Finite Group Databasebeta

← #34077162

Subgroups — #34077162

Order 19328.

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

normal subgroups only

This group has 464 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×#18012731C211yesmaximal, characteristic, complemented
2C2×#18012727C211yesmaximal, characteristic
3#23752149C212yesmaximal, complemented
4#23752139C212yesmaximal, complemented
5#23752134C214yesmaximal, complemented
6#23752133C212yesmaximal, complemented
7#23752130C212yesmaximal
8#382×C151C211yesmaximal, characteristic, complemented
9C22×Dic302C2211yescharacteristic
10C22×D604C2211yescharacteristic
11#18012731—24no—
12#18012727—24no—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×C4⋊Dic151C2211yescharacteristic
15C2×C4⋊Dic151C2214yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2214yes—
21C2×(C2×D151)⋊C4C2214yes—
22C151⋊#95C2214yes—
23C2×C4⋊C4×C151C2212yes—
24C2×C42×C151C2211yescharacteristic
25#95×C151C2212yes—
26#95×C151C2212yes—
27C23×D151C2312yes—
28C2×Dic302—22no—
29C2×Dic302—42no—
30C2×D604—22no—
31C2×D604—42no—
32C22×Dic151C2312yes—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C4⋊Dic151—22no—
36C4⋊Dic151—22no—
37C4⋊Dic151—44no—
38Dic151⋊C4—24no—
39Dic151⋊C4—24no—
40(C2×D151)⋊C4—24no—
41(C2×D151)⋊C4—24no—
42(C2×D151)⋊C4—44no—
43(C2×D151)⋊C4—44no—
44C22×C4×C151C2314yes—
45C22×C4×C151C2311yescharacteristic
46C22×C4×C151C2311yescharacteristic
47C22×C4×C151C2311yescharacteristic
48C4⋊C4×C151—42no—
49C42×C151D414yes—
50C22×D151—22no—
51C22×D151—22no—
52C22×D151—24no—
53C22×D151—24no—
54C22×D151—22no—
55Dic302—44no—
56D604—44no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—24no—
62C2×Dic151—24no—
63C2×Dic151—22no—
64C23×C151C2411yescharacteristic
65C2×C4×C151—22no—
66C2×C4×C151—21no—
67C2×C4×C151—22no—
68C2×C4×C151—21no—
69C2×C4×C151—24no—
70C2×C4×C151—24no—
71C2×C4×C151—24no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D412yes—
75C22×C151C22×D411yescharacteristic
76C22×C151H(5,𝔽2)11yescharacteristic
77C22×C151H(5,𝔽2)12yes—
78C22×C1512−1+412yes—
79C22×C1512−1+411yescharacteristic
80C2×D151—42no—
81C2×D151—42no—
82C2×D151—42no—
83C2×D151—44no—
84C2×D151—44no—
85C4×C151—22no—
86C4×C151—22no—
87C4×C151—22no—
88C4×C151—44no—
89Dic151—42no—
90Dic151—42no—
91Dic151—42no—
92C2×C151#53511yescharacteristic
93C2×C151#53611yescharacteristic
94C2×C151#53711yescharacteristic
95C2×C151#56212yes—
96C2×C151#56312yes—
97D151—82no—
98C151#282011yescharacteristic, complemented, Sylow
99#2820—1511nomaximal, Sylow
100C2×#125—1511no—
101C2×#124—1511no—
102#399—1512no—
103#397—1512no—
104#396—1514no—
105#395—1512no—
106#394—1512no—
107#382D15111yescharacteristic, complemented
108C22×Q8—1511no—
109C22×D4—1511no—
110#125—3024no—
111#124—3024no—
112C2×C4⋊C4—1512no—
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1511no—
115C2×C4⋊C4—1511no—
116C2×C4⋊C4—1514no—
117C2×C4⋊C4C2×D15112yes—
118C2×C22⋊C4—1512no—
119C2×C22⋊C4—1512no—
120C2×C22⋊C4—1514no—
121C2×C22⋊C4—1514no—
122C2×C42C2×D15111yescharacteristic
123#95—1514no—
124#95C2×D15112yes—
125#95C2×D15112yes—
126C24—1512no—
127C2×Q8—3022no—
128C2×Q8—6042no—
129C2×D4—3022no—
130C2×D4—6042no—
131C22×C4—1512no—
132C22×C4—1512no—
133C22×C4—1512no—
134C22×C4C22×D15114yes—
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15111yescharacteristic
137C22×C4C22×D15111yescharacteristic
138C4⋊C4—42no—
139C4⋊C4—3024no—
140C4⋊C4—3024no—
141C4⋊C4—3022no—
142C4⋊C4—3022no—
143C4⋊C4—6044no—
144C22⋊C4—3024no—
145C22⋊C4—3024no—
146C22⋊C4—6044no—
147C22⋊C4—6044no—
148C42D60414yes—
149C23—3022no—
150C23—3022no—
151C23—3024no—
152C23—3024no—
153C23—3022no—
154C23C23×D15111yescharacteristic
155Q8—6044no—
156D4—6044no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—3022no—
165C2×C4—3022no—
166C2×C4—3022no—
167C2×C4—3022no—
168C2×C4—3024no—
169C2×C4—3024no—
170C2×C4—3022no—
171C2×C4C2×D60412yes—
172C2×C4C2×D60412yes—
173C2×C4C2×D60412yes—
174C22—6044no—
175C22—6042no—
176C22—6042no—
177C22—6042no—
178C22—6044no—
179C22C22×D60411yescharacteristic
180C22#1801278411yescharacteristic
181C22#1801278512yes—
182C22#1801278612yes—
183C22#1801278711yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—6042no—
189C4—6042no—
190C4—6042no—
191C2—12082no—
192C2#2375278111yescharacteristic
193C2#2375278811yescharacteristic
194C2#2375279311yescharacteristic
195C2#2375295612yes—
196C2#2375296612yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#382×C151C2
prime radicalC22×D604C22
hypercenter#382D151
hypocenterC151#2820
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#18012731C2semidirect
3. #23752149C2semidirect
4. #23752139C2semidirect
5. #23752134C2semidirect
6. #23752133C2semidirect
8. #382×C151C2semidirect
98. C151#2820semidirect
107. #382D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127312
C2×#180127272
#237521492
#237521392
#237521342
#237521332
#237521302
#382×C1512
#2820151