Finite Group Databasebeta

← #34077168

Subgroups — #34077168

Order 19328.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012739C211yesmaximal, characteristic, complemented
2#23752151C212yesmaximal, complemented
3#23752148C212yesmaximal
4#23752142C212yesmaximal, complemented
5#23752137C212yesmaximal
6#23752132C212yesmaximal, complemented
7#23752124C212yesmaximal
8#23752080C211yesmaximal, characteristic, complemented
9C2×#126×C151C211yesmaximal, characteristic
10C22×Dic302C2212yes—
11#18012739—24no—
12C2×C4⋊Dic151C2212yes—
13C2×C4⋊Dic151C2212yes—
14C2×Dic151⋊C4C2214yes—
15C2×C22⋊Dic151C2214yes—
16C151⋊#95C2212yes—
17C151⋊#95C2212yes—
18C151⋊#95C2212yes—
19C151⋊#95C2214yes—
20C151⋊#95C2214yes—
21#126×C151—24no—
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24C2×C4⋊C4×C151C2211yescharacteristic
25C2×C22⋊C4×C151C2211yescharacteristic
26C2×C22⋊C4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2211yescharacteristic
28C2×C42×C151C2211yescharacteristic
29C2×Dic302—24no—
30C2×Dic302—44no—
31C22×Dic151C2314yes—
32C22×Dic151C2314yes—
33C4⋊Dic151—24no—
34C4⋊Dic151—24no—
35Dic151⋊C4—44no—
36C22⋊Dic151—44no—
37C24×C151C2311yescharacteristic
38C22×C4×C151C2311yescharacteristic
39C22×C4×C151C2311yescharacteristic
40C22×C4×C151C2311yescharacteristic
41C22×C4×C151C2311yescharacteristic
42C22×C4×C151C2311yescharacteristic
43C22×C4×C151C2311yescharacteristic
44C4⋊C4×C151—22no—
45C4⋊C4×C151—22no—
46C4⋊C4×C151—22no—
47C22⋊C4×C151—22no—
48C22⋊C4×C151—22no—
49C22⋊C4×C151—22no—
50C42×C151D414yes—
51Dic302—48no—
52C2×Dic151—24no—
53C2×Dic151—24no—
54C2×Dic151—24no—
55C2×Dic151—24no—
56C2×Dic151—24no—
57C2×Dic151—24no—
58C23×C151—21no—
59C23×C151—22no—
60C23×C151—22no—
61C23×C151—22no—
62C23×C151C2411yescharacteristic
63C2×C4×C151—22no—
64C2×C4×C151—22no—
65C2×C4×C151—22no—
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151—21no—
69C2×C4×C151—22no—
70C2×C4×C151—22no—
71C2×C4×C151—22no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D412yes—
75C22×C151—41no—
76C22×C151—41no—
77C22×C151—41no—
78C22×C151—44no—
79C22×C151C22×D411yescharacteristic
80C22×C151H(5,𝔽2)12yes—
81C22×C1512−1+412yes—
82C22×C1512−1+412yes—
83C4×C151—22no—
84C4×C151—22no—
85C4×C151—22no—
86C4×C151—41no—
87C4×C151—41no—
88C4×C151—41no—
89Dic151—44no—
90Dic151—44no—
91C2×C151—81no—
92C2×C151#53511yescharacteristic
93C2×C151#53611yescharacteristic
94C2×C151#53611yescharacteristic
95C2×C151#56314yes—
96C151#282111yescharacteristic, complemented, Sylow
97#2821—1511nomaximal, Sylow
98C2×C4⋊Q8—1511no—
99C2×#126D15111yescharacteristic
100#400—1512no—
101#399—1512no—
102#398—1512no—
103#397—1512no—
104#395—1512no—
105#393—1512no—
106#383—1511no—
107C22×Q8—1512no—
108C4⋊Q8—3024no—
109#126—24no—
110C2×C4⋊C4—1512no—
111C2×C4⋊C4—1512no—
112C2×C4⋊C4—1514no—
113C2×C4⋊C4C2×D15111yescharacteristic
114C2×C4⋊C4C2×D15111yescharacteristic
115C2×C4⋊C4C2×D15111yescharacteristic
116C2×C22⋊C4—1514no—
117C2×C22⋊C4C2×D15111yescharacteristic
118C2×C22⋊C4C2×D15111yescharacteristic
119C2×C22⋊C4C2×D15111yescharacteristic
120C2×C42C2×D15111yescharacteristic
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1514no—
125#95—1514no—
126C24C22×D15111yescharacteristic
127C2×Q8—3024no—
128C2×Q8—6044no—
129C22×C4—1514no—
130C22×C4—1514no—
131C22×C4C22×D15111yescharacteristic
132C22×C4C22×D15111yescharacteristic
133C22×C4C22×D15111yescharacteristic
134C22×C4C22×D15111yescharacteristic
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15111yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4—3024no—
141C4⋊C4—3024no—
142C4⋊C4—6044no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—6044no—
147C42C22⋊D15114yes—
148C23—21no—
149C23—22no—
150C23—22no—
151C23—22no—
152C23C23×D15111yescharacteristic
153Q8—6048no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—3024no—
164C2×C4—3024no—
165C2×C4—3024no—
166C2×C4—3024no—
167C2×C4—3024no—
168C2×C4—3024no—
169C2×C4C2×C22⋊D15112yes—
170C2×C4C2×C22⋊D15112yes—
171C2×C4C2×C22⋊D15112yes—
172C22—44no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22C22×C22⋊D15111yescharacteristic
177C22#1801278512yes—
178C22#1801278612yes—
179C22#1801278612yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4—6044no—
187C4—6044no—
188C2—81no—
189C2#2375277611yescharacteristic
190C2#2375278311yescharacteristic
191C2#2375278311yescharacteristic
192C2#2375296414yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×#126×C151C2
prime radicalC24×C151C23
hypercenterC2×#126D151
hypocenterC151#2821
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#18012739C2semidirect
2. #23752151C2semidirect
4. #23752142C2semidirect
6. #23752132C2semidirect
8. #23752080C2semidirect
96. C151#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#180127392
#237521512
#237521482
#237521422
#237521372
#237521322
#237521242
#237520802
C2×#126×C1512
#2821151