Finite Group Databasebeta

← #34099182

Subgroups — #34099182

Order 20096.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757861C211yesmaximal, characteristic
2#23757608C211yesmaximal, characteristic, complemented
3#23757591C211yesmaximal, characteristic, complemented
4#23757009C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic, complemented
6#23756997C211yesmaximal, characteristic, complemented
7#399×C157C211yesmaximal, characteristic, complemented
8#19097764—21no—
9#19097757—21no—
10#19097753—21no—
11#19097750C2211yescharacteristic
12#19097745C2211yescharacteristic
13#19097744—21no—
14#19097740—21no—
15C4×C22⋊D157—21no—
16#19097704—21no—
17#19097702—21no—
18#19097694—21no—
19#19097691—21no—
20C22⋊#11929434C2211yescharacteristic
21C22⋊#11929434C2211yescharacteristic
22C2×C4⋊C4×C157—21no—
23C2×C4⋊C4×C157C2211yescharacteristic
24C2×C22⋊C4×C157—21no—
25C2×C22⋊C4×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C2×C4×D157—21no—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157D411yescharacteristic
36C4⋊Dic157D411yescharacteristic
37#14578933—21no—
38#14578933—21no—
39C22⋊Dic157—21no—
40C22⋊Dic157—21no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44C4×Dic157—21no—
45C24×C157D411yescharacteristic
46C22×C4×C157—21no—
47C22×C4×C157—21no—
48C22×C4×C157D411yescharacteristic
49C22×C4×C157C2311yescharacteristic
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—42no—
53C22⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C22⋊C4×C157—42no—
56C22×D157—21no—
57Dic314—41no—
58D628—41no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C22⋊D157—81no—
62C22⋊D157—81no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C4×D157—81no—
67#11929434—41no—
68#11929434—41no—
69C23×C157—21no—
70C23×C157—21no—
71C23×C157—21no—
72C23×C157—41no—
73C23×C157—41no—
74C23×C157C2×D411yescharacteristic
75C2×C4×C157—22no—
76C2×C4×C157—21no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157—41no—
82C2×C4×C157—41no—
83C2×C4×C157—41no—
84C2×C4×C157C2×D411yescharacteristic
85C2×C4×C157C2×D411yescharacteristic
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—42no—
89C22×C157—41no—
90C22×C157—41no—
91C22×C157—41no—
92C22×C157—81no—
93C22×C157#12011yescharacteristic
94C22×C157#13511yescharacteristic
95C22×C157#13711yescharacteristic
96C2×D157—41no—
97C2×D157—41no—
98C2×D157—41no—
99C4×C157—21no—
100C4×C157—21no—
101C4×C157—42no—
102C4×C157—41no—
103C4×C157—81no—
104Dic157—41no—
105Dic157—41no—
106Dic157—41no—
107C2×C157—21no—
108C2×C157—21no—
109C2×C157—81no—
110C2×C157#45211yescharacteristic
111C2×C157#45311yescharacteristic
112C2×C157#45811yescharacteristic
113D157—81no—
114C157#161811yescharacteristic, complemented, Sylow
115#1618—1571nomaximal, Sylow
116#538—1571no—
117#484—1571no—
118#481—1571no—
119#399D15711yescharacteristic, complemented
120#328—1571no—
121#327—1571no—
122#323—1571no—
123#126—3141no—
124#124—3141no—
125#123—3141no—
126C22⋊Q8—1571no—
127#121—3141no—
128#121—1571no—
129#120—3141no—
130C4×D4—3141no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D15711yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4C2×D15711yescharacteristic
135#107—3141no—
136#106—3141no—
137#103—3141no—
138#102—3141no—
139C22⋊C8—1571no—
140C22⋊C8—1571no—
141#95C2×D15711yescharacteristic
142C24C22⋊D15711yescharacteristic
143C2×Q8—1571no—
144C2×D4—3141no—
145C2×D4—3141no—
146C2×D4—3141no—
147C2×D4—1571no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—3141no—
151C22×C4C22⋊D15711yescharacteristic
152C22×C4C22×D15711yescharacteristic
153C2×C8—3141no—
154C2×C8—3141no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—3141no—
159C4⋊C4—3141no—
160C4⋊C4—1571no—
161C4⋊C4—1571no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—42no—
165C22⋊C4—3141no—
166C22⋊C4—3141no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C42—3141no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—3141no—
177C23C2×C22⋊D15711yescharacteristic
178Q8—6281no—
179D4—6281no—
180D4—6281no—
181D4—6281no—
182D4—12561no—
183D4—12561no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—3141no—
194C2×C4—3141no—
195C2×C4—3141no—
196C2×C4—12561no—
197C2×C4D4×D15711yescharacteristic
198C2×C4D4×D15711yescharacteristic
199C8—6281no—
200C8—6281no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—6281no—
209C22—6281no—
210C22—6281no—
211C22#1909773911yescharacteristic
212C22#1909779111yescharacteristic
213C22#1909780211yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—81no—
219C4—6281no—
220C4—6281no—
221C4—6281no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—12561no—
226C2#2375743311yescharacteristic
227C2#2375744011yescharacteristic
228C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#399×C157C2
socleC22×C157#120
prime radical#23757861C2
hypercenter#399D157
hypocenterC157#1618
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #23757608C2semidirect
3. #23757591C2semidirect
4. #23757009C2semidirect
5. #23757006C2semidirect
6. #23756997C2semidirect
7. #399×C157C2semidirect
114. C157#1618semidirect
119. #399D157semidirect

Maximal subgroups

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

subgroupindex
#237578612
#237576082
#237575912
#237570092
#237570062
#237569972
#399×C1572
#1618157