Finite Group Databasebeta

← #34078340

Subgroups — #34078340

Order 19328.

994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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×D604C211yesmaximal, characteristic, complemented
2C2×#18012767C212yesmaximal, complemented
3#23752723C211yesmaximal, characteristic, complemented
4#23752365C214yesmaximal, complemented
5#23752348C214yesmaximal, complemented
6#23752218C212yesmaximal, complemented
7#407×C151C211yesmaximal, characteristic, complemented
8C24×D151—21no—
9C2×#14559004C2211yescharacteristic, complemented
10C22×D604—22no—
11C22×D604—21no—
12C22×D604—28no—
13C22×D604C2214yes—
14C22×D604C2212yes—
15#18012767—28no—
16C2×#14558993C2214yescomplemented
17C2×D1208C2214yescomplemented
18#18012722—21no—
19#18012718C2212yescomplemented
20#18012713C2212yescomplemented
21#18012708—21no—
22C4×C22⋊D151—22no—
23#18012698C2211yescharacteristic, complemented
24#18012661C2218yescomplemented
25C23×C4×C151C2211yescharacteristic
26C2×M16×C151C2212yescomplemented
27C22⋊C8×C151C2214yescomplemented
28C23×D151—28no—
29C23×D151—22no—
30C23×D151—24no—
31C23×D151—48no—
32#14559004—24no—
33C2×Dic302C2311yescharacteristic, complemented
34C2×D604—28no—
35C2×D604—216no—
36C2×D604—216no—
37C2×D604—24no—
38C2×D604—24no—
39C2×D604—22no—
40C2×D604D418yescomplemented
41C2×D604C2314yes—
42C2×D604C2311yescharacteristic, complemented
43C2×C22⋊D151—22no—
44C2×C22⋊D151—21no—
45C2×C4×D151—21no—
46#14558993—28no—
47D1208—28no—
48C4⋊Dic151C2312yescomplemented
49Dic151⋊C4—22no—
50C22⋊Dic151—21no—
51C22⋊Dic151—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—21no—
54C24×C151D411yescharacteristic
55C22×C4×C151—24no—
56C22×C4×C151D412yes—
57C22×C4×C151D411yescharacteristic
58C22×C4×C151C2312yes—
59C22×C4×C151C2311yescharacteristic
60M16×C151—24no—
61C2×C8×C151C2314yescomplemented
62C22×D151—216no—
63C22×D151—28no—
64C22×D151—24no—
65C22×D151—21no—
66C22×D151—432no—
67C22×D151—48no—
68C22×D151—48no—
69C22×D151—48no—
70Dic302—22no—
71D604—216no—
72D604—28no—
73D604—24no—
74D604—22no—
75D604C2×D418yes—
76C22⋊D151—42no—
77C22⋊D151—44no—
78C2×Dic151—22no—
79C2×Dic151—21no—
80C4×D151—42no—
81C23×C151—22no—
82C23×C151—24no—
83C23×C151C2×D411yescharacteristic
84C23×C151C2×D412yes—
85C2×C4×C151—22no—
86C2×C4×C151—24no—
87C2×C4×C151—24no—
88C2×C4×C151C2×D414yes—
89C2×C4×C151C2×D412yes—
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2411yescharacteristic
92C8×C151—24no—
93C22×C151—28no—
94C22×C151—22no—
95C22×C151—22no—
96C22×C151—22no—
97C22×C151#12012yes—
98C22×C151AGL(1,ℤ/8)14yescomplemented
99C22×C151C22×D411yescharacteristic
100C2×D151—28no—
101C2×D151—416no—
102C2×D151—432no—
103C2×D151—48no—
104C2×D151—41no—
105C2×D151—42no—
106C4×C151—22no—
107C4×C151#12012yes—
108C4×C151C22×D412yes—
109Dic151—41no—
110Dic151—42no—
111C2×C151—22no—
112C2×C151—24no—
113C2×C151C2×#12011yescharacteristic
114C2×C151C2×AGL(1,ℤ/8)12yes—
115D151—48no—
116D151—81no—
117C151#300311yescharacteristic, complemented, Sylow
118#3003—1511nomaximal, Sylow
119C23×D4—1511no—
120C2×AGL(1,ℤ/8)—1512no—
121#525—1511no—
122#450—1514no—
123#447—1514no—
124#418—1512no—
125#407D15111yescharacteristic, complemented
126C25—3021no—
127C2×#41—1511no—
128C22×D4—3028no—
129C22×D4—3022no—
130C22×D4—3021no—
131C22×D4—1514no—
132C22×D4—1512no—
133C23×C4C2×D15111yescharacteristic
134AGL(1,ℤ/8)—3028no—
135C2×SD16—1514no—
136C2×D8—1514no—
137C2×M16C2×D15112yescomplemented
138#123—3021no—
139C22⋊Q8—1512no—
140#121—1512no—
141#120—3021no—
142C4×D4—3022no—
143#117—1511no—
144#102—1518no—
145C22⋊C8C2×D15114yescomplemented
146C24—3028no—
147C24—3024no—
148C24—3022no—
149C24—6048no—
150C24D60411yescharacteristic
151#41—3024no—
152C2×Q8—1511no—
153C2×D4—3028no—
154C2×D4—30216no—
155C2×D4—30216no—
156C2×D4—3022no—
157C2×D4—3021no—
158C2×D4—3024no—
159C2×D4—3024no—
160C2×D4—3022no—
161C2×D4—1518no—
162C2×D4—1511no—
163C2×D4—1514no—
164C22×C4—24no—
165C22×C4—3021no—
166C22×C4D60412yes—
167C22×C4D60411yescharacteristic
168C22×C4C22×D15112yes—
169C22×C4C22×D15111yescharacteristic
170SD16—3028no—
171D8—3028no—
172M16—24no—
173C2×C8C22×D15114yescomplemented
174C4⋊C4—3022no—
175C4⋊C4—1512no—
176C22⋊C4—3021no—
177C22⋊C4—3022no—
178C22⋊C4—3022no—
179C42—3021no—
180C23—22no—
181C23—24no—
182C23—30216no—
183C23—3028no—
184C23—3024no—
185C23—3021no—
186C23—60432no—
187C23—6048no—
188C23—6048no—
189C23—6048no—
190C23C2×D60411yescharacteristic
191C23C2×D60412yes—
192Q8—3022no—
193D4—30216no—
194D4—3028no—
195D4—3024no—
196D4—3022no—
197D4—6042no—
198D4—6044no—
199D4—1518no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—24no—
203C2×C4—3022no—
204C2×C4—3021no—
205C2×C4—6042no—
206C2×C4D4×D15114yes—
207C2×C4C2×D60412yes—
208C2×C4C2×D60411yescharacteristic
209C2×C4C23×D15111yescharacteristic
210C8—24no—
211C22—28no—
212C22—22no—
213C22—22no—
214C22—22no—
215C22—3028no—
216C22—60416no—
217C22—60432no—
218C22—6048no—
219C22—6042no—
220C22—6041no—
221C22#1801270912yes—
222C22#1801276714yescomplemented
223C22C22×D60411yescharacteristic
224C4—22no—
225C4—6042no—
226C4—6041no—
227C4#1801270912yes—
228C4C2×D4×D15112yes—
229C2—22no—
230C2—24no—
231C2—6048no—
232C2—12081no—
233C2C2×#1801270911yescharacteristic
234C2C2×#1801276712yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#407×C151C2
socleC22×C151C22×D4
hypercenter#407D151
hypocenterC151#3003
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×D604C2semidirect
2. C2×#18012767C2semidirect
3. #23752723C2semidirect
4. #23752365C2semidirect
5. #23752348C2semidirect
6. #23752218C2semidirect
7. #407×C151C2semidirect
9. C2×#14559004C22semidirect
16. C2×#14558993C22semidirect
17. C2×D1208C22semidirect
19. #18012718C22semidirect
20. #18012713C22semidirect
23. #18012698C22semidirect
24. #18012661C22semidirect
26. C2×M16×C151C22semidirect
27. C22⋊C8×C151C22semidirect
33. C2×Dic302C23semidirect
40. C2×D604D4semidirect
42. C2×D604C23semidirect
48. C4⋊Dic151C23semidirect
61. C2×C8×C151C23semidirect
98. C22×C151AGL(1,ℤ/8)semidirect
117. C151#3003semidirect
125. #407D151semidirect
137. C2×M16C2×D151semidirect
145. C22⋊C8C2×D151semidirect
173. C2×C8C22×D151semidirect
222. C22#18012767semidirect

Maximal subgroups

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

subgroupindex
C23×D6042
C2×#180127672
#237527232
#237523652
#237523482
#237522182
#407×C1512
#3003151