Finite Group Databasebeta

← #34099082

Subgroups — #34099082

Order 20096.

320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757423C211yesmaximal, characteristic, complemented
2#23757406C211yesmaximal, characteristic, complemented
3#23757182C211yesmaximal, characteristic, complemented
4#23757010C211yesmaximal, characteristic, complemented
5#23757007C211yesmaximal, characteristic, complemented
6#23756997C211yesmaximal, characteristic, complemented
7#538×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C22×C22⋊D157—21no—
10C2×#14578941—21no—
11C2×#14578939—21no—
12C2×#14578931—21no—
13#19097691—21no—
14#19097691—21no—
15C22⋊#11929434C2211yescharacteristic
16C22⋊#11929434C2211yescharacteristic
17#19097678C2211yescharacteristic
18#126×C157—21no—
19#124×C157—21no—
20#123×C157—21no—
21C22⋊Q8×C157C2211yescharacteristic
22#121×C157—21no—
23#121×C157C2211yescharacteristic
24#120×C157—21no—
25C4×D4×C157—21no—
26C2×C22⋊C4×C157C2211yescharacteristic
27C23×D157—21no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—42no—
31C2×C22⋊D157—42no—
32C2×C22⋊D157—42no—
33C2×C22⋊D157—42no—
34C22×Dic157—21no—
35#14578941—42no—
36#14578939—42no—
37C2×#11929434—21no—
38C2×#11929434—21no—
39#14578931—42no—
40C24×C157D411yescharacteristic
41C2×Q8×C157D411yescharacteristic, complemented
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44C2×D4×C157—21no—
45C2×D4×C157D411yescharacteristic, complemented
46C22×C4×C157—21no—
47C22×C4×C157D411yescharacteristic
48C22×C4×C157C2311yescharacteristic
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157D411yescharacteristic, complemented
52C4⋊C4×C157D411yescharacteristic, complemented
53C22⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C22⋊C4×C157—21no—
56C22⋊C4×C157—21no—
57C22⋊C4×C157—21no—
58C22⋊C4×C157—21no—
59C22⋊C4×C157—21no—
60C42×C157—21no—
61C22×D157—22no—
62C22×D157—41no—
63C22×D157—41no—
64C22×D157—41no—
65C22×D157—41no—
66C22×D157—41no—
67C22×D157—41no—
68D628—22no—
69D628—22no—
70D628—41no—
71D628—41no—
72C22⋊D157—48no—
73C2×Dic157—22no—
74C2×Dic157—41no—
75C2×Dic157—41no—
76#11929434—41no—
77#11929434—41no—
78C23×C157—21no—
79C23×C157—21no—
80C23×C157—21no—
81C23×C157—21no—
82C23×C157—41no—
83C23×C157—41no—
84C23×C157C2×D411yescharacteristic
85Q8×C157—41no—
86D4×C157—41no—
87D4×C157—41no—
88D4×C157—41no—
89D4×C157—81no—
90D4×C157—81no—
91C2×C4×C157—21no—
92C2×C4×C157—21no—
93C2×C4×C157—21no—
94C2×C4×C157—21no—
95C2×C4×C157—41no—
96C2×C4×C157—41no—
97C2×C4×C157—81no—
98C2×C4×C157C2×D411yescharacteristic
99C2×C4×C157C2×D411yescharacteristic
100C22×C157—21no—
101C22×C157—21no—
102C22×C157—42no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157—41no—
107C22×C157—41no—
108C22×C157—41no—
109C22×C157—81no—
110C22×C157#12011yescharacteristic
111C22×C157#13511yescharacteristic
112C22×C157AGL(1,ℤ/8)11yescharacteristic
113C2×D157—42no—
114C2×D157—42no—
115C2×D157—42no—
116C2×D157—81no—
117C2×D157—81no—
118C2×D157—81no—
119C2×D157—81no—
120C4×C157—21no—
121C4×C157—21no—
122C4×C157—41no—
123C4×C157—41no—
124C4×C157—41no—
125C4×C157—41no—
126Dic157—42no—
127C2×C157—21no—
128C2×C157—21no—
129C2×C157—81no—
130C2×C157—81no—
131C2×C157#44911yescharacteristic
132C2×C157#45311yescharacteristic
133C2×C157B(4,𝔽2)11yescharacteristic
134D157—82no—
135C157#160011yescharacteristic, complemented, Sylow
136#1600—1571nomaximal, Sylow
137#538D15711yescharacteristic, complemented
138#450—1571no—
139#447—1571no—
140#392—1571no—
141#328—1571no—
142#327—1571no—
143#323—1571no—
144C22×D4—3141no—
145C22×D4—1571no—
146C2×SD16—3141no—
147C2×D8—3141no—
148#126—21no—
149#124—21no—
150#123—21no—
151C22⋊Q8C2×D15711yescharacteristic
152#121—21no—
153#121C2×D15711yescharacteristic
154#120—21no—
155C4×D4—21no—
156C2×C22⋊C4—3141no—
157C2×C22⋊C4C2×D15711yescharacteristic
158#102—3141no—
159#102—3141no—
160C22⋊C8—1571no—
161C22⋊C8—1571no—
162#95—1571no—
163C24—3141no—
164C24C22⋊D15711yescharacteristic
165C2×Q8C22⋊D15711yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—3141no—
170C2×D4—3141no—
171C2×D4—6282no—
172C2×D4—6282no—
173C2×D4—6282no—
174C2×D4—6282no—
175C2×D4C22⋊D15711yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—3141no—
178C22×C4C22⋊D15711yescharacteristic
179C22×C4C22×D15711yescharacteristic
180SD16—6282no—
181D8—6282no—
182C2×C8—3141no—
183C2×C8—3141no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4C22⋊D15711yescharacteristic, complemented
187C4⋊C4C22⋊D15711yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—21no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—6282no—
196C42—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23—3142no—
204C23—6281no—
205C23—6281no—
206C23—6281no—
207C23—6281no—
208C23—6281no—
209C23—6281no—
210C23C2×C22⋊D15711yescharacteristic
211Q8—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—3142no—
218D4—3142no—
219D4—6281no—
220D4—6281no—
221D4—6288no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—81no—
229C2×C4—3142no—
230C2×C4—6281no—
231C2×C4—6281no—
232C2×C4C2×C22⋊D15711yescharacteristic
233C2×C4C2×C22⋊D15711yescharacteristic
234C8—6281no—
235C8—6281no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—6282no—
247C22—6282no—
248C22—6282no—
249C22—12561no—
250C22—12561no—
251C22—12561no—
252C22—12561no—
253C22#1909774011yescharacteristic
254C22#1909779111yescharacteristic
255C22#1909779611yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—6282no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—81no—
267C2—12562no—
268C2#2375741811yescharacteristic
269C2#2375744111yescharacteristic
270C2#2375746011yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#538×C157C2
socleC22×C157#120
hypercenter#538D157
hypocenterC157#1600
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #23757423C2semidirect
2. #23757406C2semidirect
3. #23757182C2semidirect
4. #23757010C2semidirect
5. #23757007C2semidirect
6. #23756997C2semidirect
7. #538×C157C2semidirect
41. C2×Q8×C157D4semidirect
45. C2×D4×C157D4semidirect
51. C4⋊C4×C157D4semidirect
52. C4⋊C4×C157D4semidirect
135. C157#1600semidirect
137. #538D157semidirect
165. C2×Q8C22⋊D157semidirect
175. C2×D4C22⋊D157semidirect
186. C4⋊C4C22⋊D157semidirect
187. C4⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237574232
#237574062
#237571822
#237570102
#237570072
#237569972
#538×C1572
#1600157