Finite Group Databasebeta

← D157⋊#352 #34116385

Subgroups — D157⋊#352 #34116385

Order 20096.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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⋊#100C211yesmaximal, characteristic
2D157⋊#99C211yesmaximal, characteristic
3#23758176C212yesmaximal, complemented
4#23758175C212yesmaximal, complemented
5#123×D157C211yesmaximal, characteristic
6D157⋊M16—21no—
7C2×C22⋊#10597845—21no—
8#19097831—21no—
9#19097831C2212yes—
10#19097830—21no—
11#19097829C2212yes—
12C2×D4×D157C2211yescharacteristic
13C22×C4×D157C411yescharacteristic, complemented
14#19097756—21no—
15#19097755C2211yescharacteristic
16#19097754C2211yescharacteristic
17#19097753—21no—
18#19097752C411yescharacteristic, complemented
19C4⋊C4×D157—21no—
20C22⋊C4×D157—21no—
21C22⋊C4×D157C411yescharacteristic, complemented
22#123×C157C411yescharacteristic, complemented
23C22×#10597845—41no—
24#14578964—41no—
25#14578963—22no—
26D157⋊C8—41no—
27C22⋊#10597845—22no—
28C22⋊#10597845—41no—
29C23×D157C2×C411yescharacteristic
30C23×D157D411yescharacteristic
31C2×D628D411yescharacteristic
32C2×C22⋊D157D411yescharacteristic
33C2×C22⋊D157C2311yescharacteristic
34D4×D157—41no—
35D4×D157—41no—
36C22×Dic157C2×C411yescharacteristic, complemented
37C2×C4×D157—21no—
38C2×C4×D157—21no—
39C2×C4×D157—21no—
40C2×C4×D157—41no—
41C2×C4×D157—41no—
42C2×C4×D157D411yescharacteristic
43C4⋊Dic157—21no—
44#14578933—21no—
45#14578933—21no—
46C22⋊Dic157—21no—
47C22⋊Dic157C2×C411yescharacteristic, complemented
48#14578931—21no—
49#14578931—21no—
50#14578931—21no—
51C2×D4×C157C2×C411yescharacteristic
52C22×C4×C157C2×C411yescharacteristic, complemented
53C4⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C22⋊C4×C157C2×C411yescharacteristic, complemented
56C2×#10597845—42no—
57C2×#10597845—82no—
58#11929441—42no—
59C22×D157—21no—
60C22×D157—21no—
61C22×D157—21no—
62C22×D157—21no—
63C22×D157—42no—
64C22×D157—42no—
65C22×D157C22⋊C411yescharacteristic
66C22×D157C22⋊C411yescharacteristic
67C22×D157C2×D411yescharacteristic
68D628—41no—
69C22⋊D157—41no—
70C22⋊D157—41no—
71C2×Dic157—21no—
72C2×Dic157—21no—
73C2×Dic157—41no—
74C2×Dic157C2×D411yescharacteristic
75C4×D157—21no—
76C4×D157—21no—
77C4×D157—42no—
78C4×D157—42no—
79C4×D157—41no—
80C4×D157—41no—
81C23×C157C22⋊C411yescharacteristic
82C23×C157C22×C411yescharacteristic
83D4×C157—41no—
84C2×C4×C157—21no—
85C2×C4×C157—21no—
86C2×C4×C157—41no—
87C2×C4×C157C22⋊C411yescharacteristic
88C22×C157—21no—
89C22×C157—21no—
90C22×C157—41no—
91C22×C157—41no—
92C22×C157C2×C22⋊C411yescharacteristic
93C2×D157—22no—
94C2×D157—21no—
95C2×D157—21no—
96C2×D157—42no—
97C2×D157—42no—
98C2×D157—42no—
99C2×D157—41no—
100C2×D157—41no—
101C2×D157—81no—
102C2×D157#9911yescharacteristic
103C2×D157#9911yescharacteristic
104#10597845—82no—
105C4×C157—21no—
106C4×C157—41no—
107C4×C157—41no—
108Dic157—21no—
109Dic157—41no—
110Dic157—41no—
111C2×C157—21no—
112C2×C157—41no—
113C2×C157—41no—
114C2×C157C2×#9911yescharacteristic
115D157—21no—
116D157—41no—
117D157—41no—
118D157#35212yescomplemented
119C157C2×#35211yescharacteristic, complemented, Sylow
120C2×#352—1571nomaximal, Sylow
121C2×#123—1571no—
122C2×#100—1571no—
123C2×#99—1571no—
124#352—1572no—
125#352—1572no—
126C22×D4—1571no—
127C23×C4—1571no—
128C2×M16—3141no—
129#123—3141no—
130#123—3141no—
131#123—1571no—
132#123—1571no—
133#123—1571no—
134#123#1059784511yescharacteristic, complemented
135C2×C4⋊C4—3141no—
136C2×C22⋊C4—3141no—
137C2×C22⋊C4—3141no—
138C2×C22⋊C4—1571no—
139#100—3141no—
140#100—1572no—
141#99—3141no—
142#99—1572no—
143C24—1571no—
144C24—1571no—
145C2×D4—6281no—
146C2×D4—6281no—
147C2×D4—1571no—
148C2×D4—1571no—
149C2×D4—1571no—
150C2×D4C2×#1059784511yescharacteristic
151C22×C4—3141no—
152C22×C4—3141no—
153C22×C4—3141no—
154C22×C4—6281no—
155C22×C4—6281no—
156C22×C4—6281no—
157C22×C4—1571no—
158C22×C4—1571no—
159C22×C4C2×#1059784511yescharacteristic, complemented
160M16—3142no—
161M16—6281no—
162C2×C8—6281no—
163C4⋊C4—21no—
164C4⋊C4—3141no—
165C4⋊C4—3141no—
166C4⋊C4—3141no—
167C22⋊C4—21no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C22⋊C4—3141no—
171C22⋊C4—3141no—
172C22⋊C4—3142no—
173C22⋊C4—6281no—
174C22⋊C4—1571no—
175C22⋊C4C2×#1059784511yescharacteristic, complemented
176C23—3141no—
177C23—3141no—
178C23—3141no—
179C23—3141no—
180C23—6282no—
181C23—6282no—
182C23—1571no—
183C23—1571no—
184C23—1571no—
185C23C22⋊#1059784511yescharacteristic
186C23C22×#1059784511yescharacteristic
187D4—41no—
188D4—6281no—
189D4—6281no—
190D4—6281no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—3141no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—3141no—
198C2×C4—6282no—
199C2×C4—6282no—
200C2×C4—6281no—
201C2×C4—6281no—
202C2×C4—6281no—
203C2×C4—6282no—
204C2×C4—1571no—
205C2×C4—12562no—
206C2×C4C22⋊#1059784511yescharacteristic
207C8—6282no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—3142no—
213C22—3141no—
214C22—3141no—
215C22—6281no—
216C22—6281no—
217C22—6282no—
218C22—6282no—
219C22—6282no—
220C22—1571no—
221C22—1571no—
222C22—12561no—
223C22C2×C22⋊#1059784511yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—3141no—
228C4—6281no—
229C4—6281no—
230C4—12562no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—3141no—
235C2—6281no—
236C2—6281no—
237C2—1572no—
238C2D157⋊#9911yescharacteristic
subgroupG/H
centerC2D157⋊#99
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
Fitting#123×C157C4
socleC2×C157C2×#99
prime radicalC2×D4×D157C22
cosocleC2×C22⋊D157C23
hypercenter#123#10597845
hypocenterC157C2×#352
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #23758176C2semidirect
4. #23758175C2semidirect
13. C22×C4×D157C4semidirect
18. #19097752C4semidirect
21. C22⋊C4×D157C4semidirect
22. #123×C157C4semidirect
36. C22×Dic157C2×C4semidirect
47. C22⋊Dic157C2×C4semidirect
52. C22×C4×C157C2×C4semidirect
55. C22⋊C4×C157C2×C4semidirect
118. D157#352semidirect
119. C157C2×#352semidirect
134. #123#10597845semidirect
159. C22×C4C2×#10597845semidirect
175. C22⋊C4C2×#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊#1002
D157⋊#992
#237581762
#237581752
#123×D1572
C2×#352157