Finite Group Databasebeta

← #34098677

Subgroups — #34098677

Order 20096.

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

normal subgroups only

This group has 286 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
1#23757784C211yesmaximal, characteristic
2#23757237C211yesmaximal, characteristic, complemented
3#23757009C212yesmaximal, complemented
4#23757006C212yesmaximal, complemented
5#380×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic, complemented
7C2×#14578938—21no—
8#19097754—21no—
9#19097750C411yescharacteristic, complemented
10#19097750C2211yescharacteristic
11#19097745C411yescharacteristic, complemented
12#19097745C2211yescharacteristic
13#19097740—21no—
14C4×C22⋊D157—21no—
15C4×C22⋊D157—21no—
16#19097730C411yescharacteristic, complemented
17C22⋊#11929434—21no—
18C22⋊#11929434C2212yes—
19C23×C4×C157C2211yescharacteristic
20C2×C4⋊C4×C157—21no—
21C2×C22⋊C4×C157—21no—
22#95×C157C2212yes—
23#14578954—42no—
24C2×Dic314C2×C411yescharacteristic
25C2×D628C2×C411yescharacteristic
26C2×C22⋊D157—21no—
27C2×C22⋊D157—21no—
28C2×C22⋊D157—21no—
29C2×C4×D157—21no—
30#14578938—42no—
31C2×#11929434—22no—
32C4⋊Dic157C2×C411yescharacteristic
33C4⋊Dic157C2×C411yescharacteristic
34#14578933—21no—
35#14578933—21no—
36C22⋊Dic157—21no—
37C22⋊Dic157—21no—
38C22⋊Dic157—21no—
39#14578931—21no—
40#14578931—21no—
41C4×Dic157—21no—
42C24×C157D411yescharacteristic
43C22×C4×C157—22no—
44C22×C4×C157—42no—
45C22×C4×C157C2×C411yescharacteristic
46C22×C4×C157C2×C411yescharacteristic
47C22×C4×C157D411yescharacteristic
48C22×C4×C157D411yescharacteristic
49C22×C4×C157D411yescharacteristic
50C22×C4×C157C2311yescharacteristic
51C4⋊C4×C157—42no—
52C22⋊C4×C157—42no—
53C22×D157—21no—
54Dic314—41no—
55D628—41no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C22⋊D157—41no—
59C22⋊D157—41no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C4×D157—42no—
64#11929434—42no—
65C23×C157—21no—
66C23×C157—21no—
67C23×C157—41no—
68C23×C157—41no—
69C23×C157C22⋊C411yescharacteristic
70C23×C157C22⋊C411yescharacteristic
71C23×C157C2×D411yescharacteristic
72C2×C4×C157—22no—
73C2×C4×C157—22no—
74C2×C4×C157—22no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157—42no—
79C2×C4×C157—42no—
80C2×C4×C157—42no—
81C2×C4×C157C22⋊C411yescharacteristic
82C2×C4×C157C22⋊C411yescharacteristic
83C2×C4×C157C22×C411yescharacteristic
84C2×C4×C157C2×D411yescharacteristic
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—21no—
90C22×C157—21no—
91C22×C157—21no—
92C22×C157—21no—
93C22×C157—42no—
94C22×C157—42no—
95C22×C157C2×C22⋊C411yescharacteristic
96C22×C157AGL(1,ℤ/8)11yescharacteristic
97C22×C157#13711yescharacteristic
98C2×D157—41no—
99C2×D157—41no—
100C2×D157—41no—
101C4×C157—21no—
102C4×C157—21no—
103C4×C157—21no—
104C4×C157—82no—
105C4×C157#9912yes—
106Dic157—41no—
107Dic157—41no—
108Dic157—41no—
109C2×C157—21no—
110C2×C157—21no—
111C2×C157—41no—
112C2×C157—41no—
113C2×C157C2×#9911yescharacteristic
114C2×C157#41711yescharacteristic
115C2×C157#42111yescharacteristic
116D157—81no—
117C157#151311yescharacteristic, complemented, Sylow
118#1513—1571nomaximal, Sylow
119#525—1571no—
120#407—1571no—
121#380D15711yescharacteristic, complemented
122#328—1572no—
123#327—1572no—
124C2×#41—1571no—
125C23×C4C2×D15711yescharacteristic
126C2×M16—3141no—
127#123—3141no—
128C22⋊Q8—1571no—
129C22⋊Q8—1571no—
130#121—1571no—
131#121—1571no—
132#120—3141no—
133C4×D4—3141no—
134C4×D4—3141no—
135#117—1571no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—3141no—
139C22⋊C8—1572no—
140#95C2×D15712yes—
141C24C22⋊D15711yescharacteristic
142#41—6282no—
143C2×Q8—1571no—
144C2×D4—3141no—
145C2×D4—3141no—
146C2×D4—3141no—
147C2×D4—1571no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—3141no—
151C22×C4C4×D15711yescharacteristic
152C22×C4C4×D15711yescharacteristic
153C22×C4C22⋊D15711yescharacteristic
154C22×C4D62811yescharacteristic
155C22×C4D62811yescharacteristic
156C22×C4C22×D15711yescharacteristic
157M16—6282no—
158C2×C8—3142no—
159C4⋊C4—42no—
160C4⋊C4—3141no—
161C4⋊C4—3141no—
162C4⋊C4—1571no—
163C4⋊C4—1571no—
164C22⋊C4—42no—
165C22⋊C4—3141no—
166C22⋊C4—3141no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C42—3141no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—3141no—
176C23#1457893111yescharacteristic
177C23#1457893111yescharacteristic
178C23C2×C22⋊D15711yescharacteristic
179Q8—6281no—
180D4—6281no—
181D4—6282no—
182D4—6282no—
183D4—6281no—
184D4—6281no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—3141no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—6282no—
198C2×C4#1457893111yescharacteristic
199C2×C4#1457893111yescharacteristic
200C2×C4C2×C4×D15711yescharacteristic
201C2×C4C2×D62811yescharacteristic
202C8—6282no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—6281no—
214C22—6281no—
215C22—6281no—
216C22C2×#1457893111yescharacteristic
217C22#1909779711yescharacteristic
218C22#1909780211yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—6281no—
224C4—6281no—
225C4—6281no—
226C4#1909768512yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—12561no—
232C2C2×#1909768511yescharacteristic
233C2#2375727211yescharacteristic
234C2#2375729111yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#380×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenter#380D157
hypocenterC157#1513
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #23757237C2semidirect
3. #23757009C2semidirect
4. #23757006C2semidirect
5. #380×C157C2semidirect
6. C2×#14578954C4semidirect
9. #19097750C4semidirect
11. #19097745C4semidirect
16. #19097730C4semidirect
117. C157#1513semidirect
121. #380D157semidirect

Maximal subgroups

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

subgroupindex
#237577842
#237572372
#237570092
#237570062
#380×C1572
#1513157