Finite Group Databasebeta

← #34077161

Subgroups — #34077161

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
2#23752148C212yesmaximal, complemented
3#23752137C212yesmaximal, complemented
4#23752135C214yesmaximal, complemented
5#23752131C212yesmaximal, complemented
6#23752126C212yesmaximal
7#23752078C211yesmaximal, characteristic, complemented
8C2×#124×C151C211yesmaximal, characteristic
9#18012731—24no—
10C2×C4⋊Dic151C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2214yes—
16C2×C22⋊Dic151C2214yes—
17C2×C22⋊Dic151C2214yes—
18C151⋊#95C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2214yes—
21C22×Q8×C151C2211yescharacteristic
22C22×D4×C151C2211yescharacteristic
23#124×C151—24no—
24C2×C22⋊C4×C151C2212yes—
25C2×C22⋊C4×C151C2212yes—
26C2×C42×C151C2211yescharacteristic
27C22×Dic151C2312yes—
28C22×Dic151C2312yes—
29C22×Dic151C2314yes—
30C4⋊Dic151—22no—
31C4⋊Dic151—22no—
32C4⋊Dic151—42no—
33Dic151⋊C4—24no—
34Dic151⋊C4—24no—
35Dic151⋊C4—44no—
36C22⋊Dic151—44no—
37C22⋊Dic151—44no—
38C24×C151C2312yes—
39C2×Q8×C151—22no—
40C2×Q8×C151—42no—
41C2×D4×C151—22no—
42C2×D4×C151—42no—
43C22×C4×C151C2312yes—
44C22×C4×C151C2311yescharacteristic
45C22×C4×C151C2311yescharacteristic
46C22×C4×C151C2311yescharacteristic
47C22⋊C4×C151—24no—
48C22⋊C4×C151—24no—
49C42×C151D414yes—
50C2×Dic151—22no—
51C2×Dic151—22no—
52C2×Dic151—22no—
53C2×Dic151—24no—
54C2×Dic151—24no—
55C2×Dic151—24no—
56C2×Dic151—22no—
57C2×Dic151—24no—
58C23×C151—22no—
59C23×C151—22no—
60C23×C151—24no—
61C23×C151—24no—
62C23×C151—22no—
63C23×C151C2411yescharacteristic
64Q8×C151—44no—
65D4×C151—44no—
66C2×C4×C151—22no—
67C2×C4×C151—21no—
68C2×C4×C151—22no—
69C2×C4×C151—21no—
70C2×C4×C151—22no—
71C2×C4×C151—24no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D412yes—
74C2×C4×C151C2×D412yes—
75C22×C151—42no—
76C22×C151—42no—
77C22×C151—42no—
78C22×C151—44no—
79C22×C151—44no—
80C22×C151C22×D411yescharacteristic
81C22×C151H(5,𝔽2)12yes—
82C22×C151H(5,𝔽2)11yescharacteristic
83C22×C1512−1+412yes—
84C22×C1512−1+411yescharacteristic
85C4×C151—22no—
86C4×C151—22no—
87C4×C151—22no—
88C4×C151—42no—
89Dic151—42no—
90Dic151—42no—
91Dic151—44no—
92C2×C151—82no—
93C2×C151#53511yescharacteristic
94C2×C151#53611yescharacteristic
95C2×C151#53711yescharacteristic
96C2×C151#56212yes—
97C2×C151#56312yes—
98C151#282011yescharacteristic, complemented, Sylow
99#2820—1511nomaximal, Sylow
100C2×#125—1511no—
101C2×#124D15111yescharacteristic
102#399—1512no—
103#397—1512no—
104#396—1514no—
105#395—1512no—
106#394—1512no—
107#382—1511no—
108C22×Q8C2×D15111yescharacteristic
109C22×D4C2×D15111yescharacteristic
110#125—3024no—
111#124—24no—
112C2×C4⋊C4—1512no—
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1511no—
115C2×C4⋊C4—1511no—
116C2×C4⋊C4—1514no—
117C2×C4⋊C4—1512no—
118C2×C22⋊C4—1514no—
119C2×C22⋊C4—1514no—
120C2×C22⋊C4C2×D15112yes—
121C2×C22⋊C4C2×D15112yes—
122C2×C42C2×D15111yescharacteristic
123#95—1512no—
124#95—1512no—
125#95—1514no—
126C24C22×D15112yes—
127C2×Q8—22no—
128C2×Q8—42no—
129C2×D4—22no—
130C2×D4—42no—
131C22×C4—1514no—
132C22×C4—1512no—
133C22×C4—1512no—
134C22×C4C22×D15112yes—
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15111yescharacteristic
137C22×C4C22×D15111yescharacteristic
138C4⋊C4—3024no—
139C4⋊C4—3024no—
140C4⋊C4—3022no—
141C4⋊C4—3022no—
142C4⋊C4—6044no—
143C4⋊C4—6042no—
144C22⋊C4—24no—
145C22⋊C4—24no—
146C22⋊C4—6044no—
147C22⋊C4—6044no—
148C42C22⋊D15114yes—
149C23—22no—
150C23—24no—
151C23—22no—
152C23—22no—
153C23—24no—
154C23C23×D15111yescharacteristic
155Q8—44no—
156D4—44no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—3022no—
164C2×C4—3022no—
165C2×C4—3024no—
166C2×C4—3024no—
167C2×C4—3022no—
168C2×C4—3024no—
169C2×C4—3022no—
170C2×C4—3024no—
171C2×C4C2×C22⋊D15112yes—
172C2×C4C2×C22⋊D15112yes—
173C2×C4C2×C22⋊D15112yes—
174C22—44no—
175C22—42no—
176C22—42no—
177C22—42no—
178C22—44no—
179C22C22×C22⋊D15111yescharacteristic
180C22#1801278412yes—
181C22#1801278511yescharacteristic
182C22#1801278611yescharacteristic
183C22#1801278612yes—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—6042no—
189C4—6042no—
190C4—6044no—
191C2—82no—
192C2#2375277911yescharacteristic
193C2#2375278311yescharacteristic
194C2#2375279011yescharacteristic
195C2#2375295612yes—
196C2#2375296212yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×#124×C151C2
prime radicalC22×D4×C151C22
hypercenterC2×#124D151
hypocenterC151#2820
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#18012731C2semidirect
2. #23752148C2semidirect
3. #23752137C2semidirect
4. #23752135C2semidirect
5. #23752131C2semidirect
7. #23752078C2semidirect
98. C151#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#180127312
#237521482
#237521372
#237521352
#237521312
#237521262
#237520782
C2×#124×C1512
#2820151