Finite Group Databasebeta

← #34099176

Subgroups — #34099176

Order 20096.

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

normal subgroups only

This group has 202 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#23757608C211yesmaximal, characteristic
3#23757211C211yesmaximal, characteristic
4#23757011C211yesmaximal, characteristic
5#23757010C211yesmaximal, characteristic
6#23756998C211yesmaximal, characteristic
7#484×C157C211yesmaximal, characteristic
8#19097770—21no—
9#19097769—21no—
10#19097761—21no—
11#19097761—21no—
12#19097750C2211yescharacteristic
13#19097748—21no—
14#19097727—21no—
15C2×#14578933C2211yescharacteristic
16#19097704—21no—
17#19097694—21no—
18C22⋊#11929434C2211yescharacteristic
19#19097678—21no—
20#19097678—21no—
21#19097678C2211yescharacteristic
22C22⋊Q8×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24#107×C157—21no—
25#103×C157—21no—
26C22⋊C8×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314D411yescharacteristic
29C22×Dic157—21no—
30C22×Dic157D411yescharacteristic
31C22×Dic157D411yescharacteristic
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157D411yescharacteristic
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41#14578933—21no—
42C22⋊Dic157—21no—
43C4×Dic157—21no—
44C4×Dic157—21no—
45C2×Q8×C157D411yescharacteristic
46C22×C4×C157—21no—
47C22×C4×C157C2311yescharacteristic
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157D411yescharacteristic
53C22⋊C4×C157—21no—
54Dic314—41no—
55Dic314—81no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—21no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157Q1612yes—
66#11929434—41no—
67C23×C157C2×D411yescharacteristic
68Q8×C157—41no—
69C2×C4×C157—21no—
70C2×C4×C157—21no—
71C2×C4×C157—41no—
72C2×C4×C157—42no—
73C2×C4×C157—41no—
74C2×C4×C157C2×D411yescharacteristic
75C2×C4×C157C2×D411yescharacteristic
76C8×C157—41no—
77C22×C157—21no—
78C22×C157—21no—
79C22×C157#12011yescharacteristic
80C22×C157C2×Q1611yescharacteristic
81C22×C157#13711yescharacteristic
82C4×C157—21no—
83C4×C157—21no—
84C4×C157—41no—
85C4×C157—41no—
86C4×C157—81no—
87Dic157—22no—
88Dic157—41no—
89Dic157—41no—
90Dic157—41no—
91Dic157—81no—
92C2×C157—21no—
93C2×C157—21no—
94C2×C157#45111yescharacteristic
95C2×C157#45411yescharacteristic
96C2×C157#45811yescharacteristic
97C157#161711yescharacteristic, complemented, Sylow
98#1617—1571nomaximal, Sylow
99#544—1571no—
100#484—1571no—
101#484D15711yescharacteristic
102#400—1571no—
103#328—1571no—
104#328—1571no—
105#324—1571no—
106C4⋊Q8—3141no—
107C4⋊Q8—3141no—
108#125—3141no—
109#125—3141no—
110C22⋊Q8—3141no—
111C22⋊Q8—1571no—
112C22⋊Q8C2×D15711yescharacteristic
113#117—3141no—
114C2×C4⋊C4—1571no—
115C2×C4⋊C4C2×D15711yescharacteristic
116#107—21no—
117#107—3141no—
118#103—21no—
119#103—3141no—
120C22⋊C8—1571no—
121C22⋊C8C2×D15711yescharacteristic
122#95—3141no—
123#95—3141no—
124#95—1571no—
125C2×Q8—3141no—
126C2×Q8—1571no—
127C2×Q8C22⋊D15711yescharacteristic
128C22×C4—21no—
129C22×C4—3141no—
130C22×C4—1571no—
131C22×C4—1571no—
132C22×C4C22×D15711yescharacteristic
133C2×C8—21no—
134C2×C8—3141no—
135C4⋊C4—21no—
136C4⋊C4—21no—
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—1571no—
147C4⋊C4C22⋊D15711yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3141no—
150C42—3141no—
151C42—3141no—
152C23D4×D15711yescharacteristic
153Q8—41no—
154Q8—6281no—
155Q8—12561no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—3141no—
162C2×C4—3141no—
163C2×C4—3141no—
164C2×C4—3141no—
165C2×C4—3141no—
166C2×C4—6281no—
167C2×C4—6281no—
168C2×C4—6281no—
169C2×C4—6281no—
170C2×C4—1572no—
171C2×C4D4×D15711yescharacteristic
172C2×C4C2×C22⋊D15711yescharacteristic
173C8—41no—
174C8—6281no—
175C22—21no—
176C22—21no—
177C22#1909773911yescharacteristic
178C22Q16×D15711yescharacteristic
179C22#1909780311yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3142no—
186C4—6281no—
187C4—6281no—
188C4—6281no—
189C4—12561no—
190C2—21no—
191C2—21no—
192C2#2375742711yescharacteristic
193C2#2375744411yescharacteristic
194C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#484×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#484D157
hypocenterC157#1617
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C157#1617semidirect

Maximal subgroups

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

subgroupindex
#237579022
#237576082
#237572112
#237570112
#237570102
#237569982
#484×C1572
#1617157