Finite Group Databasebeta

← #34071490

Subgroups — #34071490

Order 19328.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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
1C23×C4×D151C211yesmaximal, characteristic
2C2×#18012695C212yesmaximal, complemented
3#23752075C211yesmaximal, characteristic, complemented
4#23752071C214yesmaximal, complemented
5#23752067C212yesmaximal
6#23752059C214yesmaximal, complemented
7#381×C151C211yesmaximal, characteristic, complemented
8C24×D151C2211yescharacteristic
9C23×Dic151C2211yescharacteristic
10C22×C4×D151—28no—
11C22×C4×D151C418yescomplemented
12C22×C4×D151C2212yes—
13C22×C4×D151C2212yes—
14#18012695—28no—
15C2×Dic151⋊C4C2214yescomplemented
16C2×C22⋊Dic151C2212yes—
17C2×(C2×D151)⋊C4C2218yes—
18C2×C4×Dic151C2214yescomplemented
19C151⋊#95C2214yescomplemented
20C23×C4×C151C2211yescharacteristic
21C2×C22⋊C4×C151C2212yes—
22#95×C151C2214yescomplemented
23C23×D151—28no—
24C23×D151—24no—
25C23×D151C2×C414yes—
26C23×D151C2312yes—
27C22×Dic151C2×C414yes—
28C22×Dic151D418yes—
29C22×Dic151C2314yes—
30C22×Dic151C2311yescharacteristic
31C22×Dic151C2311yescharacteristic
32C2×C4×D151—232no—
33C2×C4×D151—28no—
34C2×C4×D151—28no—
35C2×C4×D151C2×C418yes—
36C2×C4×D151C2×C418yes—
37Dic151⋊C4—28no—
38C22⋊Dic151—24no—
39(C2×D151)⋊C4—216no—
40C4×Dic151—28no—
41C24×C151C2311yescharacteristic
42C22×C4×C151—24no—
43C22×C4×C151C2×C414yes—
44C22×C4×C151C2314yes—
45C22×C4×C151C2312yes—
46C22⋊C4×C151—24no—
47C22×D151—232no—
48C22×D151—28no—
49C22×D151—24no—
50C22×D151—24no—
51C22×D151—216no—
52C22×D151C22×C414yes—
53C22×D151#4118yes—
54C2×Dic151—24no—
55C2×Dic151—28no—
56C2×Dic151C22⋊C4116yescomplemented
57C2×Dic151C22×C412yes—
58C2×Dic151C22×C412yes—
59C2×Dic151C2×D414yes—
60C2×Dic151C2×D414yes—
61C4×D151—216no—
62C4×D151—216no—
63C23×C151—24no—
64C23×C151C22×C412yes—
65C23×C151C2×D414yes—
66C23×C151C2411yescharacteristic
67C2×C4×C151—28no—
68C2×C4×C151—24no—
69C2×C4×C151—24no—
70C2×C4×C151—28no—
71C2×C4×C151C22×C414yes—
72C22×C151—24no—
73C22×C151—28no—
74C22×C151C2×C22⋊C414yes—
75C22×C151C23×C411yescharacteristic
76C22×C151C22×D412yes—
77C22×C151C2×#4114yes—
78C2×D151—232no—
79C2×D151—24no—
80C2×D151—24no—
81C2×D151—216no—
82C2×D151#11718yescomplemented
83C4×C151—24no—
84C4×C151—44no—
85Dic151—44no—
86Dic151C2×C22⋊C414yes—
87Dic151C2×C22⋊C414yes—
88C2×C151—24no—
89C2×C151C22×C22⋊C411yescharacteristic
90C2×C151C2×#11712yes—
91C2×C151#52514yes—
92D151—28no—
93C151#228011yescharacteristic, complemented, Sylow
94#2280—1511nomaximal, Sylow
95C24×C4—1511no—
96C2×#117—1512no—
97#381—1511no—
98#381D15111yescharacteristic, complemented
99#380—1514no—
100#379—1512no—
101C4×C22⋊C4—1514no—
102C25—1511no—
103C23×C4—3028no—
104C23×C4—1518no—
105C23×C4—1512no—
106C23×C4—1512no—
107C23×C4—1511no—
108C23×C4C2×D15111yescharacteristic
109#117—3028no—
110C2×C4⋊C4—1514no—
111C2×C22⋊C4—1512no—
112C2×C22⋊C4—1518no—
113C2×C22⋊C4C2×D15112yes—
114C2×C42—1514no—
115#95—1514no—
116#95C2×D15114yescomplemented
117C24—3028no—
118C24—3024no—
119C24—1514no—
120C24—1512no—
121C24C22×D15111yescharacteristic
122C22×C4—24no—
123C22×C4—30232no—
124C22×C4—3028no—
125C22×C4—3028no—
126C22×C4—1514no—
127C22×C4—1518no—
128C22×C4—1518no—
129C22×C4—1514no—
130C22×C4—1518no—
131C22×C4—1511no—
132C22×C4—1511no—
133C22×C4C4×D15114yes—
134C22×C4C22×D15114yes—
135C22×C4C22×D15112yes—
136C4⋊C4—3028no—
137C22⋊C4—24no—
138C22⋊C4—30216no—
139C22⋊C4—3024no—
140C42—3028no—
141C23—24no—
142C23—30232no—
143C23—30216no—
144C23—3028no—
145C23—3024no—
146C23—3024no—
147C23—1514no—
148C23—1518no—
149C23C2×C4×D15112yes—
150C23D4×D15114yes—
151C23C23×D15111yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—30216no—
157C2×C4—30216no—
158C2×C4—3024no—
159C2×C4—3028no—
160C2×C4—15116no—
161C2×C4—1512no—
162C2×C4—1512no—
163C2×C4—1514no—
164C2×C4—1514no—
165C2×C4C2×C4×D15114yes—
166C22—28no—
167C22—24no—
168C22—30232no—
169C22—30216no—
170C22—3024no—
171C22—3024no—
172C22—1518no—
173C22C22⋊C4×D15114yes—
174C22C22×C4×D15111yescharacteristic
175C22C2×D4×D15112yes—
176C22#41×D15114yes—
177C4—24no—
178C4—44no—
179C4—6044no—
180C4—1514no—
181C4—1514no—
182C2—24no—
183C2—3028no—
184C2C2×C22⋊C4×D15111yescharacteristic
185C2#117×D15112yes—
186C2#2375272014yes—
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#381×C151C2
socle, cosocleC23×C151C24
prime radicalC24×D151C22
hypercenter#381D151
hypocenterC151#2280
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#18012695C2semidirect
3. #23752075C2semidirect
4. #23752071C2semidirect
6. #23752059C2semidirect
7. #381×C151C2semidirect
11. C22×C4×D151C4semidirect
15. C2×Dic151⋊C4C22semidirect
18. C2×C4×Dic151C22semidirect
19. C151⋊#95C22semidirect
22. #95×C151C22semidirect
56. C2×Dic151C22⋊C4semidirect
82. C2×D151#117semidirect
93. C151#2280semidirect
98. #381D151semidirect
116. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1512
C2×#180126952
#237520752
#237520712
#237520672
#237520592
#381×C1512
#2280151