Finite Group Databasebeta

← #34077433

Subgroups — #34077433

Order 19328.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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×#18012722C211yesmaximal, characteristic
2C22×C4×Dic151C211yesmaximal, characteristic, complemented
3#23752104C214yesmaximal, complemented
4#23752097C214yesmaximal, complemented
5#23752089C212yesmaximal
6#23752087C212yesmaximal, complemented
7#381×C151C211yesmaximal, characteristic, complemented
8C22×C22⋊D151C2211yescharacteristic
9C23×Dic151C2212yes—
10#18012722—24no—
11C2×C4⋊Dic151C2214yes—
12C2×Dic151⋊C4C2212yes—
13C2×C22⋊Dic151C2211yescharacteristic
14C2×(C2×D151)⋊C4C2212yes—
15C2×(C2×D151)⋊C4C2214yes—
16C2×C4×Dic151—24no—
17C2×C4×Dic151C2214yes—
18C151⋊#95C2214yes—
19C151⋊#95C2214yes—
20C23×C4×C151C2211yescharacteristic
21C2×C22⋊C4×C151C2212yes—
22#95×C151C2214yes—
23C23×D151C2311yescharacteristic
24C2×C22⋊D151—22no—
25C2×C22⋊D151—24no—
26C22×Dic151—28no—
27C22×Dic151—24no—
28C22×Dic151C2312yes—
29C22×Dic151C2311yescharacteristic
30C22×Dic151C2314yes—
31C4⋊Dic151—28no—
32Dic151⋊C4—24no—
33C22⋊Dic151—22no—
34(C2×D151)⋊C4—28no—
35(C2×D151)⋊C4—24no—
36C4×Dic151—28no—
37C24×C151C2311yescharacteristic
38C22×C4×C151—24no—
39C22×C4×C151D414yes—
40C22×C4×C151C2314yes—
41C22×C4×C151C2312yes—
42C22⋊C4×C151—24no—
43C22×D151—21no—
44C22×D151—24no—
45C22×D151—22no—
46C22⋊D151—44no—
47C2×Dic151—216no—
48C2×Dic151—24no—
49C2×Dic151—24no—
50C2×Dic151—22no—
51C2×Dic151—21no—
52C2×Dic151—24no—
53C2×Dic151—22no—
54C2×Dic151#4118yes—
55C23×C151—24no—
56C23×C151C2×D412yes—
57C23×C151#4114yes—
58C23×C151C2411yescharacteristic
59C2×C4×C151—28no—
60C2×C4×C151—24no—
61C2×C4×C151—24no—
62C2×C4×C151—24no—
63C2×C4×C151—24no—
64C2×C4×C151C2×D414yes—
65C22×C151—24no—
66C22×C151—28no—
67C22×C151#12314yes—
68C22×C151C22×D411yescharacteristic
69C22×C151C2×#4114yes—
70C22×C151C2×#4112yes—
71C2×D151—41no—
72C2×D151—42no—
73C2×D151—44no—
74C4×C151—24no—
75C4×C151—44no—
76Dic151—28no—
77Dic151—41no—
78Dic151—42no—
79C2×C151—24no—
80C2×C151C2×#12311yescharacteristic
81C2×C151#52512yes—
82C2×C151#52914yes—
83D151—81no—
84C151#285311yescharacteristic, complemented, Sylow
85#2853—1511nomaximal, Sylow
86C2×#123—1511no—
87C22×C42—1511no—
88#388—1514no—
89#387—1514no—
90#386—1512no—
91#385—1512no—
92#381D15111yescharacteristic, complemented
93C22×D4—1511no—
94C23×C4—1512no—
95C23×C4C2×D15111yescharacteristic
96#123—3024no—
97C2×C4⋊C4—1512no—
98C2×C4⋊C4—1514no—
99C2×C22⋊C4—1511no—
100C2×C22⋊C4—1512no—
101C2×C22⋊C4—1514no—
102C2×C22⋊C4C2×D15112yes—
103C2×C42—3024no—
104C2×C42—1514no—
105#95—1514no—
106#95—1514no—
107#95C2×D15114yes—
108C24—1511no—
109C24C22×D15111yescharacteristic
110C2×D4—3022no—
111C2×D4—3024no—
112C22×C4—24no—
113C22×C4—3024no—
114C22×C4—3028no—
115C22×C4—1511no—
116C22×C4—1512no—
117C22×C4—1514no—
118C22×C4D60414yes—
119C22×C4C22×D15114yes—
120C22×C4C22×D15112yes—
121C4⋊C4—3028no—
122C4⋊C4—3024no—
123C22⋊C4—24no—
124C22⋊C4—3028no—
125C22⋊C4—3022no—
126C22⋊C4—3024no—
127C42—3028no—
128C23—24no—
129C23—3021no—
130C23—3024no—
131C23—3022no—
132C23C2×D60412yes—
133C23#1455900314yes—
134C23C23×D15111yescharacteristic
135D4—6044no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—30216no—
142C2×C4—3024no—
143C2×C4—3024no—
144C2×C4—3022no—
145C2×C4—3021no—
146C2×C4—3024no—
147C2×C4—3022no—
148C2×C4—1518no—
149C2×C4C2×D60414yes—
150C22—24no—
151C22—28no—
152C22—6041no—
153C22—6042no—
154C22—6044no—
155C22#1801272314yes—
156C22C22×D60411yescharacteristic
157C22#41×D15114yes—
158C22C2×#1455900312yes—
159C4—24no—
160C4—44no—
161C4—3028no—
162C4—6041no—
163C4—6042no—
164C2—24no—
165C2—12081no—
166C2C2×#1801272311yescharacteristic
167C2#2375272412yes—
168C2#2375273914yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#381×C151C2
prime radicalC22×C22⋊D151C22
hypercenter#381D151
hypocenterC151#2853
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic151C2semidirect
3. #23752104C2semidirect
4. #23752097C2semidirect
6. #23752087C2semidirect
7. #381×C151C2semidirect
84. C151#2853semidirect
92. #381D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127222
C22×C4×Dic1512
#237521042
#237520972
#237520892
#237520872
#381×C1512
#2853151