Finite Group Databasebeta

← #34080789

Subgroups — #34080789

Order 19328.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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, complemented
2#23752850C212yesmaximal, complemented
3#23752597C211yesmaximal, characteristic, complemented
4#23752450C211yesmaximal, characteristic, complemented
5#23752448C211yesmaximal, characteristic, complemented
6#23752429C212yesmaximal, complemented
7#23752361C212yesmaximal, complemented
8#23752357C212yesmaximal, complemented
9D8×Dic151C211yesmaximal, characteristic, complemented
10C8×C22⋊D151C211yesmaximal, characteristic, complemented
11C2×#135×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151C2212yes—
13C2×#14558991C2212yescomplemented
14C2×D1208C2211yescharacteristic
15C2×#14558989C2212yes—
16D8×D151—24no—
17C2×C8×D151C2211yescharacteristic
18#18012728C2212yescomplemented
19#18012722—22no—
20#18012715C2212yes—
21#18012713C2212yescomplemented
22#18012711—22no—
23#18012707—22no—
24D4×Dic151C2212yescomplemented
25C4×C22⋊D151C2211yescharacteristic
26C2×(C2×D151)⋊C4—22no—
27#18012673C2211yescharacteristic, complemented
28Dic151⋊C8C2211yescharacteristic, complemented
29#18012663C2212yescomplemented
30#18012661C2212yescomplemented
31#18012660C2212yescomplemented
32C22⋊(C151⋊C8)C2211yescharacteristic, complemented
33(C2×D151)⋊C8C2211yescharacteristic
34C8×Dic151C2211yescharacteristic, complemented
35C2×#41×C151C2212yescomplemented
36#135×C151—24no—
37C2×Q16×C151C2211yescharacteristic, complemented
38C2×SD16×C151C2212yescomplemented
39C2×D8×C151C2211yescharacteristic
40C22×C8×C151C2211yescharacteristic, complemented
41C23×D151—22no—
42C2×D604C2312yes—
43C2×C22⋊D151—22no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151D411yescharacteristic
46D4×D151—24no—
47D4×D151—42no—
48C22×Dic151—22no—
49C2×C4×D151C2311yescharacteristic
50#14558991—42no—
51D1208—22no—
52#14558989—24no—
53C2×C151⋊C8C2311yescharacteristic
54C2×C151⋊C8C2311yescharacteristic
55C8×D151—22no—
56C4⋊Dic151C2312yes—
57Dic151⋊C4—22no—
58Dic151⋊C4D411yescharacteristic
59C22⋊Dic151—22no—
60C22⋊Dic151D411yescharacteristic
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64(C2×D151)⋊C4—22no—
65(C2×D151)⋊C4D411yescharacteristic
66C4×Dic151C2311yescharacteristic
67#41×C151—24no—
68#41×C151—42no—
69C2×Q8×C151C2312yes—
70C2×D4×C151—22no—
71C2×D4×C151C2312yes—
72C22×C4×C151—22no—
73C22×C4×C151C2311yescharacteristic
74Q16×C151—22no—
75SD16×C151—24no—
76D8×C151D414yescomplemented
77C2×C8×C151—22no—
78C2×C8×C151C2311yescharacteristic
79C2×C8×C151C2311yescharacteristic
80C22×D151—22no—
81C22×D151—44no—
82C22×D151—44no—
83C22×D151—82no—
84C22×D151C2×D411yescharacteristic
85D604—22no—
86D604—22no—
87C22⋊D151—22no—
88C22⋊D151—44no—
89C22⋊D151—82no—
90C2×Dic151—22no—
91C2×Dic151—82no—
92C2×Dic151C2×D411yescharacteristic
93C2×Dic151C2×D411yescharacteristic
94C2×Dic151C2×D411yescharacteristic
95C4×D151—21no—
96C4×D151—21no—
97C151⋊C8—21no—
98C151⋊C8—21no—
99C23×C151—22no—
100C23×C151C2×D411yescharacteristic
101Q8×C151—22no—
102Q8×C151—22no—
103D4×C151—22no—
104D4×C151—44no—
105D4×C151C2×D414yes—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—22no—
109C2×C4×C151—44no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—21no—
113C8×C151C2×D412yes—
114C22×C151—21no—
115C22×C151—24no—
116C22×C151—21no—
117C22×C151—21no—
118C22×C151—42no—
119C22×C151—42no—
120C22×C151C22×D411yescharacteristic
121C2×D151—21no—
122C2×D151—21no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—42no—
126C2×D151—88no—
127C2×D151#13512yescomplemented
128C4×C151—21no—
129C4×C151—42no—
130C4×C151C22×D411yescharacteristic
131C4×C151H(5,𝔽2)11yescharacteristic
132Dic151—21no—
133Dic151—21no—
134Dic151—21no—
135Dic151—42no—
136C2×C151—44no—
137C2×C151—41no—
138C2×C151D4211yescharacteristic
139C2×C151C2×#13511yescharacteristic
140C2×C151#57611yescharacteristic
141D151—22no—
142D151—82no—
143C151#328011yescharacteristic, complemented, Sylow
144#3280—1511nomaximal, Sylow
145C2×#135D15111yescharacteristic, complemented
146C22×D8—1511no—
147#546—1512no—
148#495—1511no—
149#467—1511no—
150#466—1511no—
151#463—1512no—
152#450—1512no—
153#449—1512no—
154C4×D8—1511no—
155C8×D4—1511no—
156C2×#41C2×D15112yescomplemented
157C22×D4—1512no—
158#135—24no—
159C2×Q16C2×D15111yescharacteristic, complemented
160C2×SD16—1512no—
161C2×SD16C2×D15112yescomplemented
162C2×D8—3024no—
163C2×D8—1512no—
164C2×D8—1511no—
165C2×D8C2×D15111yescharacteristic
166C22×C8—1511no—
167C22×C8C2×D15111yescharacteristic, complemented
168#124—1512no—
169#123—3022no—
170C22⋊Q8—1512no—
171#121—3022no—
172#121—1512no—
173#120—3022no—
174C4×D4—1512no—
175C4×D4—1511no—
176C2×C22⋊C4—3022no—
177#107—1511no—
178C4⋊C8—1511no—
179#103—1512no—
180#102—1512no—
181#102—1512no—
182C22⋊C8—1511no—
183C22⋊C8—1511no—
184C4×C8—1511no—
185C24—3022no—
186#41—24no—
187#41—42no—
188C2×Q8C22×D15112yes—
189C2×D4—22no—
190C2×D4—3024no—
191C2×D4—3022no—
192C2×D4—3022no—
193C2×D4—6042no—
194C2×D4—1511no—
195C2×D4—1512no—
196C2×D4C22×D15112yes—
197C22×C4—22no—
198C22×C4—3022no—
199C22×C4—1511no—
200C22×C4C22×D15111yescharacteristic
201Q16—22no—
202SD16—24no—
203SD16—6042no—
204D8—3024no—
205D8—3022no—
206D8C22⋊D15114yescomplemented
207C2×C8—22no—
208C2×C8—3022no—
209C2×C8—1511no—
210C2×C8—1511no—
211C2×C8C22×D15111yescharacteristic
212C2×C8C22×D15111yescharacteristic
213C4⋊C4—3022no—
214C4⋊C4—1512no—
215C4⋊C4—1511no—
216C22⋊C4—3022no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4—3022no—
220C22⋊C4—3022no—
221C22⋊C4—1511no—
222C22⋊C4—1511no—
223C42—1511no—
224C23—22no—
225C23—3022no—
226C23—6044no—
227C23—6044no—
228C23—1511no—
229C23—12082no—
230C23D4×D15111yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—22no—
234D4—44no—
235D4—3022no—
236D4—3022no—
237D4—3022no—
238D4—6044no—
239D4—12082no—
240D4C2×C22⋊D15114yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—44no—
245C2×C4—3021no—
246C2×C4—3021no—
247C2×C4—3022no—
248C2×C4—1511no—
249C2×C4—1511no—
250C2×C4—1511no—
251C2×C4—12082no—
252C2×C4D4×D15111yescharacteristic
253C2×C4C23×D15111yescharacteristic
254C8—21no—
255C8—3021no—
256C8—3021no—
257C8C2×C22⋊D15112yes—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—24no—
262C22—42no—
263C22—42no—
264C22—3021no—
265C22—3021no—
266C22—6042no—
267C22—6042no—
268C22—6042no—
269C22—1512no—
270C22—12088no—
271C22C2×D4×D15111yescharacteristic
272C4—21no—
273C4—42no—
274C4—3021no—
275C4—3021no—
276C4—3021no—
277C4—6042no—
278C4C22×C22⋊D15111yescharacteristic
279C4#1801278411yescharacteristic
280C2—41no—
281C2—44no—
282C2—3022no—
283C2—12082no—
284C2D4×C22⋊D15111yescharacteristic
285C2#135×D15111yescharacteristic
286C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#135×C151C2
socleC22×C151C22×D4
hypercenterC2×#135D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×D8×D151C2semidirect
2. #23752850C2semidirect
3. #23752597C2semidirect
4. #23752450C2semidirect
5. #23752448C2semidirect
6. #23752429C2semidirect
7. #23752361C2semidirect
8. #23752357C2semidirect
9. D8×Dic151C2semidirect
10. C8×C22⋊D151C2semidirect
11. C2×#135×C151C2semidirect
13. C2×#14558991C22semidirect
18. #18012728C22semidirect
21. #18012713C22semidirect
24. D4×Dic151C22semidirect
27. #18012673C22semidirect
28. Dic151⋊C8C22semidirect
29. #18012663C22semidirect
30. #18012661C22semidirect
31. #18012660C22semidirect
32. C22⋊(C151⋊C8)C22semidirect
34. C8×Dic151C22semidirect
35. C2×#41×C151C22semidirect
37. C2×Q16×C151C22semidirect
38. C2×SD16×C151C22semidirect
40. C22×C8×C151C22semidirect
76. D8×C151D4semidirect
127. C2×D151#135semidirect
143. C151#3280semidirect
145. C2×#135D151semidirect
156. C2×#41C2×D151semidirect
159. C2×Q16C2×D151semidirect
161. C2×SD16C2×D151semidirect
167. C22×C8C2×D151semidirect
206. D8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
#237528502
#237525972
#237524502
#237524482
#237524292
#237523612
#237523572
D8×Dic1512
C8×C22⋊D1512
C2×#135×C1512
#3280151