Finite Group Databasebeta

← #34100436

Subgroups — #34100436

Order 20096.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14578938C211yesmaximal, characteristic, complemented
2#23757784C211yesmaximal, characteristic
3C2×#19097699C212yesmaximal, complemented
4#23757033C212yesmaximal, complemented
5C4×C22⋊C4×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2211yescharacteristic
7C2×#14578938—24no—
8C2×#14578938—21no—
9C2×#14578938C2212yes—
10C22×#11929434—21no—
11#19097754—21no—
12#19097750C411yescharacteristic, complemented
13#19097750C411yescharacteristic, complemented
14#19097745C411yescharacteristic, complemented
15#19097745C411yescharacteristic, complemented
16#19097740—21no—
17C4×C22⋊D157—21no—
18C4×C22⋊D157—21no—
19#19097730C2211yescharacteristic
20#19097699—24no—
21C23×C4×C157C2211yescharacteristic
22C2×C22⋊C4×C157—21no—
23C2×C42×C157C2212yes—
24#95×C157—21no—
25#14578954—22no—
26#14578954—22no—
27C2×Dic314C2×C411yescharacteristic
28C2×D628C2×C411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C2×C4×D157—21no—
33#14578938—24no—
34#14578938—22no—
35#14578938D414yescomplemented
36C2×#11929434—24no—
37C2×#11929434—22no—
38C4⋊Dic157C2×C411yescharacteristic
39C4⋊Dic157C2×C411yescharacteristic
40#14578933—21no—
41#14578933—21no—
42C22⋊Dic157—21no—
43C22⋊Dic157—21no—
44C22⋊Dic157—21no—
45#14578931—21no—
46#14578931—21no—
47C4×Dic157—21no—
48C24×C157D411yescharacteristic
49C22×C4×C157—22no—
50C22×C4×C157—22no—
51C22×C4×C157—22no—
52C22×C4×C157C2×C411yescharacteristic
53C22×C4×C157C2×C411yescharacteristic
54C22×C4×C157D411yescharacteristic
55C22×C4×C157D411yescharacteristic
56C22×C4×C157D411yescharacteristic
57C22×C4×C157C2311yescharacteristic
58C22⋊C4×C157—24no—
59C42×C157—22no—
60C42×C157—22no—
61C22×D157—21no—
62Dic314—22no—
63D628—22no—
64C22⋊D157—42no—
65C22⋊D157—42no—
66C22⋊D157—42no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—21no—
70C4×D157—41no—
71C4×D157—41no—
72#11929434—24no—
73C23×C157—22no—
74C23×C157—22no—
75C23×C157—41no—
76C23×C157C22⋊C411yescharacteristic
77C23×C157C22⋊C411yescharacteristic
78C23×C157C2×D411yescharacteristic
79C2×C4×C157—22no—
80C2×C4×C157—22no—
81C2×C4×C157—22no—
82C2×C4×C157—21no—
83C2×C4×C157—21no—
84C2×C4×C157—21no—
85C2×C4×C157—21no—
86C2×C4×C157—24no—
87C2×C4×C157—42no—
88C2×C4×C157—42no—
89C2×C4×C157C22⋊C411yescharacteristic
90C2×C4×C157C22⋊C411yescharacteristic
91C2×C4×C157C22×C411yescharacteristic
92C2×C4×C157C2×D412yes—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157#4112yes—
95C22×C157—21no—
96C22×C157—21no—
97C22×C157—21no—
98C22×C157—21no—
99C22×C157—21no—
100C22×C157—21no—
101C22×C157—21no—
102C22×C157—44no—
103C22×C157#10412yescomplemented
104C22×C157C2×C22⋊C411yescharacteristic
105C22×C157#12112yes—
106C2×D157—41no—
107C2×D157—41no—
108C2×D157—41no—
109C4×C157—21no—
110C4×C157—21no—
111C4×C157—44no—
112C4×C157C4×D412yes—
113C4×C157#12011yescharacteristic
114C4×C157#12311yescharacteristic
115Dic157—41no—
116Dic157—41no—
117Dic157—41no—
118C2×C157—22no—
119C2×C157—22no—
120C2×C157—41no—
121C2×C157#38611yescharacteristic
122C2×C157C2×#10411yescharacteristic
123C2×C157#42111yescharacteristic
124D157—81no—
125C157#187111yescharacteristic, complemented, Sylow
126#1871—1571nomaximal, Sylow
127C22×M16—1571no—
128#525—1571no—
129C2×#104—1572no—
130C4×C22⋊C4D15711yescharacteristic, complemented
131#339—1572no—
132C2×#41—1571no—
133C23×C4C2×D15711yescharacteristic
134C2×M16—3141no—
135C2×M16—3144no—
136C2×M16—1572no—
137C22×C8—3141no—
138#123—3141no—
139C22⋊Q8—1571no—
140C22⋊Q8—1571no—
141#121—1571no—
142#121—1571no—
143#120—3141no—
144C4×D4—3141no—
145C4×D4—3141no—
146#117—1571no—
147C2×C22⋊C4—21no—
148C2×C42C2×D15712yes—
149#104—3144no—
150#95—21no—
151C24C22⋊D15711yescharacteristic
152#41—3142no—
153#41—3142no—
154C2×Q8—1571no—
155C2×D4—3141no—
156C2×D4—3141no—
157C2×D4—3141no—
158C2×D4—1571no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—3141no—
163C22×C4C4×D15711yescharacteristic
164C22×C4C4×D15711yescharacteristic
165C22×C4C22⋊D15711yescharacteristic
166C22×C4D62811yescharacteristic
167C22×C4D62811yescharacteristic
168C22×C4C22×D15711yescharacteristic
169M16—3144no—
170M16—3142no—
171M16—1574no—
172C2×C8—3144no—
173C2×C8—3142no—
174C4⋊C4—3141no—
175C4⋊C4—3141no—
176C4⋊C4—1571no—
177C4⋊C4—1571no—
178C22⋊C4—24no—
179C22⋊C4—3141no—
180C22⋊C4—3141no—
181C22⋊C4—3141no—
182C22⋊C4—3141no—
183C22⋊C4—3141no—
184C42—22no—
185C42—22no—
186C42—3141no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—3141no—
191C23#1457893111yescharacteristic
192C23#1457893111yescharacteristic
193C23C2×C22⋊D15711yescharacteristic
194Q8—3142no—
195D4—3142no—
196D4—6282no—
197D4—6282no—
198D4—6282no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—3141no—
210C2×C4—3141no—
211C2×C4—3141no—
212C2×C4—6281no—
213C2×C4—6281no—
214C2×C4#1457893111yescharacteristic
215C2×C4#1457893111yescharacteristic
216C2×C4C2×C4×D15711yescharacteristic
217C2×C4D4×D15712yes—
218C2×C4C2×D62811yescharacteristic
219C2×C4#1457895312yes—
220C8—3144no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—6281no—
230C22—6281no—
231C22—6281no—
232C22#1909769912yescomplemented
233C22C2×#1457893111yescharacteristic
234C22#1909774312yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—6281no—
239C4—6281no—
240C4—6281no—
241C4#1909773112yes—
242C4#1909774111yescharacteristic
243C4#1909775511yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—12561no—
248C2#2375715011yescharacteristic
249C2C2×#1909769911yescharacteristic
250C2#2375729111yescharacteristic
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC4×C22⋊C4×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenterC4×C22⋊C4D157
hypocenterC157#1871
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14578938C2semidirect
3. C2×#19097699C2semidirect
4. #23757033C2semidirect
5. C4×C22⋊C4×C157C2semidirect
12. #19097750C4semidirect
13. #19097750C4semidirect
14. #19097745C4semidirect
15. #19097745C4semidirect
35. #14578938D4semidirect
103. C22×C157#104semidirect
125. C157#1871semidirect
130. C4×C22⋊C4D157semidirect
232. C22#19097699semidirect

Maximal subgroups

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

subgroupindex
C22×#145789382
#237577842
C2×#190976992
#237570332
C4×C22⋊C4×C1572
#1871157