Finite Group Databasebeta

← #34099075

Subgroups — #34099075

Order 20096.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757904C211yesmaximal, characteristic, complemented
2#23757424C212yesmaximal
3#23757009C212yesmaximal, complemented
4#23756999C211yesmaximal, characteristic, complemented
5#394×C157C211yesmaximal, characteristic
6C2×#14578942—22no—
7#19097770—22no—
8#19097762—22no—
9#19097750—21no—
10#19097750C2212yes—
11#19097730—21no—
12#19097692—22no—
13C22⋊#11929434C2212yes—
14C22×D4×C157C2211yescharacteristic
15C2×C4⋊C4×C157C2211yescharacteristic
16C2×C22⋊C4×C157—21no—
17C2×C22⋊C4×C157—21no—
18#95×C157C2211yescharacteristic
19C2×Dic314—21no—
20C2×Dic314D412yes—
21#14578942—44no—
22C2×#11929434—22no—
23C4⋊Dic157—21no—
24C4⋊Dic157—21no—
25C4⋊Dic157—21no—
26C4⋊Dic157D412yes—
27#14578933—22no—
28#14578933—22no—
29C22⋊Dic157—22no—
30C4×Dic157—22no—
31C24×C157—21no—
32C2×D4×C157—22no—
33C2×D4×C157—42no—
34C22×C4×C157—21no—
35C22×C4×C157D411yescharacteristic
36C22×C4×C157D411yescharacteristic
37C22×C4×C157C2311yescharacteristic
38C4⋊C4×C157—22no—
39C22⋊C4×C157—42no—
40C22⋊C4×C157—42no—
41Dic314—42no—
42Dic314—81no—
43C2×Dic157—22no—
44C2×Dic157—22no—
45#11929434—42no—
46C23×C157—22no—
47C23×C157—41no—
48C23×C157—41no—
49C23×C157—41no—
50C23×C157—41no—
51C23×C157—41no—
52C23×C157—41no—
53C23×C157C2×D411yescharacteristic
54D4×C157—24no—
55D4×C157—42no—
56C2×C4×C157—21no—
57C2×C4×C157—21no—
58C2×C4×C157—21no—
59C2×C4×C157—41no—
60C2×C4×C157—41no—
61C2×C4×C157—41no—
62C2×C4×C157—41no—
63C2×C4×C157—41no—
64C2×C4×C157SD1612yescomplemented
65C2×C4×C157C2×D412yes—
66C22×C157—21no—
67C22×C157—21no—
68C22×C157—42no—
69C22×C157—42no—
70C22×C157—42no—
71C22×C157—81no—
72C22×C157—81no—
73C22×C157—81no—
74C22×C157—81no—
75C22×C157#12011yescharacteristic
76C22×C157C2×SD1611yescharacteristic
77C22×C157#13711yescharacteristic
78C4×C157—22no—
79C4×C157—22no—
80C4×C157—41no—
81C4×C157—81no—
82Dic157—42no—
83Dic157—42no—
84C2×C157—21no—
85C2×C157—21no—
86C2×C157—82no—
87C2×C157#44811yescharacteristic
88C2×C157#45411yescharacteristic
89C2×C157B(4,𝔽2)11yescharacteristic
90C157#159911yescharacteristic, complemented, Sylow
91#1599—1571nomaximal, Sylow
92#544—1571no—
93#450—1572no—
94#394D15711yescharacteristic
95#328—1572no—
96#324—1571no—
97C22×D4C2×D15711yescharacteristic
98C2×SD16—3142no—
99C4⋊Q8—3142no—
100#125—3142no—
101C22⋊Q8—3141no—
102C22⋊Q8—1572no—
103#117—3141no—
104C2×C4⋊C4C2×D15711yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107#102—3142no—
108C22⋊C8—1572no—
109#95C2×D15711yescharacteristic
110C24—21no—
111C2×Q8—3141no—
112C2×Q8—1572no—
113C2×D4—22no—
114C2×D4—42no—
115C22×C4—21no—
116C22×C4C22⋊D15711yescharacteristic
117C22×C4C22⋊D15711yescharacteristic
118C22×C4C22×D15711yescharacteristic
119SD16—6284no—
120C2×C8—3142no—
121C4⋊C4—22no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—3142no—
126C4⋊C4—3142no—
127C4⋊C4—1572no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—3142no—
131C42—3142no—
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×C22⋊D15711yescharacteristic
140Q8—6282no—
141Q8—12561no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—3142no—
153C2×C4—3142no—
154C2×C4#1457894212yescomplemented
155C2×C4D4×D15712yes—
156C8—6282no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1909773911yescharacteristic
167C22C2×#1457894211yescharacteristic
168C22#1909780111yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—81no—
173C4—6282no—
174C4—6282no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2#2375741111yescharacteristic
179C2#2375744511yescharacteristic
180C2#2375745911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#394×C157C2
socleC22×C157#120
prime radicalC22×D4×C157C22
hypercenter#394D157
hypocenterC157#1599
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #23757904C2semidirect
3. #23757009C2semidirect
4. #23756999C2semidirect
64. C2×C4×C157SD16semidirect
90. C157#1599semidirect
154. C2×C4#14578942semidirect

Maximal subgroups

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

subgroupindex
#237579042
#237574242
#237570092
#237569992
#394×C1572
#1599157