Finite Group Databasebeta

← #34101762

Subgroups — #34101762

Order 20096.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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#131×D157C211yesmaximal, characteristic
2C2×#19097710C211yesmaximal, characteristic, complemented
3M32×D157C211yesmaximal, characteristic, complemented
4#23757058C211yesmaximal, characteristic, complemented
5#23757057C211yesmaximal, characteristic, complemented
6#23757056C211yesmaximal, characteristic, complemented
7#350×C157C211yesmaximal, characteristic, complemented
8#41×D157C411yescharacteristic
9#19097779—21no—
10#19097779C411yescharacteristic
11#19097778C411yescharacteristic
12#19097777—21no—
13#19097777C2211yescharacteristic
14M16×D157—21no—
15M16×D157C411yescharacteristic
16C2×C8×D157—21no—
17C2×C8×D157C2211yescharacteristic
18#19097711C2211yescharacteristic, complemented
19#19097710—21no—
20#19097710—21no—
21#19097710—21no—
22C2×#14578929C2211yescharacteristic, complemented
23C16×D157—21no—
24#131×C157C2211yescharacteristic
25M32×C157C2211yescharacteristic, complemented
26C2×C16×C157C2211yescharacteristic, complemented
27#14578955C811yescharacteristic
28#14578954—21no—
29#14578954C2×C411yescharacteristic
30#14578953—21no—
31#14578953C811yescharacteristic
32Q8×D157C811yescharacteristic
33D4×D157—21no—
34D4×D157C811yescharacteristic
35C2×C4×D157—21no—
36C2×C4×D157C2×C411yescharacteristic
37#14578938—21no—
38#14578938C2×C411yescharacteristic
39#14578937—21no—
40#14578937—21no—
41#14578937—21no—
42C2×#11929434—21no—
43C2×#11929434C2×C411yescharacteristic
44C8×D157—21no—
45C8×D157—21no—
46C8×D157—21no—
47C8×D157D411yescharacteristic
48C8×D157D411yescharacteristic
49C8×D157D411yescharacteristic
50C8×D157D411yescharacteristic
51#14578929—21no—
52#14578929—21no—
53#41×C157C2×C411yescharacteristic
54M16×C157—21no—
55M16×C157C2×C411yescharacteristic
56C2×C8×C157—21no—
57C2×C8×C157C2311yescharacteristic
58C16×C157—21no—
59C16×C157—21no—
60C22×D157—21no—
61C22×D157M1611yescharacteristic
62Dic314—21no—
63Dic314C2×C811yescharacteristic
64D628—21no—
65D628C2×C811yescharacteristic
66C22⋊D157—21no—
67C22⋊D157—21no—
68C22⋊D157—21no—
69C2×Dic157—21no—
70C2×Dic157M1611yescharacteristic
71C4×D157—21no—
72C4×D157—21no—
73C4×D157—21no—
74C4×D157C22⋊C411yescharacteristic
75C4×D157C22⋊C411yescharacteristic
76C4×D157C2×C811yescharacteristic
77C4×D157C2×C811yescharacteristic
78#11929434—21no—
79#11929434C22⋊C411yescharacteristic
80#11929434C22⋊C411yescharacteristic
81Q8×C157C2×C811yescharacteristic
82D4×C157—21no—
83D4×C157C2×C811yescharacteristic
84C2×C4×C157—21no—
85C2×C4×C157C22×C411yescharacteristic
86C8×C157—21no—
87C8×C157C2×D411yescharacteristic
88C8×C157C2×D411yescharacteristic
89C22×C157—21no—
90C22×C157C2×M1611yescharacteristic
91C2×D157—21no—
92C2×D157—41no—
93C2×D157—42no—
94C2×D157C22⋊C811yescharacteristic
95C2×D157C22⋊C811yescharacteristic
96C4×C157—21no—
97C4×C157C2×C22⋊C411yescharacteristic
98C4×C157C22×C811yescharacteristic
99Dic157—21no—
100Dic157C22⋊C811yescharacteristic
101Dic157C22⋊C811yescharacteristic
102C2×C157—21no—
103C2×C157—41no—
104C2×C157C2×C22⋊C811yescharacteristic
105D157—21no—
106D157—21no—
107D157—41no—
108C157#211711yescharacteristic, complemented, Sylow
109#2117—1571nomaximal, Sylow
110C2×#131—1571no—
111C2×M32—1571no—
112C2×M32—1571no—
113#350—1571no—
114#350—1571no—
115#350—1571no—
116#350D15711yescharacteristic, complemented
117C2×#41—1571no—
118#131—3141no—
119#131—3141no—
120#131—1571no—
121#131—1571no—
122#131—1571no—
123#131C2×D15711yescharacteristic
124C2×M16—3141no—
125C2×M16—1571no—
126C22×C8—3141no—
127C22×C8—1571no—
128M32—3141no—
129M32—3141no—
130M32—3141no—
131M32—1571no—
132M32C2×D15711yescharacteristic, complemented
133C2×C16—3141no—
134C2×C16—1571no—
135C2×C16C2×D15711yescharacteristic, complemented
136#41—3141no—
137#41—3141no—
138#41—1571no—
139#41—1571no—
140#41—1571no—
141#41C4×D15711yescharacteristic
142C2×Q8—1571no—
143C2×D4—3141no—
144C2×D4—1571no—
145C22×C4—3141no—
146C22×C4—1571no—
147M16—21no—
148M16—3141no—
149M16—3141no—
150M16—3141no—
151M16—3141no—
152M16—1571no—
153M16C4×D15711yescharacteristic
154C2×C8—21no—
155C2×C8—3141no—
156C2×C8—3141no—
157C2×C8—3141no—
158C2×C8—3141no—
159C2×C8—1571no—
160C2×C8—1571no—
161C2×C8—1571no—
162C2×C8—1571no—
163C2×C8—1571no—
164C2×C8C22×D15711yescharacteristic
165C16—21no—
166C16—21no—
167C16—3141no—
168C16—3141no—
169C23—3141no—
170C23—1571no—
171Q8—3141no—
172Q8—1571no—
173Q8C8×D15711yescharacteristic
174D4—21no—
175D4—3141no—
176D4—3141no—
177D4—3141no—
178D4—3141no—
179D4—1571no—
180D4C8×D15711yescharacteristic
181C2×C4—21no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—3141no—
185C2×C4—3141no—
186C2×C4—1571no—
187C2×C4—1571no—
188C2×C4—1571no—
189C2×C4—1571no—
190C2×C4—1571no—
191C2×C4C2×C4×D15711yescharacteristic
192C8—21no—
193C8—3141no—
194C8—1571no—
195C8—1571no—
196C8D4×D15711yescharacteristic
197C8D4×D15711yescharacteristic
198C22—21no—
199C22—3141no—
200C22—6281no—
201C22—6282no—
202C22—1571no—
203C22—1571no—
204C22M16×D15711yescharacteristic
205C4—21no—
206C4—3141no—
207C4—1571no—
208C4—1571no—
209C4C22⋊C4×D15711yescharacteristic
210C4C2×C8×D15711yescharacteristic
211C2—21no—
212C2—41no—
213C2—3141no—
214C2—3141no—
215C2—6281no—
216C2C22⋊C8×D15711yescharacteristic
subgroupG/H
centerC8D4×D157
commutatorC4×C157C22×C8
FrattiniC2×C8C22×D157
Fitting#350×C157C2
socleC2×C157C2×C22⋊C8
prime radical#41×D157C4
cosocleC2×C8×C157C23
hypercenter#350D157
hypocenterC157#2117
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. C2×#19097710C2semidirect
3. M32×D157C2semidirect
4. #23757058C2semidirect
5. #23757057C2semidirect
6. #23757056C2semidirect
7. #350×C157C2semidirect
18. #19097711C22semidirect
22. C2×#14578929C22semidirect
25. M32×C157C22semidirect
26. C2×C16×C157C22semidirect
108. C157#2117semidirect
116. #350D157semidirect
132. M32C2×D157semidirect
135. C2×C16C2×D157semidirect

Maximal subgroups

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

subgroupindex
#131×D1572
C2×#190977102
M32×D1572
#237570582
#237570572
#237570562
#350×C1572
#2117157