Finite Group Databasebeta

← D157⋊#327 #34115502

Subgroups — D157⋊#327 #34115502

Order 20096.

388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D157⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2C2×(C2×#10597845)⋊C4C211yesmaximal, characteristic, complemented
3#23758125C212yesmaximal, complemented
4#23758124C212yesmaximal, complemented
5#121×D157C211yesmaximal, characteristic
6C23×#10597845—21no—
7C2×D157⋊C8—21no—
8#19097828C2212yescomplemented
9C22⋊#11929441—21no—
10(C2×#10597845)⋊C4—21no—
11(C2×#10597845)⋊C4C2212yescomplemented
12C2×D4×D157—21no—
13C2×D4×D157C411yescharacteristic, complemented
14C22×C4×D157C2211yescharacteristic
15#19097746C2211yescharacteristic
16#19097745C411yescharacteristic, complemented
17#19097744—21no—
18#19097743—21no—
19#19097742C2211yescharacteristic
20C4⋊C4×D157C411yescharacteristic, complemented
21C22⋊C4×D157—21no—
22#121×C157C411yescharacteristic, complemented
23C22×#10597845—24no—
24C22×#10597845—22no—
25C22×#10597845—42no—
26C22×#10597845—42no—
27D157⋊C8—42no—
28C2×#11929441—22no—
29C23×D157—21no—
30C23×D157D411yescharacteristic
31C2×D628—21no—
32C2×D628C2×C411yescharacteristic, complemented
33C2×C22⋊D157—21no—
34C2×C22⋊D157—21no—
35C2×C22⋊D157—21no—
36D4×D157—42no—
37D4×D157—42no—
38D4×D157—42no—
39C22×Dic157D411yescharacteristic
40C2×C4×D157—21no—
41C2×C4×D157—42no—
42C2×C4×D157C2×C411yescharacteristic
43C2×C4×D157D411yescharacteristic
44C2×C4×D157D411yescharacteristic
45C2×C4×D157C2311yescharacteristic
46C4⋊Dic157C2×C411yescharacteristic, complemented
47#14578933—21no—
48C22⋊Dic157—21no—
49#14578931—21no—
50#14578931—21no—
51C2×D4×C157—21no—
52C2×D4×C157C2×C411yescharacteristic, complemented
53C22×C4×C157C2×C411yescharacteristic
54C4⋊C4×C157C2×C411yescharacteristic, complemented
55C22⋊C4×C157—21no—
56C2×#10597845—24no—
57C2×#10597845—42no—
58C2×#10597845—48no—
59C2×#10597845—42no—
60#11929441—42no—
61C22×D157—22no—
62C22×D157—22no—
63C22×D157—21no—
64C22×D157—42no—
65C22×D157—42no—
66C22×D157—42no—
67C22×D157C22⋊C411yescharacteristic
68C22×D157D812yes—
69C22×D157SD1612yes—
70C22×D157C2×D411yescharacteristic
71D628—41no—
72D628—41no—
73D628—41no—
74C22⋊D157—42no—
75C22⋊D157—42no—
76C22⋊D157—41no—
77C22⋊D157—41no—
78C2×Dic157—21no—
79C2×Dic157—41no—
80C2×Dic157C22⋊C411yescharacteristic
81C2×Dic157C2×D411yescharacteristic
82C4×D157—22no—
83C4×D157—22no—
84C4×D157—41no—
85C4×D157—41no—
86C4×D157—42no—
87C23×C157—21no—
88C23×C157C22⋊C411yescharacteristic
89D4×C157—41no—
90D4×C157—42no—
91C2×C4×C157—21no—
92C2×C4×C157—41no—
93C2×C4×C157C22⋊C411yescharacteristic
94C2×C4×C157C22×C411yescharacteristic
95C22×C157—21no—
96C22×C157—21no—
97C22×C157—41no—
98C22×C157—41no—
99C22×C157—41no—
100C22×C157#10212yes—
101C22×C157C2×C22⋊C411yescharacteristic
102C2×D157—21no—
103C2×D157—21no—
104C2×D157—24no—
105C2×D157—24no—
106C2×D157—41no—
107C2×D157—41no—
108C2×D157—41no—
109C2×D157—84no—
110C2×D157#9912yes—
111C2×D157#10212yes—
112C2×D157#10412yes—
113C2×D157C2×D811yescharacteristic
114C2×D157C2×SD1611yescharacteristic
115#10597845—44no—
116C4×C157—21no—
117C4×C157—21no—
118C4×C157—41no—
119Dic157—21no—
120Dic157—21no—
121Dic157—41no—
122C2×C157—22no—
123C2×C157—81no—
124C2×C157C2×#9911yescharacteristic
125C2×C157C2×#10211yescharacteristic
126C2×C157C2×#10411yescharacteristic
127D157—21no—
128D157—21no—
129D157—81no—
130D157#32714yescomplemented
131C157C2×#32711yescharacteristic, complemented, Sylow
132C2×#327—1571nomaximal, Sylow
133C2×#121—1571no—
134C2×C22⋊C8—1571no—
135C2×#95—1571no—
136#327—1572no—
137#327—1572no—
138C22×D4—3141no—
139C22×D4—1571no—
140C23×C4—3141no—
141C23×C4—1571no—
142C22×C8—3141no—
143#121—3141no—
144#121—3141no—
145#121—1571no—
146#121—1571no—
147#121—1571no—
148#121#1059784511yescharacteristic, complemented
149C2×C4⋊C4—1571no—
150C2×C22⋊C4—3141no—
151C22⋊C8—3141no—
152C22⋊C8—1572no—
153#95—3141no—
154#95—1572no—
155C24—3141no—
156C24—1571no—
157C2×D4—21no—
158C2×D4—3141no—
159C2×D4—3141no—
160C2×D4—3141no—
161C2×D4—3141no—
162C2×D4—6282no—
163C2×D4—6282no—
164C2×D4—6282no—
165C2×D4—1571no—
166C2×D4C2×#1059784511yescharacteristic, complemented
167C22×C4—3141no—
168C22×C4—3144no—
169C22×C4—3142no—
170C22×C4—6282no—
171C22×C4—6282no—
172C22×C4—6282no—
173C22×C4—1571no—
174C22×C4—1571no—
175C22×C4—1571no—
176C22×C4—1571no—
177C22×C4—1571no—
178C22×C4C2×#1059784511yescharacteristic
179C2×C8—3142no—
180C2×C8—6282no—
181C4⋊C4—3141no—
182C4⋊C4—1571no—
183C4⋊C4C2×#1059784511yescharacteristic, complemented
184C22⋊C4—21no—
185C22⋊C4—3141no—
186C22⋊C4—3141no—
187C22⋊C4—3141no—
188C23—21no—
189C23—3142no—
190C23—3142no—
191C23—3141no—
192C23—6282no—
193C23—6282no—
194C23—6282no—
195C23—1572no—
196C23—1572no—
197C23—1571no—
198C23—1571no—
199C23C22⋊#1059784511yescharacteristic
200D4—41no—
201D4—42no—
202D4—6281no—
203D4—6281no—
204D4—6281no—
205D4—6282no—
206D4—6281no—
207D4—6281no—
208D4—6282no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—3142no—
212C2×C4—3142no—
213C2×C4—3144no—
214C2×C4—3141no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—6282no—
218C2×C4—6281no—
219C2×C4—6288no—
220C2×C4—6282no—
221C2×C4—6282no—
222C2×C4—1571no—
223C2×C4—1571no—
224C2×C4C22⋊#1059784511yescharacteristic
225C2×C4C22×#1059784511yescharacteristic
226C8—6282no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—3144no—
233C22—3144no—
234C22—3141no—
235C22—3141no—
236C22—6281no—
237C22—6281no—
238C22—6281no—
239C22—1571no—
240C22—1571no—
241C22—1572no—
242C22—1572no—
243C22—1572no—
244C22—12564no—
245C22#1909783312yes—
246C22C2×C22⋊#1059784511yescharacteristic
247C4—21no—
248C4—21no—
249C4—41no—
250C4—3141no—
251C4—3141no—
252C4—6284no—
253C4—6281no—
254C2—22no—
255C2—81no—
256C2—3141no—
257C2—3141no—
258C2—1574no—
259C2—12561no—
260C2D157⋊#9911yescharacteristic
261C2C2×#1909783311yescharacteristic
262C2D157⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#121×C157C4
socleC22×C157C2×C22⋊C4
prime radical#121×D157C2
cosocleC2×C4×D157C23
hypercenter#121#10597845
hypocenterC157C2×#327
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. D157⋊(C22⋊C8)C2semidirect
2. C2×(C2×#10597845)⋊C4C2semidirect
3. #23758125C2semidirect
4. #23758124C2semidirect
8. #19097828C22semidirect
11. (C2×#10597845)⋊C4C22semidirect
13. C2×D4×D157C4semidirect
16. #19097745C4semidirect
20. C4⋊C4×D157C4semidirect
22. #121×C157C4semidirect
32. C2×D628C2×C4semidirect
46. C4⋊Dic157C2×C4semidirect
52. C2×D4×C157C2×C4semidirect
54. C4⋊C4×C157C2×C4semidirect
130. D157#327semidirect
131. C157C2×#327semidirect
148. #121#10597845semidirect
166. C2×D4C2×#10597845semidirect
183. C4⋊C4C2×#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊(C22⋊C8)2
C2×(C2×#10597845)⋊C42
#237581252
#237581242
#121×D1572
C2×#327157