Finite Group Databasebeta

← #34111748

Subgroups — #34111748

Order 20096.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19097799C212yesmaximal, complemented
2#23757919C212yesmaximal, complemented
3#23757657C211yesmaximal, characteristic, complemented
4#23757519C212yesmaximal, complemented
5#23757489C212yesmaximal, complemented
6#23757437C212yesmaximal, complemented
7#23757409C212yesmaximal, complemented
8C4×D1256C211yesmaximal, characteristic, complemented
9#436×C157C211yesmaximal, characteristic, complemented
10C2×#14578954C2212yes—
11C22×D628C2212yescomplemented
12#19097799—28no—
13C2×Dic628C2211yescharacteristic, complemented
14C2×#14578943C2212yescomplemented
15C2×#14578943C2212yescomplemented
16C2×D1256C2212yes—
17C2×D1256C2211yescharacteristic
18C2×D1256C2211yescharacteristic
19#19097759C2212yescomplemented
20#19097756—22no—
21#19097750C2212yescomplemented
22#19097745C2212yes—
23#19097744—22no—
24#19097739—22no—
25C4×D628C2212yescomplemented
26C22⋊C4×D157—22no—
27#19097705C2211yescharacteristic, complemented
28#19097696C2212yescomplemented
29#19097693C2212yescomplemented
30#19097693C2212yescomplemented
31C2×M16×C157C2212yescomplemented
32C4×D4×C157C2211yescharacteristic
33C4⋊C8×C157C2211yescharacteristic, complemented
34C22⋊C8×C157C2212yescomplemented
35C4×C8×C157C2211yescharacteristic, complemented
36C23×D157—22no—
37#14578954—24no—
38#14578954—42no—
39C2×Dic314C2312yes—
40C2×D628—24no—
41C2×D628—22no—
42C2×D628—42no—
43C2×D628C2312yes—
44C2×D628C2312yes—
45C2×C22⋊D157—22no—
46C2×C22⋊D157—22no—
47C2×C4×D157—22no—
48C2×C4×D157—22no—
49Dic628—41no—
50#14578943—24no—
51#14578943—24no—
52D1256—24no—
53D1256—41no—
54D1256D414yescomplemented
55C4⋊Dic157C2312yes—
56#14578933—22no—
57C22⋊Dic157—22no—
58#14578931—22no—
59#14578931—22no—
60#14578931—22no—
61#14578931—22no—
62C2×D4×C157D411yescharacteristic
63C22×C4×C157C2312yes—
64M16×C157—24no—
65C2×C8×C157C2311yescharacteristic
66C2×C8×C157C2312yes—
67C2×C8×C157C2311yescharacteristic
68C4⋊C4×C157D411yescharacteristic
69C22⋊C4×C157D412yes—
70C42×C157C2311yescharacteristic
71C22×D157—22no—
72C22×D157—22no—
73C22×D157—44no—
74C22×D157—44no—
75C22×D157—82no—
76Dic314—22no—
77Dic314—22no—
78D628—22no—
79D628—22no—
80D628—22no—
81D628—44no—
82D628C2×D414yes—
83C22⋊D157—44no—
84C22⋊D157—82no—
85C2×Dic157—22no—
86C2×Dic157—22no—
87C4×D157—44no—
88C4×D157—82no—
89C23×C157C2×D412yes—
90D4×C157—41no—
91C2×C4×C157—22no—
92C2×C4×C157—22no—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2×D412yes—
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2411yescharacteristic
97C8×C157—22no—
98C8×C157—21no—
99C8×C157C2×D412yes—
100C22×C157—22no—
101C22×C157—22no—
102C22×C157—22no—
103C22×C157C22×D411yescharacteristic
104C2×D157—24no—
105C2×D157—42no—
106C2×D157—42no—
107C2×D157—42no—
108C2×D157—42no—
109C2×D157—42no—
110C2×D157—88no—
111C4×C157—22no—
112C4×C157—21no—
113C4×C157—21no—
114C4×C157C22×D411yescharacteristic
115C4×C157H(5,𝔽2)11yescharacteristic
116Dic157—42no—
117Dic157—42no—
118C2×C157—42no—
119C2×C157D4211yescharacteristic
120C2×C157#57511yescharacteristic
121C2×C157#57611yescharacteristic
122D157—44no—
123D157—82no—
124C157#327311yescharacteristic, complemented, Sylow
125#3273—1571nomaximal, Sylow
126C2×AGL(1,ℤ/8)—1572no—
127#546—1572no—
128#495—1571no—
129#468—1572no—
130#463—1572no—
131#452—1572no—
132#447—1572no—
133C4×D8—1571no—
134#436D15711yescharacteristic, complemented
135C2×#41—1572no—
136C22×D4—1572no—
137AGL(1,ℤ/8)—3148no—
138C2×Q16—1571no—
139C2×SD16—1572no—
140C2×SD16—1572no—
141C2×D8—1572no—
142C2×D8—1571no—
143C2×D8—1571no—
144C2×M16C2×D15712yescomplemented
145#124—1572no—
146#123—3142no—
147C22⋊Q8—1572no—
148#121—3142no—
149#121—1572no—
150#120—3142no—
151C4×D4—1572no—
152C4×D4C2×D15711yescharacteristic
153C2×C22⋊C4—3142no—
154#107—1571no—
155C4⋊C8C2×D15711yescharacteristic, complemented
156#103—1572no—
157#102—1572no—
158#102—1572no—
159C22⋊C8C2×D15712yescomplemented
160C4×C8C2×D15711yescharacteristic, complemented
161C24—3142no—
162#41—3144no—
163#41—6282no—
164C2×Q8—1572no—
165C2×D4—3144no—
166C2×D4—3142no—
167C2×D4—3142no—
168C2×D4—3142no—
169C2×D4—6282no—
170C2×D4—1572no—
171C2×D4—1572no—
172C2×D4D62811yescharacteristic
173C22×C4—3142no—
174C22×C4—3142no—
175C22×C4C22×D15712yes—
176Q16—6281no—
177SD16—3144no—
178SD16—3144no—
179D8—3144no—
180D8—6281no—
181D8—1574no—
182M16—24no—
183C2×C8C22×D15711yescharacteristic
184C2×C8C22×D15712yes—
185C2×C8C22×D15711yescharacteristic
186C4⋊C4—3142no—
187C4⋊C4—1572no—
188C4⋊C4D62811yescharacteristic
189C22⋊C4—3142no—
190C22⋊C4—3142no—
191C22⋊C4—3142no—
192C22⋊C4—3142no—
193C22⋊C4—3142no—
194C22⋊C4D62812yes—
195C42C22×D15711yescharacteristic
196C23—3142no—
197C23—3142no—
198C23—6284no—
199C23—6284no—
200C23—12562no—
201C23C2×D62812yes—
202Q8—3142no—
203Q8—3142no—
204D4—41no—
205D4—3142no—
206D4—3142no—
207D4—3142no—
208D4—6284no—
209D4—6284no—
210D4—1574no—
211D4—12562no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—3142no—
215C2×C4—3142no—
216C2×C4—6284no—
217C2×C4—12562no—
218C2×C4C2×D62811yescharacteristic
219C2×C4C2×D62811yescharacteristic
220C2×C4C2×D62812yes—
221C2×C4C23×D15711yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D15712yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—3144no—
229C22—6282no—
230C22—6282no—
231C22—6282no—
232C22—6282no—
233C22—6282no—
234C22—12568no—
235C22C22×D62811yescharacteristic
236C4—22no—
237C4—21no—
238C4—21no—
239C4—6282no—
240C4—6282no—
241C4C2×D4×D15711yescharacteristic
242C4#1909781711yescharacteristic
243C2—42no—
244C2—6284no—
245C2—12562no—
246C2D4×D62811yescharacteristic
247C2#2375807311yescharacteristic
248C2#2375807811yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#436×C157C2
socleC22×C157C22×D4
hypercenter#436D157
hypocenterC157#3273
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#19097799C2semidirect
2. #23757919C2semidirect
3. #23757657C2semidirect
4. #23757519C2semidirect
5. #23757489C2semidirect
6. #23757437C2semidirect
7. #23757409C2semidirect
8. C4×D1256C2semidirect
9. #436×C157C2semidirect
11. C22×D628C22semidirect
13. C2×Dic628C22semidirect
14. C2×#14578943C22semidirect
15. C2×#14578943C22semidirect
19. #19097759C22semidirect
21. #19097750C22semidirect
25. C4×D628C22semidirect
27. #19097705C22semidirect
28. #19097696C22semidirect
29. #19097693C22semidirect
30. #19097693C22semidirect
31. C2×M16×C157C22semidirect
33. C4⋊C8×C157C22semidirect
34. C22⋊C8×C157C22semidirect
35. C4×C8×C157C22semidirect
54. D1256D4semidirect
124. C157#3273semidirect
134. #436D157semidirect
144. C2×M16C2×D157semidirect
155. C4⋊C8C2×D157semidirect
159. C22⋊C8C2×D157semidirect
160. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977992
#237579192
#237576572
#237575192
#237574892
#237574372
#237574092
C4×D12562
#436×C1572
#3273157