Finite Group Databasebeta

← #34079039

Subgroups — #34079039

Order 19328.

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

normal subgroups only

This group has 414 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×#18012698C211yesmaximal, characteristic, complemented
2#23752550C214yesmaximal, complemented
3#23752533C214yesmaximal, complemented
4#23752255C212yesmaximal, complemented
5#23752213C212yesmaximal, complemented
6#23752176C211yesmaximal, characteristic, complemented
7#525×C151C211yesmaximal, characteristic
8C2×#14558988C2212yes—
9#18012698—22no—
10#18012698C2214yes—
11C2×C4⋊Dic151C2212yes—
12C2×C22⋊Dic151—21no—
13C2×C4×Dic151—21no—
14#18012672C2214yescomplemented
15#18012670C2214yescomplemented
16#18012663C2214yescomplemented
17#18012660C2214yescomplemented
18C22⋊(C151⋊C8)C2214yes—
19C2×#41×C151C2211yescharacteristic
20C23×C4×C151C2211yescharacteristic
21#123×C151—21no—
22C22⋊Q8×C151C2212yes—
23#121×C151C2212yes—
24#120×C151—21no—
25C4×D4×C151—22no—
26#117×C151C2211yescharacteristic
27C22×Dic151—22no—
28#14558988—24no—
29C2×C151⋊C8C2314yes—
30C4⋊Dic151—22no—
31C4⋊Dic151C2314yes—
32C22⋊Dic151—24no—
33C4×Dic151—24no—
34C24×C151D411yescharacteristic
35#41×C151—24no—
36C2×Q8×C151C2311yescharacteristic
37C2×D4×C151—22no—
38C2×D4×C151—21no—
39C2×D4×C151C2311yescharacteristic
40C22×C4×C151—24no—
41C22×C4×C151—21no—
42C22×C4×C151D411yescharacteristic
43C22×C4×C151D412yes—
44C22×C4×C151C2312yes—
45C22×C4×C151C2311yescharacteristic
46C4⋊C4×C151—22no—
47C4⋊C4×C151C2312yes—
48C22⋊C4×C151—21no—
49C22⋊C4×C151—22no—
50C22⋊C4×C151—22no—
51C42×C151—21no—
52C2×Dic151—24no—
53C2×Dic151—44no—
54C151⋊C8—24no—
55C23×C151—22no—
56C23×C151—21no—
57C23×C151—42no—
58C23×C151C2×D412yes—
59C23×C151C2×D411yescharacteristic
60Q8×C151—22no—
61D4×C151—22no—
62D4×C151—44no—
63D4×C151—42no—
64C2×C4×C151—22no—
65C2×C4×C151—24no—
66C2×C4×C151—24no—
67C2×C4×C151—21no—
68C2×C4×C151—22no—
69C2×C4×C151—42no—
70C2×C4×C151C2×D412yes—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151#4114yes—
73C2×C4×C151C2411yescharacteristic
74C22×C151—22no—
75C22×C151—22no—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—44no—
79C22×C151—41no—
80C22×C151—42no—
81C22×C151#12312yes—
82C22×C151C22×D411yescharacteristic
83C4×C151—22no—
84C4×C151—41no—
85C4×C151—42no—
86C4×C151#12312yes—
87C4×C151C2×#4112yes—
88Dic151—44no—
89C2×C151—22no—
90C2×C151—42no—
91C2×C151—81no—
92C2×C151C2×#12311yescharacteristic
93C2×C151#57512yes—
94C151#309311yescharacteristic, complemented, Sylow
95#3093—1511nomaximal, Sylow
96#525D15111yescharacteristic
97C2×#117—1511no—
98#485—1514no—
99#482—1514no—
100#428—1512no—
101#417—1512no—
102#407—1511no—
103C2×#41C2×D15111yescharacteristic
104C23×C4C2×D15111yescharacteristic
105C2×M16—1512no—
106#123—21no—
107C22⋊Q8C2×D15112yes—
108#121C2×D15112yes—
109#120—21no—
110C4×D4—22no—
111#117—3022no—
112#117—1514no—
113#117C2×D15111yescharacteristic
114C2×C4⋊C4—1512no—
115C2×C22⋊C4—3021no—
116C2×C42—3021no—
117#107—1514no—
118#106—1514no—
119#103—1514no—
120#102—1514no—
121C22⋊C8—1514no—
122C24C22⋊D15111yescharacteristic
123#41—24no—
124C2×Q8C22×D15111yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D15111yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—3022no—
131C22×C4C22⋊D15111yescharacteristic
132C22×C4C22⋊D15112yes—
133C22×C4C22×D15112yes—
134C22×C4C22×D15111yescharacteristic
135M16—3024no—
136C2×C8—1514no—
137C4⋊C4—22no—
138C4⋊C4—3022no—
139C4⋊C4—1514no—
140C4⋊C4C22×D15112yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—3024no—
145C42—21no—
146C42—3024no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D15112yes—
151C23C2×C22⋊D15111yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—3024no—
163C2×C4—6044no—
164C2×C4C2×C22⋊D15112yes—
165C2×C4C2×C22⋊D15111yescharacteristic
166C2×C4#1455900314yes—
167C2×C4C23×D15111yescharacteristic
168C8—3024no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#1801272012yes—
177C22C22×C22⋊D15111yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—6044no—
182C4#1801272012yes—
183C4C2×#1455900312yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#1801272011yescharacteristic
188C2#2375301012yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#525×C151C2
socleC22×C151C22×D4
hypercenter#525D151
hypocenterC151#3093
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#18012698C2semidirect
2. #23752550C2semidirect
3. #23752533C2semidirect
4. #23752255C2semidirect
5. #23752213C2semidirect
6. #23752176C2semidirect
14. #18012672C22semidirect
15. #18012670C22semidirect
16. #18012663C22semidirect
17. #18012660C22semidirect
94. C151#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#180126982
#237525502
#237525332
#237522552
#237522132
#237521762
#525×C1512
#3093151