Finite Group Databasebeta

← #34099152

Subgroups — #34099152

Order 20096.

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

normal subgroups only

This group has 232 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#23757604C211yesmaximal, characteristic, complemented
3#23757587C211yesmaximal, characteristic, complemented
4#23757198C211yesmaximal, characteristic, complemented
5#23757011C211yesmaximal, characteristic, complemented
6#23757008C211yesmaximal, characteristic, complemented
7#323×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—
16C2×C4⋊Dic157C2211yescharacteristic
17C2×C22⋊Dic157—21no—
18#19097705—21no—
19#19097703—21no—
20#19097696—21no—
21#19097693—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24C2×C22⋊C4×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26C22⋊C8×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C22×Dic157—21no—
33C22×Dic157—21no—
34C2×C4×D157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157D411yescharacteristic
38C4⋊Dic157D411yescharacteristic
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42C22⋊Dic157—21no—
43C22⋊Dic157—21no—
44C22⋊Dic157—42no—
45#14578931—21no—
46#14578931—21no—
47C4×Dic157—21no—
48C24×C157D411yescharacteristic
49C22×C4×C157D411yescharacteristic
50C22×C4×C157C2311yescharacteristic
51C2×C8×C157—21no—
52C2×C8×C157—21no—
53C22⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C22×D157—21no—
56Dic314—41no—
57D628—41no—
58C22⋊D157—41no—
59C22⋊D157—41no—
60C22⋊D157—81no—
61C22⋊D157—81no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C2×Dic157—41no—
68C2×Dic157—41no—
69C2×Dic157—41no—
70C2×Dic157—41no—
71C4×D157—81no—
72C23×C157—21no—
73C23×C157—21no—
74C23×C157—21no—
75C23×C157—41no—
76C23×C157—41no—
77C23×C157C2×D411yescharacteristic
78C2×C4×C157—21no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C8×C157—41no—
84C8×C157—41no—
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—42no—
88C22×C157—41no—
89C22×C157—41no—
90C22×C157—41no—
91C22×C157—81no—
92C22×C157#12011yescharacteristic
93C22×C157#13511yescharacteristic
94C22×C157AGL(1,ℤ/8)11yescharacteristic
95C2×D157—41no—
96C2×D157—41no—
97C2×D157—41no—
98C4×C157—21no—
99C4×C157—21no—
100C4×C157—41no—
101Dic157—41no—
102Dic157—41no—
103Dic157—41no—
104Dic157—81no—
105Dic157—81no—
106C2×C157—21no—
107C2×C157—21no—
108C2×C157—81no—
109C2×C157#44911yescharacteristic
110C2×C157#45511yescharacteristic
111C2×C157#45811yescharacteristic
112D157—81no—
113C157#161211yescharacteristic, complemented, Sylow
114#1612—1571nomaximal, Sylow
115#538—1571no—
116#483—1571no—
117#480—1571no—
118#397—1571no—
119#328—1571no—
120#327—1571no—
121#323D15711yescharacteristic, complemented
122#126—3141no—
123#124—3141no—
124#123—3141no—
125C22⋊Q8—1571no—
126#121—3141no—
127#121—1571no—
128#120—3141no—
129C4×D4—3141no—
130C2×C4⋊C4—1571no—
131C2×C22⋊C4—3141no—
132C2×C22⋊C4C2×D15711yescharacteristic
133#107—3141no—
134#106—3141no—
135#103—3141no—
136#102—3141no—
137C22⋊C8C2×D15711yescharacteristic
138C22⋊C8C2×D15711yescharacteristic
139#95—3141no—
140#95—1571no—
141C24D62811yescharacteristic
142C2×Q8—1571no—
143C2×D4—3141no—
144C2×D4—3141no—
145C2×D4—3141no—
146C2×D4—1571no—
147C22×C4—3141no—
148C22×C4—3141no—
149C22×C4—3141no—
150C22×C4D62811yescharacteristic
151C22×C4C22×D15711yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C4⋊C4—1571no—
159C4⋊C4—1571no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C22⋊C4—3141no—
165C22⋊C4—3141no—
166C22⋊C4—3141no—
167C22⋊C4—6282no—
168C42—3141no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—3141no—
175C23C2×D62811yescharacteristic
176Q8—6281no—
177D4—6281no—
178D4—6281no—
179D4—6281no—
180D4—12561no—
181D4—12561no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—3141no—
186C2×C4—3141no—
187C2×C4—3141no—
188C2×C4—6281no—
189C2×C4—6281no—
190C2×C4—6281no—
191C2×C4—6281no—
192C2×C4—6281no—
193C2×C4—6281no—
194C2×C4—12561no—
195C2×C4D4×D15711yescharacteristic
196C2×C4D4×D15711yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—6281no—
207C22—6281no—
208C22—6281no—
209C22#1909774111yescharacteristic
210C22#1909779311yescharacteristic
211C22#1909779911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—6281no—
216C4—6281no—
217C4—6281no—
218C4—12561no—
219C4—12561no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—12561no—
224C2#2375742011yescharacteristic
225C2#2375745311yescharacteristic
226C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#323×C157C2
socleC22×C157#120
prime radical#23757861C2
hypercenter#323D157
hypocenterC157#1612
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23757604C2semidirect
3. #23757587C2semidirect
4. #23757198C2semidirect
5. #23757011C2semidirect
6. #23757008C2semidirect
7. #323×C157C2semidirect
113. C157#1612semidirect
121. #323D157semidirect

Maximal subgroups

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

subgroupindex
#237578612
#237576042
#237575872
#237571982
#237570112
#237570082
#323×C1572
#1612157