Finite Group Databasebeta

← #34079051

Subgroups — #34079051

Order 19328.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012713C211yesmaximal, characteristic
2C2×#18012698C211yesmaximal, characteristic, complemented
3#23752537C214yesmaximal, complemented
4#23752531C212yesmaximal, complemented
5#23752526C212yesmaximal, complemented
6#23752254C212yesmaximal, complemented
7#23752218C212yesmaximal, complemented
8#407×C151C211yesmaximal, characteristic, complemented
9C22×D604C2211yescharacteristic
10C22×C22⋊D151—21no—
11#18012713—21no—
12#18012713—21no—
13#18012713C2212yes—
14#18012713C2212yes—
15#18012698—21no—
16#18012698—21no—
17#18012698C2212yes—
18#18012698C2212yescomplemented
19C2×C4⋊Dic151C2211yescharacteristic
20C2×C4⋊Dic151C2211yescharacteristic, complemented
21C2×C4⋊Dic151C2211yescharacteristic, complemented
22C2×C22⋊Dic151—21no—
23C2×(C2×D151)⋊C4—21no—
24C2×C4×Dic151—21no—
25#18012673C2214yescomplemented
26#18012671C2214yescomplemented
27#18012661C2214yescomplemented
28#18012661C2214yescomplemented
29C23×C4×C151C2211yescharacteristic
30C2×M16×C151C2212yes—
31C22⋊C8×C151C2212yescomplemented
32C22⋊C8×C151C2212yescomplemented
33C23×D151—21no—
34C2×D604—21no—
35C2×D604—24no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C22⋊D151—22no—
39C2×C22⋊D151—44no—
40C22×Dic151—21no—
41C22×Dic151—21no—
42C22×Dic151—21no—
43C4⋊Dic151—21no—
44C4⋊Dic151—21no—
45C4⋊Dic151—21no—
46C4⋊Dic151C2312yes—
47C4⋊Dic151C2312yes—
48C4⋊Dic151C2312yes—
49C22⋊Dic151—22no—
50C22⋊Dic151—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C4×Dic151—22no—
55C24×C151D411yescharacteristic
56C22×C4×C151—24no—
57C22×C4×C151D411yescharacteristic
58C22×C4×C151D411yescharacteristic
59C22×C4×C151D411yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63M16×C151—24no—
64C2×C8×C151C2314yes—
65C22×D151—22no—
66C22×D151—42no—
67C22×D151—42no—
68C22×D151—42no—
69D604—24no—
70D604—42no—
71C22⋊D151—44no—
72C22⋊D151—44no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—42no—
77C2×Dic151—42no—
78C2×Dic151—42no—
79C23×C151—22no—
80C23×C151—22no—
81C23×C151—41no—
82C23×C151C2×D411yescharacteristic
83C23×C151C2×D411yescharacteristic
84C23×C151C2×D411yescharacteristic
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2×D411yescharacteristic
93C2×C4×C151#4114yes—
94C2×C4×C151C2411yescharacteristic
95C8×C151—24no—
96C22×C151—21no—
97C22×C151—21no—
98C22×C151—21no—
99C22×C151—21no—
100C22×C151—21no—
101C22×C151—21no—
102C22×C151—21no—
103C22×C151—44no—
104C22×C151#12312yes—
105C22×C151AGL(1,ℤ/8)12yes—
106C22×C151C22×D411yescharacteristic
107C2×D151—42no—
108C2×D151—42no—
109C2×D151—42no—
110C2×D151—84no—
111C4×C151—21no—
112C4×C151—21no—
113C4×C151#12312yes—
114C4×C151C2×#4112yes—
115Dic151—42no—
116Dic151—42no—
117Dic151—42no—
118C2×C151—22no—
119C2×C151—22no—
120C2×C151—41no—
121C2×C151C2×#12311yescharacteristic
122C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C151#57511yescharacteristic
124D151—82no—
125C151#309411yescharacteristic, complemented, Sylow
126#3094—1511nomaximal, Sylow
127C2×#121—1511no—
128C2×#117—1511no—
129#482—1514no—
130#481—1512no—
131#480—1512no—
132#428—1512no—
133#418—1512no—
134#407D15111yescharacteristic, complemented
135C22×D4—3021no—
136C22×D4—1511no—
137C23×C4C2×D15111yescharacteristic
138C2×M16C2×D15112yes—
139#121—3021no—
140#121—3021no—
141#121—1512no—
142#121—1512no—
143#117—3021no—
144#117—3021no—
145#117—1512no—
146#117—1512no—
147C2×C4⋊C4—1511no—
148C2×C4⋊C4—1511no—
149C2×C4⋊C4—1511no—
150C2×C22⋊C4—3021no—
151C2×C22⋊C4—3021no—
152C2×C42—3021no—
153#107—1514no—
154#106—1514no—
155#102—1514no—
156#102—1514no—
157C22⋊C8C2×D15112yescomplemented
158C22⋊C8C2×D15112yescomplemented
159C24—3021no—
160C24D60411yescharacteristic
161C2×D4—3022no—
162C2×D4—3022no—
163C2×D4—3021no—
164C2×D4—3024no—
165C2×D4—6044no—
166C2×D4—1512no—
167C22×C4—24no—
168C22×C4—3021no—
169C22×C4—3021no—
170C22×C4—3021no—
171C22×C4D60411yescharacteristic
172C22×C4D60411yescharacteristic
173C22×C4D60411yescharacteristic
174C22×C4C22×D15111yescharacteristic
175C22×C4C22×D15111yescharacteristic
176C22×C4C22×D15111yescharacteristic
177M16—24no—
178C2×C8C22×D15114yes—
179C4⋊C4—3021no—
180C4⋊C4—3021no—
181C4⋊C4—3021no—
182C4⋊C4—1512no—
183C4⋊C4—1512no—
184C4⋊C4—1512no—
185C22⋊C4—3022no—
186C22⋊C4—3022no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C42—3022no—
190C42—3022no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—3022no—
195C23—6042no—
196C23—6042no—
197C23—6042no—
198C23C2×D60411yescharacteristic
199C23C2×D60411yescharacteristic
200C23C2×D60411yescharacteristic
201D4—3024no—
202D4—6044no—
203D4—6044no—
204D4—6042no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—3022no—
211C2×C4—3022no—
212C2×C4—3022no—
213C2×C4—6042no—
214C2×C4—6042no—
215C2×C4—6042no—
216C2×C4C2×D60411yescharacteristic
217C2×C4C2×D60411yescharacteristic
218C2×C4C2×D60411yescharacteristic
219C2×C4#1455900314yes—
220C2×C4C23×D15111yescharacteristic
221C8—24no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—6042no—
231C22—6042no—
232C22—6042no—
233C22—12084no—
234C22#1801272312yes—
235C22#1801276712yes—
236C22C22×D60411yescharacteristic
237C4—21no—
238C4—21no—
239C4—6042no—
240C4—6042no—
241C4—6042no—
242C4#1801272312yes—
243C4C2×#1455900312yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—12082no—
248C2C2×#1801272311yescharacteristic
249C2C2×#1801276711yescharacteristic
250C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#407×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012713C2
hypercenter#407D151
hypocenterC151#3094
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
2. C2×#18012698C2semidirect
3. #23752537C2semidirect
4. #23752531C2semidirect
5. #23752526C2semidirect
6. #23752254C2semidirect
7. #23752218C2semidirect
8. #407×C151C2semidirect
18. #18012698C22semidirect
20. C2×C4⋊Dic151C22semidirect
21. C2×C4⋊Dic151C22semidirect
25. #18012673C22semidirect
26. #18012671C22semidirect
27. #18012661C22semidirect
28. #18012661C22semidirect
31. C22⋊C8×C151C22semidirect
32. C22⋊C8×C151C22semidirect
125. C151#3094semidirect
134. #407D151semidirect
157. C22⋊C8C2×D151semidirect
158. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127132
C2×#180126982
#237525372
#237525312
#237525262
#237522542
#237522182
#407×C1512
#3094151