Finite Group Databasebeta

← #34099145

Subgroups — #34099145

Order 20096.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#23757902C211yesmaximal, characteristic
2#23757604C211yesmaximal, characteristic
3#23757601C211yesmaximal, characteristic
4#23757205C211yesmaximal, characteristic
5#23757009C211yesmaximal, characteristic
6#23756998C211yesmaximal, characteristic
7#328×C157C211yesmaximal, characteristic
8#19097770—21no—
9#19097769—21no—
10#19097761—21no—
11#19097761—21no—
12#19097750C2211yescharacteristic
13#19097748—21no—
14#19097727—21no—
15C2×C4⋊Dic157—21no—
16C2×C4⋊Dic157C2211yescharacteristic
17C2×#14578933C2211yescharacteristic
18#19097703—21no—
19#19097702—21no—
20#19097696—21no—
21#19097695—21no—
22C22⋊#11929434C2211yescharacteristic
23#19097678—21no—
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—42no—
37C4⋊Dic157D411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43#14578933—21no—
44#14578933—21no—
45C22⋊Dic157—21no—
46C4×Dic157—21no—
47C4×Dic157—21no—
48C2×Q8×C157D411yescharacteristic
49C22×C4×C157—21no—
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157D411yescharacteristic
54C22⋊C4×C157—21no—
55Dic314—41no—
56Dic314—81no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157SD1612yes—
67#11929434—41no—
68C23×C157C2×D411yescharacteristic
69Q8×C157—41no—
70C2×C4×C157—22no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—41no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C8×C157—41no—
79C22×C157—21no—
80C22×C157—21no—
81C22×C157#12011yescharacteristic
82C22×C157C2×SD1611yescharacteristic
83C22×C157#13711yescharacteristic
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—42no—
87C4×C157—41no—
88C4×C157—41no—
89Dic157—22no—
90Dic157—41no—
91Dic157—41no—
92Dic157—41no—
93Dic157—81no—
94C2×C157—21no—
95C2×C157—21no—
96C2×C157#44811yescharacteristic
97C2×C157#45611yescharacteristic
98C2×C157#45811yescharacteristic
99C157#161111yescharacteristic, complemented, Sylow
100#1611—1571nomaximal, Sylow
101#544—1571no—
102#483—1571no—
103#483—1571no—
104#398—1571no—
105#328—1571no—
106#328D15711yescharacteristic
107#324—1571no—
108C4⋊Q8—3141no—
109C4⋊Q8—3141no—
110#125—3141no—
111#125—3141no—
112C22⋊Q8—3141no—
113C22⋊Q8—1571no—
114C22⋊Q8C2×D15711yescharacteristic
115#117—3141no—
116C2×C4⋊C4—3141no—
117C2×C4⋊C4—1571no—
118C2×C4⋊C4—1571no—
119#106—3141no—
120#106—3141no—
121#103—3141no—
122#103—3141no—
123C22⋊C8—1571no—
124C22⋊C8C2×D15711yescharacteristic
125#95—3141no—
126#95C2×D15711yescharacteristic
127C2×Q8—3141no—
128C2×Q8—1571no—
129C2×Q8D62811yescharacteristic
130C22×C4—21no—
131C22×C4—3141no—
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4C22×D15711yescharacteristic
135C2×C8—21no—
136C2×C8—3141no—
137C4⋊C4—21no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—6282no—
149C4⋊C4—1571no—
150C4⋊C4D62811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3141no—
153C42—3141no—
154C42—3141no—
155C23D4×D15711yescharacteristic
156Q8—41no—
157Q8—6281no—
158Q8—12561no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—3141no—
170C2×C4—6281no—
171C2×C4—6281no—
172C2×C4—6281no—
173C2×C4—6281no—
174C2×C4—1572no—
175C2×C4D4×D15711yescharacteristic
176C2×C4C2×D62811yescharacteristic
177C8—41no—
178C8—6281no—
179C22—21no—
180C22—21no—
181C22#1909774111yescharacteristic
182C22SD16×D15711yescharacteristic
183C22#1909780311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—3142no—
190C4—6281no—
191C4—6281no—
192C4—6281no—
193C4—12561no—
194C2—21no—
195C2—21no—
196C2#2375741311yescharacteristic
197C2#2375745711yescharacteristic
198C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#328D157
hypocenterC157#1611
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C157#1611semidirect

Maximal subgroups

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

subgroupindex
#237579022
#237576042
#237576012
#237572052
#237570092
#237569982
#328×C1572
#1611157