Finite Group Databasebeta

← #34109645

Subgroups — #34109645

Order 20096.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097797C211yesmaximal, characteristic
2#23757847C211yesmaximal, characteristic, complemented
3#23757748C211yesmaximal, characteristic, complemented
4#23757490C214yesmaximal, complemented
5#23757476C214yesmaximal, complemented
6#23757299C211yesmaximal, characteristic, complemented
7#23757282C211yesmaximal, characteristic, complemented
8#23757270C211yesmaximal, characteristic, complemented
9C22×SD16×C157C211yesmaximal, characteristic, complemented
10C2×#14578954C2211yescharacteristic
11#19097797—24no—
12C2×#14578942C2212yes—
13C2×#14578939C2212yes—
14C2×#14578938C2211yescharacteristic
15#19097769C2212yescomplemented
16#19097760C2212yescomplemented
17#19097754—22no—
18#19097747—22no—
19D4×Dic157—22no—
20D4×Dic157C2214yes—
21#19097730C2211yescharacteristic
22#19097730C2211yescharacteristic
23C2×C22⋊Dic157—22no—
24#19097700C2214yescomplemented
25#19097696C2212yescomplemented
26#19097695C2214yescomplemented
27#19097693C2212yescomplemented
28C22×Q8×C157C2211yescharacteristic
29C22×D4×C157C2211yescharacteristic
30C2×SD16×C157—24no—
31C2×SD16×C157C2214yes—
32C22×C8×C157C2211yescharacteristic
33#14578954—22no—
34#14578954—22no—
35C2×Dic314C2311yescharacteristic
36C2×D628C2311yescharacteristic
37C2×C22⋊D157—21no—
38C22×Dic157—24no—
39C2×C4×D157—21no—
40#14578942—24no—
41#14578939—24no—
42#14578938—22no—
43C2×#11929434C2312yes—
44C4⋊Dic157D412yes—
45C4⋊Dic157C2312yes—
46#14578933—24no—
47C22⋊Dic157—24no—
48C22⋊Dic157—21no—
49C22⋊Dic157D412yes—
50#14578931—24no—
51C4×Dic157—21no—
52C4×Dic157C2312yes—
53C24×C157—21no—
54C2×Q8×C157—21no—
55C2×Q8×C157—22no—
56C2×Q8×C157—22no—
57C2×Q8×C157C2312yes—
58C2×D4×C157—21no—
59C2×D4×C157—22no—
60C2×D4×C157D414yes—
61C2×D4×C157C2312yes—
62C22×C4×C157—21no—
63C22×C4×C157C2311yescharacteristic
64SD16×C157—28no—
65C2×C8×C157—22no—
66C2×C8×C157C2312yes—
67C22×D157—21no—
68Dic314—21no—
69Dic314—21no—
70D628—21no—
71D628—21no—
72C22⋊D157—42no—
73C2×Dic157—21no—
74C2×Dic157—22no—
75C2×Dic157—84no—
76C2×Dic157C2×D414yes—
77C4×D157—42no—
78#11929434—22no—
79C23×C157—22no—
80C23×C157—24no—
81C23×C157—82no—
82C23×C157C2×D411yescharacteristic
83Q8×C157—22no—
84Q8×C157—22no—
85Q8×C157—42no—
86D4×C157—24no—
87D4×C157—22no—
88D4×C157C2×D414yes—
89C2×C4×C157—22no—
90C2×C4×C157—42no—
91C2×C4×C157C2×D411yescharacteristic
92C2×C4×C157C2×D412yes—
93C2×C4×C157#4112yes—
94C2×C4×C157C2411yescharacteristic
95C8×C157—22no—
96C22×C157—22no—
97C22×C157—24no—
98C22×C157—44no—
99C22×C157—84no—
100C22×C157#12112yes—
101C22×C157C22×D411yescharacteristic
102C2×D157—41no—
103C2×D157—42no—
104C4×C157—42no—
105C4×C157#12112yes—
106C4×C157C22×D411yescharacteristic
107C4×C157C2×#4111yescharacteristic
108Dic157—24no—
109Dic157—41no—
110Dic157—42no—
111C2×C157—22no—
112C2×C157—44no—
113C2×C157C2×#12111yescharacteristic
114C2×C157#57712yes—
115D157—81no—
116C157#304211yescharacteristic, complemented, Sylow
117#3042—1571nomaximal, Sylow
118C2×AGL(1,ℤ/8)—1571no—
119C22×SD16D15711yescharacteristic, complemented
120#536—1571no—
121#518—1571no—
122#463—1574no—
123#461—1574no—
124#424—1571no—
125#419—1571no—
126#416—1571no—
127C2×#41—1571no—
128C22×Q8C2×D15711yescharacteristic
129C22×D4C2×D15711yescharacteristic
130AGL(1,ℤ/8)—3144no—
131C2×SD16—24no—
132C2×SD16—1572no—
133C2×SD16C2×D15714yes—
134C2×D8—1572no—
135C2×M16—1571no—
136C22×C8C2×D15711yescharacteristic
137C4⋊Q8—1572no—
138#124—1572no—
139#123—3142no—
140C22⋊Q8—3142no—
141C4×D4—3142no—
142C4×D4—1574no—
143#117—1571no—
144#117—1571no—
145C2×C22⋊C4—3142no—
146C4⋊C8—1574no—
147#103—1574no—
148#103—1572no—
149#102—1572no—
150C24—21no—
151#41—3142no—
152#41—3142no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—1571no—
157C2×Q8C22×D15712yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—3141no—
161C2×D4—1571no—
162C2×D4C22⋊D15714yes—
163C2×D4C22×D15712yes—
164C22×C4—21no—
165C22×C4—3141no—
166C22×C4—3144no—
167C22×C4C22×D15711yescharacteristic
168SD16—28no—
169SD16—3144no—
170D8—3144no—
171M16—3142no—
172C2×C8—22no—
173C2×C8—1572no—
174C2×C8C22×D15712yes—
175C4⋊C4—3144no—
176C4⋊C4—1572no—
177C4⋊C4—1572no—
178C22⋊C4—3144no—
179C22⋊C4—3141no—
180C22⋊C4—3144no—
181C22⋊C4—1572no—
182C42—3141no—
183C42—1572no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—3141no—
188C23D4×D15711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—3141no—
193Q8—3141no—
194D4—24no—
195D4—22no—
196D4—3141no—
197D4—3141no—
198D4—6282no—
199D4C2×C22⋊D15714yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—3142no—
203C2×C4—3141no—
204C2×C4—6282no—
205C2×C4—1574no—
206C2×C4—12564no—
207C2×C4D4×D15711yescharacteristic
208C2×C4C2×C22⋊D15712yes—
209C2×C4#1457895312yes—
210C2×C4C23×D15711yescharacteristic
211C8—22no—
212C8—3142no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—6281no—
218C22—6282no—
219C22#1909774312yes—
220C22C2×D4×D15711yescharacteristic
221C4—42no—
222C4—3144no—
223C4—6281no—
224C4—6282no—
225C4#1909774312yes—
226C4C22×C22⋊D15711yescharacteristic
227C4C2×#1457895311yescharacteristic
228C2—22no—
229C2—44no—
230C2—12561no—
231C2C2×#1909774311yescharacteristic
232C2#2375807912yes—
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC22×SD16×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097797C2
hypercenterC22×SD16D157
hypocenterC157#3042
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #23757847C2semidirect
3. #23757748C2semidirect
4. #23757490C2semidirect
5. #23757476C2semidirect
6. #23757299C2semidirect
7. #23757282C2semidirect
8. #23757270C2semidirect
9. C22×SD16×C157C2semidirect
15. #19097769C22semidirect
16. #19097760C22semidirect
24. #19097700C22semidirect
25. #19097696C22semidirect
26. #19097695C22semidirect
27. #19097693C22semidirect
116. C157#3042semidirect
119. C22×SD16D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977972
#237578472
#237577482
#237574902
#237574762
#237572992
#237572822
#237572702
C22×SD16×C1572
#3042157