Finite Group Databasebeta

← #34101511

Subgroups — #34101511

Order 20096.

284 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19097693C211yesmaximal, characteristic
4C2×#19097691C211yesmaximal, characteristic
5#23757174C211yesmaximal, characteristic
6#23757169C211yesmaximal, characteristic, complemented
7#340×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10C2×C4⋊Dic157C2211yescharacteristic
11C2×#14578933—21no—
12C2×#14578931—21no—
13C2×#14578931—21no—
14C2×C4×Dic157C2211yescharacteristic
15#19097702—22no—
16#19097700—22no—
17#19097693—22no—
18#19097691—22no—
19#19097678—21no—
20C22×C8×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22C2×C4⋊C4×C157C2211yescharacteristic
23C23×D157—21no—
24C2×D628—21no—
25C2×D628—21no—
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628Q812yes—
30C22×Dic157—21no—
31C22×Dic157D411yescharacteristic
32C22×Dic157D411yescharacteristic
33C2×#11929434—21no—
34C2×#11929434—21no—
35C2×#11929434D412yes—
36C4⋊Dic157—21no—
37C4⋊Dic157D412yes—
38#14578933—42no—
39#14578931—42no—
40#14578931—42no—
41C4×Dic157—21no—
42C4×Dic157—21no—
43C22×C4×C157—21no—
44C22×C4×C157—21no—
45C22×C4×C157C2311yescharacteristic
46C2×C8×C157—21no—
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C22×D157—22no—
54C22×D157—41no—
55C22×D157—41no—
56C22×D157—41no—
57C22×D157—41no—
58C22×D157—41no—
59C22×D157—41no—
60D628—22no—
61D628—22no—
62D628—41no—
63D628—41no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—22no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—21no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157SD1612yes—
73#11929434—22no—
74C23×C157C2×D411yescharacteristic
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157—41no—
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#12111yescharacteristic
89C22×C157#12111yescharacteristic
90C22×C157C22⋊Q811yescharacteristic
91C22×C157C2×SD1611yescharacteristic
92C22×C157#13511yescharacteristic
93C22×C157AGL(1,ℤ/8)11yescharacteristic
94C22×C157AGL(1,ℤ/8)11yescharacteristic
95C2×D157—42no—
96C2×D157—42no—
97C2×D157—42no—
98C2×D157—81no—
99C2×D157—81no—
100C2×D157—81no—
101C2×D157—81no—
102C4×C157—81no—
103C4×C157—81no—
104C4×C157#12111yescharacteristic
105C4×C157C22⋊Q811yescharacteristic
106C4×C157C22⋊Q811yescharacteristic
107C4×C157#12611yescharacteristic
108Dic157—22no—
109Dic157—42no—
110Dic157—41no—
111C2×C157#39611yescharacteristic
112C2×C157#46011yescharacteristic
113C2×C157#46311yescharacteristic
114C2×C157#46511yescharacteristic
115C2×C157#46911yescharacteristic
116C2×C157#47611yescharacteristic
117C2×C157#47811yescharacteristic
118D157—82no—
119C157#206511yescharacteristic, complemented, Sylow
120#2065—1571nomaximal, Sylow
121C2×#106—1571no—
122C2×C4⋊C8—1571no—
123C2×#102—1571no—
124C2×#102—1571no—
125#390—1571no—
126#389—1571no—
127#340D15711yescharacteristic, complemented
128C22×D4—1571no—
129C22×C8—1571no—
130C22×C8C2×D15711yescharacteristic
131C2×C4⋊C4—3141no—
132C2×C4⋊C4—1571no—
133C2×C4⋊C4C2×D15711yescharacteristic
134C2×C4⋊C4C2×D15711yescharacteristic
135C2×C22⋊C4—3141no—
136C2×C22⋊C4—3141no—
137C2×C42—1571no—
138#106—3142no—
139C4⋊C8—3142no—
140#102—3142no—
141#102—3142no—
142#95—3141no—
143C24—3141no—
144C2×D4—3141no—
145C2×D4—3141no—
146C2×D4—3141no—
147C2×D4—3141no—
148C2×D4—3141no—
149C2×D4—1572no—
150C22×C4—21no—
151C22×C4—21no—
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—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—3141no—
167C4⋊C4—6282no—
168C4⋊C4—1572no—
169C22⋊C4—6282no—
170C22⋊C4—6282no—
171C42—3141no—
172C42—3141no—
173C23—3142no—
174C23—6281no—
175C23—6281no—
176C23—6281no—
177C23—6281no—
178C23—6281no—
179C23—6281no—
180C23D4×D15711yescharacteristic
181D4—3142no—
182D4—3142no—
183D4—6281no—
184D4—6281no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—3141no—
192C2×C4—3141no—
193C2×C4—3141no—
194C2×C4—3142no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—6281no—
198C2×C4—6281no—
199C2×C4—1572no—
200C2×C4D4×D15711yescharacteristic
201C2×C4D4×D15711yescharacteristic
202C2×C4Q8×D15711yescharacteristic
203C2×C4#1457895411yescharacteristic
204C2×C4#1457895411yescharacteristic
205C2×C4#1457895411yescharacteristic
206C8—41no—
207C8—3142no—
208C22—6282no—
209C22—6282no—
210C22—6282no—
211C22—12561no—
212C22—12561no—
213C22—12561no—
214C22—12561no—
215C22#1909774411yescharacteristic
216C22#1909774411yescharacteristic
217C22#1909774911yescharacteristic
218C22SD16×D15711yescharacteristic
219C22#1909779411yescharacteristic
220C22#1909779511yescharacteristic
221C22#1909779811yescharacteristic
222C4—81no—
223C4—81no—
224C4—3142no—
225C4—6282no—
226C4—6281no—
227C4#1909774411yescharacteristic
228C4#1909774911yescharacteristic
229C4#1909774911yescharacteristic
230C4#1909776511yescharacteristic
231C2—12562no—
232C2#2375719711yescharacteristic
233C2#2375747211yescharacteristic
234C2#2375749111yescharacteristic
235C2#2375750511yescharacteristic
236C2#2375752511yescharacteristic
237C2#2375756211yescharacteristic
238C2#2375757611yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#340×C157C2
socleC23×C157C2×D4
prime radicalC22×D628C22
hypercenter#340D157
hypocenterC157#2065
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#19097702C2semidirect
2. C2×#19097700C2semidirect
6. #23757169C2semidirect
7. #340×C157C2semidirect
119. C157#2065semidirect
127. #340D157semidirect

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×#190976932
C2×#190976912
#237571742
#237571692
#340×C1572
#2065157