Finite Group Databasebeta

← #34101152

Subgroups — #34101152

Order 20096.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19097797C211yesmaximal, characteristic, complemented
2#23757842C211yesmaximal, characteristic, complemented
3C2×#19097767C211yesmaximal, characteristic, complemented
4C2×#19097697C211yesmaximal, characteristic, complemented
5C2×#19097687C211yesmaximal, characteristic, complemented
6#23757032C211yesmaximal, characteristic, complemented
7#418×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C22×D628C2211yescharacteristic
10C22×C22⋊D157—22no—
11#19097797—22no—
12#19097797—22no—
13C2×#14578942—21no—
14C2×#14578939—21no—
15C2×#14578938C2211yescharacteristic
16#19097768—21no—
17#19097767—22no—
18#19097767—22no—
19#19097759—21no—
20#19097746—22no—
21#19097741—22no—
22C2×C4×Dic157C2211yescharacteristic
23#19097697—22no—
24#19097687—22no—
25C22×D4×C157C2211yescharacteristic
26C2×M16×C157C2211yescharacteristic
27#117×C157C2211yescharacteristic
28#102×C157—22no—
29C23×D157D412yes—
30#14578954—21no—
31#14578954—21no—
32#14578954—21no—
33#14578954—21no—
34C2×Dic314D411yescharacteristic, complemented
35C2×D628—24no—
36C2×D628—21no—
37C2×D628—21no—
38C2×D628—21no—
39C2×D628—21no—
40C2×D628—21no—
41C2×D628—21no—
42C2×D628D411yescharacteristic, complemented
43C2×C22⋊D157—28no—
44C2×C22⋊D157—21no—
45C2×C22⋊D157—48no—
46C22×Dic157—21no—
47C2×C4×D157—21no—
48#14578942—24no—
49#14578939—24no—
50#14578938—21no—
51#14578938D412yescomplemented
52C2×#11929434—21no—
53#14578931—24no—
54C4×Dic157—21no—
55C4×Dic157D412yescomplemented
56C24×C157—21no—
57C2×D4×C157—21no—
58C2×D4×C157—21no—
59C2×D4×C157—21no—
60C2×D4×C157—21no—
61C2×D4×C157—21no—
62C2×D4×C157D412yescomplemented
63C22×C4×C157C2311yescharacteristic
64M16×C157—21no—
65M16×C157—21no—
66C2×C8×C157—21no—
67C4⋊C4×C157D412yescomplemented
68C22⋊C4×C157—21no—
69C42×C157—21no—
70C22×D157—21no—
71C22×D157—22no—
72C22×D157—22no—
73C22×D157—22no—
74C22×D157—44no—
75Dic314—21no—
76Dic314—21no—
77D628—21no—
78D628—21no—
79D628—41no—
80D628—41no—
81D628—41no—
82D628—41no—
83D628—84no—
84C22⋊D157—416no—
85C22⋊D157—41no—
86C22⋊D157—41no—
87C2×Dic157—24no—
88C2×Dic157—22no—
89C2×Dic157—21no—
90C4×D157—41no—
91C4×D157—41no—
92#11929434—22no—
93C23×C157—22no—
94C23×C157—44no—
95C23×C157—41no—
96C23×C157—41no—
97C23×C157C2×D411yescharacteristic
98D4×C157—22no—
99D4×C157—22no—
100D4×C157—41no—
101D4×C157—41no—
102C2×C4×C157—22no—
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157C2×D411yescharacteristic
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157C2×D411yescharacteristic
107C2×C4×C157C2×D411yescharacteristic
108C2×C4×C157#4111yescharacteristic
109C8×C157—41no—
110C22×C157—22no—
111C22×C157—44no—
112C22×C157—42no—
113C22×C157—82no—
114C22×C157—82no—
115C22×C157#12011yescharacteristic
116C22×C157#12011yescharacteristic
117C22×C157#12111yescharacteristic
118C2×D157—44no—
119C2×D157—41no—
120C2×D157—42no—
121C2×D157—42no—
122C2×D157—44no—
123C2×D157—82no—
124C4×C157—42no—
125C4×C157#12011yescharacteristic
126C4×C157#12111yescharacteristic
127C4×C157#12111yescharacteristic
128C4×C157#12711yescharacteristic
129Dic157—24no—
130Dic157—41no—
131C2×C157—21no—
132C2×C157—21no—
133C2×C157—82no—
134C2×C157#39211yescharacteristic
135C2×C157#45312yes—
136D157—81no—
137D157—82no—
138C157#200211yescharacteristic, complemented, Sylow
139#2002—1571nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1571no—
141#535—1571no—
142C2×#127—1571no—
143C2×#104—1571no—
144#418D15711yescharacteristic, complemented
145C2×#100—1571no—
146#339—1571no—
147C2×#41—1571no—
148C22×D4—3142no—
149C22×D4—1571no—
150C22×D4C2×D15711yescharacteristic
151AGL(1,ℤ/8)—3142no—
152AGL(1,ℤ/8)—3142no—
153C2×SD16—3141no—
154C2×D8—3141no—
155C2×M16—1571no—
156C2×M16C2×D15711yescharacteristic
157#127—3141no—
158#127—3142no—
159#127—3142no—
160#124—3141no—
161#121—3142no—
162#120—3142no—
163#117C2×D15711yescharacteristic
164C2×C42—1571no—
165#104—3142no—
166#102—22no—
167#100—3142no—
168C24—21no—
169C24—1572no—
170#41—3141no—
171#41—3141no—
172#41—3141no—
173#41—3141no—
174C2×Q8—1571no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—3144no—
181C2×D4—3148no—
182C2×D4—3141no—
183C2×D4—3141no—
184C2×D4—3141no—
185C2×D4—3141no—
186C2×D4—3141no—
187C2×D4—3141no—
188C2×D4—3141no—
189C2×D4—6288no—
190C2×D4—1571no—
191C2×D4D62812yescomplemented
192C22×C4—3141no—
193C22×C4—3141no—
194C22×C4C22×D15711yescharacteristic
195SD16—3144no—
196D8—3144no—
197M16—21no—
198M16—21no—
199M16—3141no—
200M16—1572no—
201C2×C8—21no—
202C2×C8—3141no—
203C4⋊C4C22⋊D15712yescomplemented
204C22⋊C4—21no—
205C22⋊C4—3144no—
206C42—21no—
207C42—3141no—
208C42—1572no—
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—3142no—
214C23—3141no—
215C23—3142no—
216C23—3142no—
217C23—6284no—
218C23D4×D15711yescharacteristic
219Q8—3141no—
220Q8—3141no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—3141no—
226D4—3141no—
227D4—62816no—
228D4—6281no—
229D4—6281no—
230D4—6281no—
231D4—6281no—
232D4—6281no—
233D4—6281no—
234D4—12564no—
235C2×C4—22no—
236C2×C4—3144no—
237C2×C4—3142no—
238C2×C4—3141no—
239C2×C4—6281no—
240C2×C4—6281no—
241C2×C4D4×D15711yescharacteristic
242C2×C4D4×D15711yescharacteristic
243C2×C4D4×D15711yescharacteristic
244C2×C4C2×C22⋊D15711yescharacteristic
245C2×C4C2×D62811yescharacteristic
246C2×C4#1457895411yescharacteristic
247C8—41no—
248C8—3142no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—6284no—
255C22—6281no—
256C22—6282no—
257C22—6282no—
258C22—6284no—
259C22—12562no—
260C22#1909773911yescharacteristic
261C22#1909774111yescharacteristic
262C22#1909774411yescharacteristic
263C4—42no—
264C4—3144no—
265C4—6281no—
266C4#1909774111yescharacteristic
267C4#1909774411yescharacteristic
268C4#1909774511yescharacteristic
269C4#1909776711yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—12562no—
274C2—12561no—
275C2#2375718211yescharacteristic
276C2#2375743912yes—
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#418×C157C2
socleC22×C157#120
hypercenter#418D157
hypocenterC157#2002
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#19097797C2semidirect
2. #23757842C2semidirect
3. C2×#19097767C2semidirect
4. C2×#19097697C2semidirect
5. C2×#19097687C2semidirect
6. #23757032C2semidirect
7. #418×C157C2semidirect
34. C2×Dic314D4semidirect
42. C2×D628D4semidirect
51. #14578938D4semidirect
55. C4×Dic157D4semidirect
62. C2×D4×C157D4semidirect
67. C4⋊C4×C157D4semidirect
138. C157#2002semidirect
144. #418D157semidirect
191. C2×D4D628semidirect
203. C4⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
#237578422
C2×#190977672
C2×#190976972
C2×#190976872
#237570322
#418×C1572
#2002157