14C4×D124C2211yescharacteristic
15#11758446C2211yescharacteristic
16C4×Dic62C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19#11758409—21no—
20#11758406—21no—
21#11758405—21no—
22#11758404—21no—
23#11758398—22no—
24C4×C31⋊C8C2211yescharacteristic
25C2×Q8×C31—21no—
26Q8×D31—42no—
27Q8×D31—42no—
28C2×D124D411yescharacteristic
29C2×C4×D31—22no—
30C2×C4×D31—21no—
31C2×Dic62—22no—
32C2×Dic62—21no—
33C2×Dic62D411yescharacteristic
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31D412yes—
38C42×C31C2311yescharacteristic
39(C2×D31)⋊C4—22no—
40(C2×D31)⋊C4—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31D411yescharacteristic
44C4⋊Dic31D411yescharacteristic
45Dic31⋊C4—22no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C2×C31⋊C8—21no—
49C22×D31—21no—
50Q8×C31—41no—
51Q8×C31—41no—
52C2×C4×C31—22no—
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—21no—
57C2×Dic31—21no—
58C2×Dic31—21no—
59C2×Dic31—41no—
60D124—21no—
61D124Q1612yes—
62C4×D31—44no—
63C4×D31—41no—
64C4×D31—41no—
65Dic62—21no—
66Dic62—44no—
67Dic62—42no—
68Dic62SD1612yes—
69C8×C31—41no—
70C8×C31—41no—
71C31⋊C8—41no—
72#1637—311nomaximal, Sylow
73C22×C31#12011yescharacteristic
74C2×D31—22no—
75C2×D31—41no—
76C2×D31—41no—
77C4×C31—21no—
78C4×C31—42no—
79C4×C31C2×SD1611yescharacteristic
80C4×C31C2×Q1611yescharacteristic
81C4×C31AGL(1,ℤ/8)11yescharacteristic
82C4×C31#13711yescharacteristic
83Dic31—22no—
84Dic31—41no—
85Dic31—41no—
86Dic31—81no—
87D4×Q8—311no—
88#487—311no—
89#477—311no—
90#476—311no—
91#332D3111yescharacteristic, complemented
92Q8⋊C8—311no—
93D4⋊C8—311no—
94C2×C31#45011yescharacteristic
95C2×C31#45111yescharacteristic
96C2×C31#45411yescharacteristic
97D31—42no—
98C22×Q8—621no—
99C4⋊Q8—311no—
100C4⋊Q8—621no—
101C4⋊Q8C2×D3111yescharacteristic
102C22⋊Q8—621no—
103C22⋊Q8—622no—
104C4×Q8—311no—
105C4×D4—311no—
106C4×D4—621no—
107#107—621no—
108#106—621no—
109C4⋊C8C2×D3111yescharacteristic
110C4⋊C8C2×D3111yescharacteristic
111#103—621no—
112#103—622no—
113#102—621no—
114C4×C8—311no—
115C31#163711yescharacteristic, complemented, Sylow
116C2×Q8—21no—
117C2×Q8—311no—
118C2×Q8—622no—
119C2×Q8—621no—
120C2×Q8—1242no—
121C2×Q8—1242no—
122C2×D4—311no—
123C22×C4—622no—
124C22×C4—621no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—621no—
128C4⋊C4—21no—
129C4⋊C4—311no—
130C4⋊C4—311no—
131C4⋊C4—622no—
132C4⋊C4—621no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C4⋊C4D12412yes—
136C22⋊C4—622no—
137C22⋊C4—621no—
138C42—621no—
139C42C22×D3111yescharacteristic
140C23—621no—
141Q8—41no—
142Q8—41no—
143Q8—312no—
144Q8—621no—
145Q8—1242no—
146Q8—1244no—
147D4—312no—
148D4—621no—
149C2×C4—22no—
150C2×C4—621no—
151C2×C4—621no—
152C2×C4—621no—
153C2×C4—1244no—
154C2×C4—1241no—
155C2×C4—1241no—
156C2×C4—1241no—
157C2×C4C2×D12411yescharacteristic
158C2×C4D4×D3111yescharacteristic
159C2×C4D4×D3111yescharacteristic
160C8—41no—
161C8—41no—
162C8—1241no—
163C22—622no—
164C22—1241no—
165C22—1241no—
166C22#1175845911yescharacteristic
167C4—21no—
168C4—42no—
169C4—622no—
170C4—1241no—
171C4—1241no—
172C4—2481no—
173C4#1175848811yescharacteristic
174C4SD16×D3111yescharacteristic
175C4#1175849211yescharacteristic
176C4Q16×D3111yescharacteristic
177C2—1242no—
178C2#1452120111yescharacteristic
179C2#1452120611yescharacteristic
180C2#1452122411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31#120
prime radicalC2×D124D4
hypercenter#332D31
hypocenterC31#1637
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14521401C2semidirect
3. #14521345C2semidirect
5. #14520779C2semidirect
7. C31×#332C2semidirect
91. #332D31semidirect
115. C31#1637semidirect

Maximal subgroups

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

subgroupindex
#145217142
#145214012
#145213452
#145213402
#145207792
#145207762
C31×#3322
#163731