Finite Group Databasebeta

← #34079048

Subgroups — #34079048

Order 19328.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#18012710C211yesmaximal, characteristic
2#117×D151C211yesmaximal, characteristic, complemented
3#23752535C212yesmaximal, complemented
4#23752534C212yesmaximal, complemented
5#23752529C212yesmaximal, complemented
6#23752524C212yesmaximal, complemented
7#23752255C211yesmaximal, characteristic, complemented
8#23752254C211yesmaximal, characteristic, complemented
9#23752217C211yesmaximal, characteristic, complemented
10#23752175C211yesmaximal, characteristic, complemented
11#418×C151C211yesmaximal, characteristic, complemented
12C22×C22⋊D151—21no—
13C22×C4×D151C2211yescharacteristic
14C2×#14558988C2211yescharacteristic
15#18012710—21no—
16#18012710—21no—
17#18012710C2212yes—
18#18012710C2212yes—
19#18012698C2211yescharacteristic
20#18012697C2211yescharacteristic, complemented
21#18012697C2211yescharacteristic, complemented
22#18012696—21no—
23#18012695—21no—
24C2×C4⋊Dic151C2211yescharacteristic
25C4⋊C4×D151C2211yescharacteristic, complemented
26C4⋊C4×D151C2211yescharacteristic, complemented
27C2×C22⋊Dic151—21no—
28C22⋊C4×D151—21no—
29C42×D151—21no—
30#18012673C2212yescomplemented
31#18012672C2212yescomplemented
32#18012671C2212yescomplemented
33#18012670C2212yescomplemented
34#18012660C2212yescomplemented
35#18012660C2212yescomplemented
36(C2×D151)⋊C8C2212yescomplemented
37(C2×D151)⋊C8C2212yescomplemented
38C22×D4×C151C2211yescharacteristic
39C2×M16×C151C2211yescharacteristic
40#117×C151C2211yescharacteristic
41#102×C151C2212yescomplemented
42#102×C151C2212yescomplemented
43C23×D151D411yescharacteristic
44C2×C22⋊D151—22no—
45C2×C22⋊D151—22no—
46C2×C22⋊D151—44no—
47C22×Dic151—21no—
48C22×Dic151D411yescharacteristic
49C2×C4×D151—21no—
50C2×C4×D151—21no—
51C2×C4×D151—22no—
52C2×C4×D151—22no—
53C2×C4×D151D411yescharacteristic
54C2×C4×D151D411yescharacteristic
55C2×C4×D151C2311yescharacteristic
56C2×C4×D151C2311yescharacteristic
57#14558988—22no—
58C2×C151⋊C8C2312yes—
59C4⋊Dic151—21no—
60C4⋊Dic151C2312yes—
61C4⋊Dic151C2311yescharacteristic
62C4⋊Dic151C2311yescharacteristic
63Dic151⋊C4—21no—
64Dic151⋊C4—21no—
65C22⋊Dic151—22no—
66C22⋊Dic151—22no—
67C22⋊Dic151—21no—
68(C2×D151)⋊C4—21no—
69(C2×D151)⋊C4—21no—
70C4×Dic151—21no—
71C4×Dic151—21no—
72C4×Dic151—21no—
73C24×C151—21no—
74C2×D4×C151—21no—
75C2×D4×C151—22no—
76C2×D4×C151—22no—
77C2×D4×C151C2312yes—
78C22×C4×C151C2311yescharacteristic
79M16×C151—22no—
80C2×C8×C151C2312yes—
81C4⋊C4×C151C2311yescharacteristic
82C4⋊C4×C151C2311yescharacteristic
83C22⋊C4×C151—21no—
84C42×C151—21no—
85C22×D151—22no—
86C22×D151—22no—
87C22×D151—41no—
88C22×D151C2×D411yescharacteristic
89C22×D151C2×D411yescharacteristic
90C22⋊D151—44no—
91C22⋊D151—44no—
92C2×Dic151—22no—
93C2×Dic151—21no—
94C2×Dic151—21no—
95C2×Dic151—22no—
96C2×Dic151—42no—
97C2×Dic151C2×D411yescharacteristic
98C2×Dic151C2×D411yescharacteristic
99C4×D151—22no—
100C4×D151—22no—
101C4×D151—21no—
102C4×D151—21no—
103C4×D151—21no—
104C4×D151—21no—
105C4×D151—42no—
106C4×D151—42no—
107C151⋊C8—22no—
108C23×C151—22no—
109C23×C151—42no—
110C23×C151—42no—
111C23×C151—42no—
112C23×C151C2×D411yescharacteristic
113D4×C151—22no—
114D4×C151—22no—
115D4×C151—42no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151C2×D411yescharacteristic
119C2×C4×C151#4112yes—
120C2×C4×C151#4112yes—
121C2×C4×C151C2411yescharacteristic
122C8×C151—22no—
123C22×C151—21no—
124C22×C151—21no—
125C22×C151—42no—
126C22×C151—42no—
127C22×C151—42no—
128C22×C151—84no—
129C22×C151#12312yes—
130C22×C151C22×D411yescharacteristic
131C2×D151—21no—
132C2×D151—21no—
133C2×D151—21no—
134C2×D151—21no—
135C2×D151—21no—
136C2×D151—44no—
137C2×D151AGL(1,ℤ/8)12yes—
138C4×C151—41no—
139C4×C151—41no—
140C4×C151#12312yes—
141C4×C151C2×#4111yescharacteristic
142C4×C151C2×#4111yescharacteristic
143Dic151—21no—
144Dic151—21no—
145Dic151—41no—
146Dic151—42no—
147Dic151—41no—
148C2×C151—22no—
149C2×C151—82no—
150C2×C151C2×#12311yescharacteristic
151C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C151#57511yescharacteristic
153D151—22no—
154D151—41no—
155C151#309411yescharacteristic, complemented, Sylow
156#3094—1511nomaximal, Sylow
157C2×#121—1511no—
158C2×#117—1511no—
159#482—1512no—
160#482—1512no—
161#481—1512no—
162#480—1512no—
163#428—1511no—
164#428—1511no—
165#418—1511no—
166#418D15111yescharacteristic, complemented
167#407—1511no—
168C22×D4—3021no—
169C22×D4C2×D15111yescharacteristic
170C23×C4—1511no—
171C2×M16—1511no—
172C2×M16C2×D15111yescharacteristic
173#121—3021no—
174#121—3021no—
175#121—1512no—
176#121—1512no—
177#117—3021no—
178#117—3021no—
179#117—1511no—
180#117—1511no—
181#117—1511no—
182#117C2×D15111yescharacteristic
183C2×C4⋊C4—1511no—
184C2×C4⋊C4—1511no—
185C2×C4⋊C4—1511no—
186C2×C22⋊C4—3021no—
187C2×C22⋊C4—3021no—
188C2×C42—3021no—
189#107—1512no—
190#107—1512no—
191#106—1512no—
192#106—1512no—
193#102—1512no—
194#102—1512no—
195#102C2×D15112yescomplemented
196#102C2×D15112yescomplemented
197C22⋊C8—1512no—
198C22⋊C8—1512no—
199C24—21no—
200C24—1511no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—3022no—
205C2×D4—3022no—
206C2×D4—6044no—
207C2×D4C22×D15112yes—
208C22×C4—3021no—
209C22×C4—3021no—
210C22×C4—3022no—
211C22×C4—3022no—
212C22×C4—3021no—
213C22×C4—1511no—
214C22×C4—1511no—
215C22×C4—1511no—
216C22×C4—1511no—
217C22×C4—1511no—
218C22×C4C22×D15111yescharacteristic
219M16—22no—
220M16—3022no—
221C2×C8—1512no—
222C2×C8C22×D15112yes—
223C4⋊C4—3021no—
224C4⋊C4—3021no—
225C4⋊C4—3021no—
226C4⋊C4—1511no—
227C4⋊C4—1511no—
228C4⋊C4—1512no—
229C4⋊C4C22×D15111yescharacteristic
230C4⋊C4C22×D15111yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—3021no—
233C22⋊C4—3021no—
234C22⋊C4—3021no—
235C22⋊C4—3022no—
236C22⋊C4—3022no—
237C42—21no—
238C42—3021no—
239C42—3021no—
240C42—3021no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—3022no—
246C23—3022no—
247C23—6041no—
248C23—1511no—
249C23—1511no—
250C23D4×D15111yescharacteristic
251D4—22no—
252D4—22no—
253D4—42no—
254D4—6044no—
255D4—6044no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—3022no—
259C2×C4—3022no—
260C2×C4—3022no—
261C2×C4—3021no—
262C2×C4—3021no—
263C2×C4—3021no—
264C2×C4—3021no—
265C2×C4—3021no—
266C2×C4—3021no—
267C2×C4—3022no—
268C2×C4—6042no—
269C2×C4—6042no—
270C2×C4—6042no—
271C2×C4—1511no—
272C2×C4—1511no—
273C2×C4D4×D15111yescharacteristic
274C2×C4#1455900312yes—
275C2×C4#1455900412yes—
276C2×C4C23×D15111yescharacteristic
277C8—22no—
278C8—3022no—
279C22—21no—
280C22—21no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—3021no—
286C22—3021no—
287C22—3021no—
288C22—3021no—
289C22—3021no—
290C22—6044no—
291C22—1512no—
292C22#1801272112yes—
293C22C2×D4×D15111yescharacteristic
294C4—41no—
295C4—41no—
296C4—3021no—
297C4—3021no—
298C4—6042no—
299C4—6041no—
300C4—6041no—
301C4#1801272112yes—
302C4C2×#1455900311yescharacteristic
303C4C2×#1455900411yescharacteristic
304C2—22no—
305C2—82no—
306C2—3022no—
307C2—6041no—
308C2C2×#1801272111yescharacteristic
309C2AGL(1,ℤ/8)×D15111yescharacteristic
310C2#2375300811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#418×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012710C2
hypercenter#418D151
hypocenterC151#3094
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #117×D151C2semidirect
3. #23752535C2semidirect
4. #23752534C2semidirect
5. #23752529C2semidirect
6. #23752524C2semidirect
7. #23752255C2semidirect
8. #23752254C2semidirect
9. #23752217C2semidirect
10. #23752175C2semidirect
11. #418×C151C2semidirect
20. #18012697C22semidirect
21. #18012697C22semidirect
25. C4⋊C4×D151C22semidirect
26. C4⋊C4×D151C22semidirect
30. #18012673C22semidirect
31. #18012672C22semidirect
32. #18012671C22semidirect
33. #18012670C22semidirect
34. #18012660C22semidirect
35. #18012660C22semidirect
36. (C2×D151)⋊C8C22semidirect
37. (C2×D151)⋊C8C22semidirect
41. #102×C151C22semidirect
42. #102×C151C22semidirect
155. C151#3094semidirect
166. #418D151semidirect
195. #102C2×D151semidirect
196. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127102
#117×D1512
#237525352
#237525342
#237525292
#237525242
#237522552
#237522542
#237522172
#237521752
#418×C1512
#3094151