Finite Group Databasebeta

← #34101485

Subgroups — #34101485

Order 20096.

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

normal subgroups only

This group has 230 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#23757901C211yesmaximal, characteristic
2#23757316C211yesmaximal, characteristic
3#23757315C211yesmaximal, characteristic
4#23757139C211yesmaximal, characteristic
5#23757041C211yesmaximal, characteristic
6#23757033C211yesmaximal, characteristic
7#339×C157C211yesmaximal, characteristic
8C2×#14578938C2211yescharacteristic
9#19097771—21no—
10#19097770—21no—
11#19097763—21no—
12#19097762—21no—
13#19097748—22no—
14#19097730C2211yescharacteristic
15C2×C4⋊Dic157C2211yescharacteristic
16C2×C4⋊Dic157C2211yescharacteristic
17#19097705—21no—
18#19097704—21no—
19#19097703—21no—
20#19097702—21no—
21#19097678—22no—
22C2×M16×C157C2211yescharacteristic
23#117×C157C2211yescharacteristic
24C2×C42×C157C2211yescharacteristic
25C2×Dic314—22no—
26C22×Dic157—21no—
27C22×Dic157D412yes—
28#14578938—21no—
29#14578938Q812yescomplemented
30C2×#11929434—21no—
31C4⋊Dic157—22no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D411yescharacteristic
38#14578933—22no—
39#14578933—22no—
40C22⋊Dic157—21no—
41C4×Dic157—21no—
42C22×C4×C157—21no—
43C22×C4×C157C2311yescharacteristic
44M16×C157—21no—
45M16×C157Q812yescomplemented
46C2×C8×C157—21no—
47C4⋊C4×C157D411yescharacteristic
48C4⋊C4×C157D411yescharacteristic
49C22⋊C4×C157—21no—
50C42×C157—21no—
51C42×C157—21no—
52C42×C157Q812yescomplemented
53Dic314—82no—
54C2×Dic157—22no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—42no—
58C2×Dic157—42no—
59C2×Dic157—41no—
60#11929434—22no—
61C23×C157C2×D411yescharacteristic
62C2×C4×C157—21no—
63C2×C4×C157—21no—
64C2×C4×C157—22no—
65C2×C4×C157—41no—
66C2×C4×C157—41no—
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×Q811yescharacteristic
70C2×C4×C157C2×Q811yescharacteristic
71C2×C4×C157C2×Q811yescharacteristic
72C2×C4×C157#4111yescharacteristic
73C8×C157—22no—
74C22×C157—21no—
75C22×C157—21no—
76C22×C157#12011yescharacteristic
77C22×C157C22⋊Q811yescharacteristic
78C22×C157C4⋊Q811yescharacteristic
79C4×C157—42no—
80C4×C157—41no—
81C4×C157—41no—
82C4×C157C22⋊Q811yescharacteristic
83C4×C157C22⋊Q811yescharacteristic
84C4×C157C4⋊Q811yescharacteristic
85C4×C157C4⋊Q811yescharacteristic
86Dic157—41no—
87Dic157—42no—
88Dic157—41no—
89Dic157—81no—
90C2×C157—21no—
91C2×C157—21no—
92C2×C157#39511yescharacteristic
93C2×C157#45411yescharacteristic
94C2×C157#45511yescharacteristic
95C157#206111yescharacteristic, complemented, Sylow
96#2061—1571nomaximal, Sylow
97#544—1571no—
98#428—1571no—
99#428—1571no—
100#382—1571no—
101#343—1571no—
102#339—1571no—
103#339D15711yescharacteristic
104C2×M16—1571no—
105C2×M16C2×D15711yescharacteristic
106C4⋊Q8—3141no—
107C4⋊Q8—3141no—
108#125—3141no—
109#125—3141no—
110C22⋊Q8—3142no—
111#117—1571no—
112#117C2×D15711yescharacteristic
113C2×C4⋊C4—1571no—
114C2×C4⋊C4—1571no—
115C2×C42C2×D15711yescharacteristic
116#107—3141no—
117#107—3141no—
118#106—3141no—
119#106—3141no—
120#95—3142no—
121C2×Q8—3142no—
122C22×C4—21no—
123C22×C4—3141no—
124C22×C4—1572no—
125C22×C4C22×D15711yescharacteristic
126M16—21no—
127M16—3141no—
128M16—1572no—
129M16Dic31412yescomplemented
130C2×C8—21no—
131C2×C8—3141no—
132C4⋊C4—3142no—
133C4⋊C4—3142no—
134C4⋊C4—3142no—
135C4⋊C4—3141no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4—3141no—
139C4⋊C4—1571no—
140C4⋊C4—1571no—
141C4⋊C4D62811yescharacteristic
142C4⋊C4D62811yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3141no—
145C42—21no—
146C42—21no—
147C42—3141no—
148C42Dic31412yescomplemented
149C23D4×D15711yescharacteristic
150Q8—12562no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3141no—
157C2×C4—3141no—
158C2×C4—3142no—
159C2×C4—6282no—
160C2×C4—6282no—
161C2×C4—6281no—
162C2×C4D4×D15711yescharacteristic
163C2×C4C2×D62811yescharacteristic
164C2×C4Q8×D15711yescharacteristic
165C2×C4C2×Dic31411yescharacteristic
166C2×C4C2×Dic31411yescharacteristic
167C2×C4#1457895311yescharacteristic
168C8—22no—
169C8—3142no—
170C22—21no—
171C22—21no—
172C22#1909774111yescharacteristic
173C22#1909774811yescharacteristic
174C22#1909777011yescharacteristic
175C4—42no—
176C4—41no—
177C4—41no—
178C4—6281no—
179C4—6282no—
180C4—6281no—
181C4—12561no—
182C4#1909774811yescharacteristic
183C4#1909775111yescharacteristic
184C4#1909777011yescharacteristic
185C4#1909777111yescharacteristic
186C2—21no—
187C2—21no—
188C2#2375719411yescharacteristic
189C2#2375744711yescharacteristic
190C2#2375745211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#339×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#339D157
hypocenterC157#2061
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #14578938Q8semidirect
45. M16×C157Q8semidirect
52. C42×C157Q8semidirect
95. C157#2061semidirect
129. M16Dic314semidirect
148. C42Dic314semidirect

Maximal subgroups

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

subgroupindex
#237579012
#237573162
#237573152
#237571392
#237570412
#237570332
#339×C1572
#2061157