Finite Group Databasebeta

← #34098571

Subgroups — #34098571

Order 20096.

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

normal subgroups only

This group has 246 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
1C4×#14578954C211yesmaximal, characteristic
2#23757330C211yesmaximal, characteristic, complemented
3#23757005C212yesmaximal, complemented
4#23757002C212yesmaximal, complemented
5#431×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic
7C4×Dic314C411yescharacteristic
8C4×Dic314C2211yescharacteristic
9C4×D628C411yescharacteristic
10C4×D628C2211yescharacteristic
11C4×C22⋊D157—21no—
12C4×C22⋊D157—21no—
13#19097730C411yescharacteristic
14#19097728—21no—
15C42×D157—21no—
16C4⋊#11929434C2212yes—
17C22⋊#11929434—21no—
18#19097682—21no—
19C2×C42×C157C2211yescharacteristic
20C4⋊C8×C157—21no—
21C22⋊C8×C157—21no—
22C4×C8×C157C2212yes—
23#14578954—22no—
24#14578954—22no—
25C2×Dic314C2×C411yescharacteristic
26C2×D628C2×C411yescharacteristic
27C2×C22⋊D157—21no—
28C2×C4×D157—21no—
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×#11929434—22no—
32C4⋊Dic157C2×C411yescharacteristic
33C4⋊Dic157C2×C411yescharacteristic
34#14578933—21no—
35#14578933—21no—
36C22⋊Dic157—21no—
37#14578931—21no—
38#14578931—21no—
39C4×Dic157—21no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C22×C4×C157C2×C411yescharacteristic
43C22×C4×C157D411yescharacteristic
44C22×C4×C157D411yescharacteristic
45C2×C8×C157—22no—
46C42×C157C2×C411yescharacteristic
47C42×C157D411yescharacteristic
48C42×C157D411yescharacteristic
49C42×C157C2311yescharacteristic
50C22×D157—21no—
51Dic314—21no—
52Dic314M1612yes—
53D628—21no—
54D628M1612yes—
55C22⋊D157—24no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C4×D157—24no—
60C4×D157—42no—
61C4×D157—42no—
62#11929434—42no—
63C23×C157C22⋊C411yescharacteristic
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157—22no—
67C2×C4×C157—41no—
68C2×C4×C157C22⋊C411yescharacteristic
69C2×C4×C157C22⋊C411yescharacteristic
70C2×C4×C157C22⋊C411yescharacteristic
71C2×C4×C157C22×C411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—42no—
75C22×C157—21no—
76C22×C157—21no—
77C22×C157—21no—
78C22×C157C2×C22⋊C411yescharacteristic
79C2×D157—22no—
80C2×D157—41no—
81C2×D157—41no—
82C4×C157—21no—
83C4×C157—21no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157C2×M1611yescharacteristic
87C4×C157C2×M1611yescharacteristic
88C4×C157#13512yes—
89Dic157—22no—
90Dic157—41no—
91Dic157—41no—
92C2×C157—41no—
93C2×C157#40711yescharacteristic
94C2×C157#41611yescharacteristic
95C2×C157#42111yescharacteristic
96D157—42no—
97C157#148811yescharacteristic, complemented, Sylow
98#1488—1571nomaximal, Sylow
99C4×#41—1571no—
100#432—1571no—
101#431D15711yescharacteristic, complemented
102Q8⋊C8—1572no—
103D4⋊C8—1572no—
104C2×#41—1571no—
105C4×Q8—1571no—
106C4×Q8—1571no—
107C4×D4—3141no—
108C4×D4—3141no—
109C4×D4—1571no—
110C4×D4—1571no—
111#117—3141no—
112#117—1571no—
113C2×C42—3141no—
114C2×C42C2×D15711yescharacteristic
115C4⋊C8—21no—
116C4⋊C8—1572no—
117C22⋊C8—21no—
118C22⋊C8—3141no—
119#97—3141no—
120C4×C8C2×D15712yes—
121#41—3142no—
122#41—3142no—
123C2×Q8—1571no—
124C2×D4—3141no—
125C2×D4—1571no—
126C22×C4—3141no—
127C22×C4—3141no—
128C22×C4—3141no—
129C22×C4C4×D15711yescharacteristic
130C22×C4C22⋊D15711yescharacteristic
131C22×C4D62811yescharacteristic
132C2×C8—22no—
133C2×C8—3142no—
134C4⋊C4—3141no—
135C4⋊C4—3141no—
136C4⋊C4—1571no—
137C4⋊C4—1571no—
138C22⋊C4—3141no—
139C22⋊C4—3141no—
140C22⋊C4—3141no—
141C42—3141no—
142C42—3141no—
143C42—3141no—
144C42C4×D15711yescharacteristic
145C42C22⋊D15711yescharacteristic
146C42D62811yescharacteristic
147C42C22×D15711yescharacteristic
148C23—3141no—
149C23#1457893111yescharacteristic
150Q8—3141no—
151Q8—1572no—
152D4—3144no—
153D4—3141no—
154D4—1572no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—3144no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—6282no—
164C2×C4—6282no—
165C2×C4#1457893111yescharacteristic
166C2×C4#1457893111yescharacteristic
167C2×C4#1457893111yescharacteristic
168C2×C4C2×C4×D15711yescharacteristic
169C2×C4C2×C22⋊D15711yescharacteristic
170C2×C4C2×D62811yescharacteristic
171C8—42no—
172C8—6282no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—3142no—
177C22—6281no—
178C22—6281no—
179C22C2×#1457893111yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—3142no—
185C4—6281no—
186C4—6281no—
187C4M16×D15711yescharacteristic
188C4M16×D15711yescharacteristic
189C4#1909779312yes—
190C2—41no—
191C2—6282no—
192C2#2375723611yescharacteristic
193C2#2375727011yescharacteristic
194C2#2375729111yescharacteristic
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#431×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×#14578954C4
cosocleC42×C157C23
hypercenter#431D157
hypocenterC157#1488
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #23757330C2semidirect
3. #23757005C2semidirect
4. #23757002C2semidirect
5. #431×C157C2semidirect
97. C157#1488semidirect
101. #431D157semidirect

Maximal subgroups

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

subgroupindex
C4×#145789542
#237573302
#237570052
#237570022
#431×C1572
#1488157