Finite Group Databasebeta

← #34099134

Subgroups — #34099134

Order 20096.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757868C211yesmaximal, characteristic
2#23757604C211yesmaximal, characteristic, complemented
3#23757584C211yesmaximal, characteristic
4#23757205C211yesmaximal, characteristic, complemented
5#23757009C211yesmaximal, characteristic, complemented
6#23756998C211yesmaximal, characteristic, complemented
7#327×C157C211yesmaximal, characteristic
8#19097764—21no—
9#19097761—21no—
10#19097752—21no—
11#19097752—21no—
12#19097750C2211yescharacteristic
13#19097748—21no—
14D4×Dic157—21no—
15C2×C4⋊Dic157—21no—
16C2×C4⋊Dic157C2211yescharacteristic
17C2×#14578933C2211yescharacteristic
18#19097704—21no—
19#19097703—21no—
20#19097696—21no—
21#19097692—21no—
22C22⋊#11929434C2211yescharacteristic
23#19097678—21no—
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C22×Dic157—21no—
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—
43C22⋊Dic157—21no—
44C22⋊Dic157—21no—
45C22⋊Dic157—21no—
46C22⋊Dic157—21no—
47C4×Dic157—21no—
48C2×D4×C157—21no—
49C2×D4×C157D411yescharacteristic
50C22×C4×C157—21no—
51C22×C4×C157C2311yescharacteristic
52C2×C8×C157—21no—
53C4⋊C4×C157D411yescharacteristic
54C22⋊C4×C157—21no—
55Dic314—41no—
56C2×Dic157—21no—
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×Dic157—81no—
67#11929434—41no—
68C23×C157—21no—
69C23×C157C2×D411yescharacteristic
70D4×C157—41no—
71D4×C157—41no—
72D4×C157—41no—
73C2×C4×C157—22no—
74C2×C4×C157—21no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C8×C157—41no—
81C22×C157—21no—
82C22×C157—21no—
83C22×C157—41no—
84C22×C157—41no—
85C22×C157—41no—
86C22×C157#12011yescharacteristic
87C22×C157#13511yescharacteristic
88C22×C157AGL(1,ℤ/8)11yescharacteristic
89C4×C157—21no—
90C4×C157—21no—
91C4×C157—42no—
92C4×C157—41no—
93Dic157—41no—
94Dic157—41no—
95Dic157—41no—
96Dic157—41no—
97Dic157—81no—
98C2×C157—21no—
99C2×C157—21no—
100C2×C157—81no—
101C2×C157#44911yescharacteristic
102C2×C157#45611yescharacteristic
103C2×C157#45811yescharacteristic
104C157#160911yescharacteristic, complemented, Sylow
105#1609—1571nomaximal, Sylow
106#539—1571no—
107#483—1571no—
108#480—1571no—
109#398—1571no—
110#328—1571no—
111#327D15711yescharacteristic
112#324—1571no—
113#126—3141no—
114#125—3141no—
115#123—3141no—
116#123—3141no—
117C22⋊Q8—3141no—
118C22⋊Q8—1571no—
119#121C2×D15711yescharacteristic
120C4×D4—3141no—
121C2×C4⋊C4—3141no—
122C2×C4⋊C4—1571no—
123C2×C4⋊C4—1571no—
124#107—3141no—
125#106—3141no—
126#103—3141no—
127#102—3141no—
128C22⋊C8—1571no—
129C22⋊C8C2×D15711yescharacteristic
130#95—3141no—
131#95C2×D15711yescharacteristic
132C2×Q8—1571no—
133C2×D4—21no—
134C2×D4D62811yescharacteristic
135C22×C4—21no—
136C22×C4—3141no—
137C22×C4—3141no—
138C22×C4—1571no—
139C22×C4—1571no—
140C22×C4C22×D15711yescharacteristic
141C2×C8—21no—
142C2×C8—3141no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—6282no—
152C4⋊C4—1571no—
153C4⋊C4D62811yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C22⋊C4—3141no—
158C22⋊C4—3141no—
159C42—3141no—
160C23—21no—
161C23D4×D15711yescharacteristic
162Q8—6281no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3141no—
172C2×C4—3141no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—6281no—
178C2×C4—6281no—
179C2×C4—6281no—
180C2×C4—6281no—
181C2×C4—12561no—
182C2×C4D4×D15711yescharacteristic
183C2×C4C2×D62811yescharacteristic
184C8—41no—
185C8—6281no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1909774111yescharacteristic
192C22#1909779211yescharacteristic
193C22#1909779511yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—6281no—
199C4—6281no—
200C4—6281no—
201C4—6281no—
202C4—12561no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2375741911yescharacteristic
207C2#2375745711yescharacteristic
208C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157#120
prime radical#121×C157C22
hypercenter#327D157
hypocenterC157#1609
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23757604C2semidirect
4. #23757205C2semidirect
5. #23757009C2semidirect
6. #23756998C2semidirect
104. C157#1609semidirect

Maximal subgroups

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

subgroupindex
#237578682
#237576042
#237575842
#237572052
#237570092
#237569982
#327×C1572
#1609157