Finite Group Databasebeta

← #34100592

Subgroups — #34100592

Order 20096.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#19097754C211yesmaximal, characteristic
2C2×#19097730C211yesmaximal, characteristic, complemented
3C2×#19097685C212yesmaximal
4#23757039C212yesmaximal, complemented
5#381×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157C2211yescharacteristic
7#19097754—22no—
8#19097754—21no—
9#19097754—21no—
10#19097730—24no—
11C2×C4⋊Dic157—21no—
12C2×#14578933C412yescomplemented
13C2×C22⋊Dic157C2212yes—
14C2×C22⋊Dic157C2211yescharacteristic
15C2×#14578931C412yescomplemented
16C2×C4×Dic157—21no—
17#19097685—24no—
18C23×C4×C157C2211yescharacteristic
19C2×C22⋊C4×C157C2212yes—
20#95×C157—22no—
21C23×D157C2×C411yescharacteristic
22C2×C22⋊D157—22no—
23C2×C22⋊D157—21no—
24C2×C22⋊D157—21no—
25C2×C22⋊D157—22no—
26C22×Dic157—22no—
27C22×Dic157C2×C411yescharacteristic
28C22×Dic157C2×C412yes—
29C4⋊Dic157—24no—
30#14578933—22no—
31#14578933—22no—
32C22⋊Dic157—22no—
33C22⋊Dic157—21no—
34C22⋊Dic157—21no—
35C22⋊Dic157D414yes—
36#14578931—22no—
37#14578931—22no—
38C4×Dic157—24no—
39C24×C157C2311yescharacteristic
40C22×C4×C157—22no—
41C22×C4×C157—22no—
42C22×C4×C157—22no—
43C22×C4×C157C2×C412yes—
44C22×C4×C157D412yes—
45C22×C4×C157D411yescharacteristic
46C22×C4×C157D411yescharacteristic
47C22⋊C4×C157—22no—
48C22⋊C4×C157—22no—
49C22×D157—21no—
50C22×D157—22no—
51C22×D157—42no—
52C22⋊D157—41no—
53C22⋊D157—42no—
54C22⋊D157—41no—
55C2×Dic157—21no—
56C2×Dic157—22no—
57C2×Dic157—22no—
58C2×Dic157—24no—
59C2×Dic157—44no—
60C2×Dic157—42no—
61C23×C157—42no—
62C23×C157C22×C411yescharacteristic
63C23×C157C2×D412yes—
64C23×C157C2×D411yescharacteristic
65C23×C157C2×D411yescharacteristic
66C23×C157#4112yes—
67C2×C4×C157—24no—
68C2×C4×C157—21no—
69C2×C4×C157—21no—
70C2×C4×C157—24no—
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—44no—
74C2×C4×C157—42no—
75C2×C4×C157C22⋊C412yes—
76C2×C4×C157C22⋊C412yes—
77C22×C157—22no—
78C22×C157—22no—
79C22×C157—22no—
80C22×C157—42no—
81C22×C157—42no—
82C22×C157C2×C22⋊C411yescharacteristic
83C22×C157C4×D412yes—
84C22×C157#12011yescharacteristic
85C22×C157#12112yes—
86C22×C157#12311yescharacteristic
87C2×D157—41no—
88C2×D157—42no—
89C2×D157—82no—
90C4×C157—22no—
91C4×C157—22no—
92C4×C157—82no—
93Dic157—44no—
94Dic157—41no—
95Dic157—42no—
96C2×C157—21no—
97C2×C157—22no—
98C2×C157—22no—
99C2×C157—21no—
100C2×C157#38611yescharacteristic
101C2×C157#41012yes—
102D157—81no—
103C157#189911yescharacteristic, complemented, Sylow
104#1899—1571nomaximal, Sylow
105C2×#123—1571no—
106C2×#117—1571no—
107C2×#99—1572no—
108#381D15711yescharacteristic, complemented
109#342—1572no—
110C22×D4—1571no—
111C23×C4C2×D15711yescharacteristic
112#123—3142no—
113#123—3141no—
114#123—3141no—
115#117—3144no—
116C2×C4⋊C4—3141no—
117C2×C4⋊C4—1572no—
118C2×C22⋊C4—1571no—
119C2×C22⋊C4—1572no—
120C2×C22⋊C4—1572no—
121C2×C22⋊C4C2×D15712yes—
122C2×C42—3141no—
123#99—3144no—
124#95—22no—
125C24—1571no—
126C24C22×D15711yescharacteristic
127C2×D4—3142no—
128C2×D4—3141no—
129C2×D4—3141no—
130C2×D4—3142no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—3142no—
135C22×C4—1571no—
136C22×C4—1572no—
137C22×C4C4×D15712yes—
138C22×C4C22⋊D15712yes—
139C22×C4D62811yescharacteristic
140C22×C4D62811yescharacteristic
141C4⋊C4—3144no—
142C4⋊C4—3142no—
143C4⋊C4—3142no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—3142no—
147C22⋊C4—3141no—
148C22⋊C4—3141no—
149C22⋊C4—3142no—
150C22⋊C4—3142no—
151C22⋊C4—1574no—
152C42—3144no—
153C23—42no—
154C23—3141no—
155C23—3142no—
156C23—6282no—
157C23C2×C4×D15711yescharacteristic
158C23D4×D15712yes—
159C23C2×C22⋊D15711yescharacteristic
160C23C2×D62811yescharacteristic
161C23#1457895312yes—
162D4—6281no—
163D4—6282no—
164D4—6281no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—3142no—
174C2×C4—3141no—
175C2×C4—3142no—
176C2×C4—3144no—
177C2×C4—6284no—
178C2×C4—6282no—
179C2×C4#1457893112yes—
180C2×C4#1457893112yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—6281no—
187C22—6282no—
188C22—12562no—
189C22C2×#1457893111yescharacteristic
190C22#1909773112yes—
191C22#1909774111yescharacteristic
192C22#1909774312yes—
193C22#1909775511yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—6284no—
198C4—6281no—
199C4—6282no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—12561no—
205C2#2375715011yescharacteristic
206C2#2375724612yes—
subgroupG/H
centerC22C2×#14578931
commutatorC23×C157C22×C4
FrattiniC24C22×D157
Fitting#381×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×C22⋊D157C22
cosocleC24×C157C23
hypercenter#381D157
hypocenterC157#1899
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#19097730C2semidirect
4. #23757039C2semidirect
5. #381×C157C2semidirect
12. C2×#14578933C4semidirect
15. C2×#14578931C4semidirect
103. C157#1899semidirect
108. #381D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977542
C2×#190977302
C2×#190976852
#237570392
#381×C1572
#1899157