Finite Group Databasebeta

← #20241776

Subgroups — #20241776

Order 6016.

264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C4×#10625350C211yesmaximal, characteristic
2C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#15688855C212yesmaximal, complemented
4#15688852C212yesmaximal, complemented
5C47×#431C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic
7C22×C47⋊C8—21no—
8C4×Dic94C411yescharacteristic
9C4×Dic94C2211yescharacteristic
10C4×D188C411yescharacteristic
11C4×D188C2211yescharacteristic
12C4×C22⋊D47—21no—
13C4×C22⋊D47—21no—
14#13093983C411yescharacteristic
15#13093981—21no—
16C42×D47—21no—
17C4⋊(C47⋊C8)—21no—
18C4⋊(C47⋊C8)C2212yes—
19C2×C42×C47C2211yescharacteristic
20C4⋊C8×C47—21no—
21C22⋊C8×C47—21no—
22C4×C8×C47C2212yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C2×C22⋊D47—21no—
27#10625350—22no—
28#10625350C814yescomplemented
29C2×D188C2×C411yescharacteristic
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47—21no—
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—22no—
35C42×C47C2×C411yescharacteristic
36C42×C47D411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47C2311yescharacteristic
39C22⋊Dic47—21no—
40(C2×D47)⋊C4—21no—
41(C2×D47)⋊C4—21no—
42C4⋊Dic47C2×C411yescharacteristic
43C4⋊Dic47C2×C411yescharacteristic
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—22no—
50C2×C47⋊C8—42no—
51C23×C47C22⋊C411yescharacteristic
52C22×D47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—41no—
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C2×C812yes—
60C2×C4×C47M1612yes—
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C22⋊D47—24no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68D188—21no—
69D188C2×C812yescomplemented
70C4×D47—24no—
71C4×D47—42no—
72C4×D47—41no—
73C4×D47—41no—
74Dic94—21no—
75Dic94C2×C812yescomplemented
76C8×C47—42no—
77C47⋊C8—42no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47C22⋊C812yes—
81C22×C47C2×C22⋊C411yescharacteristic
82C2×D47—22no—
83C2×D47—41no—
84C2×D47—41no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—21no—
88C4×C47C22⋊C812yes—
89C4×C47C22×C811yescharacteristic
90C4×C47C2×M1611yescharacteristic
91C4×C47AGL(1,ℤ/8)11yescharacteristic
92C4×C47#13711yescharacteristic
93Dic47—22no—
94Dic47—41no—
95Dic47—41no—
96#1477—471nomaximal, Sylow
97C2×C47—22no—
98C2×C47C2×C22⋊C811yescharacteristic
99C2×C47#41711yescharacteristic
100C2×C47#42111yescharacteristic
101D47—42no—
102C4×#41—471no—
103#431D4711yescharacteristic, complemented
104C2×C4⋊C8—471no—
105Q8⋊C8—472no—
106D4⋊C8—472no—
107C47#147711yescharacteristic, complemented, Sylow
108C2×#41—471no—
109C22×C8—941no—
110C4×Q8—471no—
111C4×Q8—471no—
112C4×D4—471no—
113C4×D4—471no—
114C4×D4—941no—
115C4×D4—941no—
116#117—471no—
117#117—941no—
118C2×C42—941no—
119C2×C42C2×D4711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—472no—
122C4⋊C8—941no—
123C22⋊C8—21no—
124C4×C8C2×D4712yes—
125#41—474no—
126#41—942no—
127C2×Q8—471no—
128C2×D4—471no—
129C2×D4—941no—
130C22×C4—941no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4C4×D4711yescharacteristic
134C22×C4D18811yescharacteristic
135C22×C4C22⋊D4711yescharacteristic
136C2×C8—22no—
137C2×C8—942no—
138C2×C8—1882no—
139C4⋊C4—471no—
140C4⋊C4—471no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C22⋊C4—941no—
144C22⋊C4—941no—
145C22⋊C4—941no—
146C42—941no—
147C42—941no—
148C42—941no—
149C42C4×D4711yescharacteristic
150C42D18811yescharacteristic
151C42C22⋊D4711yescharacteristic
152C42C22×D4711yescharacteristic
153C23—941no—
154C23(C2×D47)⋊C411yescharacteristic
155Q8—472no—
156Q8—941no—
157D4—472no—
158D4—944no—
159D4—941no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—941no—
164C2×C4—944no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—1882no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4C8×D4712yes—
171C2×C4#1062532412yes—
172C2×C4(C2×D47)⋊C411yescharacteristic
173C2×C4(C2×D47)⋊C411yescharacteristic
174C2×C4(C2×D47)⋊C411yescharacteristic
175C2×C4C2×C4×D4711yescharacteristic
176C2×C4C2×D18811yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C8—42no—
179C8—1882no—
180C22—21no—
181C22—21no—
182C22—942no—
183C22—1881no—
184C22—1881no—
185C22(C2×D47)⋊C812yes—
186C22C2×(C2×D47)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—942no—
191C4—1881no—
192C4—1881no—
193C4(C2×D47)⋊C812yes—
194C4C2×C8×D4711yescharacteristic
195C4C2×#1062532411yescharacteristic
196C4#1309405211yescharacteristic
197C4#1309405711yescharacteristic
198C2—22no—
199C2—1882no—
200C2C2×(C2×D47)⋊C811yescharacteristic
201C2#1568912511yescharacteristic
202C2#1568914111yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC4×C47C22×C8
FrattiniC42C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1477
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C47⋊C8)C2semidirect
3. #15688855C2semidirect
4. #15688852C2semidirect
5. C47×#431C2semidirect
28. #10625350C8semidirect
69. D188C2×C8semidirect
75. Dic94C2×C8semidirect
103. #431D47semidirect
107. C47#1477semidirect