Finite Group Databasebeta

← #481×D151 #34079006

Subgroups — #481×D151 #34079006

Order 19328.

512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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#121×D151C211yesmaximal, characteristic
2C2×C4⋊C4×D151C211yesmaximal, characteristic, complemented
3#23752532C212yesmaximal, complemented
4#23752531C211yesmaximal, characteristic, complemented
5#23752530C211yesmaximal, characteristic, complemented
6#23752529C212yesmaximal, complemented
7#23752528C211yesmaximal, characteristic, complemented
8#106×D151C212yesmaximal, complemented
9#102×D151C212yesmaximal, complemented
10C22⋊C8×D151C211yesmaximal, characteristic, complemented
11#481×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151—21no—
13C2×D4×D151C2211yescharacteristic
14C22×C4×D151—21no—
15C22×C4×D151C2211yescharacteristic
16C2×C8×D151C2212yes—
17#18012714C2211yescharacteristic
18#18012713C2211yescharacteristic
19#18012712—21no—
20#18012711—21no—
21#18012710C2211yescharacteristic
22C2×C4⋊Dic151C2211yescharacteristic, complemented
23C2×Dic151⋊C4—21no—
24C4⋊C4×D151—21no—
25C4⋊C4×D151—21no—
26C4⋊C4×D151C2212yes—
27C4⋊C4×D151C2211yescharacteristic
28C4⋊C4×D151C2212yescomplemented
29C22⋊C4×D151—21no—
30#18012671C2212yescomplemented
31#18012670C2212yescomplemented
32#18012670C2212yescomplemented
33#18012661C2212yescomplemented
34#18012660C2212yescomplemented
35#18012659C2212yescomplemented
36C22⋊(C151⋊C8)C2211yescharacteristic, complemented
37(C2×D151)⋊C8C2212yescomplemented
38#121×C151C2211yescharacteristic
39C2×C4⋊C4×C151C2211yescharacteristic, complemented
40#106×C151C2212yescomplemented
41#102×C151C2212yescomplemented
42C22⋊C8×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C23×D151D411yescharacteristic
45C2×D604—21no—
46C2×D604C2311yescharacteristic
47C2×C22⋊D151—21no—
48C2×C22⋊D151—21no—
49C2×C22⋊D151—21no—
50D4×D151—24no—
51D4×D151—44no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—24no—
55C2×C4×D151—21no—
56C2×C4×D151—22no—
57C2×C4×D151—22no—
58C2×C4×D151—44no—
59C2×C4×D151D411yescharacteristic
60C2×C4×D151D411yescharacteristic
61C2×C4×D151C2311yescharacteristic
62C2×C4×D151C2311yescharacteristic
63C2×C151⋊C8C2312yes—
64C8×D151—24no—
65C4⋊Dic151—21no—
66C4⋊Dic151C2312yes—
67C4⋊Dic151C2311yescharacteristic
68Dic151⋊C4—22no—
69Dic151⋊C4—22no—
70Dic151⋊C4—21no—
71C22⋊Dic151—21no—
72(C2×D151)⋊C4—21no—
73(C2×D151)⋊C4—21no—
74C2×D4×C151—21no—
75C2×D4×C151C2311yescharacteristic
76C22×C4×C151—21no—
77C22×C4×C151C2311yescharacteristic
78C2×C8×C151C2312yes—
79C4⋊C4×C151—21no—
80C4⋊C4×C151C2312yes—
81C4⋊C4×C151C2311yescharacteristic
82C22⋊C4×C151—21no—
83C22×D151—22no—
84C22×D151—22no—
85C22×D151—21no—
86C22×D151—42no—
87C22×D151—42no—
88C22×D151—42no—
89C22×D151SD1614yes—
90C22×D151C2×D411yescharacteristic
91C22×D151C2×D411yescharacteristic
92D604—22no—
93D604—42no—
94C22⋊D151—42no—
95C22⋊D151—42no—
96C22⋊D151—42no—
97C2×Dic151—22no—
98C2×Dic151—21no—
99C2×Dic151—22no—
100C2×Dic151—42no—
101C2×Dic151C2×D411yescharacteristic
102C2×Dic151C2×D411yescharacteristic
103C4×D151—22no—
104C4×D151—22no—
105C4×D151—22no—
106C4×D151—44no—
107C4×D151—42no—
108C4×D151—44no—
109C4×D151#4114yes—
110C151⋊C8—22no—
111C23×C151—21no—
112C23×C151C2×D411yescharacteristic
113D4×C151—22no—
114D4×C151—42no—
115C2×C4×C151—22no—
116C2×C4×C151—21no—
117C2×C4×C151—22no—
118C2×C4×C151—42no—
119C2×C4×C151C2×D411yescharacteristic
120C2×C4×C151C2411yescharacteristic
121C8×C151—22no—
122C22×C151—21no—
123C22×C151—21no—
124C22×C151—41no—
125C22×C151—41no—
126C22×C151—41no—
127C22×C151C2×SD1612yes—
128C22×C151C22×D411yescharacteristic
129C2×D151—21no—
130C2×D151—21no—
131C2×D151—28no—
132C2×D151—41no—
133C2×D151—41no—
134C2×D151—41no—
135C2×D151—84no—
136C2×D151#12312yes—
137C2×D151C2×SD1612yes—
138C2×D151C2×SD1612yes—
139C2×D151AGL(1,ℤ/8)12yes—
140C4×C151—21no—
141C4×C151—41no—
142C4×C151—42no—
143C4×C151C2×#4112yes—
144Dic151—21no—
145Dic151—41no—
146Dic151—42no—
147Dic151#12312yes—
148C2×C151—22no—
149C2×C151—81no—
150C2×C151C2×#12311yescharacteristic
151C2×C151C22×SD1611yescharacteristic
152C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
153D151—22no—
154D151—81no—
155D151#48114yesdirect product factor
156C151C2×#48111yescharacteristic, complemented, Sylow
157C2×#481—1511nomaximal, Sylow
158C2×#121—1511no—
159C22×C4⋊C4—1511no—
160#481—1511no—
161#481—1511no—
162#481—1512no—
163#481—1512no—
164#481—1511no—
165#481D15111yescharacteristic, direct product factor
166C2×#106—1512no—
167C2×#102—1512no—
168C2×C22⋊C8—1511no—
169C22×D4—3021no—
170C22×D4—1511no—
171C23×C4—3021no—
172C23×C4—1511no—
173C22×C8—1512no—
174#121—3021no—
175#121—3021no—
176#121—1511no—
177#121—1511no—
178#121—1511no—
179#121C2×D15111yescharacteristic
180C2×C4⋊C4—3021no—
181C2×C4⋊C4—3021no—
182C2×C4⋊C4—3021no—
183C2×C4⋊C4—1511no—
184C2×C4⋊C4—1512no—
185C2×C4⋊C4—1512no—
186C2×C4⋊C4—1511no—
187C2×C4⋊C4C2×D15111yescharacteristic, complemented
188C2×C22⋊C4—3021no—
189#106—1512no—
190#106—1512no—
191#106—1512no—
192#106C2×D15112yescomplemented
193#102—1512no—
194#102—1512no—
195#102—1512no—
196#102C2×D15112yescomplemented
197C22⋊C8—1511no—
198C22⋊C8—1512no—
199C22⋊C8C2×D15111yescharacteristic, complemented
200C24—3021no—
201C24—1511no—
202C2×D4—21no—
203C2×D4—3021no—
204C2×D4—3021no—
205C2×D4—3021no—
206C2×D4—3024no—
207C2×D4—3021no—
208C2×D4—6044no—
209C2×D4—1511no—
210C2×D4C22×D15111yescharacteristic
211C22×C4—21no—
212C22×C4—3024no—
213C22×C4—3021no—
214C22×C4—3022no—
215C22×C4—3022no—
216C22×C4—3021no—
217C22×C4—6044no—
218C22×C4—1511no—
219C22×C4—1511no—
220C22×C4—1511no—
221C22×C4—1511no—
222C22×C4—1511no—
223C22×C4C22×D15111yescharacteristic
224C2×C8—3024no—
225C2×C8—1512no—
226C2×C8C22×D15112yes—
227C4⋊C4—21no—
228C4⋊C4—3022no—
229C4⋊C4—3022no—
230C4⋊C4—3021no—
231C4⋊C4—3021no—
232C4⋊C4—1512no—
233C4⋊C4—1511no—
234C4⋊C4C22×D15112yes—
235C4⋊C4C22×D15111yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—3021no—
238C22⋊C4—3021no—
239C22⋊C4—3021no—
240C23—21no—
241C23—3022no—
242C23—3022no—
243C23—3021no—
244C23—6042no—
245C23—6042no—
246C23—6042no—
247C23—1514no—
248C23—1511no—
249C23—1511no—
250C23D4×D15111yescharacteristic
251D4—22no—
252D4—42no—
253D4—3022no—
254D4—6042no—
255D4—6042no—
256D4—6042no—
257D4—6042no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—3022no—
263C2×C4—3022no—
264C2×C4—3022no—
265C2×C4—3022no—
266C2×C4—3021no—
267C2×C4—3022no—
268C2×C4—6044no—
269C2×C4—6044no—
270C2×C4—6042no—
271C2×C4—6042no—
272C2×C4—1511no—
273C2×C4—1511no—
274C2×C4—1514no—
275C2×C4D4×D15111yescharacteristic
276C2×C4C23×D15111yescharacteristic
277C8—22no—
278C8—3022no—
279C22—21no—
280C22—21no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—3028no—
285C22—3021no—
286C22—3021no—
287C22—6041no—
288C22—6041no—
289C22—6041no—
290C22—1512no—
291C22—1512no—
292C22—1512no—
293C22—1512no—
294C22—12084no—
295C22SD16×D15112yes—
296C22C2×D4×D15111yescharacteristic
297C4—21no—
298C4—41no—
299C4—42no—
300C4—3021no—
301C4—6041no—
302C4—6042no—
303C4—1512no—
304C4#41×D15112yes—
305C2—22no—
306C2—81no—
307C2—3022no—
308C2—1514no—
309C2—12081no—
310C2#123×D15111yescharacteristic
311C2C2×SD16×D15111yescharacteristic
312C2AGL(1,ℤ/8)×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#481×C151C2
socleC22×C151C22×D4
prime radical#121×D151C2
hypercenter#481D151
hypocenterC151C2×#481
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D151C2semidirect
3. #23752532C2semidirect
4. #23752531C2semidirect
5. #23752530C2semidirect
6. #23752529C2semidirect
7. #23752528C2semidirect
8. #106×D151C2semidirect
9. #102×D151C2semidirect
10. C22⋊C8×D151C2semidirect
11. #481×C151C2semidirect
22. C2×C4⋊Dic151C22semidirect
28. C4⋊C4×D151C22semidirect
30. #18012671C22semidirect
31. #18012670C22semidirect
32. #18012670C22semidirect
33. #18012661C22semidirect
34. #18012660C22semidirect
35. #18012659C22semidirect
36. C22⋊(C151⋊C8)C22semidirect
37. (C2×D151)⋊C8C22semidirect
39. C2×C4⋊C4×C151C22semidirect
40. #106×C151C22semidirect
41. #102×C151C22semidirect
42. C22⋊C8×C151C22semidirect
155. D151#481direct (N × H)
156. C151C2×#481semidirect
165. #481D151direct (N × H)
187. C2×C4⋊C4C2×D151semidirect
192. #106C2×D151semidirect
196. #102C2×D151semidirect
199. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#121×D1512
C2×C4⋊C4×D1512
#237525322
#237525312
#237525302
#237525292
#237525282
#106×D1512
#102×D1512
C22⋊C8×D1512
#481×C1512
C2×#481151