Finite Group Databasebeta

← #34110490

Subgroups — #34110490

Order 20096.

404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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#23757901C211yesmaximal, characteristic, complemented
2#23757637C212yesmaximal, complemented
3#23757632C212yesmaximal, complemented
4#23757627C212yesmaximal, complemented
5#23757619C212yesmaximal, complemented
6#23757278C211yesmaximal, characteristic, complemented
7#23757274C211yesmaximal, characteristic, complemented
8#23757269C211yesmaximal, characteristic, complemented
9C2×#19097692C211yesmaximal, characteristic, complemented
10#23757229C211yesmaximal, characteristic, complemented
11#535×C157C211yesmaximal, characteristic
12C2×#14578938C2211yescharacteristic
13C22×#11929434C2211yescharacteristic
14#19097771C2212yescomplemented
15#19097770—21no—
16#19097763C2212yescomplemented
17#19097762—21no—
18#19097748—22no—
19#19097730C2211yescharacteristic
20C2×C4⋊Dic157C2211yescharacteristic
21#19097695C2211yescharacteristic, complemented
22#19097695C2212yescomplemented
23#19097695C2211yescharacteristic, complemented
24#19097692C2212yes—
25#19097692C2212yes—
26#19097692C2212yes—
27#19097692C2212yes—
28#19097692C2211yescharacteristic, complemented
29#19097692C2212yescomplemented
30#19097692C2211yescharacteristic, complemented
31#19097682C2212yescomplemented
32C4×#11929434C2212yescomplemented
33C2×#41×C157C2211yescharacteristic
34C22×D4×C157C2211yescharacteristic
35#127×C157C2212yes—
36#124×C157C2212yes—
37#121×C157—21no—
38#121×C157—21no—
39#120×C157—22no—
40#117×C157C2211yescharacteristic
41C2×Dic314—22no—
42C22×Dic157—21no—
43#14578938—22no—
44C2×#11929434—22no—
45C2×#11929434C2311yescharacteristic
46C2×#11929434C2312yes—
47C2×#11929434C2311yescharacteristic
48C4⋊Dic157—21no—
49C4⋊Dic157—22no—
50C4⋊Dic157C2312yes—
51C4⋊Dic157C2311yescharacteristic
52C4⋊Dic157C2311yescharacteristic
53#14578933—22no—
54#14578933—22no—
55C22⋊Dic157—21no—
56C4×Dic157—21no—
57C24×C157—21no—
58#41×C157—22no—
59#41×C157—22no—
60C2×Q8×C157C2311yescharacteristic
61C2×D4×C157—21no—
62C2×D4×C157—21no—
63C2×D4×C157—22no—
64C2×D4×C157—22no—
65C2×D4×C157—22no—
66C2×D4×C157—22no—
67C2×D4×C157C2312yes—
68C2×D4×C157C2311yescharacteristic
69C22×C4×C157—21no—
70C22×C4×C157C2311yescharacteristic
71C4⋊C4×C157D411yescharacteristic
72C4⋊C4×C157D411yescharacteristic
73C22⋊C4×C157—22no—
74C22⋊C4×C157—22no—
75C22⋊C4×C157D412yes—
76C42×C157C2312yes—
77Dic314—82no—
78C2×Dic157—22no—
79C2×Dic157—21no—
80C2×Dic157—21no—
81C2×Dic157—81no—
82#11929434—21no—
83#11929434—21no—
84#11929434—22no—
85C23×C157—22no—
86C23×C157—21no—
87C23×C157—42no—
88C23×C157—81no—
89C23×C157—81no—
90C23×C157C2×D411yescharacteristic
91Q8×C157—21no—
92Q8×C157—21no—
93D4×C157—22no—
94D4×C157—22no—
95D4×C157—21no—
96D4×C157—21no—
97D4×C157—42no—
98D4×C157—42no—
99D4×C157—82no—
100D4×C157—82no—
101C2×C4×C157—21no—
102C2×C4×C157—42no—
103C2×C4×C157C2×D412yes—
104C2×C4×C157C2×D412yes—
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157#4112yes—
107C2×C4×C157#4112yes—
108C2×C4×C157C2411yescharacteristic
109C22×C157—21no—
110C22×C157—21no—
111C22×C157—41no—
112C22×C157—42no—
113C22×C157—41no—
114C22×C157—42no—
115C22×C157—41no—
116C22×C157—42no—
117C22×C157—84no—
118C22×C157#12412yes—
119C22×C157C22×D411yescharacteristic
120C4×C157—22no—
121C4×C157—22no—
122C4×C157—41no—
123C4×C157#12412yes—
124C4×C157C2×#4111yescharacteristic
125C4×C157C2×#4111yescharacteristic
126Dic157—42no—
127Dic157—41no—
128Dic157—41no—
129C2×C157—22no—
130C2×C157—81no—
131C2×C157—82no—
132C2×C157C2×#12411yescharacteristic
133C2×C157#57611yescharacteristic
134C2×C157#57711yescharacteristic
135C157#313611yescharacteristic, complemented, Sylow
136#3136—1571nomaximal, Sylow
137#544—1571no—
138#535D15711yescharacteristic
139#490—1572no—
140#489—1572no—
141#488—1572no—
142#486—1572no—
143#418—1571no—
144#417—1571no—
145#416—1571no—
146C2×#102—1571no—
147#405—1571no—
148C2×#41C2×D15711yescharacteristic
149C22×D4C2×D15711yescharacteristic
150C2×M16—1571no—
151C22×C8—1571no—
152C4⋊Q8—3141no—
153C4⋊Q8—1572no—
154#127C2×D15712yes—
155#125—3141no—
156#125—1572no—
157#124C2×D15712yes—
158C22⋊Q8—3142no—
159#121—21no—
160#121—21no—
161#120—22no—
162#117—1571no—
163#117C2×D15711yescharacteristic
164C2×C4⋊C4—1571no—
165#103—1571no—
166#103—1571no—
167#103—1572no—
168#102—1572no—
169#102—1572no—
170#102—1572no—
171#102—1572no—
172#102—1571no—
173#102—1571no—
174#102—1572no—
175#97—1572no—
176C4×C8—1572no—
177C24—21no—
178#41—22no—
179#41—22no—
180C2×Q8—3142no—
181C2×Q8C22×D15711yescharacteristic
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4C22×D15712yes—
189C2×D4C22×D15711yescharacteristic
190C22×C4—21no—
191C22×C4—3141no—
192C22×C4C22×D15711yescharacteristic
193M16—3142no—
194C2×C8—3142no—
195C2×C8—1571no—
196C2×C8—1572no—
197C2×C8—1571no—
198C4⋊C4—3141no—
199C4⋊C4—3142no—
200C4⋊C4—3142no—
201C4⋊C4—3142no—
202C4⋊C4—1572no—
203C4⋊C4—1571no—
204C4⋊C4—1571no—
205C4⋊C4C22⋊D15711yescharacteristic
206C4⋊C4C22⋊D15711yescharacteristic
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—3141no—
210C22⋊C4C22⋊D15712yes—
211C42—3141no—
212C42C22×D15712yes—
213C23—22no—
214C23—21no—
215C23—42no—
216C23—81no—
217C23—81no—
218C23C2×C22⋊D15711yescharacteristic
219Q8—21no—
220Q8—21no—
221Q8—12562no—
222D4—22no—
223D4—22no—
224D4—21no—
225D4—21no—
226D4—42no—
227D4—42no—
228D4—82no—
229D4—82no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—3141no—
233C2×C4—3141no—
234C2×C4—3142no—
235C2×C4—12561no—
236C2×C4C2×C22⋊D15712yes—
237C2×C4C2×C22⋊D15712yes—
238C2×C4C2×C22⋊D15711yescharacteristic
239C2×C4#1457895312yes—
240C2×C4#1457895312yes—
241C2×C4C23×D15711yescharacteristic
242C8—3141no—
243C8—3141no—
244C8—3142no—
245C22—21no—
246C22—21no—
247C22—41no—
248C22—42no—
249C22—41no—
250C22—42no—
251C22—41no—
252C22—42no—
253C22—84no—
254C22#1909775812yes—
255C22C22×C22⋊D15711yescharacteristic
256C4—22no—
257C4—22no—
258C4—41no—
259C4—6281no—
260C4—6282no—
261C4—6281no—
262C4#1909775812yes—
263C4C2×#1457895311yescharacteristic
264C4C2×#1457895311yescharacteristic
265C2—22no—
266C2—82no—
267C2—81no—
268C2C2×#1909775811yescharacteristic
269C2#2375807611yescharacteristic
270C2#2375808411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting, prime radical#535×C157C2
socleC22×C157C22×D4
hypercenter#535D157
hypocenterC157#3136
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23757901C2semidirect
2. #23757637C2semidirect
3. #23757632C2semidirect
4. #23757627C2semidirect
5. #23757619C2semidirect
6. #23757278C2semidirect
7. #23757274C2semidirect
8. #23757269C2semidirect
9. C2×#19097692C2semidirect
10. #23757229C2semidirect
14. #19097771C22semidirect
16. #19097763C22semidirect
21. #19097695C22semidirect
22. #19097695C22semidirect
23. #19097695C22semidirect
28. #19097692C22semidirect
29. #19097692C22semidirect
30. #19097692C22semidirect
31. #19097682C22semidirect
32. C4×#11929434C22semidirect
135. C157#3136semidirect

Maximal subgroups

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

subgroupindex
#237579012
#237576372
#237576322
#237576272
#237576192
#237572782
#237572742
#237572692
C2×#190976922
#237572292
#535×C1572
#3136157