Finite Group Databasebeta

← #34101506

Subgroups — #34101506

Order 20096.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19097702C211yesmaximal, characteristic, complemented
2C2×#19097700C211yesmaximal, characteristic, complemented
3C2×#19097692C211yesmaximal, characteristic
4#23757176C211yesmaximal, characteristic
5#23757172C211yesmaximal, characteristic, complemented
6#23757036C211yesmaximal, characteristic, complemented
7C2×#102×C157C211yesmaximal, characteristic
8C22×#11929434C2211yescharacteristic
9C2×C4⋊Dic157—21no—
10C2×C4⋊Dic157C2211yescharacteristic
11C2×C4⋊Dic157C2211yescharacteristic
12C2×C22⋊Dic157—21no—
13C2×C22⋊Dic157—21no—
14C2×C4×Dic157C2211yescharacteristic
15#19097702—22no—
16#19097700—22no—
17#19097692—22no—
18#19097678—21no—
19C22×D4×C157C2211yescharacteristic
20C22×C8×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22#102×C157—22no—
23C22×Dic157—21no—
24C22×Dic157—21no—
25C22×Dic157D411yescharacteristic
26C22×Dic157D411yescharacteristic
27C2×#11929434—21no—
28C2×#11929434—21no—
29C2×#11929434D412yes—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—42no—
35C22⋊Dic157—42no—
36C22⋊Dic157—42no—
37C4×Dic157—21no—
38C4×Dic157—21no—
39C24×C157—21no—
40C2×D4×C157—21no—
41C2×D4×C157—21no—
42C2×D4×C157—21no—
43C2×D4×C157—21no—
44C2×D4×C157—21no—
45C2×D4×C157Q812yes—
46C22×C4×C157—21no—
47C22×C4×C157C2311yescharacteristic
48C2×C8×C157—21no—
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157D412yes—
53C2×Dic157—21no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—41no—
59C2×Dic157—41no—
60C2×Dic157—41no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157SD1612yes—
65#11929434—22no—
66C23×C157—22no—
67C23×C157—41no—
68C23×C157—41no—
69C23×C157—41no—
70C23×C157—41no—
71C23×C157—41no—
72C23×C157—41no—
73C23×C157C2×D411yescharacteristic
74D4×C157—22no—
75D4×C157—22no—
76D4×C157—41no—
77D4×C157—41no—
78C2×C4×C157—22no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C2×C4×C157C2×Q811yescharacteristic
84C2×C4×C157#4111yescharacteristic
85C2×C4×C157#4111yescharacteristic
86C2×C4×C157#4111yescharacteristic
87C8×C157—41no—
88C22×C157—42no—
89C22×C157—42no—
90C22×C157—42no—
91C22×C157—81no—
92C22×C157—81no—
93C22×C157—81no—
94C22×C157—81no—
95C22×C157#12111yescharacteristic
96C22×C157#12111yescharacteristic
97C22×C157C22⋊Q811yescharacteristic
98C22×C157C2×SD1611yescharacteristic
99C22×C157#13511yescharacteristic
100C22×C157AGL(1,ℤ/8)11yescharacteristic
101C22×C157AGL(1,ℤ/8)11yescharacteristic
102C4×C157—42no—
103C4×C157#12111yescharacteristic
104C4×C157C22⋊Q811yescharacteristic
105C4×C157C22⋊Q811yescharacteristic
106C4×C157#12611yescharacteristic
107Dic157—22no—
108Dic157—41no—
109Dic157—81no—
110Dic157—81no—
111C2×C157—82no—
112C2×C157#39611yescharacteristic
113C2×C157#46011yescharacteristic
114C2×C157#46311yescharacteristic
115C2×C157#46511yescharacteristic
116C2×C157#46911yescharacteristic
117C2×C157#47611yescharacteristic
118C2×C157#47811yescharacteristic
119C157#206511yescharacteristic, complemented, Sylow
120#2065—1571nomaximal, Sylow
121C2×#106—1571no—
122C2×C4⋊C8—1571no—
123C2×#102—1571no—
124C2×#102D15711yescharacteristic
125#390—1571no—
126#389—1571no—
127#340—1571no—
128C22×D4C2×D15711yescharacteristic
129C22×C8—1571no—
130C22×C8C2×D15711yescharacteristic
131C2×C4⋊C4—3141no—
132C2×C4⋊C4—1571no—
133C2×C4⋊C4—1571no—
134C2×C4⋊C4C2×D15711yescharacteristic
135C2×C22⋊C4—3141no—
136C2×C22⋊C4—3141no—
137C2×C42—1571no—
138#106—3142no—
139C4⋊C8—3142no—
140#102—22no—
141#102—3142no—
142#95—3141no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic31412yes—
150C22×C4—21no—
151C22×C4—3141no—
152C22×C4—3141no—
153C22×C4—1571no—
154C22×C4—1571no—
155C22×C4C22×D15711yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—3141no—
160C2×C8—3141no—
161C2×C8—1572no—
162C4⋊C4—21no—
163C4⋊C4—3141no—
164C4⋊C4—3141no—
165C4⋊C4—3141no—
166C4⋊C4—3141no—
167C4⋊C4—6282no—
168C4⋊C4C22⋊D15712yes—
169C22⋊C4—6282no—
170C22⋊C4—6282no—
171C42—3141no—
172C42—3141no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D15711yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—3141no—
189C2×C4—3141no—
190C2×C4—3141no—
191C2×C4—3141no—
192C2×C4—3141no—
193C2×C4—6281no—
194C2×C4—6281no—
195C2×C4—6281no—
196C2×C4—6281no—
197C2×C4—6281no—
198C2×C4—6281no—
199C2×C4—1572no—
200C2×C4D4×D15711yescharacteristic
201C2×C4C2×C22⋊D15711yescharacteristic
202C2×C4C2×Dic31411yescharacteristic
203C2×C4#1457895311yescharacteristic
204C2×C4#1457895311yescharacteristic
205C2×C4#1457895411yescharacteristic
206C8—41no—
207C8—3142no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1909774311yescharacteristic
216C22#1909774411yescharacteristic
217C22#1909774811yescharacteristic
218C22SD16×D15711yescharacteristic
219C22#1909779011yescharacteristic
220C22#1909779511yescharacteristic
221C22#1909779811yescharacteristic
222C4—42no—
223C4—3142no—
224C4—6281no—
225C4—12561no—
226C4—12561no—
227C4#1909774211yescharacteristic
228C4#1909774811yescharacteristic
229C4#1909775011yescharacteristic
230C4#1909776411yescharacteristic
231C2—82no—
232C2#2375719611yescharacteristic
233C2#2375747111yescharacteristic
234C2#2375748611yescharacteristic
235C2#2375750111yescharacteristic
236C2#2375752511yescharacteristic
237C2#2375756111yescharacteristic
238C2#2375757111yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#102×C157C2
socleC23×C157C2×D4
prime radicalC22×D4×C157C22
hypercenterC2×#102D157
hypocenterC157#2065
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#19097702C2semidirect
2. C2×#19097700C2semidirect
5. #23757172C2semidirect
6. #23757036C2semidirect
119. C157#2065semidirect

Maximal subgroups

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

subgroupindex
C2×#190977022
C2×#190977002
C2×#190976922
#237571762
#237571722
#237570362
C2×#102×C1572
#2065157