Finite Group Databasebeta

← #34111745

Subgroups — #34111745

Order 20096.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#19097798C212yesmaximal, complemented
2#23757916C212yesmaximal, complemented
3#23757516C212yesmaximal, complemented
4#23757485C212yesmaximal, complemented
5#23757434C212yesmaximal, complemented
6#23757405C212yesmaximal, complemented
7C4×D1256C211yesmaximal, characteristic, complemented
8#23757352C211yesmaximal, characteristic, complemented
9#495×C157C211yesmaximal, characteristic, complemented
10C2×#14578955C2212yes—
11C2×D4×D157C2212yescomplemented
12#19097798—28no—
13C2×#14578941C2212yescomplemented
14C2×D1256C2211yescharacteristic
15C2×#14578939C2212yes—
16C2×#14578937C2212yescomplemented
17#19097753—22no—
18#19097747C2212yescomplemented
19#19097744—22no—
20#19097742C2212yes—
21#19097741—22no—
22C4×D628C2211yescharacteristic
23C4×D628C2212yescomplemented
24C22⋊C4×D157—22no—
25#19097705C2211yescharacteristic, complemented
26C4⋊#11929434C2211yescharacteristic, complemented
27#19097695C2212yescomplemented
28#19097693C2212yescomplemented
29#19097692C2212yescomplemented
30#19097683C2212yescomplemented
31C2×Q16×C157C2211yescharacteristic, complemented
32C2×SD16×C157C2212yescomplemented
33C2×D8×C157C2211yescharacteristic
34#124×C157C2212yescomplemented
35C4×C8×C157C2211yescharacteristic, complemented
36C23×D157—22no—
37#14578955—24no—
38#14578955—42no—
39C2×D628—22no—
40C2×D628D411yescharacteristic
41C2×D628C2312yes—
42C2×C22⋊D157—22no—
43C2×C22⋊D157—22no—
44D4×D157—24no—
45D4×D157—42no—
46C2×C4×D157—22no—
47C2×C4×D157—22no—
48C2×C4×D157C2312yes—
49#14578941—24no—
50D1256D414yescomplemented
51#14578939—24no—
52#14578937—24no—
53C2×#11929434C2312yes—
54C4⋊Dic157D411yescharacteristic
55C4⋊Dic157C2312yes—
56#14578933—22no—
57C22⋊Dic157—22no—
58#14578931—22no—
59#14578931—22no—
60#14578931D412yes—
61C2×Q8×C157C2312yes—
62C2×D4×C157C2312yes—
63Q16×C157—41no—
64SD16×C157—24no—
65D8×C157—41no—
66C2×C8×C157C2311yescharacteristic
67C2×C8×C157C2311yescharacteristic
68C22⋊C4×C157—22no—
69C22⋊C4×C157—22no—
70C42×C157C2311yescharacteristic
71C22×D157—22no—
72C22×D157—44no—
73C22×D157—44no—
74C22×D157—82no—
75C22×D157C2×D412yes—
76D628—22no—
77D628—41no—
78D628—44no—
79D628C2×D414yes—
80C22⋊D157—44no—
81C22⋊D157—82no—
82C2×Dic157—22no—
83C2×Dic157C2×D412yes—
84C4×D157—22no—
85C4×D157—22no—
86C4×D157—44no—
87C4×D157—82no—
88#11929434—22no—
89C23×C157—22no—
90Q8×C157—22no—
91Q8×C157—22no—
92D4×C157—22no—
93D4×C157—22no—
94C2×C4×C157—22no—
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157C2411yescharacteristic
98C8×C157—21no—
99C8×C157C2×D412yes—
100C22×C157—42no—
101C22×C157—42no—
102C22×C157—42no—
103C22×C157C22×D411yescharacteristic
104C2×D157—22no—
105C2×D157—24no—
106C2×D157—22no—
107C2×D157—22no—
108C2×D157—42no—
109C2×D157—42no—
110C2×D157—88no—
111C4×C157—21no—
112C4×C157—21no—
113C4×C157—42no—
114C4×C157C22×D411yescharacteristic
115C4×C157H(5,𝔽2)11yescharacteristic
116Dic157—22no—
117Dic157—42no—
118C2×C157—82no—
119C2×C157D4211yescharacteristic
120C2×C157#57511yescharacteristic
121C2×C157#57611yescharacteristic
122D157—42no—
123D157—44no—
124C157#327311yescharacteristic, complemented, Sylow
125#3273—1571nomaximal, Sylow
126C2×AGL(1,ℤ/8)—1572no—
127#546—1572no—
128#495D15711yescharacteristic, complemented
129#468—1572no—
130#463—1572no—
131#452—1572no—
132#447—1572no—
133C4×D8—1571no—
134#436—1571no—
135C2×#41—1572no—
136C22×D4—1572no—
137AGL(1,ℤ/8)—3148no—
138C2×Q16C2×D15711yescharacteristic, complemented
139C2×SD16—1572no—
140C2×SD16C2×D15712yescomplemented
141C2×D8—1572no—
142C2×D8—1571no—
143C2×D8C2×D15711yescharacteristic
144C2×M16—1572no—
145#124C2×D15712yescomplemented
146#123—3142no—
147C22⋊Q8—1572no—
148#121—3142no—
149#121—1572no—
150#120—3142no—
151C4×D4—1572no—
152C4×D4—1571no—
153C2×C22⋊C4—3142no—
154#107—1571no—
155C4⋊C8—1571no—
156#103—1572no—
157#102—1572no—
158#102—1572no—
159C22⋊C8—1572no—
160C4×C8C2×D15711yescharacteristic, complemented
161C24—3142no—
162#41—3144no—
163#41—6282no—
164C2×Q8C22×D15712yes—
165C2×D4—3142no—
166C2×D4—3144no—
167C2×D4—3142no—
168C2×D4—3142no—
169C2×D4—6282no—
170C2×D4—1571no—
171C2×D4—1572no—
172C2×D4C22×D15712yes—
173C22×C4—3142no—
174C22×C4—3142no—
175C22×C4—1572no—
176Q16—41no—
177SD16—24no—
178SD16—3144no—
179D8—41no—
180D8—3144no—
181D8—1574no—
182M16—3144no—
183C2×C8—1572no—
184C2×C8C22×D15711yescharacteristic
185C2×C8C22×D15711yescharacteristic
186C4⋊C4—3142no—
187C4⋊C4—1572no—
188C4⋊C4—1571no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—3142no—
192C22⋊C4—3142no—
193C22⋊C4—3142no—
194C22⋊C4—1572no—
195C42C22×D15711yescharacteristic
196C23—22no—
197C23—3142no—
198C23—6284no—
199C23—6284no—
200C23—1572no—
201C23—12562no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—3142no—
207D4—6281no—
208D4—6284no—
209D4—6284no—
210D4—1574no—
211D4—12562no—
212C2×C4—22no—
213C2×C4—3142no—
214C2×C4—3142no—
215C2×C4—3142no—
216C2×C4—6284no—
217C2×C4—1572no—
218C2×C4—12562no—
219C2×C4D4×D15711yescharacteristic
220C2×C4D4×D15711yescharacteristic
221C2×C4C23×D15711yescharacteristic
222C8—21no—
223C8—3142no—
224C8D4×D15712yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—3142no—
229C22—3144no—
230C22—3142no—
231C22—3142no—
232C22—6282no—
233C22—6282no—
234C22—12568no—
235C22C2×D4×D15711yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—3142no—
240C4—6282no—
241C4C2×D4×D15711yescharacteristic
242C4#1909781611yescharacteristic
243C2—82no—
244C2—6282no—
245C2—6284no—
246C2#2375790811yescharacteristic
247C2#2375807011yescharacteristic
248C2#2375807511yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#495×C157C2
socleC22×C157C22×D4
hypercenter#495D157
hypocenterC157#3273
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#19097798C2semidirect
2. #23757916C2semidirect
3. #23757516C2semidirect
4. #23757485C2semidirect
5. #23757434C2semidirect
6. #23757405C2semidirect
7. C4×D1256C2semidirect
8. #23757352C2semidirect
9. #495×C157C2semidirect
11. C2×D4×D157C22semidirect
13. C2×#14578941C22semidirect
16. C2×#14578937C22semidirect
18. #19097747C22semidirect
23. C4×D628C22semidirect
25. #19097705C22semidirect
26. C4⋊#11929434C22semidirect
27. #19097695C22semidirect
28. #19097693C22semidirect
29. #19097692C22semidirect
30. #19097683C22semidirect
31. C2×Q16×C157C22semidirect
32. C2×SD16×C157C22semidirect
34. #124×C157C22semidirect
35. C4×C8×C157C22semidirect
50. D1256D4semidirect
124. C157#3273semidirect
128. #495D157semidirect
138. C2×Q16C2×D157semidirect
140. C2×SD16C2×D157semidirect
145. #124C2×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×#190977982
#237579162
#237575162
#237574852
#237574342
#237574052
C4×D12562
#237573522
#495×C1572
#3273157