Finite Group Databasebeta

← #34101372

Subgroups — #34101372

Order 20096.

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

normal subgroups only

This group has 318 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×#19097695C211yesmaximal, characteristic, complemented
2C2×#19097695C211yesmaximal, characteristic, complemented
3C2×#19097692C211yesmaximal, characteristic
4C2×#19097692C211yesmaximal, characteristic
5#23757171C211yesmaximal, characteristic, complemented
6#23757028C211yesmaximal, characteristic, complemented
7C2×#124×C157C211yesmaximal, characteristic
8C22×#11929434C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10C2×C4⋊Dic157C2211yescharacteristic
11C2×C4⋊Dic157C2211yescharacteristic
12C2×#14578933—21no—
13#19097695—22no—
14#19097695—22no—
15#19097692—22no—
16#19097692—22no—
17#19097678—21no—
18C22×Q8×C157C2211yescharacteristic
19C22×D4×C157C2211yescharacteristic
20#124×C157—22no—
21#124×C157—22no—
22C2×C22⋊C4×C157—21no—
23C2×C22⋊C4×C157—21no—
24C2×C42×C157C2211yescharacteristic
25C22×Dic157—21no—
26C22×Dic157—21no—
27C2×#11929434—21no—
28C2×#11929434—21no—
29C2×#11929434—21no—
30C2×#11929434—21no—
31C2×#11929434—21no—
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D412yes—
37#14578933—42no—
38C24×C157—21no—
39C2×Q8×C157—21no—
40C2×Q8×C157—21no—
41C2×Q8×C157—21no—
42C2×Q8×C157—21no—
43C2×Q8×C157—21no—
44C2×Q8×C157D412yes—
45C2×D4×C157—21no—
46C2×D4×C157—21no—
47C2×D4×C157—21no—
48C2×D4×C157—21no—
49C2×D4×C157—21no—
50C2×D4×C157D412yes—
51C22×C4×C157—21no—
52C22×C4×C157D411yescharacteristic
53C22×C4×C157D411yescharacteristic
54C22×C4×C157C2311yescharacteristic
55C22⋊C4×C157—24no—
56C22⋊C4×C157—24no—
57C42×C157—21no—
58C42×C157—21no—
59C2×Dic157—22no—
60C2×Dic157—41no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65#11929434—41no—
66#11929434—41no—
67C23×C157—22no—
68C23×C157—41no—
69C23×C157—41no—
70C23×C157—41no—
71C23×C157—41no—
72C23×C157—41no—
73C23×C157—41no—
74C23×C157C2×D411yescharacteristic
75Q8×C157—22no—
76Q8×C157—22no—
77Q8×C157—41no—
78Q8×C157—41no—
79D4×C157—22no—
80D4×C157—22no—
81D4×C157—41no—
82D4×C157—41no—
83C2×C4×C157—21no—
84C2×C4×C157—21no—
85C2×C4×C157—22no—
86C2×C4×C157—21no—
87C2×C4×C157—21no—
88C2×C4×C157—21no—
89C2×C4×C157—21no—
90C2×C4×C157—41no—
91C2×C4×C157—41no—
92C2×C4×C157C2×D411yescharacteristic
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2×D411yescharacteristic
95C2×C4×C157#4111yescharacteristic
96C2×C4×C157#4111yescharacteristic
97C2×C4×C157#4111yescharacteristic
98C22×C157—42no—
99C22×C157—42no—
100C22×C157—42no—
101C22×C157—81no—
102C22×C157—81no—
103C22×C157—81no—
104C22×C157—81no—
105C22×C157#12011yescharacteristic
106C22×C157#12111yescharacteristic
107C22×C157#12411yescharacteristic
108C22×C157#13511yescharacteristic
109C22×C157#13511yescharacteristic
110C22×C157AGL(1,ℤ/8)11yescharacteristic
111C22×C157#13711yescharacteristic
112C4×C157—42no—
113C4×C157—41no—
114C4×C157—41no—
115C4×C157#12111yescharacteristic
116C4×C157#12111yescharacteristic
117C4×C157#12311yescharacteristic
118C4×C157#12311yescharacteristic
119Dic157—42no—
120Dic157—81no—
121C2×C157—82no—
122C2×C157#39411yescharacteristic
123C2×C157#44911yescharacteristic
124C2×C157#45211yescharacteristic
125C2×C157#46311yescharacteristic
126C2×C157#46411yescharacteristic
127C2×C157#48811yescharacteristic
128C2×C157#48911yescharacteristic
129C157#204211yescharacteristic, complemented, Sylow
130#2042—1571nomaximal, Sylow
131C2×#124D15711yescharacteristic
132C2×#103—1571no—
133C2×#103—1571no—
134C2×#102—1571no—
135C2×#102—1571no—
136#389—1571no—
137#336—1571no—
138C22×Q8C2×D15711yescharacteristic
139C22×D4C2×D15711yescharacteristic
140C22×C8—1571no—
141C22×C8—1571no—
142#124—22no—
143#124—22no—
144C2×C4⋊C4—3141no—
145C2×C4⋊C4—1571no—
146C2×C4⋊C4—1571no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C42C2×D15711yescharacteristic
150#103—3142no—
151#103—3142no—
152#102—3142no—
153#102—3142no—
154#95—3141no—
155C24—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D15712yes—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D15712yes—
168C22×C4—21no—
169C22×C4—3141no—
170C22×C4—3141no—
171C22×C4C22⋊D15711yescharacteristic
172C22×C4C22⋊D15711yescharacteristic
173C22×C4C22×D15711yescharacteristic
174C2×C8—3141no—
175C2×C8—3141no—
176C2×C8—3141no—
177C2×C8—3141no—
178C2×C8—3141no—
179C2×C8—3141no—
180C4⋊C4—3141no—
181C4⋊C4—3141no—
182C4⋊C4—3141no—
183C4⋊C4—6282no—
184C4⋊C4—1572no—
185C22⋊C4—24no—
186C22⋊C4—24no—
187C42—21no—
188C42—21no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D15711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—3142no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—6281no—
218C2×C4—6281no—
219C2×C4—6281no—
220C2×C4D4×D15711yescharacteristic
221C2×C4C2×C22⋊D15711yescharacteristic
222C2×C4C2×C22⋊D15711yescharacteristic
223C2×C4#1457895311yescharacteristic
224C2×C4#1457895311yescharacteristic
225C2×C4#1457895311yescharacteristic
226C8—6281no—
227C8—6281no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1909774011yescharacteristic
236C22#1909774211yescharacteristic
237C22#1909775811yescharacteristic
238C22#1909779111yescharacteristic
239C22#1909779111yescharacteristic
240C22#1909779611yescharacteristic
241C22#1909780111yescharacteristic
242C4—41no—
243C4—41no—
244C4—42no—
245C4—6282no—
246C4—12561no—
247C4#1909774311yescharacteristic
248C4#1909774311yescharacteristic
249C4#1909775211yescharacteristic
250C4#1909775211yescharacteristic
251C2—82no—
252C2#2375718711yescharacteristic
253C2#2375741811yescharacteristic
254C2#2375743511yescharacteristic
255C2#2375748511yescharacteristic
256C2#2375749211yescharacteristic
257C2#2375762711yescharacteristic
258C2#2375763211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#124×C157C2
socleC23×C157C2×D4
prime radicalC22×D4×C157C22
hypercenterC2×#124D157
hypocenterC157#2042
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#19097695C2semidirect
2. C2×#19097695C2semidirect
5. #23757171C2semidirect
6. #23757028C2semidirect
129. C157#2042semidirect

Maximal subgroups

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

subgroupindex
C2×#190976952
C2×#190976922
#237571712
#237570282
C2×#124×C1572
#2042157