Finite Group Databasebeta

← #34079953

Subgroups — #34079953

Order 19328.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752725C212yesmaximal, complemented
2#23752551C212yesmaximal, complemented
3#23752538C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic, complemented
5#23752460C212yesmaximal, complemented
6#23752373C212yesmaximal, complemented
7#23752360C212yesmaximal, complemented
8#23752175C211yesmaximal, characteristic, complemented
9#470×C151C211yesmaximal, characteristic, complemented
10C2×#14559005C2212yes—
11C22×C4×D151C2211yescharacteristic
12C2×#14558991C2212yescomplemented
13C2×D1208C2211yescharacteristic, complemented
14C2×#14558988C2211yescharacteristic
15#18012724—22no—
16#18012715C2212yes—
17#18012714C2212yes—
18#18012713C2212yes—
19#18012709—22no—
20#18012701—22no—
21(C22⋊D151)⋊C4—22no—
22#18012697C2212yes—
23#18012672C2212yescomplemented
24#18012671C2211yescharacteristic, complemented
25#18012663C2212yescomplemented
26#18012661C2212yescomplemented
27#18012659C2212yescomplemented
28(C2×D151)⋊C8C2212yes—
29(C2×D151)⋊C8C2212yes—
30C2×Q16×C151C2211yescharacteristic, complemented
31C2×M16×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#106×C151C2211yescharacteristic, complemented
34#103×C151C2212yescomplemented
35C23×D151D411yescharacteristic
36#14559005—42no—
37#14559005—42no—
38C2×D604—22no—
39C2×D604—22no—
40C2×D604C2312yes—
41C2×C22⋊D151—22no—
42C22×Dic151D411yescharacteristic
43C2×C4×D151—22no—
44C2×C4×D151—41no—
45C2×C4×D151—41no—
46C2×C4×D151D412yes—
47C2×C4×D151C2312yes—
48#14558991—42no—
49D1208—41no—
50#14558988—41no—
51C2×C151⋊C8C2312yes—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54(C2×D151)⋊C4—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58C4×Dic151—22no—
59C2×Q8×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61Q16×C151—41no—
62M16×C151—41no—
63C2×C8×C151C2311yescharacteristic
64C2×C8×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—22no—
69C22×D151—41no—
70C22×D151—42no—
71C22×D151C2×D412yes—
72D604—22no—
73D604—22no—
74D604—44no—
75D604—44no—
76C22⋊D151—44no—
77C2×Dic151—22no—
78C2×Dic151—41no—
79C2×Dic151C2×D412yes—
80C4×D151—22no—
81C4×D151—22no—
82C4×D151—42no—
83C4×D151—44no—
84C151⋊C8—22no—
85C23×C151C2×D411yescharacteristic
86Q8×C151—22no—
87Q8×C151—22no—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151C2×D411yescharacteristic
93C2×C4×C151C2411yescharacteristic
94C8×C151—21no—
95C8×C151—21no—
96C22×C151—21no—
97C22×C151—22no—
98C22×C151C22×D411yescharacteristic
99C2×D151—22no—
100C2×D151—22no—
101C2×D151—22no—
102C2×D151—44no—
103C2×D151—42no—
104C2×D151—42no—
105C2×D151—42no—
106C4×C151—21no—
107C4×C151—42no—
108C4×C151—42no—
109C4×C151H(5,𝔽2)11yescharacteristic
110C4×C151H(5,𝔽2)11yescharacteristic
111Dic151—22no—
112Dic151—42no—
113C2×C151—41no—
114C2×C151#53411yescharacteristic
115C2×C151#57512yes—
116D151—42no—
117D151—82no—
118C151#319711yescharacteristic, complemented, Sylow
119#3197—1511nomaximal, Sylow
120#525—1512no—
121#485—1512no—
122#482—1512no—
123#470D15111yescharacteristic, complemented
124#469—1511no—
125#468—1512no—
126#452—1512no—
127#449—1512no—
128#407—1511no—
129C2×#41—1512no—
130C23×C4—1511no—
131C2×Q16C2×D15111yescharacteristic, complemented
132C2×SD16—1512no—
133C2×D8—1511no—
134C2×M16—1511no—
135C2×M16C2×D15111yescharacteristic
136#123—3022no—
137C22⋊Q8—1512no—
138C22⋊Q8C2×D15112yes—
139#121—1512no—
140#121—1512no—
141#120—3022no—
142C4×D4—3022no—
143C4×D4—3022no—
144#117—1512no—
145#107—1512no—
146#106—1511no—
147#106C2×D15111yescharacteristic, complemented
148#103—1512no—
149#103C2×D15112yescomplemented
150#102—1512no—
151#102—1512no—
152C22⋊C8—1512no—
153C22⋊C8—1512no—
154C24—1511no—
155#41—6042no—
156#41—6042no—
157C2×Q8C22×D15112yes—
158C2×D4—3022no—
159C2×D4—3022no—
160C2×D4—3022no—
161C2×D4—1512no—
162C22×C4—3022no—
163C22×C4—6041no—
164C22×C4—6041no—
165C22×C4—1512no—
166C22×C4—1511no—
167C22×C4—1512no—
168C22×C4C22×D15111yescharacteristic
169Q16—41no—
170SD16—6042no—
171D8—6041no—
172M16—41no—
173M16—6041no—
174C2×C8—1512no—
175C2×C8C22×D15111yescharacteristic
176C2×C8C22×D15111yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—3022no—
179C4⋊C4—1512no—
180C4⋊C4C22×D15112yes—
181C22⋊C4—22no—
182C22⋊C4—3022no—
183C22⋊C4—3022no—
184C22⋊C4—3022no—
185C22⋊C4—3022no—
186C42—3022no—
187C23—3022no—
188C23—6041no—
189C23—6042no—
190C23—1512no—
191C23D4×D15111yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—3022no—
195D4—3022no—
196D4—6044no—
197D4—6044no—
198D4—6044no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—3022no—
206C2×C4—6042no—
207C2×C4—6044no—
208C2×C4—6041no—
209C2×C4—1512no—
210C2×C4D4×D15111yescharacteristic
211C2×C4C23×D15111yescharacteristic
212C8—21no—
213C8—21no—
214C8—3022no—
215C22—22no—
216C22—21no—
217C22—3022no—
218C22—3022no—
219C22—3022no—
220C22—6044no—
221C22—6042no—
222C22—6042no—
223C22—6042no—
224C22C2×D4×D15111yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—3022no—
229C4—6042no—
230C4#1801278411yescharacteristic
231C4#1801278511yescharacteristic
232C2—41no—
233C2—6042no—
234C2—12082no—
235C2#2375277011yescharacteristic
236C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
hypercenter#470D151
hypocenterC151#3197
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23752725C2semidirect
2. #23752551C2semidirect
3. #23752538C2semidirect
4. #23752465C2semidirect
5. #23752460C2semidirect
6. #23752373C2semidirect
7. #23752360C2semidirect
8. #23752175C2semidirect
9. #470×C151C2semidirect
12. C2×#14558991C22semidirect
13. C2×D1208C22semidirect
23. #18012672C22semidirect
24. #18012671C22semidirect
25. #18012663C22semidirect
26. #18012661C22semidirect
27. #18012659C22semidirect
30. C2×Q16×C151C22semidirect
33. #106×C151C22semidirect
34. #103×C151C22semidirect
118. C151#3197semidirect
123. #470D151semidirect
131. C2×Q16C2×D151semidirect
147. #106C2×D151semidirect
149. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527252
#237525512
#237525382
#237524652
#237524602
#237523732
#237523602
#237521752
#470×C1512
#3197151