Finite Group Databasebeta

← #34080784

Subgroups — #34080784

Order 19328.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×D1208C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752846C212yesmaximal, complemented
4#23752587C211yesmaximal, characteristic, complemented
5#23752449C211yesmaximal, characteristic, complemented
6#23752406C212yesmaximal, complemented
7#23752347C212yesmaximal, complemented
8#23752345C212yesmaximal, complemented
9#23752294C211yesmaximal, characteristic, complemented
10C8×C22⋊D151C211yesmaximal, characteristic, complemented
11#466×C151C211yesmaximal, characteristic, complemented
12C22×D604C2212yescomplemented
13C2×D4×D151—22no—
14C2×D4×D151C2212yescomplemented
15C2×D1208—24no—
16C2×D1208C2211yescharacteristic
17C2×D1208C2211yescharacteristic, complemented
18C2×D1208C2212yescomplemented
19C2×#14558989C2212yescomplemented
20C2×#14558989C2212yescomplemented
21D8×D151—24no—
22C2×C8×D151C2211yescharacteristic, complemented
23#18012735C2212yescomplemented
24#18012714C2212yescomplemented
25#18012712—22no—
26#18012709—22no—
27#18012707—22no—
28#18012701C2212yescomplemented
29C4×C22⋊D151C2211yescharacteristic
30Dic151⋊C8C2211yescharacteristic, complemented
31#18012659C2212yescomplemented
32#18012659C2212yescomplemented
33C22⋊(C151⋊C8)C2211yescharacteristic, complemented
34(C2×D151)⋊C8C2211yescharacteristic, complemented
35C8×Dic151C2211yescharacteristic, complemented
36C2×D8×C151C2211yescharacteristic, complemented
37C22×C8×C151C2211yescharacteristic, complemented
38#121×C151C2212yescomplemented
39#107×C151C2211yescharacteristic, complemented
40#102×C151C2212yescomplemented
41C23×D151—22no—
42C23×D151—22no—
43C2×D604—24no—
44C2×D604—22no—
45C2×D604—22no—
46C2×D604—42no—
47C2×D604C2312yes—
48C2×D604C2312yes—
49C2×C22⋊D151—22no—
50C2×C22⋊D151—22no—
51C2×C22⋊D151—22no—
52C2×C22⋊D151D411yescharacteristic
53D4×D151—24no—
54D4×D151—42no—
55D4×D151—48no—
56C2×C4×D151—22no—
57C2×C4×D151C2311yescharacteristic
58D1208—24no—
59D1208—22no—
60D1208D414yescomplemented
61#14558989—24no—
62#14558989—42no—
63C2×C151⋊C8C2311yescharacteristic
64C2×C151⋊C8C2311yescharacteristic
65C8×D151—22no—
66Dic151⋊C4D411yescharacteristic
67C22⋊Dic151D411yescharacteristic
68(C2×D151)⋊C4—22no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4D411yescharacteristic
71C4×Dic151C2311yescharacteristic
72C2×D4×C151—22no—
73C2×D4×C151C2312yes—
74C22×C4×C151C2311yescharacteristic
75D8×C151—22no—
76C2×C8×C151—22no—
77C2×C8×C151C2311yescharacteristic
78C2×C8×C151C2311yescharacteristic
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—22no—
81C22×D151—22no—
82C22×D151—22no—
83C22×D151—44no—
84C22×D151—44no—
85C22×D151—44no—
86C22×D151—44no—
87C22×D151—82no—
88C22×D151—82no—
89C22×D151C2×D411yescharacteristic
90D604—22no—
91D604—22no—
92D604—22no—
93D604—44no—
94D604—44no—
95D604C2×D414yescomplemented
96C22⋊D151—44no—
97C22⋊D151—44no—
98C22⋊D151—82no—
99C22⋊D151D814yescomplemented
100C2×Dic151C2×D411yescharacteristic
101C2×Dic151C2×D411yescharacteristic
102C2×Dic151C2×D411yescharacteristic
103C4×D151—21no—
104C4×D151—21no—
105C4×D151—44no—
106C151⋊C8—21no—
107C151⋊C8—21no—
108C23×C151—22no—
109C23×C151C2×D411yescharacteristic
110D4×C151—22no—
111D4×C151—22no—
112D4×C151—44no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—22no—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—21no—
119C8×C151C2×D412yescomplemented
120C22×C151—21no—
121C22×C151—21no—
122C22×C151—42no—
123C22×C151—42no—
124C22×C151—42no—
125C22×C151C2×D812yescomplemented
126C22×C151C22×D411yescharacteristic
127C2×D151—21no—
128C2×D151—21no—
129C2×D151—24no—
130C2×D151—42no—
131C2×D151—42no—
132C2×D151—42no—
133C2×D151—42no—
134C2×D151—42no—
135C2×D151—88no—
136C2×D151—88no—
137C2×D151C2×D812yescomplemented
138C4×C151—21no—
139C4×C151—42no—
140C4×C151C22×D411yescharacteristic
141C4×C151H(5,𝔽2)11yescharacteristic
142Dic151—21no—
143Dic151—21no—
144Dic151C2×D812yescomplemented
145C2×C151—22no—
146C2×C151—82no—
147C2×C151D4211yescharacteristic
148C2×C151C22×D811yescharacteristic
149C2×C151#57611yescharacteristic
150D151—22no—
151D151—44no—
152D151—82no—
153C151D4×D811yescharacteristic, complemented, Sylow
154D4×D8—1511nomaximal, Sylow
155C22×D8—1511no—
156C22×D8—1511no—
157D42—1512no—
158#493—1511no—
159#466—1511no—
160#466D15111yescharacteristic, complemented
161#459—1512no—
162#447—1512no—
163#447—1512no—
164C4×D8—1511no—
165C8×D4—1511no—
166C22×D4—3022no—
167C22×D4—1512no—
168C22×D4—1512no—
169C2×D8—3024no—
170C2×D8—3024no—
171C2×D8—1512no—
172C2×D8—1512no—
173C2×D8—1512no—
174C2×D8—1511no—
175C2×D8—1511no—
176C2×D8C2×D15111yescharacteristic, complemented
177C22×C8—1511no—
178C22×C8C2×D15111yescharacteristic, complemented
179#127—1512no—
180#121—3022no—
181#121—1512no—
182#121C2×D15112yescomplemented
183#120—3022no—
184#120—3022no—
185C4×D4—1512no—
186C4×D4—1511no—
187#107C2×D15111yescharacteristic, complemented
188C4⋊C8—1511no—
189#102—1512no—
190#102—1512no—
191#102C2×D15112yescomplemented
192C22⋊C8—1511no—
193C22⋊C8—1511no—
194C4×C8—1511no—
195C24—3022no—
196C24—3022no—
197C2×D4—22no—
198C2×D4—3024no—
199C2×D4—3022no—
200C2×D4—3024no—
201C2×D4—3022no—
202C2×D4—3022no—
203C2×D4—3022no—
204C2×D4—3022no—
205C2×D4—6042no—
206C2×D4—6042no—
207C2×D4—6048no—
208C2×D4—1511no—
209C2×D4—1512no—
210C2×D4—1512no—
211C2×D4C22×D15112yes—
212C22×C4—3022no—
213C22×C4—1511no—
214C22×C4C22×D15111yescharacteristic
215D8—22no—
216D8—3024no—
217D8—3024no—
218D8—3022no—
219D8—6042no—
220D8—1514no—
221C2×C8—22no—
222C2×C8—3022no—
223C2×C8—1511no—
224C2×C8—1511no—
225C2×C8C22×D15111yescharacteristic
226C2×C8C22×D15111yescharacteristic
227C4⋊C4—1511no—
228C4⋊C4C22×D15112yes—
229C22⋊C4—22no—
230C22⋊C4—3022no—
231C22⋊C4—3022no—
232C22⋊C4—1511no—
233C22⋊C4—1511no—
234C42—1511no—
235C23—22no—
236C23—3022no—
237C23—3022no—
238C23—6044no—
239C23—6044no—
240C23—6044no—
241C23—6044no—
242C23—1511no—
243C23—12082no—
244C23—12082no—
245C23D4×D15111yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—3022no—
250D4—3022no—
251D4—3022no—
252D4—6044no—
253D4—6044no—
254D4—6044no—
255D4—6044no—
256D4—1514no—
257D4—1514no—
258D4—12082no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—3021no—
263C2×C4—3021no—
264C2×C4—6044no—
265C2×C4—1511no—
266C2×C4—1511no—
267C2×C4—1511no—
268C2×C4D4×D15111yescharacteristic
269C2×C4C23×D15111yescharacteristic
270C8—21no—
271C8—3021no—
272C8—3021no—
273C8D4×D15112yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—3021no—
280C22—3021no—
281C22—3024no—
282C22—6042no—
283C22—6042no—
284C22—6042no—
285C22—6042no—
286C22—6042no—
287C22—1512no—
288C22—12088no—
289C22—12088no—
290C22D8×D15112yescomplemented
291C22C2×D4×D15111yescharacteristic
292C4—21no—
293C4—42no—
294C4—3021no—
295C4—3021no—
296C4—1512no—
297C4C2×D4×D15111yescharacteristic
298C4#1801278511yescharacteristic
299C2—22no—
300C2—82no—
301C2—3022no—
302C2—6044no—
303C2—12082no—
304C2#2375284611yescharacteristic
305C2C2×D8×D15111yescharacteristic
306C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151D4×D8
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D1208C2semidirect
2. C2×D8×D151C2semidirect
3. #23752846C2semidirect
4. #23752587C2semidirect
5. #23752449C2semidirect
6. #23752406C2semidirect
7. #23752347C2semidirect
8. #23752345C2semidirect
9. #23752294C2semidirect
10. C8×C22⋊D151C2semidirect
11. #466×C151C2semidirect
12. C22×D604C22semidirect
14. C2×D4×D151C22semidirect
17. C2×D1208C22semidirect
18. C2×D1208C22semidirect
19. C2×#14558989C22semidirect
20. C2×#14558989C22semidirect
22. C2×C8×D151C22semidirect
23. #18012735C22semidirect
24. #18012714C22semidirect
28. #18012701C22semidirect
30. Dic151⋊C8C22semidirect
31. #18012659C22semidirect
32. #18012659C22semidirect
33. C22⋊(C151⋊C8)C22semidirect
34. (C2×D151)⋊C8C22semidirect
35. C8×Dic151C22semidirect
36. C2×D8×C151C22semidirect
37. C22×C8×C151C22semidirect
38. #121×C151C22semidirect
39. #107×C151C22semidirect
40. #102×C151C22semidirect
60. D1208D4semidirect
95. D604C2×D4semidirect
99. C22⋊D151D8semidirect
119. C8×C151C2×D4semidirect
125. C22×C151C2×D8semidirect
137. C2×D151C2×D8semidirect
144. Dic151C2×D8semidirect
153. C151D4×D8semidirect
160. #466D151semidirect
176. C2×D8C2×D151semidirect
178. C22×C8C2×D151semidirect
182. #121C2×D151semidirect
187. #107C2×D151semidirect
191. #102C2×D151semidirect
273. C8D4×D151semidirect
290. C22D8×D151semidirect

Maximal subgroups

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

subgroupindex
C22×D12082
C2×D8×D1512
#237528462
#237525872
#237524492
#237524062
#237523472
#237523452
#237522942
C8×C22⋊D1512
#466×C1512
D4×D8151