Finite Group Databasebeta

← #34067372

Subgroups — #34067372

Order 19328.

476 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 181 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×C151⋊#95C213yesmaximal
2C2×C151⋊#95C213yesmaximal
3C2×#95×C151C211yesmaximal, characteristic
4C23×Dic151C2213yes—
5C23×Dic151C2211yescharacteristic
6C151⋊#95—26no—
7C151⋊#95—26no—
8C23×C4×C151C2213yes—
9#95×C151C414yescomplemented
10C22×Dic151—23no—
11C22×Dic151—23no—
12C22×Dic151—23no—
13C22×Dic151—23no—
14C22×Dic151—23no—
15C22×Dic151—23no—
16C22×Dic151—23no—
17C22×Dic151—23no—
18C22×Dic151D416yes—
19C22×Dic151Q812yes—
20C24×C151C2311yescharacteristic
21C22×C4×C151—23no—
22C22×C4×C151—23no—
23C22×C4×C151—23no—
24C22×C4×C151—23no—
25C22×C4×C151—23no—
26C22×C4×C151—23no—
27C22×C4×C151C2×C416yes—
28C2×Dic151—26no—
29C2×Dic151—26no—
30C2×Dic151—26no—
31C2×Dic151—26no—
32C2×Dic151—43no—
33C2×Dic151—43no—
34C2×Dic151—43no—
35C2×Dic151—41no—
36C2×Dic151—43no—
37C2×Dic151—43no—
38C23×C151C22×C411yescharacteristic
39C23×C151C2×D413yes—
40C23×C151C2×Q811yescharacteristic
41C23×C151#4113yes—
42C23×C151#4113yes—
43C23×C151#4113yes—
44C23×C151#4111yescharacteristic
45C2×C4×C151—26no—
46C2×C4×C151—26no—
47C2×C4×C151—26no—
48C2×C4×C151—43no—
49C2×C4×C151—43no—
50C2×C4×C151—43no—
51C2×C4×C151—43no—
52C22×C151#11713yes—
53C22×C151C4×D413yes—
54C22×C151C4×Q811yescharacteristic
55C22×C151#12113yes—
56C22×C151C22⋊Q813yes—
57C22×C151#12313yes—
58C22×C151#12313yes—
59C22×C151#12413yes—
60C22×C151#12513yes—
61C22×C151#12613yes—
62C22×C151#12611yescharacteristic
63C22×C151#12613yes—
64C22×C151#12613yes—
65C4×C151—46no—
66Dic151—42no—
67Dic151—46no—
68C2×C151#38311yescharacteristic
69C2×C151#38713yes—
70C2×C151#38813yes—
71C2×C151#39611yescharacteristic
72C2×C151#39713yes—
73C2×C151#40013yes—
74C2×C151#40111yescharacteristic
75C151#144311yescharacteristic, complemented, Sylow
76#1443—1511nomaximal, Sylow
77C2×#95—1513no—
78C2×#95—1513no—
79C2×#95D15111yescharacteristic
80C23×C4—1511no—
81C23×C4—1513no—
82C23×C4C2×D15113yes—
83#95—3026no—
84#95—3026no—
85#95Dic15114yescomplemented
86C24C22×D15111yescharacteristic
87C22×C4—23no—
88C22×C4—23no—
89C22×C4—23no—
90C22×C4—23no—
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—3023no—
94C22×C4—3023no—
95C22×C4—3023no—
96C22×C4—3023no—
97C22×C4—3023no—
98C22×C4—3023no—
99C22×C4—3023no—
100C22×C4—3023no—
101C22×C4—1516no—
102C22×C4—1512no—
103C22×C4C2×Dic15116yes—
104C23C22×Dic15111yescharacteristic
105C23D4×D15113yes—
106C23Q8×D15111yescharacteristic
107C23#1455900313yes—
108C23#1455900413yes—
109C23#1455900413yes—
110C23#1455900511yescharacteristic
111C2×C4—26no—
112C2×C4—26no—
113C2×C4—26no—
114C2×C4—43no—
115C2×C4—43no—
116C2×C4—43no—
117C2×C4—43no—
118C2×C4—3026no—
119C2×C4—3026no—
120C2×C4—3026no—
121C2×C4—3026no—
122C2×C4—6043no—
123C2×C4—6043no—
124C2×C4—6043no—
125C2×C4—6041no—
126C2×C4—6043no—
127C2×C4—6043no—
128C22#1801269813yes—
129C22D4×Dic15113yes—
130C22Q8×Dic15111yescharacteristic
131C22#1801271213yes—
132C22#1801271713yes—
133C22#1801272113yes—
134C22#1801272413yes—
135C22#1801272513yes—
136C22#1801272913yes—
137C22#1801273213yes—
138C22#1801273311yescharacteristic
139C22#1801273313yes—
140C22#1801273413yes—
141C4—46no—
142C4—6042no—
143C4—6046no—
144C2#2375208011yescharacteristic
145C2#2375209813yes—
146C2#2375210513yes—
147C2#2375213611yescharacteristic
148C2#2375214113yes—
149C2#2375215313yes—
150C2C151⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D151
commutatorC23×C151C22×C4
FittingC2×#95×C151C2
socle, prime radical, cosocleC24×C151C23
hypercenterC2×#95D151
hypocenterC151#1443
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
9. #95×C151C4semidirect
75. C151#1443semidirect
85. #95Dic151semidirect

Maximal subgroups

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

subgroupindex
C2×C151⋊#952
C2×#95×C1512
#1443151