Finite Group Databasebeta

← #16848850

Subgroups — #16848850

Order 3968.

688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#11758530C211yesmaximal, characteristic
2#14520949C213yesmaximal, complemented
3#14520943C213yesmaximal, complemented
4#14520937C213yesmaximal, complemented
5#14520925C213yesmaximal, complemented
6#14520905C211yesmaximal, characteristic, complemented
7C31×#379C211yesmaximal, characteristic, complemented
8C25×C31C2211yescharacteristic
9C22×C22⋊D31C2213yes—
10C22×C4×D31C2211yescharacteristic, complemented
11C2×C22⋊C4×C31C2213yes—
12C2×C22⋊C4×C31C2213yes—
13#11758530C418yescomplemented
14C2×C22⋊Dic31C2213yes—
15C2×C22⋊Dic31C2213yes—
16C2×C22⋊Dic31C2213yes—
17C2×(C2×D31)⋊C4C2213yescomplemented
18C2×Dic31⋊C4C2213yescomplemented
19C2×C4×Dic31C2213yescomplemented
20C31⋊#95C2213yescomplemented
21C31⋊#95C2213yescomplemented
22C24×C31—43no—
23C24×C31—43no—
24C24×C31C2×C414yescomplemented
25C24×C31C2313yes—
26C23×D31C2311yescharacteristic
27C22×C4×C31C2311yescharacteristic
28C22×C4×C31C2313yes—
29C2×C22⋊D31—43no—
30C2×C22⋊D31—43no—
31C2×C22⋊D31C2×C4112yes—
32C22×Dic31C2311yescharacteristic
33C22×Dic31C2313yes—
34C22×Dic31C2313yes—
35C2×C4×D31—43no—
36C22⋊C4×C31—43no—
37C22⋊C4×C31—43no—
38C22⋊Dic31—43no—
39C22⋊Dic31—43no—
40C22⋊Dic31C2×C4112yescomplemented
41(C2×D31)⋊C4—43no—
42Dic31⋊C4—43no—
43C4×Dic31—43no—
44C23×C31—23no—
45C23×C31—23no—
46C23×C31—23no—
47C23×C31—23no—
48C23×C31—23no—
49C23×C31—23no—
50C23×C31—412no—
51C23×C31—412no—
52C23×C31—44no—
53C23×C31C22×C416yes—
54C23×C31C2411yescharacteristic
55C22×D31—23no—
56C22×D31—23no—
57C22×D31C22×C412yes—
58C2×C4×C31—23no—
59C2×C4×C31—23no—
60C2×C4×C31—23no—
61C2×C4×C31—23no—
62C22⋊D31—412no—
63C2×Dic31—23no—
64C2×Dic31—23no—
65C2×Dic31—23no—
66C2×Dic31—23no—
67C2×Dic31—23no—
68C2×Dic31—23no—
69C2×Dic31C22×C416yes—
70C4×D31—44no—
71#2375—311nomaximal, Sylow
72C22×C31—26no—
73C22×C31—26no—
74C22×C31—26no—
75C22×C31—416no—
76C22×C31—43no—
77C22×C31—43no—
78C22×C31—43no—
79C22×C31—43no—
80C22×C31C23×C411yescharacteristic
81C22×C31H(5,𝔽2)13yes—
82C22×C31H(5,𝔽2)13yes—
83C2×D31—26no—
84C2×D31—43no—
85C2×D31—41no—
86C4×C31—43no—
87C4×C31—41no—
88Dic31—26no—
89Dic31—43no—
90Dic31—41no—
91C2×#120—311no—
92#390—313no—
93#388—313no—
94#388—313no—
95#386—313no—
96#379—311no—
97#379D3111yescharacteristic, complemented
98C2×C31—46no—
99C2×C31#51813yes—
100C2×C31#56013yes—
101C2×C31H(3,𝔽4)11yescharacteristic
102D31—42no—
103C25C2×D3111yescharacteristic
104C22×D4—313no—
105C23×C4—311no—
106#120—318no—
107C2×C4⋊C4—313no—
108C2×C22⋊C4—313no—
109C2×C22⋊C4—313no—
110C2×C22⋊C4—313no—
111C2×C22⋊C4—313no—
112C2×C22⋊C4C2×D3113yes—
113C2×C22⋊C4C2×D3113yes—
114C2×C42—313no—
115#95—313no—
116#95—313no—
117C31#237511yescharacteristic, complemented, Sylow
118C24—43no—
119C24—43no—
120C24—311no—
121C24C4×D3114yescomplemented
122C24C22×D3113yes—
123C2×D4—3112no—
124C2×D4—1243no—
125C2×D4—1243no—
126C22×C4—313no—
127C22×C4—311no—
128C22×C4—313no—
129C22×C4—1243no—
130C22×C4C22×D3111yescharacteristic
131C22×C4C22×D3113yes—
132C4⋊C4—1243no—
133C22⋊C4—43no—
134C22⋊C4—43no—
135C22⋊C4—3112no—
136C22⋊C4—1243no—
137C22⋊C4—1243no—
138C22⋊C4—1243no—
139C42—1243no—
140C23—23no—
141C23—23no—
142C23—23no—
143C23—23no—
144C23—23no—
145C23—23no—
146C23—412no—
147C23—412no—
148C23—44no—
149C23—312no—
150C23—623no—
151C23—623no—
152C23C2×C4×D3116yes—
153C23C23×D3111yescharacteristic
154D4—12412no—
155C2×C4—23no—
156C2×C4—23no—
157C2×C4—23no—
158C2×C4—23no—
159C2×C4—316no—
160C2×C4—623no—
161C2×C4—623no—
162C2×C4—623no—
163C2×C4—623no—
164C2×C4—623no—
165C2×C4—623no—
166C2×C4—1244no—
167C22—26no—
168C22—26no—
169C22—26no—
170C22—416no—
171C22—43no—
172C22—43no—
173C22—43no—
174C22—43no—
175C22—626no—
176C22—1243no—
177C22—1241no—
178C22C22×C4×D3111yescharacteristic
179C22#1175856113yes—
180C22#1175856113yes—
181C4—43no—
182C4—41no—
183C4—626no—
184C4—1243no—
185C4—1241no—
186C2—46no—
187C2—1242no—
188C2#1452152213yes—
189C2#1452178813yes—
190C2#1452179211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#379C2
socle, cosocleC23×C31C24
prime radicalC2×#11758530C2
hypercenter#379D31
hypocenterC31#2375
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #14520949C2semidirect
3. #14520943C2semidirect
4. #14520937C2semidirect
5. #14520925C2semidirect
6. #14520905C2semidirect
7. C31×#379C2semidirect
10. C22×C4×D31C22semidirect
13. #11758530C4semidirect
17. C2×(C2×D31)⋊C4C22semidirect
18. C2×Dic31⋊C4C22semidirect
19. C2×C4×Dic31C22semidirect
20. C31⋊#95C22semidirect
21. C31⋊#95C22semidirect
24. C24×C31C2×C4semidirect
40. C22⋊Dic31C2×C4semidirect
97. #379D31semidirect
117. C31#2375semidirect
121. C24C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585302
#145209492
#145209432
#145209372
#145209252
#145209052
C31×#3792
#237531