Finite Group Databasebeta

← #16847402

Subgroups — #16847402

Order 3968.

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

normal subgroups only

This group has 262 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#14521033C211yesmaximal, characteristic, complemented
3#14520845C214yesmaximal, complemented
4C31×#413C211yesmaximal, characteristic, complemented
5C2×#41×C31C2211yescharacteristic
6C22×D124C411yescharacteristic
7C2×M16×C31—21no—
8#11758524C2212yes—
9#11758517C412yes—
10#11758514—21no—
11#11758514—21no—
12#11758507—21no—
13#11758507—21no—
14#11758503C411yescharacteristic
15C2×#92474—21no—
16C31×#101C2212yescomplemented
17C31×#100—21no—
18#11758424C2212yescomplemented
19#11758421—21no—
20C23×D31—21no—
21#41×C31—41no—
22#41×C31—41no—
23C2×Q8×C31C2311yescharacteristic
24C2×D4×C31C2×C411yescharacteristic
25C2×D4×C31D411yescharacteristic
26C2×D4×C31D411yescharacteristic
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—
36M16×C31—22no—
37M16×C31—41no—
38C2×C8×C31—41no—
39C22⋊Dic31—21no—
40(C2×D31)⋊C4—22no—
41(C2×D31)⋊C4—22no—
42C4⋊Dic31—21no—
43C4×Dic31C2×C412yes—
44#92474—22no—
45#92474—41no—
46C2×C31⋊C8—41no—
47C23×C31C22⋊C411yescharacteristic
48C23×C31C22⋊C411yescharacteristic
49C23×C31C22⋊C411yescharacteristic
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×C31C22⋊C411yescharacteristic
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C22⋊D31—82no—
68C22⋊D31—82no—
69C2×Dic31—22no—
70D124—42no—
71D124—41no—
72D124—41no—
73C8×C31—42no—
74C31⋊C8—42no—
75#2134—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#9911yescharacteristic
91C4×C31#9911yescharacteristic
92Dic31—42no—
93#535—311no—
94#413—311no—
95#413D3111yescharacteristic, complemented
96#355—314no—
97C2×C31—21no—
98C2×C31—41no—
99C2×C31—41no—
100C2×C31—41no—
101C2×C31C2×#9911yescharacteristic
102D31—82no—
103C2×#41C2×D3111yescharacteristic
104C22×D4—311no—
105C2×M16—21no—
106C2×M16—621no—
107#127—312no—
108#124—312no—
109#121—621no—
110#121—621no—
111#120—621no—
112#120—621no—
113#117—311no—
114#101—312no—
115#101C2×D3112yescomplemented
116#100—21no—
117#100—621no—
118C31#213411yescharacteristic, complemented, Sylow
119C24—621no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D3111yescharacteristic
123C2×D4—312no—
124C2×D4—622no—
125C2×D4—622no—
126C2×D4—621no—
127C2×D4—1241no—
128C2×D4—1241no—
129C2×D4C4×D3111yescharacteristic
130C2×D4D12411yescharacteristic
131C2×D4C22⋊D3111yescharacteristic
132C22×C4C4×D3111yescharacteristic
133C22×C4D12411yescharacteristic
134C22×C4C22⋊D3111yescharacteristic
135M16—22no—
136M16—41no—
137M16—622no—
138M16—1241no—
139C2×C8—41no—
140C2×C8—1241no—
141C4⋊C4—621no—
142C22⋊C4—621no—
143C22⋊C4—622no—
144C22⋊C4—622no—
145C42—312no—
146C23—622no—
147C23—1242no—
148C23—2482no—
149C23(C2×D31)⋊C411yescharacteristic
150C23(C2×D31)⋊C411yescharacteristic
151C23(C2×D31)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—1242no—
157D4—1241no—
158D4—1241no—
159D4—2482no—
160D4—2482no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—622no—
168C2×C4(C2×D31)⋊C411yescharacteristic
169C2×C4C2×C4×D3111yescharacteristic
170C2×C4C2×D12411yescharacteristic
171C2×C4C2×C22⋊D3111yescharacteristic
172C8—42no—
173C8—1242no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—1242no—
181C22—1242no—
182C22—1242no—
183C22—2484no—
184C22C2×(C2×D31)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—1242no—
189C4#1175839411yescharacteristic
190C4#1175839411yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—2482no—
196C2C2×#1175839411yescharacteristic
subgroupG/H
centerC2C2×#11758394
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#413C2
socleC2×C31C2×#99
prime radical#14521613C2
cosocleC2×Q8×C31C23
hypercenter#413D31
hypocenterC31#2134
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14521033C2semidirect
3. #14520845C2semidirect
4. C31×#413C2semidirect
16. C31×#101C22semidirect
18. #11758424C22semidirect
95. #413D31semidirect
115. #101C2×D31semidirect
118. C31#2134semidirect

Maximal subgroups

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

subgroupindex
#145216132
#145210332
#145208452
C31×#4132
#213431