Finite Group Databasebeta

← #34101490

Subgroups — #34101490

Order 20096.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#23757899C211yesmaximal, characteristic
2#23757148C212yesmaximal
3#23757145C211yesmaximal, characteristic
4#23757039C212yesmaximal
5#342×C157C211yesmaximal, characteristic
6C23×Dic157C2211yescharacteristic
7#19097750—21no—
8#19097750—21no—
9#19097748—22no—
10#19097748—22no—
11C2×C4⋊Dic157—22no—
12C2×#14578933—21no—
13C2×C22⋊Dic157C2211yescharacteristic
14C2×C22⋊Dic157C2212yes—
15#19097678—21no—
16#19097678—22no—
17C2×C22⋊C4×C157C2211yescharacteristic
18C2×C22⋊C4×C157C2212yes—
19C2×Dic314—21no—
20C2×Dic314—21no—
21C22×Dic157—21no—
22C22×Dic157—21no—
23C22×Dic157—22no—
24C22×Dic157—42no—
25C22×Dic157D412yes—
26C22×Dic157D412yes—
27C4⋊Dic157—21no—
28C4⋊Dic157—21no—
29C4⋊Dic157—44no—
30#14578933—22no—
31#14578933—22no—
32#14578933—42no—
33C22⋊Dic157—22no—
34C22⋊Dic157—22no—
35C22⋊Dic157—21no—
36C22⋊Dic157Q812yescomplemented
37C24×C157C2311yescharacteristic
38C22×C4×C157—22no—
39C22×C4×C157D411yescharacteristic
40C22×C4×C157D411yescharacteristic
41C22⋊C4×C157—22no—
42C22⋊C4×C157—22no—
43C22⋊C4×C157Q814yescomplemented
44Dic314—81no—
45Dic314—81no—
46C2×Dic157—22no—
47C2×Dic157—24no—
48C2×Dic157—22no—
49C2×Dic157—22no—
50C2×Dic157—22no—
51C2×Dic157—41no—
52C2×Dic157—41no—
53C2×Dic157—42no—
54C2×Dic157—41no—
55C2×Dic157—41no—
56C2×Dic157—42no—
57C2×Dic157—42no—
58C23×C157—41no—
59C23×C157—41no—
60C23×C157C2×D412yes—
61C23×C157C2×D411yescharacteristic
62C23×C157C2×Q811yescharacteristic
63C23×C157C2×Q812yes—
64C23×C157#4111yescharacteristic
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—24no—
68C2×C4×C157—42no—
69C2×C4×C157—42no—
70C2×C4×C157—41no—
71C2×C4×C157—41no—
72C22×C157—22no—
73C22×C157—21no—
74C22×C157—22no—
75C22×C157—21no—
76C22×C157—41no—
77C22×C157—42no—
78C22×C157—41no—
79C22×C157#12011yescharacteristic
80C22×C157C22⋊Q812yes—
81C22×C157C22⋊Q811yescharacteristic
82C22×C157C4⋊Q812yes—
83C22×C157C4⋊Q811yescharacteristic
84C4×C157—44no—
85C4×C157—41no—
86C4×C157—41no—
87Dic157—42no—
88Dic157—42no—
89Dic157—42no—
90Dic157—42no—
91C2×C157—21no—
92C2×C157—22no—
93C2×C157—22no—
94C2×C157—21no—
95C2×C157#39511yescharacteristic
96C2×C157B(4,𝔽2)11yescharacteristic
97C2×C157#45811yescharacteristic
98C157#206211yescharacteristic, complemented, Sylow
99#2062—1571nomaximal, Sylow
100#543—1571no—
101#385—1571no—
102#385—1572no—
103#342—1572no—
104#342D15711yescharacteristic
105C23×C4—1571no—
106C22⋊Q8—3142no—
107C22⋊Q8—3142no—
108C22⋊Q8—3141no—
109C22⋊Q8—3141no—
110C2×C4⋊C4—3142no—
111C2×C4⋊C4—3141no—
112C2×C22⋊C4—1572no—
113C2×C22⋊C4—1571no—
114C2×C22⋊C4C2×D15711yescharacteristic
115C2×C22⋊C4C2×D15712yes—
116#95—3142no—
117#95—3141no—
118C24C22×D15711yescharacteristic
119C2×Q8—3141no—
120C2×Q8—3141no—
121C22×C4—22no—
122C22×C4—3142no—
123C22×C4—3141no—
124C22×C4—3141no—
125C22×C4—6282no—
126C22×C4—1572no—
127C22×C4—1572no—
128C22×C4D62811yescharacteristic
129C22×C4D62811yescharacteristic
130C4⋊C4—3142no—
131C4⋊C4—3142no—
132C4⋊C4—3141no—
133C4⋊C4—3141no—
134C4⋊C4—6282no—
135C4⋊C4—6284no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—3142no—
139C22⋊C4—3142no—
140C22⋊C4—3141no—
141C22⋊C4—1572no—
142C22⋊C4Dic31414yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D15712yes—
146C23C2×D62811yescharacteristic
147C23Q8×D15711yescharacteristic
148C23C2×Dic31412yes—
149C23#1457895311yescharacteristic
150Q8—12561no—
151Q8—12561no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—3144no—
160C2×C4—3142no—
161C2×C4—3142no—
162C2×C4—3142no—
163C2×C4—3142no—
164C2×C4—6281no—
165C2×C4—6282no—
166C2×C4—6281no—
167C2×C4—6281no—
168C2×C4—6281no—
169C2×C4—6282no—
170C2×C4—6282no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—21no—
175C22—41no—
176C22—42no—
177C22—41no—
178C22#1909774111yescharacteristic
179C22#1909774812yes—
180C22#1909775111yescharacteristic
181C22#1909777012yes—
182C22#1909777111yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—6282no—
187C4—6282no—
188C4—6282no—
189C4—6282no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#2375719411yescharacteristic
195C2#2375746111yescharacteristic
196C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, prime radical, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#342×C157C2
socleC22×C157#120
hypercenter#342D157
hypocenterC157#2062
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
36. C22⋊Dic157Q8semidirect
43. C22⋊C4×C157Q8semidirect
98. C157#2062semidirect
142. C22⋊C4Dic314semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237571482
#237571452
#237570392
#342×C1572
#2062157