Finite Group Databasebeta

← #34078339

Subgroups — #34078339

Order 19328.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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×D4×D151C211yesmaximal, characteristic, complemented
2C2×#18012767C211yesmaximal, characteristic, complemented
3C2×#18012765C211yesmaximal, characteristic, complemented
4#23752724C211yesmaximal, characteristic, complemented
5#23752364C214yesmaximal, complemented
6#23752347C214yesmaximal, complemented
7#23752216C211yesmaximal, characteristic, complemented
8#23752175C211yesmaximal, characteristic, complemented
9#418×C151C211yesmaximal, characteristic, complemented
10C24×D151—21no—
11C2×#14559004C2211yescharacteristic, complemented
12C22×D604C2211yescharacteristic
13C22×C22⋊D151—21no—
14C2×D4×D151—24no—
15C2×D4×D151—24no—
16C2×D4×D151—22no—
17C2×D4×D151C2214yes—
18C22×C4×D151C2211yescharacteristic
19#18012767—24no—
20#18012765—24no—
21C2×#14558993C2212yescomplemented
22C2×#14558992C2212yescomplemented
23C2×D1208C2212yescomplemented
24C2×#14558989C2212yescomplemented
25C2×#14558988C2211yescharacteristic, complemented
26#18012723—21no—
27#18012719C2212yescomplemented
28#18012714C2212yescomplemented
29#18012709—21no—
30C4×D604—22no—
31#18012659C2214yescomplemented
32(C2×D151)⋊C8C2214yescomplemented
33C22×D4×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic, complemented
35#117×C151C2211yescharacteristic, complemented
36#102×C151C2214yescomplemented
37C23×D151—28no—
38C23×D151—24no—
39C23×D151—21no—
40C23×D151—48no—
41C23×D151D411yescharacteristic
42#14559004—22no—
43#14559004—22no—
44C2×Dic302C2311yescharacteristic, complemented
45C2×D604—22no—
46C2×D604—21no—
47C2×D604—22no—
48C2×D604D414yescomplemented
49C2×D604C2312yes—
50C2×D604C2311yescharacteristic, complemented
51C2×C22⋊D151—28no—
52C2×C22⋊D151—24no—
53C2×C22⋊D151—21no—
54D4×D151—216no—
55D4×D151—28no—
56D4×D151—28no—
57C22×Dic151D411yescharacteristic
58C2×C4×D151—22no—
59C2×C4×D151—22no—
60C2×C4×D151—21no—
61C2×C4×D151D412yes—
62C2×C4×D151C2312yes—
63#14558993—24no—
64#14558992—24no—
65D1208—24no—
66#14558989—24no—
67#14558988—22no—
68C2×C151⋊C8C2312yescomplemented
69C4⋊Dic151—22no—
70(C2×D151)⋊C4—22no—
71(C2×D151)⋊C4—22no—
72C24×C151—21no—
73C2×D4×C151—21no—
74C2×D4×C151—22no—
75C2×D4×C151D414yescomplemented
76C2×D4×C151C2312yes—
77C22×C4×C151C2311yescharacteristic
78M16×C151—22no—
79C2×C8×C151C2312yescomplemented
80C4⋊C4×C151C2312yescomplemented
81C22⋊C4×C151—21no—
82C42×C151—21no—
83C22×D151—22no—
84C22×D151—24no—
85C22×D151—216no—
86C22×D151—24no—
87C22×D151—22no—
88C22×D151—21no—
89C22×D151—432no—
90C22×D151—48no—
91C22×D151—44no—
92C22×D151—48no—
93C22×D151C2×D412yes—
94Dic302—21no—
95Dic302—21no—
96D604—24no—
97D604—22no—
98D604—21no—
99D604—21no—
100D604—44no—
101D604C2×D414yes—
102C22⋊D151—216no—
103C22⋊D151—42no—
104C2×Dic151—22no—
105C2×Dic151—21no—
106C2×Dic151C2×D412yes—
107C4×D151—24no—
108C4×D151—22no—
109C4×D151—22no—
110C4×D151—42no—
111C151⋊C8—22no—
112C23×C151—24no—
113C23×C151—22no—
114C23×C151—44no—
115C23×C151C2×D411yescharacteristic
116D4×C151—24no—
117D4×C151—22no—
118D4×C151C2×D414yes—
119C2×C4×C151—22no—
120C2×C4×C151C2×D411yescharacteristic
121C2×C4×C151C2×D412yes—
122C2×C4×C151C2×D412yes—
123C2×C4×C151C2411yescharacteristic
124C8×C151—22no—
125C22×C151—22no—
126C22×C151—24no—
127C22×C151—48no—
128C22×C151—44no—
129C22×C151#12012yes—
130C22×C151C22×D411yescharacteristic
131C2×D151—28no—
132C2×D151—22no—
133C2×D151—22no—
134C2×D151—24no—
135C2×D151—432no—
136C2×D151—48no—
137C2×D151—44no—
138C2×D151—41no—
139C2×D151—42no—
140C2×D151AGL(1,ℤ/8)14yescomplemented
141C4×C151—42no—
142C4×C151#12012yes—
143C4×C151C22×D411yescharacteristic
144C4×C151C22×D411yescharacteristic
145Dic151—22no—
146Dic151—41no—
147C2×C151—22no—
148C2×C151—44no—
149C2×C151C2×#12011yescharacteristic
150C2×C151C2×AGL(1,ℤ/8)12yes—
151D151—24no—
152D151—44no—
153D151—81no—
154C151#300311yescharacteristic, complemented, Sylow
155#3003—1511nomaximal, Sylow
156C23×D4—1511no—
157C2×AGL(1,ℤ/8)—1511no—
158C2×AGL(1,ℤ/8)—1511no—
159#525—1511no—
160#450—1514no—
161#447—1514no—
162#418—1511no—
163#418D15111yescharacteristic, complemented
164#407—1511no—
165C25—3021no—
166C2×#41—1511no—
167C22×D4—3024no—
168C22×D4—3024no—
169C22×D4—3022no—
170C22×D4—3021no—
171C22×D4—1514no—
172C22×D4—1511no—
173C22×D4C2×D15111yescharacteristic
174C23×C4—1511no—
175AGL(1,ℤ/8)—3024no—
176AGL(1,ℤ/8)—3024no—
177C2×SD16—1512no—
178C2×SD16—1512no—
179C2×D8—1512no—
180C2×D8—1512no—
181C2×M16—1511no—
182C2×M16C2×D15111yescharacteristic, complemented
183#123—3021no—
184C22⋊Q8—1512no—
185#121—1512no—
186#120—3021no—
187C4×D4—3022no—
188#117C2×D15111yescharacteristic, complemented
189#102—1514no—
190#102C2×D15114yescomplemented
191C22⋊C8—1514no—
192C24—21no—
193C24—3028no—
194C24—3024no—
195C24—3021no—
196C24—6048no—
197C24—1511no—
198#41—3022no—
199#41—3022no—
200C2×Q8—1511no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—3022no—
204C2×D4—30216no—
205C2×D4—3028no—
206C2×D4—3028no—
207C2×D4—3028no—
208C2×D4—3021no—
209C2×D4—3024no—
210C2×D4—3021no—
211C2×D4—3022no—
212C2×D4—1514no—
213C2×D4—1511no—
214C2×D4—1512no—
215C2×D4D60414yescomplemented
216C2×D4C22×D15112yes—
217C22×C4—3022no—
218C22×C4—3022no—
219C22×C4—3021no—
220C22×C4—1511no—
221C22×C4—1512no—
222C22×C4—1512no—
223C22×C4C22×D15111yescharacteristic
224SD16—3024no—
225SD16—3024no—
226D8—3024no—
227D8—3024no—
228M16—22no—
229M16—3022no—
230C2×C8—1512no—
231C2×C8C22×D15112yescomplemented
232C4⋊C4—3022no—
233C4⋊C4C22×D15112yescomplemented
234C22⋊C4—21no—
235C22⋊C4—3022no—
236C22⋊C4—3022no—
237C42—21no—
238C23—24no—
239C23—22no—
240C23—44no—
241C23—3024no—
242C23—30216no—
243C23—3022no—
244C23—3024no—
245C23—3022no—
246C23—3021no—
247C23—6044no—
248C23—60432no—
249C23—6048no—
250C23—6048no—
251C23—1512no—
252C23D4×D15111yescharacteristic
253Q8—3021no—
254Q8—3021no—
255D4—24no—
256D4—22no—
257D4—30216no—
258D4—3024no—
259D4—3021no—
260D4—3022no—
261D4—3021no—
262D4—6044no—
263D4—6042no—
264D4—1514no—
265D4C2×D60414yes—
266C2×C4—22no—
267C2×C4—3022no—
268C2×C4—3024no—
269C2×C4—3022no—
270C2×C4—3022no—
271C2×C4—3021no—
272C2×C4—6042no—
273C2×C4—1512no—
274C2×C4D4×D15111yescharacteristic
275C2×C4D4×D15112yes—
276C2×C4C2×D60412yes—
277C2×C4C23×D15111yescharacteristic
278C8—22no—
279C8—3022no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—3028no—
285C22—3022no—
286C22—3022no—
287C22—3024no—
288C22—6048no—
289C22—60432no—
290C22—6044no—
291C22—6042no—
292C22—6041no—
293C22—1514no—
294C22#1801270912yes—
295C22C2×D4×D15111yescharacteristic
296C4—42no—
297C4—3022no—
298C4—6041no—
299C4#1801270912yes—
300C4C2×D4×D15111yescharacteristic
301C4C22×D60411yescharacteristic
302C2—22no—
303C2—44no—
304C2—3024no—
305C2—6044no—
306C2—12081no—
307C2C2×#1801270911yescharacteristic
308C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#418×C151C2
socleC22×C151C22×D4
hypercenter#418D151
hypocenterC151#3003
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
1. C22×D4×D151C2semidirect
2. C2×#18012767C2semidirect
3. C2×#18012765C2semidirect
4. #23752724C2semidirect
5. #23752364C2semidirect
6. #23752347C2semidirect
7. #23752216C2semidirect
8. #23752175C2semidirect
9. #418×C151C2semidirect
11. C2×#14559004C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558992C22semidirect
23. C2×D1208C22semidirect
24. C2×#14558989C22semidirect
25. C2×#14558988C22semidirect
27. #18012719C22semidirect
28. #18012714C22semidirect
31. #18012659C22semidirect
32. (C2×D151)⋊C8C22semidirect
34. C2×M16×C151C22semidirect
35. #117×C151C22semidirect
36. #102×C151C22semidirect
44. C2×Dic302C23semidirect
48. C2×D604D4semidirect
50. C2×D604C23semidirect
68. C2×C151⋊C8C23semidirect
75. C2×D4×C151D4semidirect
79. C2×C8×C151C23semidirect
80. C4⋊C4×C151C23semidirect
140. C2×D151AGL(1,ℤ/8)semidirect
154. C151#3003semidirect
163. #418D151semidirect
182. C2×M16C2×D151semidirect
188. #117C2×D151semidirect
190. #102C2×D151semidirect
215. C2×D4D604semidirect
231. C2×C8C22×D151semidirect
233. C4⋊C4C22×D151semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1512
C2×#180127672
C2×#180127652
#237527242
#237523642
#237523472
#237522162
#237521752
#418×C1512
#3003151