Finite Group Databasebeta

← #34098599

Subgroups — #34098599

Order 20096.

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

normal subgroups only

This group has 216 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#23757807C211yesmaximal, characteristic
2#23757326C211yesmaximal, characteristic, complemented
3#23757003C212yesmaximal, complemented
4#23757000C212yesmaximal, complemented
5#423×C157C211yesmaximal, characteristic, complemented
6#19097765—21no—
7#19097763C411yescharacteristic
8#19097759C411yescharacteristic
9#19097754—21no—
10#19097750C411yescharacteristic
11#19097745C411yescharacteristic
12C4×Dic314C2211yescharacteristic
13C4×D628C2211yescharacteristic
14C4×C22⋊D157—21no—
15#19097728—21no—
16C4⋊#11929434—21no—
17C22⋊#11929434—21no—
18C4×#11929434C2212yes—
19C2×M16×C157—21no—
20C2×C42×C157C2211yescharacteristic
21C4⋊C8×C157—21no—
22C4⋊C8×C157C2212yes—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157—21no—
26C2×C4×D157—21no—
27C2×#11929434—22no—
28C4⋊Dic157C2×C411yescharacteristic
29C4⋊Dic157C2×C411yescharacteristic
30#14578933—21no—
31#14578933—21no—
32#14578933—21no—
33#14578933—21no—
34C22⋊Dic157—21no—
35#14578931—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39C4×Dic157—21no—
40C22×C4×C157C2×C411yescharacteristic
41C22×C4×C157D411yescharacteristic
42C22×C4×C157D411yescharacteristic
43M16×C157—42no—
44C2×C8×C157—22no—
45C42×C157C2×C411yescharacteristic
46C42×C157D411yescharacteristic
47C42×C157D411yescharacteristic
48C42×C157C2311yescharacteristic
49C22×D157—21no—
50Dic314—22no—
51D628—22no—
52C22⋊D157—42no—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C4×D157—41no—
57C4×D157—41no—
58#11929434—42no—
59C23×C157C22⋊C411yescharacteristic
60C2×C4×C157—22no—
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—41no—
64C2×C4×C157C22⋊C411yescharacteristic
65C2×C4×C157C22⋊C411yescharacteristic
66C2×C4×C157C22⋊C411yescharacteristic
67C2×C4×C157C22×C411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C8×C157—42no—
71C22×C157—21no—
72C22×C157—21no—
73C22×C157—21no—
74C22×C157C2×C22⋊C411yescharacteristic
75C2×D157—41no—
76C2×D157—41no—
77C2×D157—41no—
78C4×C157—21no—
79C4×C157—21no—
80C4×C157—21no—
81C4×C157—21no—
82C4×C157#13112yes—
83C4×C157AGL(1,ℤ/8)11yescharacteristic
84C4×C157#13711yescharacteristic
85Dic157—41no—
86Dic157—41no—
87Dic157—41no—
88C2×C157—41no—
89C2×C157#40811yescharacteristic
90C2×C157#41711yescharacteristic
91C2×C157#42111yescharacteristic
92D157—81no—
93C157#149511yescharacteristic, complemented, Sylow
94#1495—1571nomaximal, Sylow
95#529—1571no—
96#431—1571no—
97#423D15711yescharacteristic, complemented
98Q8⋊C8—1572no—
99D4⋊C8—1572no—
100C2×M16—21no—
101#126—3141no—
102#125—1571no—
103#124—1571no—
104#123—3141no—
105C22⋊Q8—1571no—
106#121—1571no—
107C4×Q8—1571no—
108C4×D4—3141no—
109C4×D4—1571no—
110#117—3141no—
111C2×C42C2×D15711yescharacteristic
112C4⋊C8—21no—
113C4⋊C8—3141no—
114C4⋊C8C2×D15712yes—
115C22⋊C8—3141no—
116C4×C8—1572no—
117C2×Q8—1571no—
118C2×D4—3141no—
119C2×D4—1571no—
120C22×C4—3141no—
121C22×C4C4×D15711yescharacteristic
122C22×C4C22⋊D15711yescharacteristic
123C22×C4D62811yescharacteristic
124M16—42no—
125C2×C8—22no—
126C2×C8—3142no—
127C4⋊C4—3141no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C4⋊C4—1571no—
132C4⋊C4—1571no—
133C22⋊C4—3141no—
134C22⋊C4—3141no—
135C22⋊C4—3141no—
136C22⋊C4—3141no—
137C22⋊C4—3141no—
138C42—3141no—
139C42C4×D15711yescharacteristic
140C42C22⋊D15711yescharacteristic
141C42D62811yescharacteristic
142C42C22×D15711yescharacteristic
143C23—3141no—
144C23#1457893111yescharacteristic
145Q8—3142no—
146D4—3142no—
147D4—6282no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—3141no—
153C2×C4—3141no—
154C2×C4—3141no—
155C2×C4—6281no—
156C2×C4—6281no—
157C2×C4#1457893111yescharacteristic
158C2×C4#1457893111yescharacteristic
159C2×C4#1457893111yescharacteristic
160C2×C4C2×C4×D15711yescharacteristic
161C2×C4C2×C22⋊D15711yescharacteristic
162C2×C4C2×D62811yescharacteristic
163C8—42no—
164C8—6282no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—6281no—
169C22—6281no—
170C22—6281no—
171C22C2×#1457893111yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—6281no—
177C4—6281no—
178C4—6281no—
179C4#1909777912yes—
180C4#1909779711yescharacteristic
181C4#1909780211yescharacteristic
182C2—41no—
183C2—12561no—
184C2#2375724111yescharacteristic
185C2#2375727211yescharacteristic
186C2#2375728911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#423×C157C2
socleC22×C157C2×C22⋊C4
prime radical#19097745C4
cosocleC42×C157C23
hypercenter#423D157
hypocenterC157#1495
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #23757326C2semidirect
3. #23757003C2semidirect
4. #23757000C2semidirect
5. #423×C157C2semidirect
93. C157#1495semidirect
97. #423D157semidirect

Maximal subgroups

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

subgroupindex
#237578072
#237573262
#237570032
#237570002
#423×C1572
#1495157