Finite Group Databasebeta

← #34099140

Subgroups — #34099140

Order 20096.

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

normal subgroups only

This group has 254 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#23757587C211yesmaximal, characteristic, complemented
3#23757584C211yesmaximal, characteristic, complemented
4#23757205C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic, complemented
6#23756998C211yesmaximal, characteristic, complemented
7#327×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9#19097749—21no—
10#19097748—21no—
11#19097745C2211yescharacteristic
12#19097744—21no—
13#19097743—21no—
14#19097743—21no—
15C2×C4⋊Dic157—21no—
16C2×C4⋊Dic157C2211yescharacteristic
17C2×#14578933C2211yescharacteristic
18#19097705—21no—
19#19097704—21no—
20#19097693—21no—
21#19097692—21no—
22C22⋊#11929434C2211yescharacteristic
23#19097678—21no—
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×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⋊Dic157—21no—
41C4⋊Dic157—21no—
42C4⋊Dic157—42no—
43C4⋊Dic157D411yescharacteristic
44#14578933—21no—
45#14578933—21no—
46#14578933—21no—
47C22⋊Dic157—21no—
48#14578931—21no—
49#14578931—21no—
50C2×D4×C157—21no—
51C2×D4×C157D411yescharacteristic
52C22×C4×C157—21no—
53C22×C4×C157C2311yescharacteristic
54C2×C8×C157—21no—
55C4⋊C4×C157D411yescharacteristic
56C22⋊C4×C157—21no—
57C22×D157—21no—
58Dic314—42no—
59D628—41no—
60C22⋊D157—42no—
61C22⋊D157—41no—
62C22⋊D157—41no—
63C22⋊D157—81no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C2×Dic157—42no—
69C2×Dic157—41no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157—41no—
73C2×Dic157D812yes—
74C4×D157—42no—
75#11929434—41no—
76C23×C157—21no—
77C23×C157C2×D411yescharacteristic
78D4×C157—41no—
79D4×C157—41no—
80D4×C157—41no—
81C2×C4×C157—22no—
82C2×C4×C157—21no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C2×C4×C157—41no—
86C2×C4×C157C2×D411yescharacteristic
87C2×C4×C157C2×D411yescharacteristic
88C8×C157—41no—
89C22×C157—21no—
90C22×C157—21no—
91C22×C157—41no—
92C22×C157—41no—
93C22×C157—41no—
94C22×C157#12011yescharacteristic
95C22×C157C2×D811yescharacteristic
96C22×C157AGL(1,ℤ/8)11yescharacteristic
97C2×D157—41no—
98C2×D157—41no—
99C2×D157—41no—
100C4×C157—21no—
101C4×C157—21no—
102C4×C157—42no—
103C4×C157—41no—
104Dic157—22no—
105Dic157—41no—
106Dic157—41no—
107Dic157—81no—
108C2×C157—21no—
109C2×C157—21no—
110C2×C157—81no—
111C2×C157#44711yescharacteristic
112C2×C157#45611yescharacteristic
113C2×C157#45811yescharacteristic
114D157—81no—
115C157#161011yescharacteristic, complemented, Sylow
116#1610—1571nomaximal, Sylow
117#537—1571no—
118#480—1571no—
119#480—1571no—
120#398—1571no—
121#327—1571no—
122#327D15711yescharacteristic, complemented
123#324—1571no—
124C2×#41—3141no—
125C22⋊Q8—3141no—
126C22⋊Q8—3141no—
127#121—3141no—
128#121—3141no—
129#121—3141no—
130#121—1571no—
131#121C2×D15711yescharacteristic
132C2×C4⋊C4—3141no—
133C2×C4⋊C4—1571no—
134C2×C4⋊C4—1571no—
135#107—3141no—
136#107—3141no—
137#102—3141no—
138#102—3141no—
139C22⋊C8—1571no—
140C22⋊C8C2×D15711yescharacteristic
141#95—3141no—
142#95C2×D15711yescharacteristic
143#41—6282no—
144#41—6282no—
145C2×Q8—3141no—
146C2×D4—21no—
147C2×D4—3141no—
148C2×D4—3141no—
149C2×D4—3141no—
150C2×D4—1571no—
151C2×D4D62811yescharacteristic
152C22×C4—21no—
153C22×C4—3141no—
154C22×C4—3141no—
155C22×C4—3141no—
156C22×C4—1571no—
157C22×C4—1571no—
158C22×C4C22×D15711yescharacteristic
159C2×C8—21no—
160C2×C8—3141no—
161C4⋊C4—3141no—
162C4⋊C4—3141no—
163C4⋊C4—3141no—
164C4⋊C4—3141no—
165C4⋊C4—3141no—
166C4⋊C4—6282no—
167C4⋊C4—1571no—
168C4⋊C4D62811yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—3141no—
171C22⋊C4—3141no—
172C22⋊C4—3141no—
173C23—21no—
174C23—3141no—
175C23D4×D15711yescharacteristic
176Q8—6282no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—6281no—
181D4—6282no—
182D4—6281no—
183D4—6281no—
184D4—12561no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—3141no—
191C2×C4—3141no—
192C2×C4—3141no—
193C2×C4—3141no—
194C2×C4—6282no—
195C2×C4—6282no—
196C2×C4—6281no—
197C2×C4—6281no—
198C2×C4—6281no—
199C2×C4—6281no—
200C2×C4—1572no—
201C2×C4D4×D15711yescharacteristic
202C2×C4C2×D62811yescharacteristic
203C8—41no—
204C8—6281no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—6281no—
211C22—6281no—
212C22—6281no—
213C22#1909774111yescharacteristic
214C22D8×D15711yescharacteristic
215C22#1909779811yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—3142no—
221C4—6281no—
222C4—6281no—
223C4—12561no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—12561no—
228C2#2375740811yescharacteristic
229C2#2375745711yescharacteristic
230C2#2375746411yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157#120
prime radical#23757850C2
hypercenter#327D157
hypocenterC157#1610
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #23757587C2semidirect
3. #23757584C2semidirect
4. #23757205C2semidirect
5. #23757006C2semidirect
6. #23756998C2semidirect
7. #327×C157C2semidirect
115. C157#1610semidirect
122. #327D157semidirect

Maximal subgroups

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

subgroupindex
#237578502
#237575872
#237575842
#237572052
#237570062
#237569982
#327×C1572
#1610157