Finite Group Databasebeta

← #34098628

Subgroups — #34098628

Order 20096.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×C22⋊Dic157C211yesmaximal, characteristic, complemented
3#23757011C212yesmaximal, complemented
4#23757008C212yesmaximal, complemented
5C2×C22⋊C8×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic, complemented
7#19097754—21no—
8#19097750C411yescharacteristic, complemented
9#19097750C2211yescharacteristic
10#19097745C411yescharacteristic, complemented
11#19097745C2211yescharacteristic
12#19097740—21no—
13C4×C22⋊D157—21no—
14C4×C22⋊D157—21no—
15#19097730C411yescharacteristic, complemented
16C2×C22⋊Dic157—21no—
17C2×C4×Dic157—21no—
18#19097678C2212yes—
19C23×C4×C157C2211yescharacteristic
20C22×C8×C157—21no—
21C22⋊C8×C157—21no—
22C22⋊C8×C157C2212yes—
23#14578954—42no—
24C2×Dic314C2×C411yescharacteristic
25C2×D628C2×C411yescharacteristic
26C2×C22⋊D157—21no—
27C2×C22⋊D157—21no—
28C2×C22⋊D157—21no—
29C22×Dic157—22no—
30C2×C4×D157—21no—
31C4⋊Dic157C2×C411yescharacteristic
32C4⋊Dic157C2×C411yescharacteristic
33#14578933—21no—
34#14578933—21no—
35C22⋊Dic157—24no—
36C22⋊Dic157—21no—
37C22⋊Dic157—21no—
38C22⋊Dic157—21no—
39#14578931—21no—
40#14578931—21no—
41C4×Dic157—21no—
42C4×Dic157—42no—
43C24×C157D411yescharacteristic
44C22×C4×C157—42no—
45C22×C4×C157C2×C411yescharacteristic
46C22×C4×C157C2×C411yescharacteristic
47C22×C4×C157D411yescharacteristic
48C22×C4×C157D411yescharacteristic
49C22×C4×C157D411yescharacteristic
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—22no—
52C2×C8×C157—42no—
53C22×D157—21no—
54Dic314—41no—
55D628—41no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C22⋊D157—42no—
59C2×Dic157—24no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—42no—
64C2×Dic157—42no—
65C4×D157—42no—
66C23×C157—22no—
67C23×C157—22no—
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×C157C22⋊C411yescharacteristic
79C2×C4×C157C22⋊C411yescharacteristic
80C2×C4×C157C22×C411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C8×C157—42no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—21no—
90C22×C157—44no—
91C22×C157#10412yes—
92C22×C157C2×C22⋊C411yescharacteristic
93C22×C157#13512yes—
94C2×D157—41no—
95C2×D157—41no—
96C2×D157—41no—
97C4×C157—21no—
98C4×C157—21no—
99C4×C157—21no—
100C4×C157#9912yes—
101Dic157—44no—
102Dic157—41no—
103Dic157—41no—
104Dic157—41no—
105C2×C157—22no—
106C2×C157—22no—
107C2×C157—41no—
108C2×C157C2×#9911yescharacteristic
109C2×C157#41611yescharacteristic
110C2×C157C2×#10411yescharacteristic
111D157—81no—
112C157#150111yescharacteristic, complemented, Sylow
113#1501—1571nomaximal, Sylow
114#525—1571no—
115C2×C22⋊C8D15711yescharacteristic, complemented
116C4×C22⋊C4—1571no—
117#328—1572no—
118#327—1572no—
119C2×#41—1571no—
120C23×C4C2×D15711yescharacteristic
121C22×C8—21no—
122#123—3141no—
123C22⋊Q8—1571no—
124C22⋊Q8—1571no—
125#121—1571no—
126#121—1571no—
127#120—3141no—
128C4×D4—3141no—
129C4×D4—3141no—
130#117—1571no—
131C2×C22⋊C4—3141no—
132C2×C42—3141no—
133C22⋊C8—21no—
134C22⋊C8C2×D15712yes—
135#95—1572no—
136C24D62811yescharacteristic
137#41—6282no—
138C2×Q8—1571no—
139C2×D4—3141no—
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—1571no—
143C22×C4—42no—
144C22×C4—3142no—
145C22×C4—3141no—
146C22×C4C4×D15711yescharacteristic
147C22×C4C4×D15711yescharacteristic
148C22×C4C22⋊D15711yescharacteristic
149C22×C4C22⋊D15711yescharacteristic
150C22×C4D62811yescharacteristic
151C22×C4C22×D15711yescharacteristic
152C2×C8—22no—
153C2×C8—42no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—1571no—
157C4⋊C4—1571no—
158C22⋊C4—3144no—
159C22⋊C4—3141no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C42—3141no—
165C42—6282no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—3141no—
170C23#1457893111yescharacteristic
171C23#1457893111yescharacteristic
172C23C2×D62811yescharacteristic
173Q8—6281no—
174D4—6281no—
175D4—6282no—
176D4—6282no—
177D4—6282no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—3144no—
185C2×C4—3141no—
186C2×C4—3141no—
187C2×C4—3141no—
188C2×C4—6282no—
189C2×C4—6282no—
190C2×C4—6282no—
191C2×C4#1457893111yescharacteristic
192C2×C4#1457893111yescharacteristic
193C2×C4C2×C4×D15711yescharacteristic
194C2×C4C2×C22⋊D15711yescharacteristic
195C8—42no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—6281no—
205C22—6281no—
206C22—6281no—
207C22#1909769712yes—
208C22C2×#1457893111yescharacteristic
209C22#1909779312yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—6284no—
214C4—6281no—
215C4—6281no—
216C4—6281no—
217C4#1909768512yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—12561no—
222C2C2×#1909768511yescharacteristic
223C2#2375727011yescharacteristic
224C2C2×#1909769711yescharacteristic
subgroupG/H
centerC2×C4#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×C22⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenterC2×C22⋊C8D157
hypocenterC157#1501
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic157C2semidirect
3. #23757011C2semidirect
4. #23757008C2semidirect
5. C2×C22⋊C8×C157C2semidirect
6. C2×#14578954C4semidirect
8. #19097750C4semidirect
10. #19097745C4semidirect
15. #19097730C4semidirect
112. C157#1501semidirect
115. C2×C22⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237577842
C4×C22⋊Dic1572
#237570112
#237570082
C2×C22⋊C8×C1572
#1501157