Finite Group Databasebeta

← #34100352

Subgroups — #34100352

Order 20096.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#23757750C211yesmaximal, characteristic
2#23757316C211yesmaximal, characteristic
3#23757315C211yesmaximal, characteristic
4C2×#19097689C211yesmaximal, characteristic
5#23757179C211yesmaximal, characteristic
6#23757033C211yesmaximal, characteristic
7#339×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10C4×Dic314—21no—
11C4×Dic314—21no—
12#19097736—21no—
13#19097736—21no—
14#19097730C2211yescharacteristic
15#19097727—22no—
16C2×C4⋊Dic157C2211yescharacteristic
17#19097705—21no—
18#19097704—21no—
19#19097703—21no—
20#19097702—21no—
21#19097689C414yescomplemented
22#19097678—22no—
23C2×M16×C157C2211yescharacteristic
24#117×C157C2211yescharacteristic
25C2×C42×C157C2211yescharacteristic
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314C2×C412yes—
31C2×Dic314Q812yes—
32C22×Dic157—21no—
33C22×Dic157D412yes—
34#14578938—21no—
35#14578938C2×C412yes—
36C2×#11929434—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157—21no—
39C4⋊Dic157D411yescharacteristic
40C4⋊Dic157D411yescharacteristic
41#14578933—22no—
42#14578933—22no—
43C22⋊Dic157—21no—
44C4×Dic157—22no—
45C4×Dic157—22no—
46C4×Dic157—21no—
47C22×C4×C157—21no—
48C22×C4×C157C2311yescharacteristic
49M16×C157—21no—
50M16×C157C2×C412yes—
51C2×C8×C157—21no—
52C4⋊C4×C157D411yescharacteristic
53C4⋊C4×C157D411yescharacteristic
54C22⋊C4×C157—21no—
55C42×C157—21no—
56C42×C157—21no—
57C42×C157—21no—
58Dic314—22no—
59Dic314—22no—
60Dic314—22no—
61Dic314—22no—
62C2×Dic157—22no—
63C2×Dic157—22no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—42no—
67C2×Dic157—41no—
68C2×Dic157C4⋊C414yes—
69#11929434—22no—
70C23×C157C2×D411yescharacteristic
71C2×C4×C157—22no—
72C2×C4×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157—41no—
75C2×C4×C157—41no—
76C2×C4×C157C22×C411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×Q811yescharacteristic
80C2×C4×C157#4111yescharacteristic
81C2×C4×C157#4111yescharacteristic
82C8×C157—22no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157C2×C4⋊C411yescharacteristic
86C22×C157#12011yescharacteristic
87C22×C157#12311yescharacteristic
88C4×C157—42no—
89C4×C157—41no—
90C4×C157—41no—
91C4×C157C4×D411yescharacteristic
92C4×C157C4×D411yescharacteristic
93C4×C157C22⋊Q811yescharacteristic
94C4×C157C22⋊Q811yescharacteristic
95Dic157—24no—
96Dic157—41no—
97Dic157—41no—
98Dic157—81no—
99C2×C157—21no—
100C2×C157—21no—
101C2×C157#38511yescharacteristic
102C2×C157#45411yescharacteristic
103C2×C157#45611yescharacteristic
104C157#185711yescharacteristic, complemented, Sylow
105#1857—1571nomaximal, Sylow
106#519—1571no—
107#428—1571no—
108#428—1571no—
109C2×#101—1571no—
110#391—1571no—
111#339—1571no—
112#339D15711yescharacteristic
113C22×Q8—1571no—
114C2×M16—1571no—
115C2×M16C2×D15711yescharacteristic
116C4×Q8—3141no—
117C4×Q8—3141no—
118C4×Q8—3141no—
119C4×Q8—3141no—
120#117—3142no—
121#117—1571no—
122#117C2×D15711yescharacteristic
123C2×C4⋊C4—1571no—
124C2×C42C2×D15711yescharacteristic
125#107—3141no—
126#107—3141no—
127#106—3141no—
128#106—3141no—
129#101—1574no—
130#95—3142no—
131C2×Q8—3141no—
132C2×Q8—3141no—
133C2×Q8—3141no—
134C2×Q8—3141no—
135C2×Q8—1572no—
136C2×Q8—1572no—
137C22×C4—21no—
138C22×C4—3141no—
139C22×C4—1572no—
140C22×C4C22×D15711yescharacteristic
141M16—21no—
142M16—3141no—
143M16—1572no—
144M16C4×D15712yes—
145C2×C8—21no—
146C2×C8—3141no—
147C4⋊C4—3142no—
148C4⋊C4—3142no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C4⋊C4—1571no—
152C4⋊C4—1571no—
153C4⋊C4D62811yescharacteristic
154C4⋊C4D62811yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—3141no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—3142no—
161C42—3142no—
162C42—3141no—
163C23D4×D15711yescharacteristic
164Q8—3142no—
165Q8—3142no—
166Q8—3142no—
167Q8—3142no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3142no—
174C2×C4—3142no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—6282no—
178C2×C4—6281no—
179C2×C4—1574no—
180C2×C4C2×C4×D15711yescharacteristic
181C2×C4D4×D15711yescharacteristic
182C2×C4C2×D62811yescharacteristic
183C2×C4Q8×D15711yescharacteristic
184C2×C4#1457895311yescharacteristic
185C2×C4#1457895411yescharacteristic
186C8—22no—
187C8—3142no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D15711yescharacteristic
191C22#1909774111yescharacteristic
192C22#1909775311yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—3144no—
197C4—6281no—
198C4—6281no—
199C4—12561no—
200C4#1909773111yescharacteristic
201C4C4×D62811yescharacteristic
202C4#1909774911yescharacteristic
203C4#1909775111yescharacteristic
204C2—21no—
205C2—21no—
206C2#2375714711yescharacteristic
207C2#2375744711yescharacteristic
208C2#2375745711yescharacteristic
subgroupG/H
centerC22#19097741
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#339×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenter#339D157
hypocenterC157#1857
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #19097689C4semidirect
104. C157#1857semidirect

Maximal subgroups

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

subgroupindex
#237577502
#237573162
#237573152
C2×#190976892
#237571792
#237570332
#339×C1572
#1857157