Finite Group Databasebeta

← #16847382

Subgroups — #16847382

Order 3968.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521613C211yesmaximal, characteristic
2#14521023C211yesmaximal, characteristic, complemented
3#14520841C214yesmaximal, complemented
4C31×#410C211yesmaximal, characteristic, complemented
5C2×#41×C31C2211yescharacteristic
6C22×D124C411yescharacteristic, complemented
7C31×#117—21no—
8#11758524C412yescomplemented
9#11758517C2212yes—
10#11758514—21no—
11#11758514—21no—
12#11758507—21no—
13#11758507—21no—
14#11758503—21no—
15#11758503C411yescharacteristic, complemented
16C31×#99—21no—
17C31×#99C2212yescomplemented
18#11758422—21no—
19#11758422C2212yescomplemented
20C23×D31—21no—
21#41×C31—41no—
22#41×C31—41no—
23C2×Q8×C31C2×C411yescharacteristic
24C2×D4×C31D411yescharacteristic
25C2×D4×C31D411yescharacteristic
26C2×D4×C31C2311yescharacteristic
27C22×C4×C31C2×C411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C2×C22⋊D31—22no—
31C2×C22⋊D31—22no—
32C2×D124—21no—
33C2×D124—41no—
34C2×D124—41no—
35C2×D124C2×C412yes—
36C4⋊C4×C31—41no—
37C22⋊C4×C31—22no—
38C42×C31—41no—
39C22⋊Dic31—21no—
40C22⋊Dic31—22no—
41(C2×D31)⋊C4—22no—
42(C2×D31)⋊C4—22no—
43C4⋊Dic31—21no—
44C4⋊Dic31—41no—
45C4×Dic31—41no—
46C4×Dic31C2×C412yes—
47C23×C31C22⋊C411yescharacteristic
48C23×C31C2×D411yescharacteristic
49C23×C31C2×D411yescharacteristic
50C22×D31—22no—
51C22×D31—42no—
52C22×D31—82no—
53Q8×C31—41no—
54D4×C31—41no—
55D4×C31—41no—
56D4×C31—41no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—42no—
64C2×C4×C31C22⋊C411yescharacteristic
65C2×C4×C31C22⋊C411yescharacteristic
66C2×C4×C31C22⋊C411yescharacteristic
67C2×C4×C31C22×C411yescharacteristic
68C22⋊D31—82no—
69C22⋊D31—82no—
70C2×Dic31—22no—
71C2×Dic31—42no—
72D124—42no—
73D124—41no—
74D124—41no—
75#2128—311nomaximal, Sylow
76C22×C31—21no—
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—41no—
80C22×C31—41no—
81C22×C31—41no—
82C22×C31C2×C22⋊C411yescharacteristic
83C2×D31—42no—
84C2×D31—42no—
85C2×D31—42no—
86C2×D31—84no—
87C4×C31—21no—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31—82no—
91C4×C31#9911yescharacteristic
92C4×C31#9911yescharacteristic
93Dic31—42no—
94Dic31—82no—
95#535—311no—
96#410—311no—
97#410D3111yescharacteristic, complemented
98#353—314no—
99C2×C31—21no—
100C2×C31—41no—
101C2×C31—41no—
102C2×C31—41no—
103C2×C31C2×#9911yescharacteristic
104D31—82no—
105C2×#41C2×D3111yescharacteristic
106C22×D4—311no—
107#127—312no—
108#124—312no—
109#121—621no—
110#121—621no—
111#120—621no—
112#120—621no—
113#117—21no—
114#117—311no—
115#117—621no—
116#99—21no—
117#99—312no—
118#99—621no—
119#99C2×D3112yescomplemented
120C31#212811yescharacteristic, complemented, Sylow
121C24—621no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D3111yescharacteristic
125C2×D4—312no—
126C2×D4—622no—
127C2×D4—622no—
128C2×D4—621no—
129C2×D4—1241no—
130C2×D4—1241no—
131C2×D4D12411yescharacteristic
132C2×D4C22⋊D3111yescharacteristic
133C2×D4C22×D3111yescharacteristic
134C22×C4C4×D3111yescharacteristic
135C22×C4D12411yescharacteristic
136C22×C4C22⋊D3111yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—621no—
139C4⋊C4—1241no—
140C22⋊C4—22no—
141C22⋊C4—621no—
142C22⋊C4—622no—
143C22⋊C4—622no—
144C22⋊C4—622no—
145C42—41no—
146C42—312no—
147C42—1241no—
148C23—622no—
149C23—1242no—
150C23—2482no—
151C23(C2×D31)⋊C411yescharacteristic
152C23C2×D12411yescharacteristic
153C23C2×C22⋊D3111yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—1242no—
159D4—1241no—
160D4—1241no—
161D4—2482no—
162D4—2482no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—622no—
171C2×C4—1242no—
172C2×C4(C2×D31)⋊C411yescharacteristic
173C2×C4(C2×D31)⋊C411yescharacteristic
174C2×C4(C2×D31)⋊C411yescharacteristic
175C2×C4C2×C4×D3111yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—1242no—
183C22—1242no—
184C22—1242no—
185C22—2484no—
186C22C2×(C2×D31)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—1242no—
192C4—2482no—
193C4#1175839411yescharacteristic
194C4#1175839411yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—2482no—
200C2C2×#1175839411yescharacteristic
subgroupG/H
centerC2C2×#11758394
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#410C2
socleC2×C31C2×#99
prime radical#14521613C2
cosocleC2×D4×C31C23
hypercenter#410D31
hypocenterC31#2128
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14521023C2semidirect
3. #14520841C2semidirect
4. C31×#410C2semidirect
6. C22×D124C4semidirect
8. #11758524C4semidirect
15. #11758503C4semidirect
17. C31×#99C22semidirect
19. #11758422C22semidirect
97. #410D31semidirect
119. #99C2×D31semidirect
120. C31#2128semidirect

Maximal subgroups

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

subgroupindex
#145216132
#145210232
#145208412
C31×#4102
#212831