Finite Group Databasebeta

← #34077105

Subgroups — #34077105

Order 19328.

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

normal subgroups only

This group has 712 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×#18012708C211yesmaximal, characteristic, complemented
2#23752140C213yesmaximal, complemented
3#23752127C213yesmaximal, complemented
4#23752126C213yesmaximal, complemented
5#23752120C213yesmaximal, complemented
6#23752068C211yesmaximal, characteristic, complemented
7C2×#120×C151C211yesmaximal, characteristic, complemented
8C22×C22⋊D151C2213yes—
9C22×C22⋊D151C2211yescharacteristic, complemented
10#18012708—24no—
11C2×Dic151⋊C4C2213yescomplemented
12C2×C22⋊Dic151C2213yes—
13C2×C22⋊Dic151C2213yes—
14C2×C22⋊Dic151C2213yes—
15C2×C22⋊Dic151C2213yescomplemented
16C2×(C2×D151)⋊C4C2213yescomplemented
17C151⋊#95C2213yescomplemented
18C151⋊#95C2213yescomplemented
19C25×C151C2211yescharacteristic
20C22×D4×C151C2213yes—
21#120×C151—24no—
22C2×C22⋊C4×C151C2213yes—
23C23×D151C2311yescharacteristic
24C2×C22⋊D151—26no—
25C2×C22⋊D151—43no—
26C2×C22⋊D151—43no—
27C2×C22⋊D151—43no—
28C22×Dic151C2313yes—
29C22×Dic151C2311yescharacteristic
30C22×Dic151C2313yes—
31Dic151⋊C4—43no—
32C22⋊Dic151—26no—
33C22⋊Dic151—43no—
34C22⋊Dic151—43no—
35C22⋊Dic151—43no—
36(C2×D151)⋊C4—43no—
37C24×C151—43no—
38C24×C151—43no—
39C24×C151D414yescomplemented
40C24×C151C2311yescharacteristic
41C24×C151C2313yes—
42C2×D4×C151—26no—
43C2×D4×C151—43no—
44C2×D4×C151—43no—
45C22×C4×C151C2313yes—
46C22⋊C4×C151—26no—
47C22×D151—21no—
48C22×D151—23no—
49C22×D151—23no—
50C22⋊D151—412no—
51C22⋊D151—44no—
52C2×Dic151—23no—
53C2×Dic151—23no—
54C2×Dic151—23no—
55C2×Dic151—23no—
56C2×Dic151—23no—
57C2×Dic151—23no—
58C2×Dic151—23no—
59C23×C151—23no—
60C23×C151—23no—
61C23×C151—23no—
62C23×C151—23no—
63C23×C151—23no—
64C23×C151—23no—
65C23×C151—21no—
66C23×C151—23no—
67C23×C151—23no—
68C23×C151—412no—
69C23×C151—412no—
70C23×C151—44no—
71C23×C151C2×D416yes—
72C23×C151C2411yescharacteristic
73D4×C151—412no—
74C2×C4×C151—23no—
75C2×C4×C151—23no—
76C2×C4×C151—23no—
77C22×C151—26no—
78C22×C151—26no—
79C22×C151—26no—
80C22×C151—416no—
81C22×C151—43no—
82C22×C151—43no—
83C22×C151—43no—
84C22×C151—43no—
85C22×C151—43no—
86C22×C151—43no—
87C22×C151—41no—
88C22×C151C22×D411yescharacteristic
89C22×C151H(5,𝔽2)13yes—
90C22×C151H(5,𝔽2)13yes—
91C2×D151—43no—
92C2×D151—43no—
93C2×D151—41no—
94C4×C151—43no—
95Dic151—43no—
96Dic151—43no—
97Dic151—41no—
98C2×C151—46no—
99C2×C151—81no—
100C2×C151#53413yes—
101C2×C151#56013yes—
102C2×C151H(3,𝔽4)11yescharacteristic
103D151—81no—
104C151#281211yescharacteristic, complemented, Sylow
105#2812—1511nomaximal, Sylow
106C2×#120—1511no—
107C2×#120D15111yescharacteristic, complemented
108#397—1513no—
109#394—1513no—
110#394—1513no—
111#392—1513no—
112#379—1511no—
113C25C2×D15111yescharacteristic
114C22×D4—1513no—
115C22×D4—1511no—
116C22×D4C2×D15113yes—
117#120—24no—
118#120—3024no—
119C2×C4⋊C4—1513no—
120C2×C22⋊C4—1513no—
121C2×C22⋊C4—1513no—
122C2×C22⋊C4—1513no—
123C2×C22⋊C4—1513no—
124C2×C22⋊C4—1513no—
125C2×C22⋊C4C2×D15113yes—
126#95—1513no—
127#95—1513no—
128C24—43no—
129C24—43no—
130C24—1511no—
131C24C22⋊D15114yescomplemented
132C24C22×D15111yescharacteristic
133C24C22×D15113yes—
134C2×D4—26no—
135C2×D4—43no—
136C2×D4—43no—
137C2×D4—3026no—
138C2×D4—6043no—
139C2×D4—6043no—
140C2×D4—6043no—
141C22×C4—1511no—
142C22×C4—1513no—
143C22×C4—1513no—
144C22×C4C22×D15113yes—
145C4⋊C4—6043no—
146C22⋊C4—26no—
147C22⋊C4—3026no—
148C22⋊C4—6043no—
149C22⋊C4—6043no—
150C22⋊C4—6043no—
151C22⋊C4—6043no—
152C23—23no—
153C23—23no—
154C23—23no—
155C23—23no—
156C23—23no—
157C23—23no—
158C23—21no—
159C23—23no—
160C23—23no—
161C23—412no—
162C23—412no—
163C23—44no—
164C23—3021no—
165C23—3023no—
166C23—3023no—
167C23C2×C22⋊D15116yes—
168C23C23×D15111yescharacteristic
169D4—412no—
170D4—60412no—
171D4—6044no—
172C2×C4—23no—
173C2×C4—23no—
174C2×C4—23no—
175C2×C4—3023no—
176C2×C4—3023no—
177C2×C4—3023no—
178C2×C4—3023no—
179C2×C4—3023no—
180C2×C4—3023no—
181C2×C4—3023no—
182C22—26no—
183C22—26no—
184C22—26no—
185C22—416no—
186C22—43no—
187C22—43no—
188C22—43no—
189C22—43no—
190C22—43no—
191C22—43no—
192C22—41no—
193C22—6043no—
194C22—6043no—
195C22—6041no—
196C22C22×C22⋊D15111yescharacteristic
197C22#1801278413yes—
198C22#1801278413yes—
199C4—43no—
200C4—6043no—
201C4—6043no—
202C4—6041no—
203C2—46no—
204C2—81no—
205C2—12081no—
206C2#2375277113yes—
207C2#2375295113yes—
208C2#2375295511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×#120×C151C2
hypercenterC2×#120D151
hypocenterC151#2812
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#18012708C2semidirect
2. #23752140C2semidirect
3. #23752127C2semidirect
4. #23752126C2semidirect
5. #23752120C2semidirect
6. #23752068C2semidirect
7. C2×#120×C151C2semidirect
9. C22×C22⋊D151C22semidirect
11. C2×Dic151⋊C4C22semidirect
15. C2×C22⋊Dic151C22semidirect
16. C2×(C2×D151)⋊C4C22semidirect
17. C151⋊#95C22semidirect
18. C151⋊#95C22semidirect
39. C24×C151D4semidirect
104. C151#2812semidirect
107. C2×#120D151semidirect
131. C24C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127082
#237521402
#237521272
#237521262
#237521202
#237520682
C2×#120×C1512
#2812151