Finite Group Databasebeta

← #34080792

Subgroups — #34080792

Order 19328.

526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18012762C211yesmaximal, characteristic, complemented
2C22×D1208C211yesmaximal, characteristic, complemented
3#23752853C212yesmaximal, complemented
4#23752597C211yesmaximal, characteristic, complemented
5#23752449C211yesmaximal, characteristic, complemented
6#23752430C212yesmaximal, complemented
7#23752362C212yesmaximal, complemented
8#23752360C212yesmaximal, complemented
9#23752294C211yesmaximal, characteristic, complemented
10C8×C22⋊D151C211yesmaximal, characteristic, complemented
11#467×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2212yescomplemented
13C22×D604C2212yes—
14#18012762—24no—
15C2×#14558991C2212yescomplemented
16C2×#14558991C2212yescomplemented
17C2×D1208—24no—
18C2×D1208C2211yescharacteristic
19C2×D1208C2212yes—
20C2×D1208C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic, complemented
22#18012728C2212yescomplemented
23#18012724—22no—
24#18012714—22no—
25#18012714C2212yescomplemented
26#18012709—22no—
27#18012701C2212yescomplemented
28C4×C22⋊D151C2211yescharacteristic
29C22⋊C4×D151—22no—
30Dic151⋊C8C2211yescharacteristic, complemented
31#18012659C2212yescomplemented
32#18012659C2212yescomplemented
33C22⋊(C151⋊C8)C2211yescharacteristic
34(C2×D151)⋊C8C2211yescharacteristic, complemented
35C8×Dic151C2211yescharacteristic, complemented
36C2×Q16×C151C2211yescharacteristic, complemented
37C22×C8×C151C2211yescharacteristic
38C22⋊Q8×C151C2212yes—
39#107×C151C2211yescharacteristic, complemented
40#103×C151C2212yescomplemented
41C23×D151—22no—
42#14559005—24no—
43#14559005—42no—
44C2×D604—24no—
45C2×D604—22no—
46C2×D604—22no—
47C2×D604—22no—
48C2×D604—42no—
49C2×D604C2312yes—
50C2×D604C2312yes—
51C2×C22⋊D151D411yescharacteristic
52C2×C4×D151—22no—
53C2×C4×D151—22no—
54C2×C4×D151C2311yescharacteristic
55#14558991—24no—
56#14558991—42no—
57D1208—24no—
58D1208—22no—
59D1208D414yescomplemented
60C2×C151⋊C8C2311yescharacteristic
61C2×C151⋊C8C2311yescharacteristic
62C8×D151—22no—
63Dic151⋊C4D411yescharacteristic
64C22⋊Dic151D411yescharacteristic
65(C2×D151)⋊C4—22no—
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4D411yescharacteristic
70C4×Dic151C2311yescharacteristic
71C2×Q8×C151C2312yes—
72C22×C4×C151C2311yescharacteristic
73Q16×C151—22no—
74C2×C8×C151—22no—
75C2×C8×C151C2311yescharacteristic
76C2×C8×C151C2311yescharacteristic
77C4⋊C4×C151—22no—
78C4⋊C4×C151C2312yes—
79C22⋊C4×C151—22no—
80C22×D151—22no—
81C22×D151—22no—
82C22×D151—44no—
83C22×D151—44no—
84C22×D151—82no—
85C22×D151C2×D411yescharacteristic
86D604—22no—
87D604—22no—
88D604—22no—
89D604—44no—
90D604—44no—
91D604—82no—
92D604C2×D414yes—
93C22⋊D151—22no—
94C2×Dic151C2×D411yescharacteristic
95C2×Dic151C2×D411yescharacteristic
96C2×Dic151C2×D411yescharacteristic
97C4×D151—21no—
98C4×D151—21no—
99C4×D151—44no—
100C4×D151—82no—
101C151⋊C8—21no—
102C151⋊C8—21no—
103C23×C151C2×D411yescharacteristic
104Q8×C151—22no—
105Q8×C151—22no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—22no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—21no—
113C8×C151C2×D412yes—
114C22×C151—21no—
115C22×C151—21no—
116C22×C151#13512yescomplemented
117C22×C151C22×D411yescharacteristic
118C2×D151—21no—
119C2×D151—24no—
120C2×D151—21no—
121C2×D151—21no—
122C2×D151—42no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—42no—
126C2×D151—42no—
127C2×D151—88no—
128C4×C151—21no—
129C4×C151—42no—
130C4×C151—42no—
131C4×C151C22×D411yescharacteristic
132C4×C151H(5,𝔽2)11yescharacteristic
133Dic151—21no—
134Dic151—21no—
135Dic151—21no—
136C2×C151—22no—
137C2×C151D4211yescharacteristic
138C2×C151C2×#13511yescharacteristic
139C2×C151#57611yescharacteristic
140D151—41no—
141D151—44no—
142D151—82no—
143C151#328011yescharacteristic, complemented, Sylow
144#3280—1511nomaximal, Sylow
145C2×#135—1511no—
146C22×D8—1511no—
147#546—1512no—
148#495—1511no—
149#467D15111yescharacteristic, complemented
150#466—1511no—
151#463—1512no—
152#450—1512no—
153#449—1512no—
154C4×D8—1511no—
155C8×D4—1511no—
156C2×#41—1512no—
157C22×D4—1512no—
158#135—3024no—
159C2×Q16C2×D15111yescharacteristic, complemented
160C2×SD16—1512no—
161C2×SD16—1512no—
162C2×D8—3024no—
163C2×D8—1512no—
164C2×D8—1511no—
165C2×D8—1511no—
166C22×C8—1511no—
167C22×C8C2×D15111yescharacteristic
168#124—1512no—
169#123—3022no—
170C22⋊Q8C2×D15112yes—
171#121—3022no—
172#121—1512no—
173#120—3022no—
174C4×D4—1512no—
175C4×D4—1511no—
176C2×C22⋊C4—3022no—
177#107C2×D15111yescharacteristic, complemented
178C4⋊C8—1511no—
179#103C2×D15112yescomplemented
180#102—1512no—
181#102—1512no—
182C22⋊C8—1511no—
183C22⋊C8—1511no—
184C4×C8—1511no—
185C24—3022no—
186#41—3024no—
187#41—6042no—
188C2×Q8C22×D15112yes—
189C2×D4—3024no—
190C2×D4—3022no—
191C2×D4—3022no—
192C2×D4—3022no—
193C2×D4—6042no—
194C2×D4—1511no—
195C2×D4—1512no—
196C2×D4—1512no—
197C22×C4—3022no—
198C22×C4—3022no—
199C22×C4—1511no—
200C22×C4C22×D15111yescharacteristic
201Q16—22no—
202SD16—3024no—
203SD16—6042no—
204D8—3024no—
205D8—3022no—
206D8—1514no—
207C2×C8—22no—
208C2×C8—3022no—
209C2×C8—1511no—
210C2×C8—1511no—
211C2×C8C22×D15111yescharacteristic
212C2×C8C22×D15111yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—1511no—
215C4⋊C4C22×D15112yes—
216C22⋊C4—22no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4—3022no—
220C22⋊C4—3022no—
221C22⋊C4—1511no—
222C22⋊C4—1511no—
223C42—1511no—
224C23—3022no—
225C23—3022no—
226C23—6044no—
227C23—6044no—
228C23—1511no—
229C23—12082no—
230C23D4×D15111yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—3022no—
234D4—3022no—
235D4—3022no—
236D4—3022no—
237D4—6044no—
238D4—6044no—
239D4—1514no—
240D4—12082no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—3021no—
246C2×C4—3021no—
247C2×C4—6044no—
248C2×C4—1511no—
249C2×C4—1511no—
250C2×C4—1511no—
251C2×C4—12082no—
252C2×C4D4×D15111yescharacteristic
253C2×C4C23×D15111yescharacteristic
254C8—21no—
255C8—3021no—
256C8—3021no—
257C8D4×D15112yes—
258C22—21no—
259C22—21no—
260C22—3021no—
261C22—3021no—
262C22—3021no—
263C22—3024no—
264C22—6042no—
265C22—6042no—
266C22—6042no—
267C22—6042no—
268C22—6042no—
269C22—12088no—
270C22#1801276212yescomplemented
271C22C2×D4×D15111yescharacteristic
272C4—21no—
273C4—42no—
274C4—42no—
275C4—3021no—
276C4—3021no—
277C4—3021no—
278C4C2×D4×D15111yescharacteristic
279C4#1801278511yescharacteristic
280C2—22no—
281C2—6041no—
282C2—6044no—
283C2—12082no—
284C2#2375284611yescharacteristic
285C2C2×#1801276211yescharacteristic
286C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#467×C151C2
socleC22×C151C22×D4
hypercenter#467D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#18012762C2semidirect
2. C22×D1208C2semidirect
3. #23752853C2semidirect
4. #23752597C2semidirect
5. #23752449C2semidirect
6. #23752430C2semidirect
7. #23752362C2semidirect
8. #23752360C2semidirect
9. #23752294C2semidirect
10. C8×C22⋊D151C2semidirect
11. #467×C151C2semidirect
12. C2×#14559005C22semidirect
15. C2×#14558991C22semidirect
16. C2×#14558991C22semidirect
21. C2×C8×D151C22semidirect
22. #18012728C22semidirect
25. #18012714C22semidirect
27. #18012701C22semidirect
30. Dic151⋊C8C22semidirect
31. #18012659C22semidirect
32. #18012659C22semidirect
34. (C2×D151)⋊C8C22semidirect
35. C8×Dic151C22semidirect
36. C2×Q16×C151C22semidirect
39. #107×C151C22semidirect
40. #103×C151C22semidirect
59. D1208D4semidirect
116. C22×C151#135semidirect
143. C151#3280semidirect
149. #467D151semidirect
159. C2×Q16C2×D151semidirect
177. #107C2×D151semidirect
179. #103C2×D151semidirect
270. C22#18012762semidirect

Maximal subgroups

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

subgroupindex
C2×#180127622
C22×D12082
#237528532
#237525972
#237524492
#237524302
#237523622
#237523602
#237522942
C8×C22⋊D1512
#467×C1512
#3280151