Finite Group Databasebeta

← #34099171

Subgroups — #34099171

Order 20096.

246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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#23757850C211yesmaximal, characteristic
2#23757591C211yesmaximal, characteristic, complemented
3#23757211C211yesmaximal, characteristic, complemented
4#23757008C211yesmaximal, characteristic, complemented
5#23757007C211yesmaximal, characteristic, complemented
6#23756998C211yesmaximal, characteristic, complemented
7#481×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9#19097749—21no—
10#19097748—21no—
11#19097745C2211yescharacteristic
12#19097744—21no—
13#19097743—21no—
14#19097743—21no—
15C2×#14578933C2211yescharacteristic
16#19097702—21no—
17#19097691—21no—
18C22⋊#11929434C2211yescharacteristic
19#19097678—21no—
20#19097678—21no—
21#19097678C2211yescharacteristic
22#121×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24#106×C157—21no—
25#102×C157—21no—
26C22⋊C8×C157C2211yescharacteristic
27#14578953—42no—
28#14578953—42no—
29C2×Dic314—21no—
30C2×D628D411yescharacteristic
31C2×C22⋊D157—21no—
32C2×C22⋊D157—21no—
33C2×C22⋊D157—21no—
34C22×Dic157—21no—
35C22×Dic157—21no—
36C22×Dic157D411yescharacteristic
37C22×Dic157D411yescharacteristic
38C2×C4×D157—21no—
39C2×#11929434—21no—
40C4⋊Dic157D411yescharacteristic
41#14578933—21no—
42#14578933—21no—
43#14578933—21no—
44C22⋊Dic157—21no—
45#14578931—21no—
46#14578931—21no—
47C2×D4×C157—21no—
48C2×D4×C157D411yescharacteristic
49C22×C4×C157—21no—
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157—21no—
54C4⋊C4×C157D411yescharacteristic
55C22⋊C4×C157—21no—
56C22×D157—21no—
57Dic314—42no—
58D628—41no—
59C22⋊D157—42no—
60C22⋊D157—41no—
61C22⋊D157—41no—
62C22⋊D157—81no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—42no—
68C2×Dic157—41no—
69C2×Dic157—41no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157SD1612yes—
73C4×D157—42no—
74#11929434—41no—
75C23×C157—21no—
76C23×C157C2×D411yescharacteristic
77D4×C157—41no—
78D4×C157—41no—
79D4×C157—41no—
80C2×C4×C157—21no—
81C2×C4×C157—41no—
82C2×C4×C157—42no—
83C2×C4×C157—41no—
84C2×C4×C157C2×D411yescharacteristic
85C2×C4×C157C2×D411yescharacteristic
86C8×C157—41no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—41no—
90C22×C157—41no—
91C22×C157—41no—
92C22×C157#12011yescharacteristic
93C22×C157C2×SD1611yescharacteristic
94C22×C157AGL(1,ℤ/8)11yescharacteristic
95C2×D157—41no—
96C2×D157—41no—
97C2×D157—41no—
98C4×C157—21no—
99C4×C157—21no—
100C4×C157—41no—
101C4×C157—81no—
102Dic157—22no—
103Dic157—41no—
104Dic157—41no—
105Dic157—81no—
106C2×C157—21no—
107C2×C157—21no—
108C2×C157—81no—
109C2×C157#45011yescharacteristic
110C2×C157#45411yescharacteristic
111C2×C157#45811yescharacteristic
112D157—81no—
113C157#161611yescharacteristic, complemented, Sylow
114#1616—1571nomaximal, Sylow
115#537—1571no—
116#481—1571no—
117#481D15711yescharacteristic, complemented
118#400—1571no—
119#327—1571no—
120#327—1571no—
121#324—1571no—
122C2×#41—3141no—
123C22⋊Q8—3141no—
124C22⋊Q8—3141no—
125#121—3141no—
126#121—3141no—
127#121—3141no—
128#121—1571no—
129#121C2×D15711yescharacteristic
130C2×C4⋊C4—1571no—
131C2×C4⋊C4C2×D15711yescharacteristic
132#106—21no—
133#106—3141no—
134#102—21no—
135#102—3141no—
136C22⋊C8—1571no—
137C22⋊C8C2×D15711yescharacteristic
138#95—3141no—
139#95—3141no—
140#95—1571no—
141#41—6282no—
142#41—6282no—
143C2×Q8—3141no—
144C2×D4—21no—
145C2×D4—3141no—
146C2×D4—3141no—
147C2×D4—3141no—
148C2×D4—1571no—
149C2×D4C22⋊D15711yescharacteristic
150C22×C4—21no—
151C22×C4—3141no—
152C22×C4—3141no—
153C22×C4—3141no—
154C22×C4—1571no—
155C22×C4—1571no—
156C22×C4C22×D15711yescharacteristic
157C2×C8—21no—
158C2×C8—3141no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—3141no—
162C4⋊C4—3141no—
163C4⋊C4—3141no—
164C4⋊C4—1571no—
165C4⋊C4C22⋊D15711yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C23—21no—
171C23—3141no—
172C23D4×D15711yescharacteristic
173Q8—6282no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—6281no—
178D4—6282no—
179D4—6281no—
180D4—6281no—
181D4—12561no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—3141no—
187C2×C4—3141no—
188C2×C4—3141no—
189C2×C4—3141no—
190C2×C4—6282no—
191C2×C4—6282no—
192C2×C4—6281no—
193C2×C4—6281no—
194C2×C4—6281no—
195C2×C4—6281no—
196C2×C4—1572no—
197C2×C4D4×D15711yescharacteristic
198C2×C4C2×C22⋊D15711yescharacteristic
199C8—41no—
200C8—6281no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—6281no—
207C22—6281no—
208C22—6281no—
209C22#1909773911yescharacteristic
210C22SD16×D15711yescharacteristic
211C22#1909779811yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—3142no—
217C4—6281no—
218C4—6281no—
219C4—12561no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—12561no—
224C2#2375742211yescharacteristic
225C2#2375744411yescharacteristic
226C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#481×C157C2
socleC22×C157#120
prime radical#23757850C2
hypercenter#481D157
hypocenterC157#1616
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #23757591C2semidirect
3. #23757211C2semidirect
4. #23757008C2semidirect
5. #23757007C2semidirect
6. #23756998C2semidirect
7. #481×C157C2semidirect
113. C157#1616semidirect
117. #481D157semidirect

Maximal subgroups

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

subgroupindex
#237578502
#237575912
#237572112
#237570082
#237570072
#237569982
#481×C1572
#1616157