Finite Group Databasebeta

← #34098621

Subgroups — #34098621

Order 20096.

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

normal subgroups only

This group has 238 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#23757809C211yesmaximal, characteristic
2#23757323C211yesmaximal, characteristic, complemented
3#23757118C211yesmaximal, characteristic, complemented
4#23757010C211yesmaximal, characteristic, complemented
5#23757008C211yesmaximal, characteristic
6#23757006C211yesmaximal, characteristic
7#328×C157C211yesmaximal, characteristic, complemented
8#19097766—21no—
9#19097762C411yescharacteristic, complemented
10#19097760C411yescharacteristic, complemented
11#19097755—21no—
12#19097745C2211yescharacteristic
13Q8×Dic157C411yescharacteristic, complemented
14#19097733C411yescharacteristic, complemented
15#19097731—21no—
16#19097729—21no—
17C2×C4×Dic157—21no—
18C2×C4×Dic157C2211yescharacteristic
19#19097700—21no—
20C22⋊#11929434C2211yescharacteristic
21C8×Dic157—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×D628C2×C411yescharacteristic
28C2×C22⋊D157—21no—
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×C4×D157—21no—
33C2×#11929434—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157C2×C411yescharacteristic
37#14578933—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42C4×Dic157—24no—
43C4×Dic157—21no—
44C4×Dic157C2×C411yescharacteristic
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C2×Q8×C157C2×C411yescharacteristic
49C22×C4×C157—21no—
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C22⋊C4×C157—21no—
55C22×D157—21no—
56D628—41no—
57C22⋊D157—41no—
58C22⋊D157—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—21no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C4×D157—42no—
71#11929434—41no—
72C23×C157C2×D411yescharacteristic
73Q8×C157—41no—
74C2×C4×C157—22no—
75C2×C4×C157—21no—
76C2×C4×C157—21no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157C22×C411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C8×C157—41no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157C2×C22⋊C411yescharacteristic
86C22×C157#13511yescharacteristic
87C22×C157#13511yescharacteristic
88C2×D157—41no—
89C2×D157—41no—
90C2×D157—41no—
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—42no—
94C4×C157—41no—
95C4×C157—41no—
96Dic157—21no—
97Dic157—21no—
98Dic157—21no—
99Dic157—42no—
100Dic157—41no—
101Dic157#10412yes—
102C2×C157—21no—
103C2×C157—21no—
104C2×C157#41011yescharacteristic
105C2×C157#41611yescharacteristic
106C2×C157C2×#10411yescharacteristic
107D157—81no—
108C157#150011yescharacteristic, complemented, Sylow
109#1500—1571nomaximal, Sylow
110#529—1571no—
111#431—1571no—
112#376—1571no—
113#328—1571no—
114#328D15711yescharacteristic, complemented
115#327—1571no—
116#327—1571no—
117#126—3141no—
118#125—1571no—
119#124—1571no—
120#123—3141no—
121C22⋊Q8C2×D15711yescharacteristic
122#121—1571no—
123C4×Q8—1571no—
124C4×D4—3141no—
125C4×D4—1571no—
126#117—3141no—
127C2×C42—3141no—
128C2×C42—1571no—
129C4⋊C8—3141no—
130C22⋊C8—1571no—
131C22⋊C8C2×D15711yescharacteristic
132C4×C8—3141no—
133#95—3141no—
134#95—1571no—
135#95C2×D15711yescharacteristic
136C2×Q8C4×D15711yescharacteristic
137C2×D4—3141no—
138C2×D4—1571no—
139C22×C4—21no—
140C22×C4—3141no—
141C22×C4—3141no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4C22×D15711yescharacteristic
145C2×C8—21no—
146C2×C8—3141no—
147C4⋊C4—21no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—1571no—
152C4⋊C4C4×D15711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C42—3144no—
159C42—3141no—
160C42—1571no—
161C42—1571no—
162C42—1571no—
163C42—1571no—
164C23—3141no—
165C23D4×D15711yescharacteristic
166Q8—41no—
167D4—6281no—
168D4—6281no—
169D4—6281no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—3142no—
179C2×C4—3142no—
180C2×C4—3141no—
181C2×C4—6282no—
182C2×C4—6281no—
183C2×C4—6281no—
184C2×C4—1571no—
185C2×C4—1571no—
186C2×C4—1571no—
187C2×C4—1571no—
188C2×C4C2×C4×D15711yescharacteristic
189C2×C4D4×D15711yescharacteristic
190C8—41no—
191C8—6281no—
192C22—21no—
193C22—21no—
194C22—6281no—
195C22—6281no—
196C22—6281no—
197C22C22⋊C4×D15711yescharacteristic
198C22#1909779211yescharacteristic
199C22#1909779411yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3141no—
206C4—3141no—
207C4—3141no—
208C4—6282no—
209C4—6281no—
210C4—1572no—
211C2—21no—
212C2—21no—
213C2—12561no—
214C2#2375724511yescharacteristic
215C2#2375726811yescharacteristic
216C2#104×D15711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097745C22
cosocleC22×C4×C157C23
hypercenter#328D157
hypocenterC157#1500
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. #23757323C2semidirect
3. #23757118C2semidirect
4. #23757010C2semidirect
7. #328×C157C2semidirect
9. #19097762C4semidirect
10. #19097760C4semidirect
13. Q8×Dic157C4semidirect
14. #19097733C4semidirect
108. C157#1500semidirect
114. #328D157semidirect

Maximal subgroups

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

subgroupindex
#237578092
#237573232
#237571182
#237570102
#237570082
#237570062
#328×C1572
#1500157