Finite Group Databasebeta

← #34068165

Subgroups — #34068165

Order 19328.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752847C211yesmaximal, characteristic, complemented
2#23752588C211yesmaximal, characteristic, complemented
3#23752408C212yesmaximal, complemented
4#23751939C212yesmaximal, complemented
5#331×C151C211yesmaximal, characteristic, complemented
6C2×D4×D151—22no—
7C2×D1208—22no—
8C2×#14558989—22no—
9#18012736C2211yescharacteristic, complemented
10#18012710—22no—
11#18012707—22no—
12C4×D604C2212yes—
13#18012661—22no—
14C4×C151⋊C8C2211yescharacteristic, complemented
15#127×C151C2211yescharacteristic
16C4⋊C8×C151C2212yescomplemented
17C23×D151—22no—
18C2×D604—21no—
19C2×D604—22no—
20C2×D604D412yes—
21C2×C22⋊D151—24no—
22D4×D151—44no—
23D4×D151—44no—
24C2×C4×D151—22no—
25D1208—44no—
26#14558989—44no—
27C2×C151⋊C8—21no—
28C4⋊Dic151D412yes—
29C22⋊Dic151—22no—
30(C2×D151)⋊C4—22no—
31C2×D4×C151—22no—
32C2×D4×C151D412yes—
33C2×C8×C151—22no—
34C42×C151C2311yescharacteristic
35C22×D151—22no—
36C22×D151—48no—
37C22×D151—41no—
38C22×D151—82no—
39D604—22no—
40D604—42no—
41D604—42no—
42D604—42no—
43D604D814yescomplemented
44C22⋊D151—48no—
45C2×Dic151—22no—
46C4×D151—42no—
47C4×D151—42no—
48C151⋊C8—22no—
49C23×C151—22no—
50D4×C151—42no—
51D4×C151—42no—
52D4×C151—42no—
53C2×C4×C151C2×D412yes—
54C2×C4×C151C2×D411yescharacteristic
55C8×C151—42no—
56C22×C151—44no—
57C22×C151—42no—
58C22×C151#12011yescharacteristic
59C2×D151—24no—
60C2×D151—42no—
61C2×D151—42no—
62C2×D151—88no—
63C2×D151—82no—
64C2×D151—81no—
65C4×C151—21no—
66C4×C151C2×D812yes—
67C4×C151AGL(1,ℤ/8)12yes—
68Dic151—42no—
69C2×C151—82no—
70C2×C151#44712yes—
71C2×C151#45311yescharacteristic
72D151—44no—
73D151—161no—
74C151#161911yescharacteristic, complemented, Sylow
75#1619—1511nomaximal, Sylow
76D42—1511no—
77#493—1511no—
78#459—1512no—
79#331D15111yescharacteristic, complemented
80D4⋊C8—1512no—
81C22×D4—3022no—
82C2×D8—3022no—
83C2×D8—3022no—
84#127—1511no—
85#127C2×D15111yescharacteristic
86#121—3022no—
87#120—3022no—
88C4×D4—1512no—
89C4⋊C8C2×D15112yescomplemented
90#102—3022no—
91C4×C8—1511no—
92C24—3022no—
93C2×D4—22no—
94C2×D4—3024no—
95C2×D4—3022no—
96C2×D4—3021no—
97C2×D4—6044no—
98C2×D4—6044no—
99C2×D4—1512no—
100C2×D4D60412yes—
101C22×C4—3022no—
102D8—6044no—
103D8—6044no—
104C2×C8—22no—
105C2×C8—3021no—
106C4⋊C4—1512no—
107C22⋊C4—3022no—
108C22⋊C4—3022no—
109C42C22×D15111yescharacteristic
110C23—22no—
111C23—3022no—
112C23—6048no—
113C23—6041no—
114C23—12082no—
115D4—42no—
116D4—42no—
117D4—42no—
118D4—3022no—
119D4—6042no—
120D4—6048no—
121D4—6042no—
122D4—6042no—
123D4—1514no—
124C2×C4—3022no—
125C2×C4—6042no—
126C2×C4—6042no—
127C2×C4D4×D15112yes—
128C2×C4C2×D60411yescharacteristic
129C8—42no—
130C8—3022no—
131C22—44no—
132C22—42no—
133C22—3024no—
134C22—6042no—
135C22—6042no—
136C22—12088no—
137C22—12082no—
138C22—12081no—
139C22#1801270911yescharacteristic
140C4—21no—
141C4—6042no—
142C4D8×D15112yes—
143C4#1801276612yes—
144C2—82no—
145C2—6044no—
146C2—24161no—
147C2#2375234712yes—
148C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#331×C151C2
socleC22×C151#120
hypercenter#331D151
hypocenterC151#1619
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #23752847C2semidirect
2. #23752588C2semidirect
3. #23752408C2semidirect
4. #23751939C2semidirect
5. #331×C151C2semidirect
9. #18012736C22semidirect
14. C4×C151⋊C8C22semidirect
16. C4⋊C8×C151C22semidirect
43. D604D8semidirect
74. C151#1619semidirect
79. #331D151semidirect
89. C4⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528472
#237525882
#237524082
#237519392
#331×C1512
#1619151