Finite Group Databasebeta

← #34100966

Subgroups — #34100966

Order 20096.

320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#23757819C211yesmaximal, characteristic
2#23757296C211yesmaximal, characteristic, complemented
3C2×#19097699C211yesmaximal, characteristic, complemented
4C2×#19097698C211yesmaximal, characteristic, complemented
5C2×#19097697C211yesmaximal, characteristic, complemented
6#23757119C211yesmaximal, characteristic, complemented
7C2×#104×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10#19097769C411yescharacteristic, complemented
11#19097767C411yescharacteristic, complemented
12#19097760C411yescharacteristic, complemented
13#19097758C411yescharacteristic, complemented
14#19097743—22no—
15C4×C22⋊D157—22no—
16C2×C4×Dic157C2211yescharacteristic
17C2×C4×Dic157C2211yescharacteristic
18#19097700—22no—
19#19097699—22no—
20#19097698—22no—
21#19097697—22no—
22#19097678—22no—
23C2×#41×C157C2211yescharacteristic
24C2×M16×C157C2211yescharacteristic
25C2×C42×C157C2211yescharacteristic
26#104×C157—22no—
27#14578954—21no—
28#14578954—21no—
29#14578954—21no—
30#14578954—21no—
31C2×Dic314C2×C411yescharacteristic
32C2×D628C2×C411yescharacteristic
33C2×C22⋊D157—22no—
34C2×C22⋊D157—21no—
35C22×Dic157—21no—
36C22×Dic157D412yes—
37C2×C4×D157—21no—
38#14578938—21no—
39#14578938—21no—
40C2×#11929434—21no—
41#14578933—22no—
42C22⋊Dic157—22no—
43#14578931—22no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic
46C4×Dic157C2×C411yescharacteristic
47C4×Dic157D412yes—
48C4×Dic157D412yescomplemented
49#41×C157—21no—
50#41×C157—21no—
51#41×C157—21no—
52#41×C157—21no—
53C2×Q8×C157C2×C411yescharacteristic
54C2×D4×C157—21no—
55C2×D4×C157C2×C411yescharacteristic
56C22×C4×C157—21no—
57C22×C4×C157—21no—
58C22×C4×C157C2311yescharacteristic
59M16×C157—21no—
60M16×C157—21no—
61C2×C8×C157—21no—
62C42×C157—21no—
63C42×C157D412yescomplemented
64C22×D157—21no—
65Dic314—21no—
66Dic314—21no—
67D628—21no—
68D628—21no—
69C22⋊D157—44no—
70C22⋊D157—41no—
71C22⋊D157—41no—
72C2×Dic157—21no—
73C2×Dic157—22no—
74C2×Dic157—42no—
75C2×Dic157—42no—
76C2×Dic157C22⋊C412yes—
77C2×Dic157C22⋊C412yes—
78C4×D157—41no—
79C4×D157—41no—
80#11929434—41no—
81C23×C157—21no—
82C23×C157C2×D411yescharacteristic
83Q8×C157—21no—
84Q8×C157—21no—
85D4×C157—21no—
86D4×C157—21no—
87D4×C157—41no—
88D4×C157—41no—
89C2×C4×C157—21no—
90C2×C4×C157—22no—
91C2×C4×C157—42no—
92C2×C4×C157—41no—
93C2×C4×C157—41no—
94C2×C4×C157C22×C411yescharacteristic
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157C2×D411yescharacteristic
98C2×C4×C157#4111yescharacteristic
99C2×C4×C157#4111yescharacteristic
100C8×C157—41no—
101C22×C157—22no—
102C22×C157—41no—
103C22×C157—42no—
104C22×C157C2×C22⋊C411yescharacteristic
105C22×C157#12111yescharacteristic
106C22×C157#12111yescharacteristic
107C2×D157—41no—
108C2×D157—42no—
109C4×C157—42no—
110C4×C157—41no—
111C4×C157C4×D411yescharacteristic
112C4×C157C4×D411yescharacteristic
113C4×C157#12411yescharacteristic
114C4×C157#12711yescharacteristic
115Dic157—22no—
116Dic157—22no—
117Dic157—42no—
118Dic157—41no—
119C2×C157—21no—
120C2×C157—21no—
121C2×C157—81no—
122C2×C157#39011yescharacteristic
123C2×C157#42112yes—
124D157—81no—
125C157#196311yescharacteristic, complemented, Sylow
126#1963—1571nomaximal, Sylow
127#532—1571no—
128#423—1571no—
129C2×#104—1571no—
130C2×#104—1571no—
131C2×#104—1571no—
132C2×#104D15711yescharacteristic, complemented
133#376—1571no—
134C2×#41—1571no—
135C2×#41C2×D15711yescharacteristic
136C2×M16—1571no—
137C2×M16C2×D15711yescharacteristic
138C4⋊Q8—1571no—
139#127—1571no—
140#124—1571no—
141#124—1571no—
142#121—3142no—
143C4×D4—3142no—
144C2×C42—1571no—
145C2×C42—1571no—
146C2×C42C2×D15711yescharacteristic
147C4⋊C8—3142no—
148#104—22no—
149#104—3142no—
150#104—3142no—
151#104—3142no—
152#95—3142no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—3141no—
158#41—3141no—
159#41—3141no—
160#41—3141no—
161C2×Q8—1571no—
162C2×Q8C4×D15711yescharacteristic
163C2×D4—21no—
164C2×D4—3141no—
165C2×D4—3142no—
166C2×D4—1571no—
167C2×D4C4×D15711yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—3141no—
171C22×C4—3141no—
172C22×C4—1572no—
173C22×C4C22×D15711yescharacteristic
174M16—21no—
175M16—21no—
176M16—3141no—
177M16—3141no—
178C2×C8—21no—
179C2×C8—3141no—
180C4⋊C4—3142no—
181C22⋊C4—3142no—
182C22⋊C4—3142no—
183C42—21no—
184C42—3141no—
185C42—1572no—
186C42—1571no—
187C42—1571no—
188C42—1572no—
189C42C22⋊D15712yescomplemented
190C23—21no—
191C23—3141no—
192C23D4×D15711yescharacteristic
193Q8—21no—
194Q8—21no—
195Q8—3141no—
196Q8—3141no—
197D4—21no—
198D4—21no—
199D4—41no—
200D4—41no—
201D4—3141no—
202D4—3141no—
203D4—6284no—
204D4—6281no—
205D4—6281no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3141no—
212C2×C4—3142no—
213C2×C4—6282no—
214C2×C4—6282no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—1572no—
218C2×C4—1572no—
219C2×C4C2×C4×D15711yescharacteristic
220C2×C4D4×D15711yescharacteristic
221C2×C4D4×D15711yescharacteristic
222C2×C4C2×C22⋊D15711yescharacteristic
223C2×C4#1457895311yescharacteristic
224C2×C4#1457895411yescharacteristic
225C8—41no—
226C8—6281no—
227C22—22no—
228C22—41no—
229C22—42no—
230C22—6281no—
231C22—6282no—
232C22C22⋊C4×D15711yescharacteristic
233C22#1909774311yescharacteristic
234C22#1909774411yescharacteristic
235C4—42no—
236C4—41no—
237C4—3142no—
238C4—3142no—
239C4—6282no—
240C4—6281no—
241C4#1909773111yescharacteristic
242C4C4×C22⋊D15711yescharacteristic
243C4#1909775711yescharacteristic
244C4#1909776711yescharacteristic
245C2—21no—
246C2—21no—
247C2—81no—
248C2—12561no—
249C2#2375717311yescharacteristic
250C2#2375728812yes—
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#104×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757819C2
cosocleC22×C4×C157C23
hypercenterC2×#104D157
hypocenterC157#1963
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #23757296C2semidirect
3. C2×#19097699C2semidirect
4. C2×#19097698C2semidirect
5. C2×#19097697C2semidirect
6. #23757119C2semidirect
7. C2×#104×C157C2semidirect
10. #19097769C4semidirect
11. #19097767C4semidirect
12. #19097760C4semidirect
13. #19097758C4semidirect
48. C4×Dic157D4semidirect
63. C42×C157D4semidirect
125. C157#1963semidirect
132. C2×#104D157semidirect
189. C42C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237578192
#237572962
C2×#190976992
C2×#190976982
C2×#190976972
#237571192
C2×#104×C1572
#1963157