Finite Group Databasebeta

← #34101455

Subgroups — #34101455

Order 20096.

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

normal subgroups only

This group has 324 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
1C22×#14578943C211yesmaximal, characteristic
2C2×#19097700C211yesmaximal, characteristic, complemented
3C2×#19097694C211yesmaximal, characteristic, complemented
4C2×#19097691C211yesmaximal, characteristic
5#23757178C211yesmaximal, characteristic, complemented
6#23757174C211yesmaximal, characteristic
7#340×C157C211yesmaximal, characteristic, complemented
8C22×Dic314C2211yescharacteristic
9C22×D628C2211yescharacteristic
10C2×#14578943—22no—
11C2×#14578943—22no—
12C2×#14578943—22no—
13C22×#11929434C2211yescharacteristic
14C2×#14578931—21no—
15C2×#14578931—21no—
16C2×C4×Dic157C2211yescharacteristic
17#19097700—22no—
18#19097694—22no—
19#19097691—22no—
20#19097678—21no—
21#19097678—21no—
22C22×C8×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24C2×C4⋊C4×C157C2211yescharacteristic
25C23×D157—21no—
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314—21no—
31C2×Dic314D412yes—
32C2×D628—21no—
33C2×D628—21no—
34C2×D628—21no—
35C2×D628—21no—
36C2×D628—21no—
37C2×D628D412yes—
38C22×Dic157—21no—
39C22×Dic157D411yescharacteristic
40C22×Dic157D411yescharacteristic
41#14578943—28no—
42C2×#11929434—21no—
43C2×#11929434—21no—
44C2×#11929434—21no—
45#14578931—42no—
46#14578931—42no—
47C4×Dic157—21no—
48C4×Dic157—21no—
49C22×C4×C157—21no—
50C22×C4×C157—21no—
51C22×C4×C157C2311yescharacteristic
52C2×C8×C157—21no—
53C2×C8×C157—21no—
54C2×C8×C157D412yes—
55C4⋊C4×C157—21no—
56C4⋊C4×C157—21no—
57C4⋊C4×C157—21no—
58C4⋊C4×C157—21no—
59C22×D157—22no—
60C22×D157—41no—
61C22×D157—41no—
62C22×D157—41no—
63C22×D157—41no—
64C22×D157—41no—
65C22×D157—41no—
66Dic314—22no—
67Dic314—22no—
68Dic314—41no—
69Dic314—41no—
70D628—22no—
71D628—22no—
72D628—41no—
73D628—41no—
74C2×Dic157—21no—
75C2×Dic157—21no—
76C2×Dic157—22no—
77C2×Dic157—21no—
78C2×Dic157—21no—
79C2×Dic157—21no—
80C2×Dic157—41no—
81C2×Dic157—41no—
82C2×Dic157SD1612yescomplemented
83#11929434—41no—
84C23×C157C2×D411yescharacteristic
85C2×C4×C157—41no—
86C2×C4×C157—41no—
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—22no—
98C22×C157#12111yescharacteristic
99C22×C157#12111yescharacteristic
100C22×C157#12111yescharacteristic
101C22×C157C2×SD1611yescharacteristic
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—81no—
113C4×C157—81no—
114C4×C157#12011yescharacteristic
115C4×C157#12311yescharacteristic
116C4×C157#12311yescharacteristic
117C4×C157#12411yescharacteristic
118Dic157—22no—
119Dic157—42no—
120Dic157—41no—
121C2×C157#39411yescharacteristic
122C2×C157#46011yescharacteristic
123C2×C157#46111yescharacteristic
124C2×C157#46311yescharacteristic
125C2×C157#46411yescharacteristic
126C2×C157#46511yescharacteristic
127C2×C157#46811yescharacteristic
128D157—82no—
129C157#205511yescharacteristic, complemented, Sylow
130#2055—1571nomaximal, Sylow
131C22×SD16—1571no—
132C2×C4⋊C8—1571no—
133C2×#103—1571no—
134C2×#102—1571no—
135#391—1571no—
136#390—1571no—
137#340D15711yescharacteristic, complemented
138C22×Q8—1571no—
139C22×D4—1571no—
140C2×SD16—3142no—
141C2×SD16—3142no—
142C2×SD16—3142no—
143C22×C8—1571no—
144C22×C8C2×D15711yescharacteristic
145C2×C4⋊C4C2×D15711yescharacteristic
146C2×C4⋊C4C2×D15711yescharacteristic
147C2×C22⋊C4—3141no—
148C2×C22⋊C4—3141no—
149C2×C42—1571no—
150C4⋊C8—3142no—
151#103—3142no—
152#102—3142no—
153#95—3141no—
154#95—3141no—
155C24—3141no—
156C2×Q8—3141no—
157C2×Q8—3141no—
158C2×Q8—3141no—
159C2×Q8—3141no—
160C2×Q8—3141no—
161C2×Q8—1572no—
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
174SD16—3148no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—3141no—
178C2×C8—3141no—
179C2×C8—3141no—
180C2×C8D62812yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C22⋊C4—6282no—
186C22⋊C4—6282no—
187C42—3141no—
188C42—3141no—
189C23—3142no—
190C23—6281no—
191C23—6281no—
192C23—6281no—
193C23—6281no—
194C23—6281no—
195C23—6281no—
196C23D4×D15711yescharacteristic
197Q8—3142no—
198Q8—3142no—
199Q8—6281no—
200Q8—6281no—
201D4—3142no—
202D4—3142no—
203D4—6281no—
204D4—6281no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3141no—
212C2×C4—3141no—
213C2×C4—3142no—
214C2×C4—3141no—
215C2×C4—3141no—
216C2×C4—3141no—
217C2×C4—6281no—
218C2×C4—6281no—
219C2×C4—1572no—
220C2×C4D4×D15711yescharacteristic
221C2×C4D4×D15711yescharacteristic
222C2×C4C2×D62811yescharacteristic
223C2×C4#1457895411yescharacteristic
224C2×C4#1457895411yescharacteristic
225C2×C4#1457895511yescharacteristic
226C8—22no—
227C8—6281no—
228C22—6282no—
229C22—6282no—
230C22—6282no—
231C22—12561no—
232C22—12561no—
233C22—12561no—
234C22—12561no—
235C22#1909774411yescharacteristic
236C22#1909774411yescharacteristic
237C22#1909774611yescharacteristic
238C22SD16×D15711yescharacteristic
239C22#1909779211yescharacteristic
240C22#1909779511yescharacteristic
241C22#1909780311yescharacteristic
242C4—81no—
243C4—81no—
244C4—3142no—
245C4—6282no—
246C4—6281no—
247C4#1909774111yescharacteristic
248C4#1909775611yescharacteristic
249C4#1909775611yescharacteristic
250C4#1909775911yescharacteristic
251C2—12562no—
252C2#2375719111yescharacteristic
253C2#2375747211yescharacteristic
254C2#2375747711yescharacteristic
255C2#2375748711yescharacteristic
256C2#2375749811yescharacteristic
257C2#2375750311yescharacteristic
258C2#2375752011yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#340×C157C2
socleC23×C157C2×D4
prime radicalC22×D628C22
hypercenter#340D157
hypocenterC157#2055
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
2. C2×#19097700C2semidirect
3. C2×#19097694C2semidirect
5. #23757178C2semidirect
7. #340×C157C2semidirect
82. C2×Dic157SD16semidirect
129. C157#2055semidirect
137. #340D157semidirect

Maximal subgroups

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

subgroupindex
C22×#145789432
C2×#190977002
C2×#190976942
C2×#190976912
#237571782
#237571742
#340×C1572
#2055157