Finite Group Databasebeta

← #34079972

Subgroups — #34079972

Order 19328.

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

normal subgroups only

This group has 442 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#23752778C212yesmaximal, complemented
2#23752538C212yesmaximal, complemented
3#23752535C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic, complemented
5#23752446C212yesmaximal, complemented
6#23752347C212yesmaximal, complemented
7#23752344C212yesmaximal, complemented
8#23752180C211yesmaximal, characteristic, complemented
9#469×C151C211yesmaximal, characteristic, complemented
10C2×#14559004C2211yescharacteristic
11C2×D4×D151C2212yescomplemented
12C2×D1208C2211yescharacteristic
13C2×#14558989C2212yes—
14C22×C151⋊C8C2211yescharacteristic, complemented
15#18012735—22no—
16#18012725—22no—
17#18012714C2212yes—
18#18012713C2212yescomplemented
19#18012710C2212yes—
20#18012709—22no—
21#18012707—22no—
22#18012697C2212yescomplemented
23#18012672C2212yescomplemented
24#18012671C2211yescharacteristic, complemented
25#18012661C2212yescomplemented
26#18012660C2212yescomplemented
27#18012659C2212yescomplemented
28(C2×D151)⋊C8C2212yescomplemented
29(C2×D151)⋊C8C2212yescomplemented
30C2×D8×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic, complemented
32#121×C151C2212yescomplemented
33#106×C151C2211yescharacteristic, complemented
34#102×C151C2212yescomplemented
35C23×D151—22no—
36#14559004—41no—
37#14559004—41no—
38C2×Dic302D411yescharacteristic
39C2×D604—22no—
40C2×D604D411yescharacteristic
41C2×D604C2312yes—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151D412yes—
46D4×D151—42no—
47D4×D151—42no—
48C2×C4×D151C2312yes—
49D1208—41no—
50#14558989—42no—
51C2×C151⋊C8—41no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151C2312yes—
54C22⋊Dic151—22no—
55(C2×D151)⋊C4—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58C4×Dic151—22no—
59C2×D4×C151—22no—
60C2×D4×C151C2312yes—
61C22×C4×C151C2311yescharacteristic
62D8×C151—41no—
63M16×C151—41no—
64C2×C8×C151C2311yescharacteristic
65C2×C8×C151C2311yescharacteristic
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—22no—
69C22×D151—44no—
70C22×D151—82no—
71C22×D151—82no—
72C22×D151C2×D412yes—
73Dic302—41no—
74D604—22no—
75D604—22no—
76D604—41no—
77D604—82no—
78C22⋊D151—42no—
79C22⋊D151—44no—
80C22⋊D151—82no—
81C22⋊D151—82no—
82C2×Dic151—22no—
83C2×Dic151C2×D412yes—
84C4×D151—22no—
85C4×D151—22no—
86C151⋊C8—22no—
87C23×C151—22no—
88C23×C151C2×D411yescharacteristic
89D4×C151—22no—
90D4×C151—22no—
91D4×C151—82no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—22no—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2411yescharacteristic
97C8×C151—21no—
98C8×C151—21no—
99C22×C151—21no—
100C22×C151—22no—
101C22×C151—42no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151C22×D411yescharacteristic
105C2×D151—22no—
106C2×D151—22no—
107C2×D151—22no—
108C2×D151—42no—
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—88no—
112C4×C151—21no—
113C4×C151—42no—
114C4×C151H(5,𝔽2)11yescharacteristic
115C4×C151H(5,𝔽2)11yescharacteristic
116Dic151—22no—
117Dic151—42no—
118C2×C151—41no—
119C2×C151—82no—
120C2×C151#53411yescharacteristic
121C2×C151#57612yes—
122D151—42no—
123D151—82no—
124C151#319911yescharacteristic, complemented, Sylow
125#3199—1511nomaximal, Sylow
126#535—1512no—
127#482—1512no—
128#482—1512no—
129#469—1511no—
130#469D15111yescharacteristic, complemented
131#466—1512no—
132#447—1512no—
133#447—1512no—
134#408—1511no—
135C2×#41—1511no—
136C22×D4—1512no—
137C2×D8—1512no—
138C2×D8—1511no—
139C2×D8C2×D15111yescharacteristic
140C2×M16C2×D15111yescharacteristic, complemented
141C22×C8—1511no—
142#127—3022no—
143#124—3022no—
144#121—1512no—
145#121—1512no—
146#121—1512no—
147#121C2×D15112yescomplemented
148#120—3022no—
149#120—3022no—
150#117—1512no—
151#107—1512no—
152#106—1511no—
153#106C2×D15111yescharacteristic, complemented
154#102—1512no—
155#102—1512no—
156#102—1512no—
157#102C2×D15112yescomplemented
158C22⋊C8—1512no—
159C22⋊C8—1512no—
160C24—3022no—
161#41—6041no—
162#41—6041no—
163C2×Q8—1511no—
164C2×D4—22no—
165C2×D4—3022no—
166C2×D4—3022no—
167C2×D4—3022no—
168C2×D4—3022no—
169C2×D4—6042no—
170C2×D4—6042no—
171C2×D4—1512no—
172C2×D4—1511no—
173C2×D4—1512no—
174C2×D4C22×D15112yes—
175C22×C4—1512no—
176C22×C4C22×D15111yescharacteristic
177D8—41no—
178D8—6041no—
179D8—6042no—
180M16—41no—
181C2×C8—6041no—
182C2×C8—1512no—
183C2×C8C22×D15111yescharacteristic
184C2×C8C22×D15111yescharacteristic
185C4⋊C4—1512no—
186C4⋊C4C22×D15112yes—
187C22⋊C4—22no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—3022no—
191C22⋊C4—3022no—
192C42—3022no—
193C23—22no—
194C23—3022no—
195C23—6044no—
196C23—1512no—
197C23—12082no—
198C23—12082no—
199C23D4×D15111yescharacteristic
200Q8—6041no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—3022no—
205D4—3022no—
206D4—6041no—
207D4—6042no—
208D4—6044no—
209D4—12082no—
210D4—12082no—
211D4—12082no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—3022no—
216C2×C4—3022no—
217C2×C4—3022no—
218C2×C4—1512no—
219C2×C4D4×D15111yescharacteristic
220C2×C4C23×D15111yescharacteristic
221C8—21no—
222C8—21no—
223C8—3022no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—3022no—
230C22—3022no—
231C22—3022no—
232C22—6042no—
233C22—6042no—
234C22—6042no—
235C22—12088no—
236C22C2×D4×D15111yescharacteristic
237C4—21no—
238C4—42no—
239C4—3022no—
240C4—6042no—
241C4#1801278411yescharacteristic
242C4#1801278511yescharacteristic
243C2—41no—
244C2—82no—
245C2—6042no—
246C2—12082no—
247C2#2375277011yescharacteristic
248C2#2375301612yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3199
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23752778C2semidirect
2. #23752538C2semidirect
3. #23752535C2semidirect
4. #23752465C2semidirect
5. #23752446C2semidirect
6. #23752347C2semidirect
7. #23752344C2semidirect
8. #23752180C2semidirect
9. #469×C151C2semidirect
11. C2×D4×D151C22semidirect
14. C22×C151⋊C8C22semidirect
18. #18012713C22semidirect
22. #18012697C22semidirect
23. #18012672C22semidirect
24. #18012671C22semidirect
25. #18012661C22semidirect
26. #18012660C22semidirect
27. #18012659C22semidirect
28. (C2×D151)⋊C8C22semidirect
29. (C2×D151)⋊C8C22semidirect
31. C2×M16×C151C22semidirect
32. #121×C151C22semidirect
33. #106×C151C22semidirect
34. #102×C151C22semidirect
124. C151#3199semidirect
130. #469D151semidirect
140. C2×M16C2×D151semidirect
147. #121C2×D151semidirect
153. #106C2×D151semidirect
157. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527782
#237525382
#237525352
#237524652
#237524462
#237523472
#237523442
#237521802
#469×C1512
#3199151