Finite Group Databasebeta

← #34068086

Subgroups — #34068086

Order 19328.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752843C211yesmaximal, characteristic
2#23752370C212yesmaximal
3#23752132C211yesmaximal, characteristic
4#23751950C212yesmaximal
5#324×C151C211yesmaximal, characteristic
6C22×Dic302C2211yescharacteristic
7C2×Dic604—22no—
8#18012738—22no—
9#18012730—22no—
10#18012718—21no—
11#18012718C2212yes—
12#18012698—21no—
13C2×Dic151⋊C4—21no—
14#18012664—22no—
15C151⋊#95—21no—
16C151⋊#95C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yes—
19C2×Dic302—21no—
20C2×Dic302—22no—
21C2×Dic302—42no—
22C2×Dic302D412yes—
23C22×Dic151—21no—
24C22×Dic151—21no—
25Dic604—44no—
26C4⋊Dic151—21no—
27C4⋊Dic151—21no—
28C4⋊Dic151—21no—
29C4⋊Dic151D412yes—
30Dic151⋊C4—22no—
31Dic151⋊C4—22no—
32Dic151⋊C4—42no—
33C22⋊Dic151—22no—
34C4×Dic151—22no—
35C22×C4×C151D411yescharacteristic
36C22×C4×C151D411yescharacteristic
37C22×C4×C151C2311yescharacteristic
38C2×C8×C151—22no—
39C4⋊C4×C151—22no—
40Dic302—24no—
41Dic302—42no—
42Dic302—42no—
43Dic302—81no—
44C2×Dic151—22no—
45C2×Dic151—22no—
46C2×Dic151—22no—
47C2×Dic151—22no—
48C2×Dic151—41no—
49C2×Dic151—41no—
50C2×Dic151—41no—
51C2×Dic151—41no—
52C23×C151C2×D411yescharacteristic
53C2×C4×C151—21no—
54C2×C4×C151—21no—
55C2×C4×C151—21no—
56C2×C4×C151—41no—
57C2×C4×C151—41no—
58C2×C4×C151Q1612yescomplemented
59C2×C4×C151C2×D412yes—
60C8×C151—42no—
61C22×C151—21no—
62C22×C151—21no—
63C22×C151#12011yescharacteristic
64C22×C151C2×Q1611yescharacteristic
65C22×C151#13711yescharacteristic
66C4×C151—22no—
67C4×C151—22no—
68C4×C151—41no—
69Dic151—42no—
70Dic151—42no—
71Dic151—42no—
72Dic151—42no—
73C2×C151—21no—
74C2×C151—21no—
75C2×C151#45111yescharacteristic
76C2×C151#45611yescharacteristic
77C2×C151B(4,𝔽2)11yescharacteristic
78C151#160511yescharacteristic, complemented, Sylow
79#1605—1511nomaximal, Sylow
80#544—1511no—
81#451—1512no—
82#395—1511no—
83#328—1512no—
84#324D15111yescharacteristic
85C22×Q8—1511no—
86C2×Q16—3022no—
87C4⋊Q8—3022no—
88#125—3022no—
89C22⋊Q8—3021no—
90C22⋊Q8—1512no—
91#117—3021no—
92C2×C4⋊C4—3021no—
93C2×C4⋊C4C2×D15111yescharacteristic
94#103—3022no—
95C22⋊C8C2×D15112yes—
96#95—3021no—
97#95—1511no—
98C2×Q8—3021no—
99C2×Q8—3022no—
100C2×Q8—6042no—
101C2×Q8—1512no—
102C22×C4—3021no—
103C22×C4—3021no—
104C22×C4D60411yescharacteristic
105C22×C4D60411yescharacteristic
106C22×C4C22×D15111yescharacteristic
107Q16—6044no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—3022no—
111C4⋊C4—3021no—
112C4⋊C4—3021no—
113C4⋊C4—3021no—
114C4⋊C4—3022no—
115C4⋊C4—6042no—
116C4⋊C4—1512no—
117C22⋊C4—3022no—
118C42—3022no—
119C23C2×D60411yescharacteristic
120Q8—3024no—
121Q8—6042no—
122Q8—6042no—
123Q8—12081no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—3022no—
130C2×C4—3022no—
131C2×C4—3022no—
132C2×C4—3022no—
133C2×C4—6041no—
134C2×C4—6041no—
135C2×C4—6041no—
136C2×C4—6041no—
137C2×C4Dic60412yescomplemented
138C2×C4D4×D15112yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1801270911yescharacteristic
143C22C2×Dic60411yescharacteristic
144C22#1801277211yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—6042no—
149C4—6042no—
150C4—6042no—
151C4—6042no—
152C2—21no—
153C2—21no—
154C2#2375237011yescharacteristic
155C2#2375239711yescharacteristic
156C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#324D151
hypocenterC151#1605
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
58. C2×C4×C151Q16semidirect
78. C151#1605semidirect
137. C2×C4Dic604semidirect

Maximal subgroups

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

subgroupindex
#237528432
#237523702
#237521322
#237519502
#324×C1512
#1605151