Finite Group Databasebeta

← #34100548

Subgroups — #34100548

Order 20096.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19097755C211yesmaximal, characteristic
2#23757746C211yesmaximal, characteristic
3C2×#19097685C211yesmaximal, characteristic
4#23757134C211yesmaximal, characteristic, complemented
5#23757134C211yesmaximal, characteristic, complemented
6#23757039C211yesmaximal, characteristic, complemented
7#342×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157C2211yescharacteristic
9C23×Dic157C2211yescharacteristic
10#19097755—22no—
11#19097755C414yescomplemented
12C4×C22⋊D157—22no—
13#19097731—22no—
14#19097727—21no—
15C2×C4⋊Dic157—21no—
16C2×C22⋊Dic157C2211yescharacteristic
17C2×C22⋊Dic157C2211yescharacteristic
18C2×#14578931—21no—
19C22⋊C4×D157—21no—
20#19097685—22no—
21#19097678—22no—
22#19097678—22no—
23C2×C22⋊C4×C157C2211yescharacteristic
24C2×C22⋊C4×C157C2211yescharacteristic
25C2×C22⋊C4×C157C2211yescharacteristic
26C23×D157D411yescharacteristic
27C2×C22⋊D157—21no—
28C2×C22⋊D157—21no—
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C2×C22⋊D157C2×C412yes—
32C2×C22⋊D157D412yes—
33C22×Dic157—21no—
34C22×Dic157—21no—
35C22×Dic157—21no—
36C22×Dic157—21no—
37C22×Dic157—21no—
38C22×Dic157—21no—
39C22×Dic157—21no—
40C22×Dic157C2×C412yescomplemented
41C22×Dic157D411yescharacteristic
42C22×Dic157D412yes—
43C2×C4×D157—22no—
44C4⋊Dic157—24no—
45#14578933—22no—
46C22⋊Dic157—21no—
47C22⋊Dic157—21no—
48C22⋊Dic157—21no—
49C22⋊Dic157—21no—
50#14578931—22no—
51#14578931—24no—
52C4×Dic157—22no—
53C24×C157C2311yescharacteristic
54C22×C4×C157—21no—
55C22×C4×C157—21no—
56C22×C4×C157D412yes—
57C22⋊C4×C157—21no—
58C22⋊C4×C157—21no—
59C22⋊C4×C157—21no—
60C22⋊C4×C157—21no—
61C22⋊C4×C157—21no—
62C22⋊C4×C157C2×C412yescomplemented
63C22×D157—21no—
64C22×D157—21no—
65C22×D157—42no—
66C22×D157C22⋊C412yes—
67C22⋊D157—22no—
68C22⋊D157—22no—
69C22⋊D157—22no—
70C22⋊D157—22no—
71C2×Dic157—21no—
72C2×Dic157—21no—
73C2×Dic157—22no—
74C2×Dic157—22no—
75C2×Dic157—22no—
76C2×Dic157—22no—
77C2×Dic157—41no—
78C2×Dic157—41no—
79C2×Dic157—41no—
80C2×Dic157—41no—
81C2×Dic157—42no—
82C2×Dic157—42no—
83C2×Dic157—41no—
84C2×Dic157C22⋊C412yes—
85C4×D157—82no—
86C23×C157—42no—
87C23×C157C22×C411yescharacteristic
88C23×C157C2×D411yescharacteristic
89C23×C157C2×D411yescharacteristic
90C23×C157C2×D411yescharacteristic
91C23×C157C2×D411yescharacteristic
92C23×C157#4111yescharacteristic
93C23×C157#4111yescharacteristic
94C2×C4×C157—22no—
95C2×C4×C157—22no—
96C2×C4×C157—42no—
97C2×C4×C157—42no—
98C2×C4×C157—42no—
99C2×C4×C157—41no—
100C22×C157—22no—
101C22×C157—22no—
102C22×C157—22no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157—41no—
107C22×C157C2×C22⋊C411yescharacteristic
108C22×C157C4×D411yescharacteristic
109C22×C157C4×D411yescharacteristic
110C22×C157#12011yescharacteristic
111C22×C157#12111yescharacteristic
112C22×C157#12111yescharacteristic
113C22×C157#12311yescharacteristic
114C2×D157—22no—
115C2×D157—42no—
116C2×D157—42no—
117C2×D157—81no—
118C4×C157—42no—
119C4×C157—42no—
120C4×C157—81no—
121Dic157—22no—
122Dic157—42no—
123Dic157—42no—
124Dic157—81no—
125C2×C157—21no—
126C2×C157—21no—
127C2×C157—21no—
128C2×C157—21no—
129C2×C157—21no—
130C2×C157—21no—
131C2×C157#38611yescharacteristic
132C2×C157#45812yes—
133D157—42no—
134C157#189011yescharacteristic, complemented, Sylow
135#1890—1571nomaximal, Sylow
136C2×#123—1571no—
137#518—1571no—
138C2×#99—1571no—
139#381—1571no—
140#381—1571no—
141#342—1571no—
142#342D15711yescharacteristic, complemented
143C22×D4—1571no—
144C23×C4—1571no—
145#123—3142no—
146#123—1574no—
147C4×D4—3142no—
148C4×D4—3142no—
149#117—3141no—
150C2×C4⋊C4—3141no—
151C2×C22⋊C4—3141no—
152C2×C22⋊C4—3141no—
153C2×C22⋊C4—1571no—
154C2×C22⋊C4—1571no—
155C2×C22⋊C4C2×D15711yescharacteristic
156C2×C22⋊C4C2×D15711yescharacteristic
157C2×C22⋊C4C2×D15711yescharacteristic
158#99—3142no—
159#95—3142no—
160#95—3142no—
161C24—1571no—
162C24C22×D15711yescharacteristic
163C2×D4—3141no—
164C2×D4—3141no—
165C2×D4—3141no—
166C2×D4—3141no—
167C2×D4—1572no—
168C2×D4—1572no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—3142no—
172C22×C4—3141no—
173C22×C4—3141no—
174C22×C4—3141no—
175C22×C4—3141no—
176C22×C4—3141no—
177C22×C4—3141no—
178C22×C4—3141no—
179C22×C4—1572no—
180C22×C4—1571no—
181C22×C4—1572no—
182C22×C4D62812yes—
183C4⋊C4—3142no—
184C4⋊C4—3144no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—3142no—
191C22⋊C4—3144no—
192C22⋊C4—3141no—
193C22⋊C4—3141no—
194C22⋊C4—3141no—
195C22⋊C4—3141no—
196C22⋊C4C4×D15712yescomplemented
197C42—3142no—
198C23—42no—
199C23—3141no—
200C23—3141no—
201C23—6282no—
202C23—1572no—
203C23C2×C4×D15711yescharacteristic
204C23D4×D15711yescharacteristic
205C23D4×D15711yescharacteristic
206C23D4×D15711yescharacteristic
207C23C2×D62811yescharacteristic
208C23#1457895411yescharacteristic
209C23#1457895511yescharacteristic
210D4—3142no—
211D4—3142no—
212D4—3142no—
213D4—3142no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—3141no—
221C2×C4—3141no—
222C2×C4—3142no—
223C2×C4—3142no—
224C2×C4—3142no—
225C2×C4—3142no—
226C2×C4—6281no—
227C2×C4—6281no—
228C2×C4—6281no—
229C2×C4—6281no—
230C2×C4—6282no—
231C2×C4—6282no—
232C2×C4—6281no—
233C2×C4—1572no—
234C2×C4—12562no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—3142no—
243C22—6282no—
244C22—6282no—
245C22—12561no—
246C22C22⋊C4×D15711yescharacteristic
247C22#1909773311yescharacteristic
248C22C4×D62811yescharacteristic
249C22#1909774111yescharacteristic
250C22#1909774411yescharacteristic
251C22#1909774611yescharacteristic
252C22#1909775611yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—3142no—
257C4—6282no—
258C4—6282no—
259C4—12561no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—6282no—
267C2#2375715111yescharacteristic
268C2#2375746412yes—
subgroupG/H
centerC22#19097741
commutatorC23×C157C22×C4
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157#120
prime radicalC22×C22⋊D157C22
cosocleC24×C157C23
hypercenter#342D157
hypocenterC157#1890
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #23757134C2semidirect
5. #23757134C2semidirect
6. #23757039C2semidirect
7. #342×C157C2semidirect
11. #19097755C4semidirect
40. C22×Dic157C2×C4semidirect
62. C22⋊C4×C157C2×C4semidirect
134. C157#1890semidirect
142. #342D157semidirect
196. C22⋊C4C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977552
#237577462
C2×#190976852
#237571342
#237570392
#342×C1572
#1890157