Finite Group Databasebeta

← #34078356

Subgroups — #34078356

Order 19328.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14559005C211yesmaximal, characteristic, complemented
2C2×#18012770C211yesmaximal, characteristic, complemented
3C2×#18012767C211yesmaximal, characteristic, complemented
4#23752724C211yesmaximal, characteristic, complemented
5#23752377C214yesmaximal, complemented
6#23752360C214yesmaximal, complemented
7#23752216C211yesmaximal, characteristic, complemented
8#23752175C211yesmaximal, characteristic, complemented
9#419×C151C211yesmaximal, characteristic, complemented
10C2×#14559005—24no—
11C2×#14559005—22no—
12C2×#14559005—24no—
13C2×#14559005C2214yes—
14C2×#14559004C2211yescharacteristic
15C22×D604—21no—
16C22×D604C2211yescharacteristic
17C22×C4×D151—21no—
18C22×C4×D151C2211yescharacteristic
19#18012770—24no—
20#18012767—24no—
21C2×#14558994C2212yescomplemented
22C2×#14558993C2212yescomplemented
23C2×#14558991C2212yescomplemented
24C2×D1208C2212yescomplemented
25C2×#14558988C2211yescharacteristic
26#18012723—21no—
27#18012719C2212yescomplemented
28#18012714C2212yescomplemented
29#18012709—21no—
30C4×D604—22no—
31#18012659C2214yescomplemented
32(C2×D151)⋊C8C2214yescomplemented
33C22×Q8×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic
35#117×C151C2211yescharacteristic
36#103×C151C2214yescomplemented
37C23×D151—21no—
38C23×D151D411yescharacteristic
39#14559005—216no—
40#14559005—28no—
41#14559005—28no—
42#14559004—22no—
43#14559004—22no—
44C2×Dic302C2311yescharacteristic
45C2×D604—28no—
46C2×D604—24no—
47C2×D604—22no—
48C2×D604—21no—
49C2×D604—22no—
50C2×D604D414yescomplemented
51C2×D604C2311yescharacteristic
52C2×D604C2312yes—
53C2×C22⋊D151—21no—
54C22×Dic151D411yescharacteristic
55C2×C4×D151—28no—
56C2×C4×D151—24no—
57C2×C4×D151—22no—
58C2×C4×D151—22no—
59C2×C4×D151—21no—
60C2×C4×D151D412yes—
61C2×C4×D151C2312yes—
62#14558994—24no—
63#14558993—24no—
64#14558991—24no—
65D1208—24no—
66#14558988—22no—
67C2×C151⋊C8C2312yes—
68C4⋊Dic151—22no—
69(C2×D151)⋊C4—22no—
70(C2×D151)⋊C4—22no—
71C2×Q8×C151—22no—
72C2×Q8×C151—21no—
73C2×Q8×C151D414yescomplemented
74C2×Q8×C151C2312yes—
75C22×C4×C151—21no—
76C22×C4×C151C2311yescharacteristic
77M16×C151—22no—
78C2×C8×C151C2312yes—
79C4⋊C4×C151C2312yes—
80C22⋊C4×C151—21no—
81C42×C151—21no—
82C22×D151—22no—
83C22×D151—24no—
84C22×D151—22no—
85C22×D151—21no—
86C22×D151—42no—
87C22×D151—44no—
88C22×D151C2×D412yes—
89Dic302—21no—
90Dic302—21no—
91D604—216no—
92D604—24no—
93D604—22no—
94D604—21no—
95D604—21no—
96D604—44no—
97D604C2×D414yes—
98C22⋊D151—42no—
99C2×Dic151—22no—
100C2×Dic151—21no—
101C2×Dic151C2×D412yes—
102C4×D151—216no—
103C4×D151—24no—
104C4×D151—22no—
105C4×D151—22no—
106C4×D151—42no—
107C151⋊C8—22no—
108C23×C151C2×D411yescharacteristic
109Q8×C151—24no—
110Q8×C151—22no—
111Q8×C151C2×D414yes—
112C2×C4×C151—24no—
113C2×C4×C151—22no—
114C2×C4×C151—22no—
115C2×C4×C151C2×D411yescharacteristic
116C2×C4×C151C2×D412yes—
117C2×C4×C151C2×D412yes—
118C2×C4×C151C2411yescharacteristic
119C8×C151—22no—
120C22×C151—22no—
121C22×C151#12012yes—
122C22×C151C22×D411yescharacteristic
123C2×D151—22no—
124C2×D151—24no—
125C2×D151—22no—
126C2×D151—22no—
127C2×D151—44no—
128C2×D151—48no—
129C2×D151—44no—
130C2×D151—41no—
131C2×D151—42no—
132C4×C151—24no—
133C4×C151—42no—
134C4×C151#12012yes—
135C4×C151C22×D411yescharacteristic
136C4×C151C22×D411yescharacteristic
137Dic151—22no—
138Dic151—41no—
139C2×C151—22no—
140C2×C151C2×#12011yescharacteristic
141C2×C151#57512yes—
142D151—42no—
143D151—44no—
144D151—81no—
145C151#300511yescharacteristic, complemented, Sylow
146#3005—1511nomaximal, Sylow
147C22×#41—1511no—
148C2×#137—1511no—
149C2×AGL(1,ℤ/8)—1511no—
150#525—1511no—
151#452—1514no—
152#449—1514no—
153#419D15111yescharacteristic, complemented
154#418—1511no—
155#407—1511no—
156C2×#41—3024no—
157C2×#41—3024no—
158C2×#41—3022no—
159C2×#41—1514no—
160C2×#41—1511no—
161C22×Q8C2×D15111yescharacteristic
162C22×D4—3021no—
163C22×D4—1511no—
164C23×C4—3021no—
165C23×C4—1511no—
166#137—3024no—
167AGL(1,ℤ/8)—3024no—
168C2×Q16—1512no—
169C2×SD16—1512no—
170C2×SD16—1512no—
171C2×D8—1512no—
172C2×M16—1511no—
173C2×M16C2×D15111yescharacteristic
174#123—3021no—
175C22⋊Q8—1512no—
176#121—1512no—
177#120—3021no—
178C4×D4—3022no—
179#117C2×D15111yescharacteristic
180#103C2×D15114yescomplemented
181#102—1514no—
182C22⋊C8—1514no—
183C24—3021no—
184C24—1511no—
185#41—30216no—
186#41—3028no—
187#41—3028no—
188#41—3022no—
189#41—3022no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—1511no—
193C2×Q8D60414yescomplemented
194C2×Q8C22×D15112yes—
195C2×D4—3028no—
196C2×D4—3024no—
197C2×D4—3022no—
198C2×D4—3021no—
199C2×D4—3021no—
200C2×D4—3022no—
201C2×D4—1514no—
202C2×D4—1511no—
203C2×D4—1512no—
204C22×C4—21no—
205C22×C4—3028no—
206C22×C4—3024no—
207C22×C4—3022no—
208C22×C4—3022no—
209C22×C4—3021no—
210C22×C4—1511no—
211C22×C4—1512no—
212C22×C4—1512no—
213C22×C4C22×D15111yescharacteristic
214Q16—3024no—
215SD16—3024no—
216SD16—3024no—
217D8—3024no—
218M16—22no—
219M16—3022no—
220C2×C8—1512no—
221C2×C8C22×D15112yes—
222C4⋊C4—3022no—
223C4⋊C4C22×D15112yes—
224C22⋊C4—21no—
225C22⋊C4—3022no—
226C22⋊C4—3022no—
227C42—21no—
228C23—3022no—
229C23—3024no—
230C23—3022no—
231C23—3021no—
232C23—6042no—
233C23—6044no—
234C23—1512no—
235C23D4×D15111yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—3021no—
239Q8—3021no—
240Q8C2×D60414yes—
241D4—30216no—
242D4—3024no—
243D4—3021no—
244D4—3022no—
245D4—3021no—
246D4—6044no—
247D4—6042no—
248D4—1514no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—30216no—
253C2×C4—3022no—
254C2×C4—3024no—
255C2×C4—3022no—
256C2×C4—3022no—
257C2×C4—3021no—
258C2×C4—6042no—
259C2×C4—1512no—
260C2×C4D4×D15111yescharacteristic
261C2×C4D4×D15112yes—
262C2×C4C2×D60412yes—
263C2×C4C23×D15111yescharacteristic
264C8—22no—
265C8—3022no—
266C22—22no—
267C22—3022no—
268C22—3022no—
269C22—3022no—
270C22—3024no—
271C22—6044no—
272C22—6048no—
273C22—6044no—
274C22—6042no—
275C22—6041no—
276C22#1801270912yes—
277C22C2×D4×D15111yescharacteristic
278C4—24no—
279C4—42no—
280C4—3022no—
281C4—6041no—
282C4#1801270912yes—
283C4C2×D4×D15111yescharacteristic
284C4C22×D60411yescharacteristic
285C2—22no—
286C2—6042no—
287C2—6044no—
288C2—12081no—
289C2C2×#1801270911yescharacteristic
290C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#419×C151C2
socleC22×C151C22×D4
hypercenter#419D151
hypocenterC151#3005
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#14559005C2semidirect
2. C2×#18012770C2semidirect
3. C2×#18012767C2semidirect
4. #23752724C2semidirect
5. #23752377C2semidirect
6. #23752360C2semidirect
7. #23752216C2semidirect
8. #23752175C2semidirect
9. #419×C151C2semidirect
21. C2×#14558994C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558991C22semidirect
24. C2×D1208C22semidirect
27. #18012719C22semidirect
28. #18012714C22semidirect
31. #18012659C22semidirect
32. (C2×D151)⋊C8C22semidirect
36. #103×C151C22semidirect
50. C2×D604D4semidirect
73. C2×Q8×C151D4semidirect
145. C151#3005semidirect
153. #419D151semidirect
180. #103C2×D151semidirect
193. C2×Q8D604semidirect

Maximal subgroups

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

subgroupindex
C22×#145590052
C2×#180127702
C2×#180127672
#237527242
#237523772
#237523602
#237522162
#237521752
#419×C1512
#3005151