Finite Group Databasebeta

← #34078355

Subgroups — #34078355

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×#14559004C211yesmaximal, characteristic, complemented
2C2×#18012772C211yesmaximal, characteristic, complemented
3C2×#18012767C211yesmaximal, characteristic, complemented
4#23752723C211yesmaximal, characteristic, complemented
5#23752376C214yesmaximal, complemented
6#23752359C214yesmaximal, complemented
7#23752222C211yesmaximal, characteristic, complemented
8#23752218C211yesmaximal, characteristic, complemented
9#407×C151C211yesmaximal, characteristic, complemented
10C2×#14559004—22no—
11C2×#14559004—24no—
12C2×#14559004—24no—
13C2×#14559004C2211yescharacteristic
14C2×#14559004C2214yes—
15C22×Dic302C2211yescharacteristic
16C22×D604C2211yescharacteristic
17C22×C22⋊D151—21no—
18C22×C4×D151—21no—
19#18012772—24no—
20#18012767—24no—
21C2×Dic604C2212yescomplemented
22C2×#14558993C2212yescomplemented
23C2×#14558993C2212yescomplemented
24C2×D1208C2212yescomplemented
25#18012722—21no—
26#18012718C2212yescomplemented
27#18012713C2212yescomplemented
28#18012708—21no—
29C4×C22⋊D151—22no—
30#18012698C2211yescharacteristic
31#18012664C2214yescomplemented
32#18012661C2214yescomplemented
33C23×C4×C151C2211yescharacteristic
34C2×M16×C151C2211yescharacteristic
35C2×M16×C151C2211yescharacteristic
36C22⋊C8×C151C2214yescomplemented
37C23×D151—21no—
38#14559004—216no—
39#14559004—28no—
40#14559004—28no—
41#14559004—22no—
42#14559004—22no—
43C2×Dic302—22no—
44C2×Dic302—21no—
45C2×Dic302D414yescomplemented
46C2×Dic302C2311yescharacteristic
47C2×Dic302C2312yes—
48C2×D604—22no—
49C2×D604—21no—
50C2×D604D414yescomplemented
51C2×D604C2311yescharacteristic
52C2×D604C2312yes—
53C2×C22⋊D151—28no—
54C2×C22⋊D151—24no—
55C2×C22⋊D151—22no—
56C2×C22⋊D151—21no—
57C22×Dic151—21no—
58C2×C4×D151—28no—
59C2×C4×D151—24no—
60C2×C4×D151—21no—
61Dic604—24no—
62#14558993—24no—
63#14558993—24no—
64D1208—24no—
65C4⋊Dic151C2312yes—
66Dic151⋊C4—22no—
67C22⋊Dic151—21no—
68C22⋊Dic151—22no—
69(C2×D151)⋊C4—22no—
70C4×Dic151—21no—
71C24×C151D411yescharacteristic
72C22×C4×C151—22no—
73C22×C4×C151—22no—
74C22×C4×C151D412yes—
75C22×C4×C151D411yescharacteristic
76C22×C4×C151C2312yes—
77C22×C4×C151C2311yescharacteristic
78M16×C151—22no—
79M16×C151—22no—
80C2×C8×C151C2312yes—
81C2×C8×C151C2312yes—
82C22×D151—24no—
83C22×D151—22no—
84C22×D151—21no—
85C22×D151—44no—
86Dic302—24no—
87Dic302—22no—
88Dic302—21no—
89Dic302—21no—
90Dic302C2×D414yes—
91D604—24no—
92D604—22no—
93D604—21no—
94D604—21no—
95D604C2×D414yes—
96C22⋊D151—216no—
97C22⋊D151—44no—
98C22⋊D151—42no—
99C2×Dic151—24no—
100C2×Dic151—22no—
101C2×Dic151—22no—
102C2×Dic151—21no—
103C4×D151—216no—
104C4×D151—42no—
105C23×C151—22no—
106C23×C151—42no—
107C23×C151C2×D412yes—
108C23×C151C2×D411yescharacteristic
109C2×C4×C151—22no—
110C2×C4×C151—24no—
111C2×C4×C151—22no—
112C2×C4×C151—22no—
113C2×C4×C151C2×D412yes—
114C2×C4×C151C2×D412yes—
115C2×C4×C151C2×D412yes—
116C2×C4×C151C2×D411yescharacteristic
117C2×C4×C151C2411yescharacteristic
118C8×C151—22no—
119C8×C151—22no—
120C22×C151—22no—
121C22×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—44no—
125C22×C151#12012yes—
126C22×C151C22×D411yescharacteristic
127C2×D151—24no—
128C2×D151—48no—
129C2×D151—44no—
130C2×D151—41no—
131C2×D151—42no—
132C4×C151—22no—
133C4×C151#12012yes—
134C4×C151C22×D411yescharacteristic
135C4×C151C22×D411yescharacteristic
136Dic151—24no—
137Dic151—41no—
138Dic151—42no—
139C2×C151—22no—
140C2×C151—42no—
141C2×C151C2×#12011yescharacteristic
142C2×C151#57512yes—
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#419—1511no—
154#418—1511no—
155#407D15111yescharacteristic, complemented
156C2×#41—3024no—
157C2×#41—3024no—
158C2×#41—3022no—
159C2×#41—1511no—
160C2×#41—1514no—
161C22×Q8—1511no—
162C22×D4—3021no—
163C22×D4—1511no—
164C23×C4—3021no—
165C23×C4C2×D15111yescharacteristic
166#137—3024no—
167AGL(1,ℤ/8)—3024no—
168C2×Q16—1512no—
169C2×SD16—1512no—
170C2×SD16—1512no—
171C2×D8—1512no—
172C2×M16C2×D15111yescharacteristic
173C2×M16C2×D15111yescharacteristic
174#123—3021no—
175C22⋊Q8—1512no—
176#121—1512no—
177#120—3021no—
178C4×D4—3022no—
179#117—1511no—
180#103—1514no—
181#102—1514no—
182C22⋊C8C2×D15114yescomplemented
183C24—3021no—
184C24D60411yescharacteristic
185#41—30216no—
186#41—3028no—
187#41—3028no—
188#41—3022no—
189#41—3022no—
190C2×Q8—3022no—
191C2×Q8—3021no—
192C2×Q8—1514no—
193C2×Q8—1511no—
194C2×Q8—1512no—
195C2×D4—3028no—
196C2×D4—3024no—
197C2×D4—3022no—
198C2×D4—3021no—
199C2×D4—3022no—
200C2×D4—3021no—
201C2×D4—1514no—
202C2×D4—1511no—
203C2×D4—1512no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—3028no—
207C22×C4—3021no—
208C22×C4—3024no—
209C22×C4—3021no—
210C22×C4D60412yes—
211C22×C4D60411yescharacteristic
212C22×C4C22×D15112yes—
213C22×C4C22×D15111yescharacteristic
214Q16—3024no—
215SD16—3024no—
216SD16—3024no—
217D8—3024no—
218M16—22no—
219M16—22no—
220C2×C8C22×D15112yes—
221C2×C8C22×D15112yes—
222C4⋊C4—3022no—
223C4⋊C4—1512no—
224C22⋊C4—3021no—
225C22⋊C4—3022no—
226C22⋊C4—3022no—
227C42—3021no—
228C23—22no—
229C23—42no—
230C23—3024no—
231C23—3022no—
232C23—3021no—
233C23—6044no—
234C23C2×D60412yes—
235C23C2×D60411yescharacteristic
236Q8—3024no—
237Q8—3022no—
238Q8—3021no—
239Q8—3021no—
240Q8—1514no—
241D4—30216no—
242D4—3024no—
243D4—3022no—
244D4—3021no—
245D4—3021no—
246D4—6044no—
247D4—6042no—
248D4—1514no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—30216no—
254C2×C4—3024no—
255C2×C4—3022no—
256C2×C4—3022no—
257C2×C4—3021no—
258C2×C4—6042no—
259C2×C4D4×D15112yes—
260C2×C4D4×D15112yes—
261C2×C4C2×D60412yes—
262C2×C4C2×D60411yescharacteristic
263C2×C4C23×D15111yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—3024no—
272C22—6048no—
273C22—6044no—
274C22—6042no—
275C22—6041no—
276C22#1801270912yes—
277C22C22×D60411yescharacteristic
278C4—22no—
279C4—3024no—
280C4—6042no—
281C4—6041no—
282C4#1801270912yes—
283C4C2×D4×D15111yescharacteristic
284C4C2×D4×D15111yescharacteristic
285C2—22no—
286C2—42no—
287C2—6044no—
288C2—12081no—
289C2C2×#1801270911yescharacteristic
290C2#2375301212yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#407×C151C2
socleC22×C151C22×D4
hypercenter#407D151
hypocenterC151#3005
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#14559004C2semidirect
2. C2×#18012772C2semidirect
3. C2×#18012767C2semidirect
4. #23752723C2semidirect
5. #23752376C2semidirect
6. #23752359C2semidirect
7. #23752222C2semidirect
8. #23752218C2semidirect
9. #407×C151C2semidirect
21. C2×Dic604C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558993C22semidirect
24. C2×D1208C22semidirect
26. #18012718C22semidirect
27. #18012713C22semidirect
31. #18012664C22semidirect
32. #18012661C22semidirect
36. C22⋊C8×C151C22semidirect
45. C2×Dic302D4semidirect
50. C2×D604D4semidirect
145. C151#3005semidirect
155. #407D151semidirect
182. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
C22×#145590042
C2×#180127722
C2×#180127672
#237527232
#237523762
#237523592
#237522222
#237522182
#407×C1512
#3005151