Finite Group Databasebeta

← #34101803

Subgroups — #34101803

Order 20096.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#23757840C211yesmaximal, characteristic
2C2×#19097686C211yesmaximal, characteristic, complemented
3#23757067C212yesmaximal, complemented
4#23757065C212yesmaximal, complemented
5C2×#99×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic, complemented
7#19097767C411yescharacteristic, complemented
8#19097767C2211yescharacteristic
9#19097758C411yescharacteristic, complemented
10#19097758C2211yescharacteristic
11#19097742—21no—
12#19097742—21no—
13#19097740—21no—
14#19097740—21no—
15#19097730C411yescharacteristic, complemented
16C2×C22⋊Dic157—21no—
17#19097686—21no—
18#19097686C2212yes—
19C22×D4×C157C2211yescharacteristic
20C2×C22⋊C4×C157—21no—
21#99×C157—21no—
22#99×C157C2212yes—
23#14578954—41no—
24#14578954—41no—
25C2×Dic314C2×C411yescharacteristic, complemented
26C2×D628C2×C411yescharacteristic, complemented
27C2×C22⋊D157—21no—
28C2×C22⋊D157—21no—
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C22×Dic157—41no—
33C2×C4×D157—21no—
34C4⋊Dic157—21no—
35C22⋊Dic157—21no—
36C22⋊Dic157—21no—
37C22⋊Dic157—21no—
38C22⋊Dic157—21no—
39C22⋊Dic157—21no—
40C22⋊Dic157—22no—
41C22⋊Dic157—41no—
42C4×Dic157C2×C411yescharacteristic, complemented
43C4×Dic157C2×C411yescharacteristic, complemented
44C24×C157D411yescharacteristic
45C24×C157D411yescharacteristic
46C2×D4×C157—41no—
47C2×D4×C157—41no—
48C2×D4×C157C2×C411yescharacteristic
49C2×D4×C157D411yescharacteristic
50C2×D4×C157D411yescharacteristic
51C2×D4×C157C2311yescharacteristic
52C22×C4×C157—41no—
53C22×C4×C157C2×C411yescharacteristic
54C22⋊C4×C157—22no—
55C22⋊C4×C157—41no—
56C22×D157—21no—
57Dic314—41no—
58D628—41no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C22⋊D157—81no—
62C22⋊D157—81no—
63C22⋊D157—81no—
64C22⋊D157—81no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C2×Dic157—42no—
69C2×Dic157—82no—
70C4×D157—42no—
71C23×C157—21no—
72C23×C157—21no—
73C23×C157—21no—
74C23×C157—21no—
75C23×C157—81no—
76C23×C157—81no—
77C23×C157C22⋊C411yescharacteristic
78C23×C157C22⋊C411yescharacteristic
79C23×C157C22⋊C411yescharacteristic
80C23×C157C2×D411yescharacteristic
81C23×C157C2×D411yescharacteristic
82D4×C157—41no—
83D4×C157—41no—
84D4×C157—41no—
85D4×C157—41no—
86C2×C4×C157—21no—
87C2×C4×C157—21no—
88C2×C4×C157—42no—
89C2×C4×C157—82no—
90C2×C4×C157C22⋊C411yescharacteristic
91C2×C4×C157C22×C411yescharacteristic
92C22×C157—21no—
93C22×C157—21no—
94C22×C157—21no—
95C22×C157—21no—
96C22×C157—41no—
97C22×C157—41no—
98C22×C157—41no—
99C22×C157—41no—
100C22×C157—41no—
101C22×C157—42no—
102C22×C157—42no—
103C22×C157—81no—
104C22×C157—81no—
105C22×C157#9911yescharacteristic
106C22×C157#9911yescharacteristic
107C22×C157C2×C22⋊C411yescharacteristic
108C2×D157—41no—
109C2×D157—41no—
110C2×D157—41no—
111C4×C157—21no—
112C4×C157—21no—
113C4×C157—82no—
114Dic157—41no—
115Dic157—41no—
116Dic157—41no—
117Dic157—82no—
118C2×C157—21no—
119C2×C157—21no—
120C2×C157—21no—
121C2×C157—41no—
122C2×C157—41no—
123C2×C157—41no—
124C2×C157—41no—
125C2×C157C2×#9911yescharacteristic
126D157—81no—
127C157#212711yescharacteristic, complemented, Sylow
128#2127—1571nomaximal, Sylow
129#535—1571no—
130C2×#99—1571no—
131C2×#99D15711yescharacteristic, complemented
132#354—1572no—
133#353—1572no—
134C2×#41—1571no—
135C22×D4C2×D15711yescharacteristic
136#127—1571no—
137#127—1571no—
138#124—1571no—
139#124—1571no—
140#121—3141no—
141#121—3141no—
142#120—3141no—
143#120—3141no—
144#117—1571no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—3141no—
147#99—21no—
148#99—3141no—
149#99—1572no—
150#99C2×D15712yes—
151C24C22⋊D15711yescharacteristic
152C24D62811yescharacteristic
153#41—6281no—
154#41—6281no—
155C2×Q8—1571no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—3141no—
159C2×D4—3141no—
160C2×D4—3141no—
161C2×D4—3141no—
162C2×D4—3141no—
163C2×D4—1571no—
164C2×D4C4×D15711yescharacteristic
165C2×D4C22⋊D15711yescharacteristic
166C2×D4D62811yescharacteristic
167C2×D4C22×D15711yescharacteristic
168C22×C4—41no—
169C22×C4—3141no—
170C22×C4—6281no—
171C22×C4C4×D15711yescharacteristic
172C4⋊C4—3141no—
173C22⋊C4—22no—
174C22⋊C4—41no—
175C22⋊C4—3141no—
176C22⋊C4—3141no—
177C22⋊C4—3141no—
178C22⋊C4—3141no—
179C22⋊C4—3141no—
180C22⋊C4—3142no—
181C22⋊C4—6281no—
182C42—1571no—
183C42—1571no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—81no—
189C23—81no—
190C23—3141no—
191C23#1457893111yescharacteristic
192C23#1457893111yescharacteristic
193C23#1457893111yescharacteristic
194C23C2×C22⋊D15711yescharacteristic
195C23C2×D62811yescharacteristic
196Q8—6281no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—6281no—
202D4—6281no—
203D4—6281no—
204D4—12561no—
205D4—12561no—
206D4—12561no—
207D4—12561no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—3141no—
213C2×C4—3141no—
214C2×C4—3141no—
215C2×C4—6282no—
216C2×C4—6282no—
217C2×C4—12562no—
218C2×C4#1457893111yescharacteristic
219C2×C4C2×C4×D15711yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—6281no—
234C22—6281no—
235C22—6281no—
236C22#1909768511yescharacteristic
237C22#1909768511yescharacteristic
238C22C2×#1457893111yescharacteristic
239C4—21no—
240C4—21no—
241C4—82no—
242C4—6281no—
243C4—6281no—
244C4—6281no—
245C4—12562no—
246C2—21no—
247C2—21no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—41no—
252C2—41no—
253C2—12561no—
254C2C2×#1909768511yescharacteristic
subgroupG/H
centerC2C2×#19097685
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
FittingC2×#99×C157C2
socleC2×C157C2×#99
prime radical#23757840C2
cosocleC2×D4×C157C23
hypercenterC2×#99D157
hypocenterC157#2127
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#19097686C2semidirect
3. #23757067C2semidirect
4. #23757065C2semidirect
5. C2×#99×C157C2semidirect
6. C2×#14578954C4semidirect
7. #19097767C4semidirect
9. #19097758C4semidirect
15. #19097730C4semidirect
25. C2×Dic314C2×C4semidirect
26. C2×D628C2×C4semidirect
42. C4×Dic157C2×C4semidirect
43. C4×Dic157C2×C4semidirect
127. C157#2127semidirect
131. C2×#99D157semidirect

Maximal subgroups

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

subgroupindex
#237578402
C2×#190976862
#237570672
#237570652
C2×#99×C1572
#2127157