Finite Group Databasebeta

← #34098678

Subgroups — #34098678

Order 20096.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#23757786C211yesmaximal, characteristic
2#23757235C211yesmaximal, characteristic, complemented
3#23757132C211yesmaximal, characteristic, complemented
4#23757010C211yesmaximal, characteristic, complemented
5#23757008C211yesmaximal, characteristic, complemented
6#23757006C211yesmaximal, characteristic, complemented
7#328×C157C211yesmaximal, characteristic, complemented
8C2×#14578955C411yescharacteristic, complemented
9C22×C4×D157C2211yescharacteristic
10C2×#14578937—21no—
11#19097756—21no—
12#19097747C411yescharacteristic, complemented
13#19097746C411yescharacteristic, complemented
14#19097745C2211yescharacteristic
15#19097741—21no—
16#19097733—21no—
17#19097731—21no—
18#19097729C411yescharacteristic, complemented
19C2×#14578933—21no—
20C2×#14578931—21no—
21C22⋊#11929434C2211yescharacteristic
22#19097683—21no—
23#19097678C2211yescharacteristic
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C23×D157D411yescharacteristic
28#14578955—42no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628C2×C411yescharacteristic
32C2×C22⋊D157—21no—
33C22×Dic157—21no—
34C22×Dic157D411yescharacteristic
35C2×C4×D157—21no—
36C2×C4×D157—42no—
37C2×C4×D157C2×C411yescharacteristic
38C2×C4×D157C2×C411yescharacteristic
39C2×C4×D157D411yescharacteristic
40C2×C4×D157D411yescharacteristic
41#14578937—42no—
42C2×#11929434—21no—
43C4⋊Dic157C2×C411yescharacteristic
44#14578933—21no—
45#14578933—42no—
46#14578931—21no—
47#14578931—21no—
48#14578931—21no—
49#14578931—21no—
50#14578931—42no—
51C4×Dic157—21no—
52C2×Q8×C157C2×C411yescharacteristic
53C22×C4×C157—21no—
54C22×C4×C157C2311yescharacteristic
55C2×C8×C157—21no—
56C4⋊C4×C157—21no—
57C4⋊C4×C157C2×C411yescharacteristic
58C22⋊C4×C157—21no—
59C22×D157—21no—
60C22×D157—21no—
61C22×D157—21no—
62C22×D157—41no—
63C22×D157—41no—
64C22×D157C22⋊C411yescharacteristic
65C22×D157C22⋊C411yescharacteristic
66D628—41no—
67D628—42no—
68D628—42no—
69C22⋊D157—41no—
70C22⋊D157—41no—
71C2×Dic157—22no—
72C2×Dic157—21no—
73C2×Dic157—41no—
74C2×Dic157—41no—
75C2×Dic157—41no—
76C2×Dic157C22⋊C411yescharacteristic
77C2×Dic157C22⋊C411yescharacteristic
78C4×D157—22no—
79C4×D157—22no—
80C4×D157—41no—
81C4×D157—41no—
82C4×D157—42no—
83#11929434—41no—
84C23×C157C2×D411yescharacteristic
85Q8×C157—41no—
86C2×C4×C157—21no—
87C2×C4×C157—21no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157—41no—
91C2×C4×C157—41no—
92C2×C4×C157C22×C411yescharacteristic
93C2×C4×C157C2×D411yescharacteristic
94C8×C157—41no—
95C22×C157—21no—
96C22×C157—21no—
97C22×C157C2×C22⋊C411yescharacteristic
98C22×C157AGL(1,ℤ/8)11yescharacteristic
99C22×C157#13711yescharacteristic
100C2×D157—21no—
101C2×D157—21no—
102C2×D157—21no—
103C2×D157—21no—
104C2×D157—21no—
105C2×D157—21no—
106C2×D157—42no—
107C2×D157—42no—
108C2×D157—41no—
109C2×D157—41no—
110C2×D157—41no—
111C4×C157—21no—
112C4×C157—21no—
113C4×C157—41no—
114C4×C157—41no—
115C4×C157—81no—
116Dic157—21no—
117Dic157—41no—
118Dic157—81no—
119Dic157#9912yes—
120C2×C157—21no—
121C2×C157—21no—
122C2×C157C2×#9911yescharacteristic
123C2×C157#41711yescharacteristic
124C2×C157#42111yescharacteristic
125D157—41no—
126D157—41no—
127D157—81no—
128C157#151311yescharacteristic, complemented, Sylow
129#1513—1571nomaximal, Sylow
130#525—1571no—
131#407—1571no—
132#380—1571no—
133#328—1571no—
134#328D15711yescharacteristic, complemented
135#327—1571no—
136#327—1571no—
137C2×#41—1571no—
138C23×C4—1571no—
139C2×M16—3141no—
140#123—3141no—
141C22⋊Q8—1571no—
142C22⋊Q8C2×D15711yescharacteristic
143#121—1571no—
144#121—1571no—
145#120—3141no—
146C4×D4—3141no—
147C4×D4—3141no—
148#117—1571no—
149C2×C4⋊C4—3141no—
150C2×C22⋊C4—3141no—
151C22⋊C8—3141no—
152C22⋊C8—1571no—
153C22⋊C8C2×D15711yescharacteristic
154#95—1571no—
155#95C2×D15711yescharacteristic
156C24—1571no—
157#41—6282no—
158C2×Q8C4×D15711yescharacteristic
159C2×D4—3141no—
160C2×D4—3141no—
161C2×D4—3141no—
162C2×D4—1571no—
163C22×C4—21no—
164C22×C4—3141no—
165C22×C4—3141no—
166C22×C4—6282no—
167C22×C4—1571no—
168C22×C4—1571no—
169C22×C4—1571no—
170C22×C4—1571no—
171C22×C4—1571no—
172C22×C4C22×D15711yescharacteristic
173M16—6282no—
174C2×C8—21no—
175C2×C8—3141no—
176C4⋊C4—21no—
177C4⋊C4—3141no—
178C4⋊C4—6282no—
179C4⋊C4—1571no—
180C4⋊C4C4×D15711yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—3141no—
183C22⋊C4—3141no—
184C22⋊C4—3141no—
185C22⋊C4—3141no—
186C22⋊C4—6282no—
187C42—3141no—
188C23—3141no—
189C23—3141no—
190C23—3141no—
191C23—6281no—
192C23—6281no—
193C23—1571no—
194C23—1571no—
195C23D4×D15711yescharacteristic
196Q8—41no—
197D4—6281no—
198D4—6282no—
199D4—6282no—
200D4—6281no—
201D4—6281no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3142no—
209C2×C4—3142no—
210C2×C4—3142no—
211C2×C4—3141no—
212C2×C4—6281no—
213C2×C4—6281no—
214C2×C4—6282no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—6281no—
218C2×C4—1571no—
219C2×C4—1571no—
220C2×C4C2×C4×D15711yescharacteristic
221C2×C4D4×D15711yescharacteristic
222C8—41no—
223C8—6281no—
224C22—21no—
225C22—21no—
226C22—3141no—
227C22—3141no—
228C22—3141no—
229C22—3141no—
230C22—3141no—
231C22—3141no—
232C22—6282no—
233C22—6282no—
234C22—6281no—
235C22—6281no—
236C22—6281no—
237C22C22⋊C4×D15711yescharacteristic
238C22#1909779811yescharacteristic
239C22#1909780311yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—3141no—
246C4—6281no—
247C4—1572no—
248C4—12561no—
249C2—21no—
250C2—21no—
251C2—6281no—
252C2—6281no—
253C2—12561no—
254C2#99×D15711yescharacteristic
255C2#2375727311yescharacteristic
256C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757786C2
cosocleC22×C4×C157C23
hypercenter#328D157
hypocenterC157#1513
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23757235C2semidirect
3. #23757132C2semidirect
4. #23757010C2semidirect
5. #23757008C2semidirect
6. #23757006C2semidirect
7. #328×C157C2semidirect
8. C2×#14578955C4semidirect
12. #19097747C4semidirect
13. #19097746C4semidirect
18. #19097729C4semidirect
128. C157#1513semidirect
134. #328D157semidirect

Maximal subgroups

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

subgroupindex
#237577862
#237572352
#237571322
#237570102
#237570082
#237570062
#328×C1572
#1513157