Finite Group Databasebeta

← #34101452

Subgroups — #34101452

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×#14578942C211yesmaximal, characteristic
2C2×#19097700C211yesmaximal, characteristic, complemented
3C2×#19097696C211yesmaximal, characteristic, complemented
4#23757178C211yesmaximal, characteristic, complemented
5#23757176C211yesmaximal, characteristic
6#23757035C211yesmaximal, characteristic, complemented
7C2×#102×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C2×#14578942—22no—
10C2×#14578942—22no—
11C2×#14578942—22no—
12C22×#11929434C2211yescharacteristic
13C2×C4⋊Dic157C2211yescharacteristic
14C2×C22⋊Dic157—21no—
15C2×C22⋊Dic157—21no—
16C2×C4×Dic157C2211yescharacteristic
17#19097700—22no—
18#19097696—22no—
19#19097678—21no—
20#19097678—21no—
21C22×D4×C157C2211yescharacteristic
22C22×C8×C157C2211yescharacteristic
23C2×C4⋊C4×C157C2211yescharacteristic
24#102×C157—22no—
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314D412yes—
31C22×Dic157—21no—
32C22×Dic157—21no—
33C22×Dic157D411yescharacteristic
34C22×Dic157D411yescharacteristic
35#14578942—28no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C2×#11929434D412yes—
39C4⋊Dic157—21no—
40C4⋊Dic157—21no—
41C22⋊Dic157—42no—
42C22⋊Dic157—42no—
43C4×Dic157—21no—
44C4×Dic157—21no—
45C24×C157—21no—
46C2×D4×C157—21no—
47C2×D4×C157—21no—
48C2×D4×C157—21no—
49C2×D4×C157—21no—
50C2×D4×C157—21no—
51C2×D4×C157D412yes—
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×C157—21no—
59Dic314—22no—
60Dic314—22no—
61Dic314—41no—
62Dic314—41no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—22no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—41no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157—41no—
73C2×Dic157—41no—
74C2×Dic157SD1612yescomplemented
75#11929434—22no—
76C23×C157—22no—
77C23×C157—41no—
78C23×C157—41no—
79C23×C157—41no—
80C23×C157—41no—
81C23×C157—41no—
82C23×C157—41no—
83C23×C157C2×D411yescharacteristic
84D4×C157—22no—
85D4×C157—22no—
86D4×C157—41no—
87D4×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—42no—
99C22×C157—42no—
100C22×C157—42no—
101C22×C157—81no—
102C22×C157—81no—
103C22×C157—81no—
104C22×C157—81no—
105C22×C157#12111yescharacteristic
106C22×C157#12111yescharacteristic
107C22×C157#12111yescharacteristic
108C22×C157C2×SD1611yescharacteristic
109C22×C157#13511yescharacteristic
110C22×C157AGL(1,ℤ/8)11yescharacteristic
111C22×C157#13711yescharacteristic
112C4×C157—81no—
113C4×C157#12011yescharacteristic
114C4×C157#12311yescharacteristic
115C4×C157#12311yescharacteristic
116C4×C157#12411yescharacteristic
117Dic157—22no—
118Dic157—42no—
119Dic157—41no—
120Dic157—81no—
121C2×C157—82no—
122C2×C157#39411yescharacteristic
123C2×C157#46011yescharacteristic
124C2×C157#46111yescharacteristic
125C2×C157#46311yescharacteristic
126C2×C157#46411yescharacteristic
127C2×C157#46511yescharacteristic
128C2×C157#46811yescharacteristic
129C157#205511yescharacteristic, complemented, Sylow
130#2055—1571nomaximal, Sylow
131C22×SD16—1571no—
132C2×C4⋊C8—1571no—
133C2×#103—1571no—
134C2×#102D15711yescharacteristic
135#391—1571no—
136#390—1571no—
137#340—1571no—
138C22×Q8—1571no—
139C22×D4C2×D15711yescharacteristic
140C2×SD16—3142no—
141C2×SD16—3142no—
142C2×SD16—3142no—
143C22×C8—1571no—
144C22×C8C2×D15711yescharacteristic
145C2×C4⋊C4—1571no—
146C2×C4⋊C4C2×D15711yescharacteristic
147C2×C22⋊C4—3141no—
148C2×C22⋊C4—3141no—
149C2×C42—1571no—
150C4⋊C8—3142no—
151#103—3142no—
152#102—22no—
153#95—3141no—
154#95—3141no—
155C24—21no—
156C2×Q8—3141no—
157C2×Q8—3141no—
158C2×Q8—3141no—
159C2×Q8—3141no—
160C2×Q8—3141no—
161C2×Q8—1572no—
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×C4—1571no—
172C22×C4—1571no—
173C22×C4C22×D15711yescharacteristic
174SD16—3148no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—3141no—
179C2×C8—3141no—
180C2×C8—1572no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—3141no—
184C4⋊C4—3141no—
185C22⋊C4—6282no—
186C22⋊C4—6282no—
187C42—3141no—
188C42—3141no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23D4×D15711yescharacteristic
197Q8—3142no—
198Q8—3142no—
199Q8—6281no—
200Q8—6281no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3141no—
209C2×C4—3141no—
210C2×C4—3141no—
211C2×C4—3142no—
212C2×C4—3141no—
213C2×C4—3141no—
214C2×C4—6281no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—6281no—
218C2×C4—6281no—
219C2×C4—1572no—
220C2×C4D4×D15711yescharacteristic
221C2×C4D4×D15711yescharacteristic
222C2×C4C2×C22⋊D15711yescharacteristic
223C2×C4#1457895311yescharacteristic
224C2×C4#1457895411yescharacteristic
225C2×C4#1457895411yescharacteristic
226C8—41no—
227C8—3142no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#1909774311yescharacteristic
236C22#1909774411yescharacteristic
237C22#1909774411yescharacteristic
238C22SD16×D15711yescharacteristic
239C22#1909779011yescharacteristic
240C22#1909779511yescharacteristic
241C22#1909780011yescharacteristic
242C4—81no—
243C4—3142no—
244C4—6282no—
245C4—6281no—
246C4—12561no—
247C4#1909773911yescharacteristic
248C4#1909775311yescharacteristic
249C4#1909775411yescharacteristic
250C4#1909775711yescharacteristic
251C2—82no—
252C2#2375718811yescharacteristic
253C2#2375747211yescharacteristic
254C2#2375747611yescharacteristic
255C2#2375748611yescharacteristic
256C2#2375749411yescharacteristic
257C2#2375750111yescharacteristic
258C2#2375751811yescharacteristic
subgroupG/H
centerC23D4×D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#102×C157C2
socleC23×C157C2×D4
prime radicalC22×D4×C157C22
hypercenterC2×#102D157
hypocenterC157#2055
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#19097700C2semidirect
3. C2×#19097696C2semidirect
4. #23757178C2semidirect
6. #23757035C2semidirect
74. C2×Dic157SD16semidirect
129. C157#2055semidirect

Maximal subgroups

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

subgroupindex
C22×#145789422
C2×#190977002
C2×#190976962
#237571782
#237571762
#237570352
C2×#102×C1572
#2055157