Finite Group Databasebeta

← #34067617

Subgroups — #34067617

Order 19328.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#23752762C211yesmaximal, characteristic
2#23752269C211yesmaximal, characteristic, complemented
3#23751945C214yesmaximal, complemented
4#376×C151C211yesmaximal, characteristic, complemented
5C2×#14559004—21no—
6#18012739C411yescharacteristic, complemented
7#18012736C411yescharacteristic, complemented
8#18012727—21no—
9#18012713—21no—
10#18012713C2212yes—
11C4×D604—21no—
12C4×D604C412yescomplemented
13C4⋊(C151⋊C8)—21no—
14C22⋊(C151⋊C8)C2212yes—
15#18012650—21no—
16C2×C42×C151—21no—
17C2×C42×C151C2211yescharacteristic
18#95×C151—21no—
19#95×C151C2212yes—
20#14559004—44no—
21C2×Dic302—21no—
22C2×D604—21no—
23C2×D604—21no—
24C2×D604C2×C412yes—
25C2×C22⋊D151—22no—
26C2×C4×D151—22no—
27C2×C151⋊C8—22no—
28C4⋊Dic151—21no—
29C4⋊Dic151C2×C412yes—
30(C2×D151)⋊C4—22no—
31(C2×D151)⋊C4—22no—
32C22×C4×C151—22no—
33C22×C4×C151D411yescharacteristic
34C22×C4×C151D411yescharacteristic
35C22×C4×C151C2311yescharacteristic
36C42×C151—24no—
37C42×C151C2×C411yescharacteristic
38C42×C151C2×C411yescharacteristic
39C42×C151D411yescharacteristic
40C42×C151D411yescharacteristic
41C22×D151—22no—
42Dic302—42no—
43D604—42no—
44D604—42no—
45D604—42no—
46C22⋊D151—44no—
47C2×Dic151—22no—
48C4×D151—44no—
49C151⋊C8—42no—
50C23×C151C2×D411yescharacteristic
51C2×C4×C151—22no—
52C2×C4×C151—22no—
53C2×C4×C151—24no—
54C2×C4×C151—41no—
55C2×C4×C151—42no—
56C2×C4×C151—42no—
57C2×C4×C151C22⋊C411yescharacteristic
58C2×C4×C151C22⋊C411yescharacteristic
59C2×C4×C151C22⋊C411yescharacteristic
60C2×C4×C151C22⋊C411yescharacteristic
61C2×C4×C151C22×C411yescharacteristic
62C2×C4×C151C2×D411yescharacteristic
63C22×C151—21no—
64C22×C151—21no—
65C22×C151C2×C22⋊C411yescharacteristic
66C22×C151AGL(1,ℤ/8)12yes—
67C2×D151—42no—
68C2×D151—42no—
69C2×D151—42no—
70C4×C151—21no—
71C4×C151—21no—
72C4×C151—21no—
73C4×C151—21no—
74C4×C151—21no—
75C4×C151—44no—
76C4×C151#10412yes—
77Dic151—42no—
78C2×C151—22no—
79C2×C151#41011yescharacteristic
80C2×C151#41811yescharacteristic
81C2×C151C2×#10411yescharacteristic
82D151—82no—
83C151#150511yescharacteristic, complemented, Sylow
84#1505—1511nomaximal, Sylow
85#532—1511no—
86#432—1511no—
87#376D15111yescharacteristic, complemented
88#327—1514no—
89C2×#41—3021no—
90C4⋊Q8—1511no—
91#127—1511no—
92#124—3021no—
93#121—3021no—
94#121—1512no—
95C4×D4—3021no—
96C4×D4—1512no—
97C2×C42—21no—
98C2×C42C2×D15111yescharacteristic
99C4⋊C8—3021no—
100C22⋊C8—1512no—
101#97—3021no—
102#95—21no—
103#95C2×D15112yes—
104#41—6044no—
105C2×Q8—3021no—
106C2×D4—3022no—
107C2×D4—3021no—
108C2×D4—3021no—
109C2×D4—1512no—
110C22×C4—22no—
111C22×C4—3022no—
112C22×C4C22⋊D15111yescharacteristic
113C22×C4C22⋊D15111yescharacteristic
114C22×C4C22×D15111yescharacteristic
115C2×C8—3022no—
116C4⋊C4—3021no—
117C4⋊C4—1512no—
118C22⋊C4—3022no—
119C22⋊C4—3022no—
120C42—24no—
121C42C4×D15111yescharacteristic
122C42C4×D15111yescharacteristic
123C42D60411yescharacteristic
124C42D60411yescharacteristic
125C23—3022no—
126C23C2×C22⋊D15111yescharacteristic
127Q8—6042no—
128D4—6042no—
129D4—6042no—
130D4—6044no—
131D4—6042no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—3022no—
139C2×C4—6044no—
140C2×C4(C2×D151)⋊C411yescharacteristic
141C2×C4(C2×D151)⋊C411yescharacteristic
142C2×C4(C2×D151)⋊C411yescharacteristic
143C2×C4(C2×D151)⋊C411yescharacteristic
144C2×C4C2×C4×D15111yescharacteristic
145C2×C4C2×D60411yescharacteristic
146C8—6042no—
147C22—21no—
148C22—21no—
149C22—6042no—
150C22—6042no—
151C22—6042no—
152C22C2×(C2×D151)⋊C411yescharacteristic
153C22#1801276412yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—6042no—
161C4#1801266712yes—
162C2—22no—
163C2—12082no—
164C2#2375218511yescharacteristic
165C2#2375221611yescharacteristic
166C2C2×#1801266711yescharacteristic
subgroupG/H
centerC22C2×(C2×D151)⋊C4
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#376×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752762C2
cosocleC22×C4×C151C23
hypercenter#376D151
hypocenterC151#1505
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #23752269C2semidirect
3. #23751945C2semidirect
4. #376×C151C2semidirect
6. #18012739C4semidirect
7. #18012736C4semidirect
12. C4×D604C4semidirect
83. C151#1505semidirect
87. #376D151semidirect

Maximal subgroups

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

subgroupindex
#237527622
#237522692
#237519452
#376×C1512
#1505151