Finite Group Databasebeta

← #34098482

Subgroups — #34098482

Order 20096.

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

normal subgroups only

This group has 280 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
1C2×#19097754C211yesmaximal, characteristic
2#23757237C211yesmaximal, characteristic, complemented
3#23756998C212yesmaximal, complemented
4#23756996C212yesmaximal, complemented
5C2×C22⋊C8×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157C411yescharacteristic
7C2×#14578938—21no—
8#19097754—21no—
9#19097754—21no—
10#19097754—21no—
11#19097754—21no—
12C2×#14578933C411yescharacteristic
13C2×#14578933C2211yescharacteristic
14C2×C22⋊Dic157C411yescharacteristic
15C2×#14578931C411yescharacteristic
16C2×#14578931C2211yescharacteristic
17C22⋊#11929434—21no—
18C22⋊#11929434C2212yes—
19C23×C4×C157C2211yescharacteristic
20C22×C8×C157—21no—
21C22⋊C8×C157—21no—
22C22⋊C8×C157C2212yes—
23C23×D157C2×C411yescharacteristic
24C2×C22⋊D157—21no—
25C2×C22⋊D157—21no—
26C2×C22⋊D157—42no—
27C22×Dic157C2×C411yescharacteristic
28C22×Dic157C2×C411yescharacteristic
29C22×Dic157C2×C411yescharacteristic
30#14578938—42no—
31C2×#11929434—22no—
32#14578933—21no—
33#14578933—21no—
34#14578933—21no—
35#14578933—21no—
36C22⋊Dic157—21no—
37C22⋊Dic157—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42C24×C157C2×C411yescharacteristic
43C22×C4×C157—42no—
44C22×C4×C157C2×C411yescharacteristic
45C22×C4×C157D411yescharacteristic
46C22×C4×C157D411yescharacteristic
47C22×C4×C157D411yescharacteristic
48C22×C4×C157D411yescharacteristic
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—22no—
51C2×C8×C157—42no—
52C22×D157—21no—
53C22×D157—22no—
54C22×D157—41no—
55C22×D157—41no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—22no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64#11929434—42no—
65C23×C157—22no—
66C23×C157—22no—
67C23×C157—41no—
68C23×C157C22⋊C411yescharacteristic
69C23×C157C22⋊C411yescharacteristic
70C23×C157C22×C411yescharacteristic
71C2×C4×C157—22no—
72C2×C4×C157—22no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C22⋊C411yescharacteristic
78C2×C4×C157C22⋊C411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C8×C157—42no—
82C22×C157—21no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—44no—
90C22×C157#9912yes—
91C22×C157C2×C22⋊C411yescharacteristic
92C22×C157#13112yes—
93C2×D157—41no—
94C2×D157—41no—
95C2×D157—41no—
96C2×D157—82no—
97C4×C157—21no—
98C4×C157—21no—
99C4×C157—21no—
100C4×C157—21no—
101Dic157—41no—
102Dic157—41no—
103Dic157—41no—
104C2×C157—22no—
105C2×C157—22no—
106C2×C157—41no—
107C2×C157#40811yescharacteristic
108C2×C157C2×#9911yescharacteristic
109C2×C157#41311yescharacteristic
110D157—81no—
111C157#146811yescharacteristic, complemented, Sylow
112#1468—1571nomaximal, Sylow
113C2×#123—1571no—
114#407—1571no—
115C2×C22⋊C8D15711yescharacteristic, complemented
116#324—1572no—
117#323—1572no—
118C22×D4—1571no—
119C23×C4C2×D15711yescharacteristic
120C2×M16—3141no—
121C22×C8—21no—
122#123—3141no—
123#123—3141no—
124#123—3141no—
125#123—3141no—
126C2×C4⋊C4—1571no—
127C2×C4⋊C4—1571no—
128C2×C22⋊C4—1571no—
129C2×C22⋊C4—1571no—
130C2×C22⋊C4—1571no—
131C22⋊C8—21no—
132C22⋊C8—3141no—
133C22⋊C8—1572no—
134C22⋊C8C2×D15712yes—
135C24—1571no—
136C24C4×D15711yescharacteristic
137C2×D4—3141no—
138C2×D4—3141no—
139C2×D4—6282no—
140C22×C4—42no—
141C22×C4—1571no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4C4×D15711yescharacteristic
145C22×C4C22⋊D15711yescharacteristic
146C22×C4C22⋊D15711yescharacteristic
147C22×C4D62811yescharacteristic
148C22×C4D62811yescharacteristic
149C22×C4C22×D15711yescharacteristic
150M16—6282no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—3142no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C22⋊C4—3141no—
159C22⋊C4—3141no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—3141no—
168C23—3142no—
169C23—6281no—
170C23—6281no—
171C23#1457893111yescharacteristic
172C23#1457893111yescharacteristic
173C23C2×C4×D15711yescharacteristic
174D4—6282no—
175D4—6282no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—3141no—
185C2×C4—3142no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4#1457893111yescharacteristic
189C2×C4#1457893111yescharacteristic
190C2×C4C2×C22⋊D15711yescharacteristic
191C2×C4C2×D62811yescharacteristic
192C8—42no—
193C8—6282no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—6281no—
203C22—6281no—
204C22—6281no—
205C22—12562no—
206C22#1909768512yes—
207C22C2×#1457893111yescharacteristic
208C22#1909777712yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—6281no—
214C4—6281no—
215C4—6281no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—12561no—
220C2#2375723911yescharacteristic
221C2C2×#1909768511yescharacteristic
222C2#2375725511yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×C22⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×C22⋊D157C4
cosocleC22×C4×C157C23
hypercenterC2×C22⋊C8D157
hypocenterC157#1468
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #23757237C2semidirect
3. #23756998C2semidirect
4. #23756996C2semidirect
5. C2×C22⋊C8×C157C2semidirect
111. C157#1468semidirect
115. C2×C22⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977542
#237572372
#237569982
#237569962
C2×C22⋊C8×C1572
#1468157