Finite Group Databasebeta

← #34068154

Subgroups — #34068154

Order 19328.

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

normal subgroups only

This group has 202 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#23752548C212yesmaximal
3#23752151C211yesmaximal, characteristic
4#23751950C212yesmaximal
5#324×C151C211yesmaximal, characteristic
6#18012738—22no—
7#18012730—22no—
8#18012718—21no—
9#18012718C2212yes—
10#18012698—21no—
11C2×C4⋊Dic151C2211yescharacteristic
12#18012673—22no—
13#18012664—22no—
14C151⋊#95—21no—
15C151⋊#95—21no—
16C151⋊#95C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yes—
19C2×Dic302—21no—
20C2×Dic302D412yes—
21C22×Dic151—21no—
22C22×Dic151—21no—
23C4⋊Dic151—21no—
24C4⋊Dic151—21no—
25C4⋊Dic151—21no—
26C4⋊Dic151—22no—
27C4⋊Dic151D412yes—
28Dic151⋊C4—22no—
29Dic151⋊C4—22no—
30C22⋊Dic151—22no—
31C4×Dic151—22no—
32C22×C4×C151D411yescharacteristic
33C22×C4×C151D411yescharacteristic
34C22×C4×C151C2311yescharacteristic
35C2×C8×C151—22no—
36C4⋊C4×C151—22no—
37Dic302—42no—
38Dic302—81no—
39C2×Dic151—22no—
40C2×Dic151—22no—
41C2×Dic151—41no—
42C2×Dic151—41no—
43C2×Dic151—42no—
44C2×Dic151—41no—
45C2×Dic151—41no—
46C23×C151C2×D411yescharacteristic
47C2×C4×C151—21no—
48C2×C4×C151—21no—
49C2×C4×C151—21no—
50C2×C4×C151—41no—
51C2×C4×C151—41no—
52C2×C4×C151Q1612yes—
53C2×C4×C151C2×D412yes—
54C8×C151—42no—
55C22×C151—21no—
56C22×C151—21no—
57C22×C151#12011yescharacteristic
58C22×C151C2×Q1611yescharacteristic
59C22×C151#13711yescharacteristic
60C4×C151—22no—
61C4×C151—22no—
62C4×C151—41no—
63Dic151—42no—
64Dic151—42no—
65Dic151—81no—
66Dic151—81no—
67C2×C151—21no—
68C2×C151—21no—
69C2×C151#45111yescharacteristic
70C2×C151#45411yescharacteristic
71C2×C151#45811yescharacteristic
72C151#161711yescharacteristic, complemented, Sylow
73#1617—1511nomaximal, Sylow
74#544—1511no—
75#484—1512no—
76#400—1511no—
77#328—1512no—
78#324D15111yescharacteristic
79C4⋊Q8—3022no—
80#125—3022no—
81C22⋊Q8—3021no—
82C22⋊Q8—1512no—
83#117—3021no—
84C2×C4⋊C4—1511no—
85C2×C4⋊C4C2×D15111yescharacteristic
86#107—3022no—
87#103—3022no—
88C22⋊C8C2×D15112yes—
89#95—3021no—
90#95—3021no—
91#95—1511no—
92C2×Q8—3021no—
93C2×Q8—1512no—
94C22×C4—3021no—
95C22×C4—3021no—
96C22×C4D60411yescharacteristic
97C22×C4D60411yescharacteristic
98C22×C4C22×D15111yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—3022no—
102C4⋊C4—3021no—
103C4⋊C4—3021no—
104C4⋊C4—3021no—
105C4⋊C4—3022no—
106C4⋊C4—3022no—
107C4⋊C4—1512no—
108C22⋊C4—3022no—
109C42—3022no—
110C23C2×D60411yescharacteristic
111Q8—6042no—
112Q8—12081no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—3022no—
119C2×C4—3022no—
120C2×C4—6041no—
121C2×C4—6041no—
122C2×C4—6042no—
123C2×C4—6041no—
124C2×C4—6041no—
125C2×C4Dic60412yes—
126C2×C4D4×D15112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1801270911yescharacteristic
131C22C2×Dic60411yescharacteristic
132C22#1801277211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—6042no—
137C4—6042no—
138C4—12081no—
139C4—12081no—
140C2—21no—
141C2—21no—
142C2#2375237011yescharacteristic
143C2#2375238711yescharacteristic
144C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#324D151
hypocenterC151#1617
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
72. C151#1617semidirect

Maximal subgroups

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

subgroupindex
#237528432
#237525482
#237521512
#237519502
#324×C1512
#1617151