Finite Group Databasebeta

← #16844271

Subgroups — #16844271

Order 3968.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521102C211yesmaximal, characteristic, complemented
2#14520915C211yesmaximal, characteristic, complemented
3#14520783C214yesmaximal, complemented
4C31×#532C211yesmaximal, characteristic
5C2×#41×C31—21no—
6C31×C4⋊Q8C411yescharacteristic, complemented
7C31×#127C411yescharacteristic, complemented
8C31×#124—21no—
9C31×#121—21no—
10C31×#121C2212yes—
11C4×D4×C31—21no—
12C4×D4×C31C412yescomplemented
13C2×C42×C31C2211yescharacteristic
14C2×C4⋊Dic31—21no—
15C31⋊#95—21no—
16C31⋊#95C2212yes—
17C22⋊(C31⋊C8)C2212yes—
18C4⋊(C31⋊C8)—21no—
19C4×C31⋊C8—21no—
20#41×C31—42no—
21#41×C31—42no—
22C2×Q8×C31—21no—
23C2×D4×C31—22no—
24C2×D4×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31C2×C412yes—
27C22×C4×C31—22no—
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31C2311yescharacteristic
31C22×Dic31—22no—
32C4⋊C4×C31—21no—
33C4⋊C4×C31C2×C412yes—
34C22⋊C4×C31—22no—
35C22⋊C4×C31—22no—
36C42×C31C2×C411yescharacteristic
37C42×C31C2×C411yescharacteristic
38C42×C31D411yescharacteristic
39C42×C31D411yescharacteristic
40C4⋊Dic31—42no—
41C2×C31⋊C8—22no—
42C23×C31—22no—
43C23×C31C2×D411yescharacteristic
44Q8×C31—42no—
45D4×C31—42no—
46D4×C31—42no—
47D4×C31—42no—
48D4×C31—42no—
49D4×C31—42no—
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—44no—
54C2×C4×C31C22⋊C411yescharacteristic
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31D812yes—
59C2×C4×C31SD1612yes—
60C2×C4×C31C22×C411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×Dic31—42no—
63C2×Dic31—42no—
64C2×Dic31—42no—
65C31⋊C8—42no—
66#1517—311nomaximal, Sylow
67C22×C31—21no—
68C22×C31—21no—
69C22×C31—42no—
70C22×C31—42no—
71C22×C31—42no—
72C22×C31C2×C22⋊C411yescharacteristic
73C22×C31C2×D811yescharacteristic
74C22×C31C2×SD1611yescharacteristic
75C4×C31—21no—
76C4×C31—21no—
77C4×C31—21no—
78C4×C31—21no—
79C4×C31—42no—
80C4×C31#10212yes—
81C4×C31#10212yes—
82Dic31—82no—
83#532D3111yescharacteristic
84#431—311no—
85#382—311no—
86#327—314no—
87C2×C31—21no—
88C2×C31—21no—
89C2×C31—82no—
90C2×C31#41011yescharacteristic
91C2×C31C2×#10211yescharacteristic
92C2×C31#42111yescharacteristic
93C2×#41—21no—
94C4⋊Q8Dic3111yescharacteristic, complemented
95#127Dic3111yescharacteristic, complemented
96#124—21no—
97#121—21no—
98#121C2×D3112yes—
99C4×D4—21no—
100C4×D4Dic3112yescomplemented
101C2×C4⋊C4—621no—
102C2×C42C2×D3111yescharacteristic
103C4⋊C8—621no—
104C22⋊C8—312no—
105C4×C8—621no—
106#95—312no—
107#95—621no—
108C31#151711yescharacteristic, complemented, Sylow
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×Dic3112yes—
116C22×C4—22no—
117C22×C4—622no—
118C22×C4C22⋊D3111yescharacteristic
119C22×C4C22⋊D3111yescharacteristic
120C22×C4C22×D3111yescharacteristic
121C2×C8—622no—
122C4⋊C4—21no—
123C4⋊C4—1242no—
124C4⋊C4C2×Dic3112yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×Dic3111yescharacteristic
128C42C2×Dic3111yescharacteristic
129C42C22⋊D3111yescharacteristic
130C42C22⋊D3111yescharacteristic
131C23—22no—
132C23C2×C22⋊D3111yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—1242no—
144C2×C4—1242no—
145C2×C4—1242no—
146C2×C4#9247912yes—
147C2×C4#9248012yes—
148C2×C4C22⋊Dic3111yescharacteristic
149C2×C4C22⋊Dic3111yescharacteristic
150C2×C4C22⋊Dic3111yescharacteristic
151C2×C4C22⋊Dic3111yescharacteristic
152C2×C4C22×Dic3111yescharacteristic
153C2×C4C2×C22⋊D3111yescharacteristic
154C8—1242no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×#9247911yescharacteristic
161C22C2×#9248011yescharacteristic
162C22C2×C22⋊Dic3111yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—2482no—
169C4#1175842012yes—
170C4#1175842012yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1452102311yescharacteristic
175C2C2×#1175842011yescharacteristic
176C2#1452106611yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#532C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#532D31
hypocenterC31#1517
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14521102C2semidirect
2. #14520915C2semidirect
3. #14520783C2semidirect
6. C31×C4⋊Q8C4semidirect
7. C31×#127C4semidirect
12. C4×D4×C31C4semidirect
94. C4⋊Q8Dic31semidirect
95. #127Dic31semidirect
100. C4×D4Dic31semidirect
108. C31#1517semidirect

Maximal subgroups

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

subgroupindex
#145211022
#145209152
#145207832
C31×#5322
#151731