Finite Group Databasebeta

← #16844226

Subgroups — #16844226

Order 3968.

346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#11758507C211yesmaximal, characteristic
2#14521013C211yesmaximal, characteristic, complemented
3#14520782C214yesmaximal, complemented
4C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
5C23×C4×C31C2211yescharacteristic
6C22×C22⋊D31—21no—
7C22×D124C411yescharacteristic, complemented
8C2×C22⋊C4×C31—21no—
9C2×C42×C31—21no—
10#11758507—21no—
11#11758507—21no—
12#11758507C412yescomplemented
13#11758507C2212yes—
14C2×(C2×D31)⋊C4—21no—
15C2×C4⋊Dic31C411yescharacteristic, complemented
16C2×#92474—21no—
17C31×#95C2212yescomplemented
18C22⋊(C31⋊C8)—21no—
19C22⋊(C31⋊C8)C2212yescomplemented
20C24×C31D411yescharacteristic
21C23×D31—21no—
22C22×C4×C31—22no—
23C22×C4×C31—42no—
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—22no—
31C2×C22⋊D31—22no—
32C2×C22⋊D31—44no—
33C22×Dic31—21no—
34C2×D124—21no—
35C2×D124—42no—
36C2×D124C2×C412yes—
37C22⋊C4×C31—24no—
38C42×C31—42no—
39(C2×D31)⋊C4—22no—
40(C2×D31)⋊C4—22no—
41C4⋊Dic31—21no—
42C4⋊Dic31C2×C412yes—
43#92474—42no—
44C2×C31⋊C8—22no—
45C23×C31—22no—
46C23×C31—22no—
47C23×C31—41no—
48C23×C31C22⋊C411yescharacteristic
49C23×C31C22⋊C411yescharacteristic
50C23×C31C2×D411yescharacteristic
51C22×D31—22no—
52C22×D31—42no—
53C22×D31—42no—
54C22×D31—42no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—24no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—42no—
63C2×C4×C31—42no—
64C2×C4×C31C22⋊C411yescharacteristic
65C2×C4×C31C22⋊C411yescharacteristic
66C2×C4×C31C22×C411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C22⋊D31—44no—
69C22⋊D31—44no—
70C2×Dic31—22no—
71C2×Dic31—42no—
72D124—42no—
73D124—42no—
74C31⋊C8—42no—
75#1507—311nomaximal, Sylow
76C22×C31—21no—
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—21no—
83C22×C31—44no—
84C22×C31#10412yes—
85C22×C31C2×C22⋊C411yescharacteristic
86C22×C31AGL(1,ℤ/8)12yes—
87C2×D31—42no—
88C2×D31—42no—
89C2×D31—42no—
90C2×D31—84no—
91C4×C31—21no—
92C4×C31—21no—
93C4×C31—21no—
94C4×C31—44no—
95C4×C31#9912yes—
96Dic31—42no—
97C2×#121—311no—
98#407—311no—
99C4×C22⋊C4D3111yescharacteristic, complemented
100#327—314no—
101C2×C31—22no—
102C2×C31—22no—
103C2×C31—41no—
104C2×C31C2×#9911yescharacteristic
105C2×C31#41811yescharacteristic
106C2×C31C2×#10411yescharacteristic
107D31—82no—
108C22×D4—311no—
109C22×D4—621no—
110C23×C4C2×D3111yescharacteristic
111C2×M16—621no—
112#121—312no—
113#121—312no—
114#121—621no—
115#121—621no—
116C2×C4⋊C4—311no—
117C2×C22⋊C4—21no—
118C2×C22⋊C4—621no—
119C2×C42—21no—
120C22⋊C8—312no—
121C22⋊C8—621no—
122#95C2×D3112yescomplemented
123C31#150711yescharacteristic, complemented, Sylow
124C24—621no—
125C24C22⋊D3111yescharacteristic
126C2×D4—312no—
127C2×D4—622no—
128C2×D4—622no—
129C2×D4—621no—
130C2×D4—1242no—
131C2×D4—1244no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—621no—
135C22×C4C4×D3111yescharacteristic
136C22×C4C4×D3111yescharacteristic
137C22×C4D12411yescharacteristic
138C22×C4D12411yescharacteristic
139C22×C4C22⋊D3111yescharacteristic
140C22×C4C22×D3111yescharacteristic
141M16—1242no—
142C2×C8—622no—
143C4⋊C4—312no—
144C4⋊C4—621no—
145C22⋊C4—24no—
146C22⋊C4—622no—
147C22⋊C4—622no—
148C42—42no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—622no—
153C23—1242no—
154C23—1242no—
155C23—1242no—
156C23(C2×D31)⋊C411yescharacteristic
157C23(C2×D31)⋊C411yescharacteristic
158C23C2×C22⋊D3111yescharacteristic
159D4—1242no—
160D4—1244no—
161D4—1244no—
162D4—1242no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—622no—
173C2×C4—1242no—
174C2×C4(C2×D31)⋊C411yescharacteristic
175C2×C4(C2×D31)⋊C411yescharacteristic
176C2×C4C2×C4×D3111yescharacteristic
177C2×C4C2×D12411yescharacteristic
178C8—1242no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—1242no—
188C22—1242no—
189C22—1242no—
190C22—2484no—
191C22#1175839312yes—
192C22C2×(C2×D31)⋊C411yescharacteristic
193C22#1175852612yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—44no—
198C4—1242no—
199C4#1175839412yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—2482no—
204C2C2×#1175839411yescharacteristic
205C2#1452105311yescharacteristic
206C2C2×#1175839311yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC4×C22⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#11758507C2
cosocleC22×C4×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#1507
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14521013C2semidirect
3. #14520782C2semidirect
4. C4×C22⋊C4×C31C2semidirect
7. C22×D124C4semidirect
12. #11758507C4semidirect
15. C2×C4⋊Dic31C4semidirect
17. C31×#95C22semidirect
19. C22⋊(C31⋊C8)C22semidirect
99. C4×C22⋊C4D31semidirect
122. #95C2×D31semidirect
123. C31#1507semidirect

Maximal subgroups

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

subgroupindex
C2×#117585072
#145210132
#145207822
C4×C22⋊C4×C312
#150731