Finite Group Databasebeta

← #34080796

Subgroups — #34080796

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×#18012758C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752857C212yesmaximal, complemented
4#23752596C211yesmaximal, characteristic, complemented
5#23752454C211yesmaximal, characteristic, complemented
6#23752449C211yesmaximal, characteristic, complemented
7#23752427C212yesmaximal, complemented
8#23752364C212yesmaximal, complemented
9#23752358C212yesmaximal, complemented
10C8×D604C211yesmaximal, characteristic, complemented
11C4×D8×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2212yescomplemented
13C2×D4×D151C2212yes—
14#18012758—24no—
15C2×Dic604C2211yescharacteristic, complemented
16C2×#14558993C2212yescomplemented
17C2×#14558992C2212yescomplemented
18C2×D1208C2211yescharacteristic
19C2×#14558989C2212yes—
20D8×D151—24no—
21C2×C8×D151C2211yescharacteristic
22C2×C8×D151C2211yescharacteristic, complemented
23#18012727C2212yescomplemented
24#18012723—22no—
25#18012719C2212yes—
26#18012714C2212yescomplemented
27#18012713—22no—
28#18012709—22no—
29C4×D604C2211yescharacteristic
30C2×(C2×D151)⋊C4—22no—
31C4⋊(C151⋊C8)C2211yescharacteristic, complemented
32#18012662C2212yescomplemented
33#18012659C2212yescomplemented
34(C2×D151)⋊C8C2211yescharacteristic
35(C2×D151)⋊C8C2211yescharacteristic, complemented
36C2×D8×C151C2211yescharacteristic
37C4×D4×C151C2212yescomplemented
38#107×C151C2211yescharacteristic, complemented
39#102×C151C2212yescomplemented
40C4×C8×C151C2211yescharacteristic, complemented
41C23×D151—22no—
42#14559003—24no—
43#14559003—42no—
44C2×Dic302C2312yes—
45C2×D604—22no—
46C2×D604D411yescharacteristic
47C2×D604C2312yes—
48C2×C22⋊D151—22no—
49C2×C22⋊D151—22no—
50D4×D151—24no—
51D4×D151—42no—
52C22×Dic151—22no—
53C2×C4×D151C2311yescharacteristic
54C2×C4×D151C2311yescharacteristic
55Dic604—22no—
56#14558993—42no—
57#14558992—24no—
58D1208—22no—
59#14558989—24no—
60C2×C151⋊C8C2311yescharacteristic
61C2×C151⋊C8C2311yescharacteristic
62C8×D151—22no—
63C8×D151—22no—
64C4⋊Dic151—22no—
65C4⋊Dic151D411yescharacteristic
66(C2×D151)⋊C4—22no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4D411yescharacteristic
71(C2×D151)⋊C4D411yescharacteristic
72C2×D4×C151C2312yes—
73C22×C4×C151—22no—
74D8×C151D414yescomplemented
75C2×C8×C151C2311yescharacteristic
76C2×C8×C151C2311yescharacteristic
77C4⋊C4×C151C2312yes—
78C22⋊C4×C151—22no—
79C42×C151C2311yescharacteristic
80C22×D151—22no—
81C22×D151—44no—
82C22×D151—44no—
83C22×D151—82no—
84C22×D151C2×D411yescharacteristic
85C22×D151C2×D411yescharacteristic
86Dic302—22no—
87Dic302—22no—
88D604—22no—
89D604—22no—
90D604—22no—
91D604—82no—
92C22⋊D151—44no—
93C22⋊D151—44no—
94C2×Dic151—22no—
95C2×Dic151—44no—
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C4×D151—21no—
99C4×D151—21no—
100C4×D151—21no—
101C4×D151—21no—
102C151⋊C8—21no—
103C151⋊C8—21no—
104C23×C151—22no—
105D4×C151—22no—
106D4×C151C2×D414yes—
107C2×C4×C151—22no—
108C2×C4×C151—82no—
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2411yescharacteristic
112C8×C151—21no—
113C8×C151C2×D412yes—
114C22×C151—24no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151C22×D411yescharacteristic
118C2×D151—21no—
119C2×D151—21no—
120C2×D151—21no—
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—21no—
130C4×C151—42no—
131C4×C151C22×D411yescharacteristic
132C4×C151H(5,𝔽2)11yescharacteristic
133Dic151—21no—
134Dic151—21no—
135Dic151—42no—
136C2×C151—44no—
137C2×C151D4211yescharacteristic
138C2×C151C2×#13511yescharacteristic
139C2×C151#57611yescharacteristic
140D151—22no—
141D151—41no—
142D151—82no—
143C151#328011yescharacteristic, complemented, Sylow
144#3280—1511nomaximal, Sylow
145C2×#135—1511no—
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×D8D15111yescharacteristic, complemented
155C8×D4—1511no—
156C2×#41—1512no—
157C22×D4—1512no—
158#135—3024no—
159C2×Q16—1511no—
160C2×SD16—1512no—
161C2×SD16—1512no—
162C2×D8—3024no—
163C2×D8—1512no—
164C2×D8—1511no—
165C2×D8C2×D15111yescharacteristic
166C22×C8—1511no—
167C22×C8—1511no—
168#124—1512no—
169#123—3022no—
170C22⋊Q8—1512no—
171#121—3022no—
172#121—1512no—
173#120—3022no—
174C4×D4—1511no—
175C4×D4C2×D15112yescomplemented
176C2×C22⋊C4—3022no—
177#107C2×D15111yescharacteristic, complemented
178C4⋊C8—1511no—
179#103—1512no—
180#102—1512no—
181#102C2×D15112yescomplemented
182C22⋊C8—1511no—
183C22⋊C8—1511no—
184C4×C8C2×D15111yescharacteristic, complemented
185C24—3022no—
186#41—3024no—
187#41—6042no—
188C2×Q8—1512no—
189C2×D4—3022no—
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×C4—1511no—
201Q16—3022no—
202SD16—3024no—
203SD16—6042no—
204D8—3024no—
205D8—3022no—
206D8D60414yescomplemented
207C2×C8—3022no—
208C2×C8—3022no—
209C2×C8—1511no—
210C2×C8—1511no—
211C2×C8C22×D15111yescharacteristic
212C2×C8C22×D15111yescharacteristic
213C4⋊C4—3022no—
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—
223C42C22×D15111yescharacteristic
224C23—22no—
225C23—3022no—
226C23—6044no—
227C23—6044no—
228C23—1511no—
229C23—1511no—
230C23—12082no—
231Q8—3022no—
232Q8—3022no—
233D4—22no—
234D4—3022no—
235D4—3022no—
236D4—3022no—
237D4—6044no—
238D4—6044no—
239D4—12082no—
240D4C2×D60414yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—3021no—
244C2×C4—3021no—
245C2×C4—3021no—
246C2×C4—3021no—
247C2×C4—3022no—
248C2×C4—6044no—
249C2×C4—1511no—
250C2×C4—1511no—
251C2×C4D4×D15111yescharacteristic
252C2×C4D4×D15111yescharacteristic
253C2×C4C23×D15111yescharacteristic
254C8—21no—
255C8—3021no—
256C8—3021no—
257C8C2×D60412yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—3021no—
262C22—3021no—
263C22—3021no—
264C22—3021no—
265C22—3021no—
266C22—6042no—
267C22—6042no—
268C22—6042no—
269C22—1512no—
270C22—12088no—
271C22C2×D4×D15111yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—3021no—
276C4—3021no—
277C4—6042no—
278C4C22×D60411yescharacteristic
279C4#1801278511yescharacteristic
280C2—44no—
281C2—3022no—
282C2—6041no—
283C2—12082no—
284C2D4×D60411yescharacteristic
285C2#135×D15111yescharacteristic
286C2#2375301311yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC4×D8×C151C2
socleC22×C151C22×D4
hypercenterC4×D8D151
hypocenterC151#3280
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18012758C2semidirect
2. C2×D8×D151C2semidirect
3. #23752857C2semidirect
4. #23752596C2semidirect
5. #23752454C2semidirect
6. #23752449C2semidirect
7. #23752427C2semidirect
8. #23752364C2semidirect
9. #23752358C2semidirect
10. C8×D604C2semidirect
11. C4×D8×C151C2semidirect
12. C2×#14559003C22semidirect
15. C2×Dic604C22semidirect
16. C2×#14558993C22semidirect
17. C2×#14558992C22semidirect
22. C2×C8×D151C22semidirect
23. #18012727C22semidirect
26. #18012714C22semidirect
31. C4⋊(C151⋊C8)C22semidirect
32. #18012662C22semidirect
33. #18012659C22semidirect
35. (C2×D151)⋊C8C22semidirect
37. C4×D4×C151C22semidirect
38. #107×C151C22semidirect
39. #102×C151C22semidirect
40. C4×C8×C151C22semidirect
74. D8×C151D4semidirect
127. C2×D151#135semidirect
143. C151#3280semidirect
154. C4×D8D151semidirect
175. C4×D4C2×D151semidirect
177. #107C2×D151semidirect
181. #102C2×D151semidirect
184. C4×C8C2×D151semidirect
206. D8D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127582
C2×D8×D1512
#237528572
#237525962
#237524542
#237524492
#237524272
#237523642
#237523582
C8×D6042
C4×D8×C1512
#3280151