Finite Group Databasebeta

← #34101519

Subgroups — #34101519

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×#19097700C211yesmaximal, characteristic, complemented
2C2×#19097693C211yesmaximal, characteristic
3C2×#19097691C211yesmaximal, characteristic
4#23757174C211yesmaximal, characteristic
5#23757172C211yesmaximal, characteristic, complemented
6#23757035C211yesmaximal, characteristic, complemented
7C2×#107×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10C2×C4⋊Dic157—21no—
11C2×C4⋊Dic157C2211yescharacteristic
12C2×#14578931—21no—
13C2×#14578931—21no—
14C2×C4×Dic157C2211yescharacteristic
15#19097700—22no—
16#19097693—22no—
17#19097691—22no—
18#19097678—21no—
19C22×C8×C157C2211yescharacteristic
20C2×C4⋊C4×C157C2211yescharacteristic
21C2×C4⋊C4×C157C2211yescharacteristic
22#107×C157—22no—
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×#11929434—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157—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×C157D412yes—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157D412yes—
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—21no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—41no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157D812yes—
73#11929434—41no—
74C23×C157C2×D411yescharacteristic
75C2×C4×C157—22no—
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—22no—
88C22×C157#12111yescharacteristic
89C22×C157#12111yescharacteristic
90C22×C157C22⋊Q811yescharacteristic
91C22×C157C2×D811yescharacteristic
92C22×C157#13511yescharacteristic
93C22×C157AGL(1,ℤ/8)11yescharacteristic
94C22×C157#13711yescharacteristic
95C2×D157—42no—
96C2×D157—42no—
97C2×D157—42no—
98C2×D157—81no—
99C2×D157—81no—
100C2×D157—81no—
101C2×D157—81no—
102C4×C157—42no—
103C4×C157—81no—
104C4×C157#12111yescharacteristic
105C4×C157C22⋊Q811yescharacteristic
106C4×C157C22⋊Q811yescharacteristic
107C4×C157#12611yescharacteristic
108Dic157—22no—
109Dic157—41no—
110Dic157—81no—
111C2×C157#39611yescharacteristic
112C2×C157#45911yescharacteristic
113C2×C157#46411yescharacteristic
114C2×C157#46611yescharacteristic
115C2×C157#46811yescharacteristic
116C2×C157#47411yescharacteristic
117C2×C157#47811yescharacteristic
118D157—82no—
119C157#206711yescharacteristic, complemented, Sylow
120#2067—1571nomaximal, Sylow
121C2×#107D15711yescharacteristic, complemented
122C2×C4⋊C8—1571no—
123C2×#102—1571no—
124C2×#102—1571no—
125#390—1571no—
126#389—1571no—
127#340—1571no—
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#107—22no—
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—3141no—
159C2×C8—3141no—
160C2×C8—3141no—
161C2×C8D62812yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—3141no—
166C4⋊C4—3141no—
167C4⋊C4—6282no—
168C4⋊C4C22⋊D15712yes—
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—22no—
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—3141no—
195C2×C4—3141no—
196C2×C4—6281no—
197C2×C4—6281no—
198C2×C4—6281no—
199C2×C4—1572no—
200C2×C4C2×C22⋊D15711yescharacteristic
201C2×C4C2×D62811yescharacteristic
202C2×C4Q8×D15711yescharacteristic
203C2×C4#1457895311yescharacteristic
204C2×C4#1457895411yescharacteristic
205C2×C4#1457895511yescharacteristic
206C8—22no—
207C8—6281no—
208C22—6282no—
209C22—6282no—
210C22—6282no—
211C22—12561no—
212C22—12561no—
213C22—12561no—
214C22—12561no—
215C22#1909774311yescharacteristic
216C22#1909774611yescharacteristic
217C22#1909774911yescharacteristic
218C22D8×D15711yescharacteristic
219C22#1909779411yescharacteristic
220C22#1909779511yescharacteristic
221C22#1909780311yescharacteristic
222C4—42no—
223C4—81no—
224C4—3142no—
225C4—6281no—
226C4—12561no—
227C4#1909774511yescharacteristic
228C4#1909774711yescharacteristic
229C4#1909775111yescharacteristic
230C4#1909776611yescharacteristic
231C2—12562no—
232C2#2375719511yescharacteristic
233C2#2375746611yescharacteristic
234C2#2375749711yescharacteristic
235C2#2375751011yescharacteristic
236C2#2375752011yescharacteristic
237C2#2375755211yescharacteristic
238C2#2375757611yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#107×C157C2
socleC23×C157C2×D4
prime radicalC22×D628C22
hypercenterC2×#107D157
hypocenterC157#2067
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#19097700C2semidirect
5. #23757172C2semidirect
6. #23757035C2semidirect
7. C2×#107×C157C2semidirect
119. C157#2067semidirect
121. C2×#107D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977002
C2×#190976932
C2×#190976912
#237571742
#237571722
#237570352
C2×#107×C1572
#2067157