Finite Group Databasebeta

← #34079483

Subgroups — #34079483

Order 19328.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#23752768C211yesmaximal, characteristic, complemented
2#127×D151C211yesmaximal, characteristic
3#23752578C211yesmaximal, characteristic, complemented
4#23752577C211yesmaximal, characteristic, complemented
5#23752576C211yesmaximal, characteristic, complemented
6#23752557C214yesmaximal, complemented
7#23752215C214yesmaximal, complemented
8#23752164C211yesmaximal, characteristic, complemented
9#490×C151C211yesmaximal, characteristic, complemented
10C2×D4×D151—22no—
11C2×D4×D151C2212yes—
12C2×#14558987C2212yes—
13#18012738C2212yescomplemented
14#18012736C2211yescharacteristic
15#18012735—22no—
16#18012735C2212yes—
17#18012731C2211yescharacteristic, complemented
18#18012717—22no—
19#18012704—22no—
20#18012697C2212yes—
21C42×D151C2211yescharacteristic
22#18012661C2214yescomplemented
23#18012660C2214yescomplemented
24#18012659C2214yescomplemented
25#18012650C2211yescharacteristic, complemented
26C8×Dic151C2212yescomplemented
27#127×C151C2211yescharacteristic
28#125×C151C2211yescharacteristic, complemented
29#102×C151C2214yescomplemented
30#97×C151C2211yescharacteristic, complemented
31C23×D151—22no—
32C2×Dic302—22no—
33C2×D604—22no—
34C2×D604C2312yes—
35C2×C22⋊D151—22no—
36C2×C22⋊D151—24no—
37D4×D151—28no—
38D4×D151—48no—
39C2×C4×D151D412yes—
40C2×C4×D151C2311yescharacteristic
41#14558987—24no—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45Dic151⋊C4—22no—
46(C2×D151)⋊C4—22no—
47C4×Dic151—22no—
48C4×Dic151D412yes—
49C4×Dic151C2311yescharacteristic
50C2×D4×C151—22no—
51C2×D4×C151C2312yes—
52C2×C8×C151C2312yes—
53C4⋊C4×C151—22no—
54C4⋊C4×C151C2312yes—
55C42×C151C2311yescharacteristic
56C22×D151—22no—
57C22×D151—48no—
58C22×D151—44no—
59C22×D151C2×D411yescharacteristic
60Dic302—44no—
61D604—24no—
62D604—44no—
63C22⋊D151—44no—
64C22⋊D151—48no—
65C2×Dic151—22no—
66C2×Dic151C2×D411yescharacteristic
67C2×Dic151C2×D412yes—
68C4×D151—24no—
69C4×D151#4114yes—
70C151⋊C8—22no—
71C23×C151—22no—
72D4×C151—24no—
73D4×C151—44no—
74C2×C4×C151—22no—
75C2×C4×C151C2×D412yes—
76C2×C4×C151C2411yescharacteristic
77C8×C151—22no—
78C22×C151—42no—
79C22×C151—44no—
80C22×C151C22×D411yescharacteristic
81C2×D151—22no—
82C2×D151—42no—
83C2×D151—44no—
84C2×D151—88no—
85C2×D151#12412yes—
86C4×C151—22no—
87C4×C151—42no—
88C4×C151C2×#4112yes—
89Dic151—42no—
90Dic151#12412yes—
91Dic151AGL(1,ℤ/8)14yes—
92C2×C151—82no—
93C2×C151C2×#12411yescharacteristic
94C2×C151C2×AGL(1,ℤ/8)12yes—
95D151—22no—
96D151—82no—
97C151#313811yescharacteristic, complemented, Sylow
98#3138—1511nomaximal, Sylow
99#533—1511no—
100C2×#127—1511no—
101#490—1511no—
102#490—1511no—
103#490—1511no—
104#490D15111yescharacteristic, complemented
105#486—1514no—
106#418—1514no—
107C4×M16—1511no—
108C22×D4—3022no—
109C22×D4—1512no—
110C2×M16—1512no—
111C4⋊Q8—1512no—
112#127—3022no—
113#127—1512no—
114#127—1511no—
115#127C2×D15111yescharacteristic
116#125—1511no—
117#125C2×D15111yescharacteristic, complemented
118C22⋊Q8—3022no—
119C4×Q8—3022no—
120#117—1512no—
121C2×C42—1511no—
122#102—1514no—
123#102—1514no—
124#102—1514no—
125#102C2×D15114yescomplemented
126#97—1511no—
127#97C2×D15111yescharacteristic, complemented
128C4×C8—1512no—
129C24—3022no—
130C2×Q8—3022no—
131C2×D4—22no—
132C2×D4—3028no—
133C2×D4—3022no—
134C2×D4—3024no—
135C2×D4—3022no—
136C2×D4—6048no—
137C2×D4—1512no—
138C2×D4C22×D15112yes—
139C22×C4—1512no—
140C22×C4—1511no—
141M16—3024no—
142C2×C8—1512no—
143C2×C8C22×D15112yes—
144C4⋊C4—22no—
145C4⋊C4—3022no—
146C4⋊C4—3022no—
147C4⋊C4—1512no—
148C4⋊C4C22×D15112yes—
149C22⋊C4—3022no—
150C42—3022no—
151C42—1512no—
152C42—1511no—
153C42C22×D15111yescharacteristic
154C23—22no—
155C23—3022no—
156C23—6048no—
157C23—6044no—
158C23—1511no—
159Q8—6044no—
160D4—24no—
161D4—44no—
162D4—3024no—
163D4—6044no—
164D4—6044no—
165D4—6048no—
166C2×C4—22no—
167C2×C4—3024no—
168C2×C4—3022no—
169C2×C4—1511no—
170C2×C4—1512no—
171C2×C4—1514no—
172C2×C4D4×D15112yes—
173C2×C4C23×D15111yescharacteristic
174C8—22no—
175C8—3022no—
176C22—42no—
177C22—44no—
178C22—3022no—
179C22—6042no—
180C22—6044no—
181C22—1512no—
182C22—12088no—
183C22C2×D4×D15111yescharacteristic
184C4—22no—
185C4—42no—
186C4—6042no—
187C4—1512no—
188C4—1514no—
189C4#41×D15112yes—
190C2—82no—
191C2—3022no—
192C2—12082no—
193C2#124×D15111yescharacteristic
194C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#490×C151C2
socleC22×C151C22×D4
prime radical#127×D151C2
hypercenter#490D151
hypocenterC151#3138
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23752768C2semidirect
3. #23752578C2semidirect
4. #23752577C2semidirect
5. #23752576C2semidirect
6. #23752557C2semidirect
7. #23752215C2semidirect
8. #23752164C2semidirect
9. #490×C151C2semidirect
13. #18012738C22semidirect
17. #18012731C22semidirect
22. #18012661C22semidirect
23. #18012660C22semidirect
24. #18012659C22semidirect
25. #18012650C22semidirect
26. C8×Dic151C22semidirect
28. #125×C151C22semidirect
29. #102×C151C22semidirect
30. #97×C151C22semidirect
97. C151#3138semidirect
104. #490D151semidirect
117. #125C2×D151semidirect
125. #102C2×D151semidirect
127. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527682
#127×D1512
#237525782
#237525772
#237525762
#237525572
#237522152
#237521642
#490×C1512
#3138151