Finite Group Databasebeta

← #34080904

Subgroups — #34080904

Order 19328.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#23753024C212yesmaximal, complemented
2#23753019C212yesmaximal, complemented
3#23752585C211yesmaximal, characteristic, complemented
4#23752476C212yesmaximal, complemented
5#23752475C212yesmaximal, complemented
6#23752396C212yesmaximal, complemented
7#23752381C212yesmaximal, complemented
8#23752330C211yesmaximal, characteristic, complemented
9#443×C151C211yesmaximal, characteristic, complemented
10#18012786C2212yes—
11#18012785C2212yescomplemented
12#18012772—22no—
13#18012772C2212yescomplemented
14#18012771—22no—
15#18012769C2212yescomplemented
16#18012767—22no—
17#18012767C2212yes—
18#18012764C2212yes—
19#18012763—22no—
20#18012761—22no—
21#18012761C2211yescharacteristic
22#18012760—22no—
23C2×#14558993—22no—
24C2×#14558993C2212yescomplemented
25C2×#14558993C2212yescomplemented
26SD16×D151—22no—
27#18012745C2212yescomplemented
28#18012739C2211yescharacteristic, complemented
29#18012736C2211yescharacteristic
30#18012675C2211yescharacteristic, complemented
31#18012667C2212yescomplemented
32#18012657C2212yescomplemented
33#18012655C2212yescomplemented
34#135×C151C2211yescharacteristic
35#131×C151C2212yescomplemented
36#108×C151C2211yescharacteristic, complemented
37#104×C151C2212yescomplemented
38C4×C8×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559004—22no—
41#14559004—22no—
42#14559004C2312yes—
43#14559003—22no—
44#14559003—42no—
45C2×Dic302—22no—
46C2×Dic302C2312yes—
47Q8×D151—22no—
48C2×D604—22no—
49C2×D604—41no—
50C2×D604C2312yes—
51D4×D151—22no—
52D4×D151—42no—
53Dic604—22no—
54Dic604D411yescharacteristic, complemented
55#14558994—22no—
56#14558993—22no—
57#14558993—22no—
58#14558993—22no—
59#14558993—22no—
60#14558993—22no—
61#14558993—22no—
62#14558993D412yescomplemented
63#14558992—22no—
64#14558991—22no—
65D1208—22no—
66D1208D411yescharacteristic, complemented
67#14558989—22no—
68#14558988C2312yes—
69#14558987—22no—
70C8×D151—22no—
71C4⋊Dic151—41no—
72#41×C151C2312yes—
73Q16×C151D411yescharacteristic, complemented
74SD16×C151D412yescomplemented
75D8×C151D411yescharacteristic, complemented
76M16×C151—22no—
77M16×C151C2312yes—
78C2×C8×C151—22no—
79C2×C8×C151C2311yescharacteristic
80C2×C8×C151C2311yescharacteristic
81C42×C151C2311yescharacteristic
82C22×D151—22no—
83C22×D151—42no—
84Dic302—22no—
85Dic302—22no—
86Dic302—42no—
87Dic302C2×D412yes—
88D604—22no—
89D604—22no—
90D604—42no—
91D604—82no—
92D604C2×D412yes—
93C22⋊D151—22no—
94C22⋊D151—42no—
95C22⋊D151—42no—
96C2×Dic151—22no—
97C2×Dic151—42no—
98C4×D151—22no—
99C4×D151—42no—
100C4×D151—42no—
101C151⋊C8—22no—
102Q8×C151C2×D412yes—
103D4×C151—22no—
104D4×C151C2×D412yes—
105C2×C4×C151—21no—
106C2×C4×C151—22no—
107C2×C4×C151C2411yescharacteristic
108C8×C151—22no—
109C8×C151C2×D411yescharacteristic
110C8×C151C2×D411yescharacteristic
111C8×C151C2×D411yescharacteristic
112C8×C151C2×D411yescharacteristic
113C22×C151—22no—
114C22×C151H(5,𝔽2)11yescharacteristic
115C2×D151—22no—
116C2×D151—42no—
117C2×D151—82no—
118C2×D151—162no—
119C4×C151—22no—
120C4×C151—22no—
121C4×C151C22×D411yescharacteristic
122C4×C151C22×D411yescharacteristic
123Dic151—22no—
124Dic151—42no—
125C2×C151—21no—
126C2×C151—42no—
127C2×C151D4211yescharacteristic
128D151—42no—
129D151—82no—
130C151#329111yescharacteristic, complemented, Sylow
131#3291—1511nomaximal, Sylow
132#577—1512no—
133#577—1512no—
134#492—1511no—
135#471—1512no—
136#471—1512no—
137#456—1512no—
138#453—1512no—
139#443—1511no—
140#443D15111yescharacteristic, complemented
1412−1+4—1512no—
142H(5,𝔽2)—1512no—
143#137—3022no—
144#137—3022no—
145#137—1512no—
146#137—1512no—
147AGL(1,ℤ/8)—3022no—
148AGL(1,ℤ/8)—3022no—
149AGL(1,ℤ/8)—1512no—
150AGL(1,ℤ/8)—1512no—
151#135—3022no—
152#135—3022no—
153#135—1511no—
154#135C2×D15111yescharacteristic
155C2×SD16—3022no—
156C2×SD16—3022no—
157C2×SD16—1512no—
158C2×SD16—1512no—
159#131—1512no—
160#131C2×D15112yescomplemented
161C4⋊Q8—1511no—
162#127—1511no—
163#108—1511no—
164#108C2×D15111yescharacteristic, complemented
165#104—1512no—
166#104C2×D15112yescomplemented
167#101—1512no—
168#100—1512no—
169C4×C8C2×D15111yescharacteristic, complemented
170#41—3022no—
171#41—3022no—
172#41—3022no—
173#41—3022no—
174#41—6042no—
175#41—1512no—
176#41C22×D15112yes—
177C2×Q8—3022no—
178C2×Q8—3022no—
179C2×Q8—1512no—
180C2×D4—3022no—
181C2×D4—3022no—
182C2×D4—6041no—
183C2×D4—6042no—
184C2×D4—1512no—
185Q16—3022no—
186Q16—3022no—
187Q16—1511no—
188Q16D60411yescharacteristic, complemented
189SD16—3022no—
190SD16—3022no—
191SD16—3022no—
192SD16—3022no—
193SD16—3022no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—1512no—
198SD16D60412yescomplemented
199D8—3022no—
200D8—3022no—
201D8—1511no—
202D8D60411yescharacteristic, complemented
203M16—22no—
204M16—3022no—
205M16—1512no—
206M16C22×D15112yes—
207C2×C8—22no—
208C2×C8—3022no—
209C2×C8C22×D15111yescharacteristic
210C2×C8C22×D15111yescharacteristic
211C4⋊C4—6041no—
212C42C22×D15111yescharacteristic
213C23—3022no—
214C23—6042no—
215Q8—3022no—
216Q8—3022no—
217Q8—6042no—
218Q8—1512no—
219Q8C2×D60412yes—
220D4—22no—
221D4—3022no—
222D4—3022no—
223D4—3022no—
224D4—6042no—
225D4—6042no—
226D4—6042no—
227D4—1512no—
228D4—12082no—
229D4C2×D60412yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—6042no—
235C2×C4—6042no—
236C2×C4—6042no—
237C2×C4C23×D15111yescharacteristic
238C8—22no—
239C8—3022no—
240C8D4×D15111yescharacteristic
241C8D4×D15111yescharacteristic
242C8C2×D60411yescharacteristic
243C8C2×D60411yescharacteristic
244C22—22no—
245C22—3022no—
246C22—6042no—
247C22—24162no—
248C22—12082no—
249C22#1801278511yescharacteristic
250C4—22no—
251C4—22no—
252C4—3022no—
253C4—6042no—
254C4C2×D4×D15111yescharacteristic
255C4C22×D60411yescharacteristic
256C2—21no—
257C2—42no—
258C2—6042no—
259C2—12082no—
260C2D4×D60411yescharacteristic
subgroupG/H
centerC2D4×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#443×C151C2
socleC2×C151D42
hypercenter#443D151
hypocenterC151#3291
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #23753024C2semidirect
2. #23753019C2semidirect
3. #23752585C2semidirect
4. #23752476C2semidirect
5. #23752475C2semidirect
6. #23752396C2semidirect
7. #23752381C2semidirect
8. #23752330C2semidirect
9. #443×C151C2semidirect
11. #18012785C22semidirect
13. #18012772C22semidirect
15. #18012769C22semidirect
24. C2×#14558993C22semidirect
25. C2×#14558993C22semidirect
27. #18012745C22semidirect
28. #18012739C22semidirect
30. #18012675C22semidirect
31. #18012667C22semidirect
32. #18012657C22semidirect
33. #18012655C22semidirect
35. #131×C151C22semidirect
36. #108×C151C22semidirect
37. #104×C151C22semidirect
38. C4×C8×C151C22semidirect
54. Dic604D4semidirect
62. #14558993D4semidirect
66. D1208D4semidirect
73. Q16×C151D4semidirect
74. SD16×C151D4semidirect
75. D8×C151D4semidirect
130. C151#3291semidirect
140. #443D151semidirect
160. #131C2×D151semidirect
164. #108C2×D151semidirect
166. #104C2×D151semidirect
169. C4×C8C2×D151semidirect
188. Q16D604semidirect
198. SD16D604semidirect
202. D8D604semidirect

Maximal subgroups

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

subgroupindex
#237530242
#237530192
#237525852
#237524762
#237524752
#237523962
#237523812
#237523302
#443×C1512
#3291151