Finite Group Databasebeta

← #34077959

Subgroups — #34077959

Order 19328.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D151C211yesmaximal, characteristic
2#23752684C212yesmaximal, complemented
3#23752325C211yesmaximal, characteristic, complemented
4#23752324C211yesmaximal, characteristic, complemented
5#23752323C211yesmaximal, characteristic, complemented
6C4×#14558989C212yesmaximal, complemented
7#23752292C212yesmaximal, complemented
8#23752247C211yesmaximal, characteristic, complemented
9#23752215C212yesmaximal, complemented
10#23752169C211yesmaximal, characteristic, complemented
11#442×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151C2212yes—
13C2×D1208C2211yescharacteristic
14C2×#14558989C2212yes—
15D8×D151C418yescomplemented
16C2×#14558987C2211yescharacteristic
17C2×C8×D151C2211yescharacteristic
18C4×D604C2212yescomplemented
19D4×Dic151C2212yescomplemented
20#18012701C2212yescomplemented
21C4×C22⋊D151—22no—
22(C22⋊D151)⋊C4—22no—
23#18012697C2212yes—
24#18012696C2211yescharacteristic
25C2×(C2×D151)⋊C4—22no—
26C22⋊C4×D151—22no—
27#18012672C2212yescomplemented
28#18012671C2211yescharacteristic, complemented
29#18012661C2212yescomplemented
30#18012660C2212yescomplemented
31#18012659C2212yescomplemented
32#18012649C2211yescharacteristic, complemented
33C4×C151⋊C8C2211yescharacteristic, complemented
34C8×Dic151C2211yescharacteristic, complemented
35C2×D8×C151C2211yescharacteristic
36C4×D4×C151C2212yescomplemented
37#106×C151C2211yescharacteristic, complemented
38#102×C151C2212yescomplemented
39#97×C151C2211yescharacteristic, complemented
40C23×D151—22no—
41C2×D604C2312yes—
42C2×C22⋊D151—22no—
43D4×D151—24no—
44D4×D151C2×C418yescomplemented
45C22×Dic151—22no—
46C2×C4×D151—22no—
47C2×C4×D151—22no—
48C2×C4×D151C2311yescharacteristic
49D1208C2×C414yescomplemented
50#14558989C2×C418yescomplemented
51#14558987—22no—
52C2×C151⋊C8C2311yescharacteristic
53C2×C151⋊C8C2311yescharacteristic
54C8×D151C2×C414yescomplemented
55C4⋊Dic151C2312yes—
56Dic151⋊C4D412yes—
57C22⋊Dic151—22no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4D412yes—
62C4×Dic151—22no—
63C4×Dic151C2311yescharacteristic
64C2×D4×C151C2312yes—
65C22×C4×C151—22no—
66D8×C151C2×C414yescomplemented
67C2×C8×C151C2311yescharacteristic
68C2×C8×C151C2311yescharacteristic
69C4⋊C4×C151C2312yes—
70C22⋊C4×C151—22no—
71C42×C151C2311yescharacteristic
72C22×D151—22no—
73C22×D151—28no—
74C22×D151—82no—
75C22×D151—82no—
76C22×D151C2×D411yescharacteristic
77D604—22no—
78D604C22×C414yes—
79C22⋊D151—28no—
80C2×Dic151—22no—
81C2×Dic151—82no—
82C2×Dic151C2×D412yes—
83C2×Dic151C2×D411yescharacteristic
84C4×D151—82no—
85C4×D151—82no—
86C4×D151C22×C412yes—
87C4×D151#4112yes—
88C151⋊C8—21no—
89C151⋊C8C22×C412yes—
90C23×C151—22no—
91D4×C151—22no—
92D4×C151C22×C414yes—
93C2×C4×C151—22no—
94C2×C4×C151—82no—
95C2×C4×C151C2×D412yes—
96C2×C4×C151C2411yescharacteristic
97C8×C151—21no—
98C8×C151C22×C412yes—
99C22×C151—24no—
100C22×C151—42no—
101C22×C151—42no—
102C22×C151C22×D411yescharacteristic
103C2×D151—22no—
104C2×D151—24no—
105C2×D151—42no—
106C2×D151—42no—
107C2×D151—88no—
108C2×D151C4×D412yes—
109C4×C151—22no—
110C4×C151—42no—
111C4×C151C23×C411yescharacteristic
112C4×C151C2×#4111yescharacteristic
113Dic151—22no—
114Dic151—42no—
115Dic151C4×D412yes—
116C2×C151—44no—
117C2×C151C2×C4×D411yescharacteristic
118C2×C151#57612yes—
119D151—22no—
120D151—44no—
121C151#294811yescharacteristic, complemented, Sylow
122#2948—1511nomaximal, Sylow
123C22×D8—1511no—
124#518—1512no—
125#442—1511no—
126#442—1511no—
127#442—1511no—
128#442D15111yescharacteristic, complemented
129C4×D8—1512no—
130C4×D8—1512no—
131#427—1511no—
132#418—1512no—
133#405—1511no—
134C22×D4—1512no—
135C2×D8—1512no—
136C2×D8—1518no—
137C2×D8—1511no—
138C2×D8C2×D15111yescharacteristic
139C2×M16—1511no—
140C22×C8—1511no—
141C4×D4—3022no—
142C4×D4—3022no—
143C4×D4—1512no—
144C4×D4—1512no—
145C4×D4—1512no—
146C4×D4C2×D15112yescomplemented
147#117—1512no—
148#117—1511no—
149C2×C22⋊C4—3022no—
150C2×C22⋊C4—3022no—
151#107—1512no—
152#106—1511no—
153#106C2×D15111yescharacteristic, complemented
154#102—1512no—
155#102—1512no—
156#102—1512no—
157#102C2×D15112yescomplemented
158#97—1511no—
159#97C2×D15111yescharacteristic, complemented
160C4×C8—1511no—
161C4×C8—1511no—
162C24—3022no—
163C2×D4—3024no—
164C2×D4—3022no—
165C2×D4—1518no—
166C2×D4—1512no—
167C2×D4C22×D15112yes—
168C22×C4—22no—
169C22×C4—3022no—
170C22×C4—3022no—
171C22×C4—3022no—
172C22×C4—1511no—
173D8—1518no—
174D8—1514no—
175D8C4×D15114yescomplemented
176M16—3022no—
177C2×C8—1511no—
178C2×C8—1511no—
179C2×C8—1514no—
180C2×C8C22×D15111yescharacteristic
181C2×C8C22×D15111yescharacteristic
182C4⋊C4—1512no—
183C4⋊C4—1512no—
184C4⋊C4C22×D15112yes—
185C22⋊C4—22no—
186C22⋊C4—3022no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—1512no—
191C42—3022no—
192C42—1511no—
193C42C22×D15111yescharacteristic
194C23—22no—
195C23—3028no—
196C23—3022no—
197C23—1511no—
198C23—12082no—
199C23—12082no—
200D4—22no—
201D4—3028no—
202D4—3022no—
203D4—1514no—
204D4C2×C4×D15114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—3022no—
208C2×C4—1512no—
209C2×C4—1511no—
210C2×C4—1512no—
211C2×C4—1512no—
212C2×C4—12082no—
213C2×C4—12082no—
214C2×C4—12082no—
215C2×C4D4×D15112yes—
216C2×C4C23×D15111yescharacteristic
217C8—21no—
218C8—3021no—
219C8—1512no—
220C8C2×C4×D15112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—3022no—
225C22—3024no—
226C22—6042no—
227C22—6042no—
228C22—1512no—
229C22—12088no—
230C22C2×D4×D15111yescharacteristic
231C4—22no—
232C4—42no—
233C4—3022no—
234C4—6042no—
235C4—1512no—
236C4C22×C4×D15111yescharacteristic
237C4#41×D15111yescharacteristic
238C2—44no—
239C2—3022no—
240C2—6044no—
241C2C4×D4×D15111yescharacteristic
242C2#2375301612yes—
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
prime radicalC2×D8×D151C2
cosocleC2×C4×C151C24
hypercenter#442D151
hypocenterC151#2948
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #23752684C2semidirect
3. #23752325C2semidirect
4. #23752324C2semidirect
5. #23752323C2semidirect
6. C4×#14558989C2semidirect
7. #23752292C2semidirect
8. #23752247C2semidirect
9. #23752215C2semidirect
10. #23752169C2semidirect
11. #442×C151C2semidirect
15. D8×D151C4semidirect
18. C4×D604C22semidirect
19. D4×Dic151C22semidirect
20. #18012701C22semidirect
27. #18012672C22semidirect
28. #18012671C22semidirect
29. #18012661C22semidirect
30. #18012660C22semidirect
31. #18012659C22semidirect
32. #18012649C22semidirect
33. C4×C151⋊C8C22semidirect
34. C8×Dic151C22semidirect
36. C4×D4×C151C22semidirect
37. #106×C151C22semidirect
38. #102×C151C22semidirect
39. #97×C151C22semidirect
44. D4×D151C2×C4semidirect
49. D1208C2×C4semidirect
50. #14558989C2×C4semidirect
54. C8×D151C2×C4semidirect
66. D8×C151C2×C4semidirect
121. C151#2948semidirect
128. #442D151semidirect
146. C4×D4C2×D151semidirect
153. #106C2×D151semidirect
157. #102C2×D151semidirect
159. #97C2×D151semidirect
175. D8C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
#237526842
#237523252
#237523242
#237523232
C4×#145589892
#237522922
#237522472
#237522152
#237521692
#442×C1512
#2948151