Finite Group Databasebeta

← #34080129

Subgroups — #34080129

Order 19328.

490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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#127×D151C211yesmaximal, characteristic, complemented
2#23752747C211yesmaximal, characteristic, complemented
3#23752601C211yesmaximal, characteristic, complemented
4#23752599C211yesmaximal, characteristic, complemented
5#23752578C211yesmaximal, characteristic, complemented
6#23752411C212yesmaximal, complemented
7#23752406C212yesmaximal, complemented
8#23752364C212yesmaximal, complemented
9#23752347C212yesmaximal, complemented
10#23752267C211yesmaximal, characteristic, complemented
11#490×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—21no—
13C2×D4×D151—21no—
14C2×D4×D151C2212yes—
15C2×#14558993C2212yescomplemented
16C2×#14558992C2212yescomplemented
17C2×D1208C2212yescomplemented
18C2×#14558989C2212yescomplemented
19#18012736C2211yescharacteristic
20#18012735—21no—
21#18012735—21no—
22#18012735C2212yes—
23#18012734—21no—
24#18012727C2211yescharacteristic, complemented
25#18012724—21no—
26#18012719C2211yescharacteristic
27#18012714C2211yescharacteristic
28#18012704C2211yescharacteristic, complemented
29#18012701—21no—
30#18012701C2211yescharacteristic, complemented
31#18012697—21no—
32C42×D151C2211yescharacteristic
33Dic151⋊C8C2212yescomplemented
34#18012659C2212yescomplemented
35#18012659C2212yescomplemented
36(C2×D151)⋊C8C2212yes—
37#18012650C2211yescharacteristic, complemented
38#127×C151C2211yescharacteristic
39#125×C151C2211yescharacteristic, complemented
40#102×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42#97×C151C2211yescharacteristic, complemented
43C23×D151—22no—
44C2×Dic302C2311yescharacteristic
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—21no—
48C2×D604C2311yescharacteristic
49C2×D604C2312yes—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—22no—
52C2×C22⋊D151—22no—
53D4×D151—42no—
54D4×D151—42no—
55D4×D151—44no—
56D4×D151—44no—
57C2×C4×D151—21no—
58C2×C4×D151D411yescharacteristic
59C2×C4×D151D411yescharacteristic
60C2×C4×D151C2311yescharacteristic
61#14558993—42no—
62#14558992—42no—
63D1208—42no—
64#14558989—42no—
65C2×C151⋊C8C2312yes—
66C4⋊Dic151—21no—
67Dic151⋊C4—21no—
68(C2×D151)⋊C4—21no—
69(C2×D151)⋊C4—21no—
70(C2×D151)⋊C4—21no—
71(C2×D151)⋊C4—21no—
72(C2×D151)⋊C4—21no—
73C4×Dic151—21no—
74C4×Dic151D411yescharacteristic
75C4×Dic151D411yescharacteristic
76C4×Dic151C2311yescharacteristic
77C2×D4×C151—21no—
78C2×D4×C151—21no—
79C2×D4×C151C2312yes—
80C2×C8×C151C2312yes—
81C4⋊C4×C151—21no—
82C4⋊C4×C151—21no—
83C4⋊C4×C151C2311yescharacteristic
84C4⋊C4×C151C2311yescharacteristic
85C42×C151C2311yescharacteristic
86C22×D151—21no—
87C22×D151—22no—
88C22×D151—44no—
89C22×D151—44no—
90C22×D151—44no—
91C22×D151C2×D411yescharacteristic
92Dic302—22no—
93D604—22no—
94D604—22no—
95D604—22no—
96D604—42no—
97D604—42no—
98D604—42no—
99C22⋊D151—44no—
100C22⋊D151—44no—
101C22⋊D151—44no—
102C2×Dic151—21no—
103C2×Dic151C2×D411yescharacteristic
104C2×Dic151C2×D411yescharacteristic
105C2×Dic151C2×D411yescharacteristic
106C4×D151—22no—
107C4×D151—22no—
108C4×D151—22no—
109C4×D151—42no—
110C151⋊C8—22no—
111C23×C151—22no—
112D4×C151—22no—
113D4×C151—22no—
114D4×C151—42no—
115D4×C151—42no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2411yescharacteristic
121C8×C151—22no—
122C22×C151—42no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151C22×D411yescharacteristic
126C2×D151—21no—
127C2×D151—21no—
128C2×D151—42no—
129C2×D151—41no—
130C2×D151—41no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—41no—
134C2×D151—88no—
135C2×D151AGL(1,ℤ/8)12yes—
136C4×C151—21no—
137C4×C151—21no—
138C4×C151—41no—
139C4×C151—41no—
140C4×C151H(5,𝔽2)12yes—
141Dic151—21no—
142Dic151—21no—
143Dic151—41no—
144Dic151AGL(1,ℤ/8)12yes—
145C2×C151—82no—
146C2×C151#53511yescharacteristic
147C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
149D151—22no—
150D151—81no—
151D151—82no—
152C151#321711yescharacteristic, complemented, Sylow
153#3217—1511nomaximal, Sylow
154C2×#127—1511no—
155#529—1511no—
156#496—1511no—
157#496—1511no—
158#490—1511no—
159#490D15111yescharacteristic, complemented
160#460—1512no—
161#459—1512no—
162#450—1512no—
163#447—1512no—
164#432—1511no—
165C22×D4—3021no—
166C22×D4—3021no—
167C22×D4—1512no—
168C2×SD16—1512no—
169C2×SD16—1512no—
170C2×D8—1512no—
171C2×D8—1512no—
172#127—3021no—
173#127—3021no—
174#127—1512no—
175#127—1511no—
176#127C2×D15111yescharacteristic
177#126—3021no—
178#125C2×D15111yescharacteristic, complemented
179#124—1511no—
180#123—3021no—
181C22⋊Q8—1511no—
182#121—1511no—
183C4×Q8—1511no—
184C4×D4—3021no—
185C4×D4—1511no—
186#117—3021no—
187C2×C42—1511no—
188C4⋊C8—1512no—
189#102—1512no—
190#102—1512no—
191#102C2×D15112yescomplemented
192#102C2×D15112yescomplemented
193C22⋊C8—1512no—
194#97—1511no—
195#97C2×D15111yescharacteristic, complemented
196C24—3022no—
197C2×Q8—1511no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—3021no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—3022no—
204C2×D4—3021no—
205C2×D4—3021no—
206C2×D4—6042no—
207C2×D4—6042no—
208C2×D4—6044no—
209C2×D4—6044no—
210C2×D4—1512no—
211C2×D4—1511no—
212C2×D4C22×D15112yes—
213C22×C4—3021no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4—1511no—
217SD16—6042no—
218SD16—6042no—
219D8—6042no—
220D8—6042no—
221C2×C8—1512no—
222C2×C8C22×D15112yes—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—3021no—
226C4⋊C4—3021no—
227C4⋊C4C22×D15111yescharacteristic
228C4⋊C4C22×D15111yescharacteristic
229C22⋊C4—3021no—
230C22⋊C4—3021no—
231C22⋊C4—3021no—
232C22⋊C4—3021no—
233C22⋊C4—3021no—
234C42—3021no—
235C42—1511no—
236C42—1511no—
237C42—1511no—
238C42C22×D15111yescharacteristic
239C23—22no—
240C23—3021no—
241C23—3022no—
242C23—6044no—
243C23—6044no—
244C23—6044no—
245C23—1511no—
246Q8—3022no—
247D4—22no—
248D4—22no—
249D4—42no—
250D4—42no—
251D4—3022no—
252D4—3022no—
253D4—3022no—
254D4—6042no—
255D4—6042no—
256D4—6042no—
257D4—6044no—
258D4—6044no—
259D4—6044no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—3022no—
263C2×C4—3022no—
264C2×C4—3022no—
265C2×C4—3021no—
266C2×C4—6042no—
267C2×C4—1511no—
268C2×C4—1511no—
269C2×C4—1511no—
270C2×C4D4×D15111yescharacteristic
271C2×C4D4×D15111yescharacteristic
272C2×C4C23×D15111yescharacteristic
273C8—22no—
274C8—3022no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—3021no—
279C22—3021no—
280C22—6041no—
281C22—6042no—
282C22—6042no—
283C22—6041no—
284C22—6042no—
285C22—6041no—
286C22—1512no—
287C22—12088no—
288C22C2×D4×D15111yescharacteristic
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—3021no—
294C4—3021no—
295C4—6041no—
296C4—1512no—
297C4#1801278512yes—
298C2—82no—
299C2—3022no—
300C2—12082no—
301C2—12081no—
302C2#2375278011yescharacteristic
303C2AGL(1,ℤ/8)×D15111yescharacteristic
304C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#490×C151C2
socleC22×C151C22×D4
hypercenter#490D151
hypocenterC151#3217
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #127×D151C2semidirect
2. #23752747C2semidirect
3. #23752601C2semidirect
4. #23752599C2semidirect
5. #23752578C2semidirect
6. #23752411C2semidirect
7. #23752406C2semidirect
8. #23752364C2semidirect
9. #23752347C2semidirect
10. #23752267C2semidirect
11. #490×C151C2semidirect
15. C2×#14558993C22semidirect
16. C2×#14558992C22semidirect
17. C2×D1208C22semidirect
18. C2×#14558989C22semidirect
24. #18012727C22semidirect
28. #18012704C22semidirect
30. #18012701C22semidirect
33. Dic151⋊C8C22semidirect
34. #18012659C22semidirect
35. #18012659C22semidirect
37. #18012650C22semidirect
39. #125×C151C22semidirect
40. #102×C151C22semidirect
41. #102×C151C22semidirect
42. #97×C151C22semidirect
152. C151#3217semidirect
159. #490D151semidirect
178. #125C2×D151semidirect
191. #102C2×D151semidirect
192. #102C2×D151semidirect
195. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#127×D1512
#237527472
#237526012
#237525992
#237525782
#237524112
#237524062
#237523642
#237523472
#237522672
#490×C1512
#3217151