Finite Group Databasebeta

← #34101374

Subgroups — #34101374

Order 20096.

318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19097760C211yesmaximal, characteristic
2C2×#19097695C211yesmaximal, characteristic, complemented
3C2×#19097693C211yesmaximal, characteristic
4C2×#19097691C211yesmaximal, characteristic
5#23757172C211yesmaximal, characteristic, complemented
6#23757027C211yesmaximal, characteristic, complemented
7C2×#103×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10#19097760—22no—
11#19097760—22no—
12C2×C4⋊Dic157—21no—
13C2×C4⋊Dic157C2211yescharacteristic
14C2×#14578931—21no—
15C2×#14578931—21no—
16C2×C4×Dic157C2211yescharacteristic
17#19097695—22no—
18#19097693—22no—
19#19097691—22no—
20#19097678—21no—
21C22×Q8×C157C2211yescharacteristic
22C22×C8×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24#103×C157—22no—
25C23×D157—21no—
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628D412yes—
32C22×Dic157—21no—
33C22×Dic157D411yescharacteristic
34C22×Dic157D411yescharacteristic
35C2×#11929434—21no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C4⋊Dic157—21no—
39C4⋊Dic157—21no—
40C4⋊Dic157—42no—
41#14578931—24no—
42#14578931—24no—
43C4×Dic157—21no—
44C4×Dic157—21no—
45C2×Q8×C157—21no—
46C2×Q8×C157—21no—
47C2×Q8×C157—21no—
48C2×Q8×C157—21no—
49C2×Q8×C157—21no—
50C2×Q8×C157D412yes—
51C22×C4×C157—21no—
52C22×C4×C157—21no—
53C22×C4×C157C2311yescharacteristic
54C2×C8×C157—21no—
55C2×C8×C157—21no—
56C2×C8×C157—21no—
57C4⋊C4×C157—21no—
58C4⋊C4×C157D412yes—
59C22×D157—22no—
60C22×D157—41no—
61C22×D157—41no—
62C22×D157—41no—
63C22×D157—41no—
64C22×D157—41no—
65C22×D157—41no—
66D628—22no—
67D628—22no—
68D628—41no—
69D628—41no—
70C2×Dic157—21no—
71C2×Dic157—21no—
72C2×Dic157—21no—
73C2×Dic157—21no—
74C2×Dic157—21no—
75C2×Dic157—21no—
76C2×Dic157—41no—
77C2×Dic157—41no—
78C2×Dic157—41no—
79#11929434—41no—
80C23×C157C2×D411yescharacteristic
81Q8×C157—22no—
82Q8×C157—22no—
83Q8×C157—41no—
84Q8×C157—41no—
85C2×C4×C157—22no—
86C2×C4×C157—22no—
87C2×C4×C157—41no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157—41no—
91C2×C4×C157C2×D411yescharacteristic
92C2×C4×C157C2×D411yescharacteristic
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157#4111yescharacteristic
95C2×C4×C157#4111yescharacteristic
96C2×C4×C157#4111yescharacteristic
97C8×C157—41no—
98C22×C157#12011yescharacteristic
99C22×C157#12111yescharacteristic
100C22×C157#12411yescharacteristic
101C22×C157#13511yescharacteristic
102C22×C157#13511yescharacteristic
103C22×C157AGL(1,ℤ/8)11yescharacteristic
104C22×C157#13711yescharacteristic
105C2×D157—42no—
106C2×D157—42no—
107C2×D157—42no—
108C2×D157—81no—
109C2×D157—81no—
110C2×D157—81no—
111C2×D157—81no—
112C4×C157—42no—
113C4×C157—42no—
114C4×C157#12111yescharacteristic
115C4×C157#12111yescharacteristic
116C4×C157#12311yescharacteristic
117C4×C157#12311yescharacteristic
118Dic157—41no—
119Dic157—41no—
120Dic157—81no—
121C2×C157#39411yescharacteristic
122C2×C157#44911yescharacteristic
123C2×C157#45211yescharacteristic
124C2×C157#46311yescharacteristic
125C2×C157#46411yescharacteristic
126C2×C157#48811yescharacteristic
127C2×C157#48911yescharacteristic
128D157—82no—
129C157#204211yescharacteristic, complemented, Sylow
130#2042—1571nomaximal, Sylow
131C2×#124—1571no—
132C2×#103—1571no—
133C2×#103D15711yescharacteristic, complemented
134C2×#102—1571no—
135C2×#102—1571no—
136#389—1571no—
137#336—1571no—
138C22×Q8C2×D15711yescharacteristic
139C22×D4—1571no—
140C22×C8—1571no—
141C22×C8C2×D15711yescharacteristic
142#124—3142no—
143#124—3142no—
144C2×C4⋊C4—3141no—
145C2×C4⋊C4—1571no—
146C2×C4⋊C4C2×D15711yescharacteristic
147C2×C22⋊C4—3141no—
148C2×C22⋊C4—3141no—
149C2×C42—1571no—
150#103—22no—
151#103—3142no—
152#102—3142no—
153#102—3142no—
154#95—3141no—
155C24—3141no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8D62812yes—
162C2×D4—3141no—
163C2×D4—3141no—
164C2×D4—3141no—
165C2×D4—3141no—
166C2×D4—3141no—
167C2×D4—1572no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—3141no—
171C22×C4—1571no—
172C22×C4—1571no—
173C22×C4C22×D15711yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—3141no—
178C2×C8—3141no—
179C2×C8—3141no—
180C4⋊C4—21no—
181C4⋊C4—3141no—
182C4⋊C4—3141no—
183C4⋊C4—6282no—
184C4⋊C4C22⋊D15712yes—
185C22⋊C4—3144no—
186C22⋊C4—3144no—
187C42—3141no—
188C42—3141no—
189C23—3142no—
190C23—6281no—
191C23—6281no—
192C23—6281no—
193C23—6281no—
194C23—6281no—
195C23—6281no—
196C23D4×D15711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—3142no—
202D4—3142no—
203D4—6281no—
204D4—6281no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3141no—
212C2×C4—3141no—
213C2×C4—3141no—
214C2×C4—3141no—
215C2×C4—3141no—
216C2×C4—3141no—
217C2×C4—6281no—
218C2×C4—6281no—
219C2×C4—6281no—
220C2×C4D4×D15711yescharacteristic
221C2×C4C2×C22⋊D15711yescharacteristic
222C2×C4C2×D62811yescharacteristic
223C2×C4#1457895311yescharacteristic
224C2×C4#1457895311yescharacteristic
225C2×C4#1457895411yescharacteristic
226C8—41no—
227C8—6281no—
228C22—6282no—
229C22—6282no—
230C22—6282no—
231C22—12561no—
232C22—12561no—
233C22—12561no—
234C22—12561no—
235C22#1909774111yescharacteristic
236C22#1909774311yescharacteristic
237C22#1909775711yescharacteristic
238C22#1909779211yescharacteristic
239C22#1909779411yescharacteristic
240C22#1909779811yescharacteristic
241C22#1909780311yescharacteristic
242C4—42no—
243C4—42no—
244C4—6281no—
245C4—6281no—
246C4—12561no—
247C4#1909774211yescharacteristic
248C4#1909774511yescharacteristic
249C4#1909775311yescharacteristic
250C4#1909775511yescharacteristic
251C2—12562no—
252C2#2375718911yescharacteristic
253C2#2375742111yescharacteristic
254C2#2375743811yescharacteristic
255C2#2375749011yescharacteristic
256C2#2375749711yescharacteristic
257C2#2375762911yescharacteristic
258C2#2375763411yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#103×C157C2
socleC23×C157C2×D4
prime radicalC22×D628C22
hypercenterC2×#103D157
hypocenterC157#2042
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#19097695C2semidirect
5. #23757172C2semidirect
6. #23757027C2semidirect
7. C2×#103×C157C2semidirect
129. C157#2042semidirect
133. C2×#103D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977602
C2×#190976952
C2×#190976932
C2×#190976912
#237571722
#237570272
C2×#103×C1572
#2042157