Finite Group Databasebeta

← #34101163

Subgroups — #34101163

Order 20096.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19097801C211yesmaximal, characteristic, complemented
2C2×#19097758C211yesmaximal, characteristic, complemented
3C2×#19097698C211yesmaximal, characteristic, complemented
4#23757281C211yesmaximal, characteristic, complemented
5C2×#19097688C211yesmaximal, characteristic, complemented
6#23757032C211yesmaximal, characteristic, complemented
7#535×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9#19097801—22no—
10#19097801—22no—
11C2×#14578944—21no—
12C2×#14578942—21no—
13C2×#14578938C2211yescharacteristic
14C2×#14578938C2211yescharacteristic
15#19097758—22no—
16#19097758—22no—
17C2×C22⋊Dic157—22no—
18C2×C4×Dic157C2211yescharacteristic
19#19097698—22no—
20#19097694—22no—
21#19097688—22no—
22C2×#41×C157C2211yescharacteristic
23C22×D4×C157C2211yescharacteristic
24#127×C157—21no—
25#124×C157—21no—
26#121×C157—22no—
27#120×C157—22no—
28#117×C157C2211yescharacteristic
29C2×Dic314—21no—
30C2×Dic314—21no—
31C2×Dic314—21no—
32C2×Dic314—21no—
33C2×Dic314—21no—
34C2×Dic314D412yescomplemented
35C22×Dic157—21no—
36C22×Dic157—21no—
37#14578944—24no—
38#14578942—24no—
39#14578938—21no—
40#14578938—21no—
41#14578938—21no—
42#14578938D412yescomplemented
43C2×#11929434—21no—
44C2×#11929434—21no—
45C22⋊Dic157—28no—
46C4×Dic157—21no—
47C4×Dic157D412yescomplemented
48C24×C157D412yes—
49#41×C157—21no—
50#41×C157—21no—
51#41×C157—21no—
52#41×C157—21no—
53C2×Q8×C157D411yescharacteristic
54C2×D4×C157—21no—
55C2×D4×C157—24no—
56C2×D4×C157—21no—
57C2×D4×C157—21no—
58C2×D4×C157—21no—
59C2×D4×C157—21no—
60C2×D4×C157—21no—
61C2×D4×C157—21no—
62C2×D4×C157D411yescharacteristic
63C22×C4×C157—21no—
64C22×C4×C157C2311yescharacteristic
65C4⋊C4×C157D412yes—
66C22⋊C4×C157—24no—
67C22⋊C4×C157—21no—
68C42×C157—21no—
69Dic314—22no—
70Dic314—22no—
71Dic314—41no—
72Dic314—41no—
73C2×Dic157—22no—
74C2×Dic157—22no—
75C2×Dic157—42no—
76C2×Dic157—41no—
77C2×Dic157—41no—
78#11929434—22no—
79#11929434—41no—
80C23×C157—22no—
81C23×C157—21no—
82C23×C157—22no—
83C23×C157—22no—
84C23×C157—44no—
85C23×C157C2×D411yescharacteristic
86Q8×C157—21no—
87Q8×C157—21no—
88D4×C157—21no—
89D4×C157—21no—
90D4×C157—41no—
91D4×C157—41no—
92D4×C157—41no—
93D4×C157—41no—
94D4×C157—41no—
95D4×C157—41no—
96D4×C157—84no—
97C2×C4×C157—22no—
98C2×C4×C157—21no—
99C2×C4×C157—41no—
100C2×C4×C157—41no—
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157C2×D411yescharacteristic
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157C2×D411yescharacteristic
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157#4111yescharacteristic
107C22×C157—22no—
108C22×C157—44no—
109C22×C157—41no—
110C22×C157—42no—
111C22×C157—42no—
112C22×C157—44no—
113C22×C157—82no—
114C22×C157#12011yescharacteristic
115C22×C157#12011yescharacteristic
116C22×C157#12111yescharacteristic
117C4×C157—41no—
118C4×C157—42no—
119C4×C157#12011yescharacteristic
120C4×C157#12111yescharacteristic
121C4×C157#12111yescharacteristic
122C4×C157#12711yescharacteristic
123Dic157—42no—
124Dic157—42no—
125C2×C157—21no—
126C2×C157—21no—
127C2×C157—81no—
128C2×C157—82no—
129C2×C157#39211yescharacteristic
130C2×C157#45512yes—
131C157#200411yescharacteristic, complemented, Sylow
132#2004—1571nomaximal, Sylow
133C2×#137—1571no—
134#535D15711yescharacteristic
135C2×#124—1571no—
136C2×#104—1571no—
137#419—1571no—
138C2×#100—1571no—
139#339—1571no—
140C2×#41C2×D15711yescharacteristic
141C22×Q8—1571no—
142C22×D4C2×D15711yescharacteristic
143#137—3142no—
144#137—3142no—
145C2×Q16—3141no—
146C2×SD16—3141no—
147C2×M16—1571no—
148C2×M16—1571no—
149#127—21no—
150#124—21no—
151#124—3142no—
152#124—3142no—
153#121—22no—
154#120—22no—
155#117C2×D15711yescharacteristic
156C2×C22⋊C4—3142no—
157C2×C42—1571no—
158#104—3142no—
159#103—3142no—
160#100—3142no—
161C24C22⋊D15712yes—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—3141no—
167C2×Q8—3141no—
168C2×Q8—3141no—
169C2×Q8—3141no—
170C2×Q8—3141no—
171C2×Q8—1572no—
172C2×Q8C22⋊D15711yescharacteristic
173C2×D4—21no—
174C2×D4—24no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4C22⋊D15711yescharacteristic
182C22×C4—21no—
183C22×C4—3141no—
184C22×C4—3141no—
185C22×C4C22×D15711yescharacteristic
186Q16—3144no—
187SD16—3144no—
188M16—3141no—
189M16—3141no—
190M16—3141no—
191M16—1572no—
192C2×C8—3141no—
193C2×C8—3141no—
194C4⋊C4C22⋊D15712yes—
195C22⋊C4—24no—
196C22⋊C4—21no—
197C22⋊C4—3148no—
198C42—21no—
199C42—3141no—
200C42—1572no—
201C23—22no—
202C23—22no—
203C23—21no—
204C23—22no—
205C23—44no—
206C23C2×C22⋊D15711yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—3142no—
210Q8—3142no—
211Q8—6281no—
212Q8—6281no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—84no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—3142no—
227C2×C4—3142no—
228C2×C4—6282no—
229C2×C4—6281no—
230C2×C4—6281no—
231C2×C4D4×D15711yescharacteristic
232C2×C4D4×D15711yescharacteristic
233C2×C4D4×D15711yescharacteristic
234C2×C4C2×C22⋊D15711yescharacteristic
235C2×C4C2×C22⋊D15711yescharacteristic
236C2×C4#1457895311yescharacteristic
237C8—3142no—
238C8—6281no—
239C22—22no—
240C22—44no—
241C22—41no—
242C22—42no—
243C22—42no—
244C22—44no—
245C22—82no—
246C22#1909773911yescharacteristic
247C22#1909774011yescharacteristic
248C22#1909774311yescharacteristic
249C4—41no—
250C4—42no—
251C4—6282no—
252C4—6282no—
253C4#1909773911yescharacteristic
254C4#1909774211yescharacteristic
255C4#1909774311yescharacteristic
256C4#1909776711yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—81no—
261C2#2375718111yescharacteristic
262C2#2375745112yes—
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting, prime radical#535×C157C2
socleC22×C157#120
hypercenter#535D157
hypocenterC157#2004
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#19097801C2semidirect
2. C2×#19097758C2semidirect
3. C2×#19097698C2semidirect
4. #23757281C2semidirect
5. C2×#19097688C2semidirect
6. #23757032C2semidirect
34. C2×Dic314D4semidirect
42. #14578938D4semidirect
47. C4×Dic157D4semidirect
131. C157#2004semidirect

Maximal subgroups

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

subgroupindex
C2×#190978012
C2×#190977582
C2×#190976982
#237572812
C2×#190976882
#237570322
#535×C1572
#2004157