Finite Group Databasebeta

← #34110263

Subgroups — #34110263

Order 20096.

380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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#23757825C211yesmaximal, characteristic
2C2×#19097736C211yesmaximal, characteristic
3#23757603C211yesmaximal, characteristic
4#23757557C212yesmaximal, complemented
5#23757482C212yesmaximal, complemented
6#23757431C211yesmaximal, characteristic
7#23757428C211yesmaximal, characteristic
8#23757379C212yesmaximal, complemented
9#23757377C212yesmaximal, complemented
10#23757327C211yesmaximal, characteristic
11#483×C157C211yesmaximal, characteristic
12C22×Dic314C2211yescharacteristic
13C2×Dic628C2212yes—
14C2×#14578944C2212yes—
15#19097770C2211yescharacteristic
16#19097769C2211yescharacteristic
17#19097761—21no—
18#19097750C2211yescharacteristic
19#19097748—21no—
20Q8×Dic157C2211yescharacteristic
21#19097736—21no—
22#19097736—21no—
23#19097736—21no—
24#19097736C2211yescharacteristic
25#19097736C2212yes—
26#19097736C2212yes—
27#19097727—21no—
28C2×#14578933—21no—
29C2×C4×Dic157—21no—
30C2×C4×Dic157C2211yescharacteristic
31#19097702C2212yes—
32#19097700C2212yes—
33#19097696C2212yes—
34#19097694C2212yes—
35#19097694C2212yes—
36C22⋊#11929434C2211yescharacteristic
37#19097681C2212yes—
38C22⋊Q8×C157C2211yescharacteristic
39C2×C4⋊C4×C157C2211yescharacteristic
40#106×C157C2212yes—
41#103×C157C2212yes—
42C22⋊C8×C157C2211yescharacteristic
43C2×Dic314—24no—
44C2×Dic314—21no—
45C2×Dic314—21no—
46C2×Dic314C2311yescharacteristic
47C2×Dic314C2312yes—
48C22×Dic157—21no—
49C22×Dic157D411yescharacteristic
50C22×Dic157D411yescharacteristic
51Dic628—24no—
52#14578944—24no—
53C2×#11929434C2312yes—
54C4⋊Dic157—21no—
55C4⋊Dic157C2311yescharacteristic
56#14578933—22no—
57#14578933—22no—
58#14578933—21no—
59#14578933—21no—
60#14578933—21no—
61#14578933—21no—
62#14578933—21no—
63C22⋊Dic157—21no—
64C4×Dic157—22no—
65C4×Dic157—22no—
66C4×Dic157—21no—
67C4×Dic157—21no—
68C4×Dic157D411yescharacteristic
69C4×Dic157D411yescharacteristic
70C4×Dic157C2311yescharacteristic
71C4×Dic157C2311yescharacteristic
72C2×Q8×C157C2311yescharacteristic
73C22×C4×C157—21no—
74C22×C4×C157C2311yescharacteristic
75C2×C8×C157C2312yes—
76C4⋊C4×C157—21no—
77C4⋊C4×C157—21no—
78C4⋊C4×C157C2312yes—
79C4⋊C4×C157C2311yescharacteristic
80C22⋊C4×C157—21no—
81Dic314—24no—
82Dic314—22no—
83Dic314—22no—
84Dic314—42no—
85Dic314#4114yes—
86C2×Dic157—24no—
87C2×Dic157—22no—
88C2×Dic157—22no—
89C2×Dic157—22no—
90C2×Dic157—21no—
91C2×Dic157—21no—
92C2×Dic157C2×D411yescharacteristic
93C2×Dic157C2×D411yescharacteristic
94C2×Dic157C2×D411yescharacteristic
95C2×Dic157C2×D411yescharacteristic
96#11929434—22no—
97C23×C157C2×D411yescharacteristic
98Q8×C157—22no—
99C2×C4×C157—22no—
100C2×C4×C157—21no—
101C2×C4×C157—21no—
102C2×C4×C157—22no—
103C2×C4×C157—42no—
104C2×C4×C157C2×D411yescharacteristic
105C2×C4×C157C2411yescharacteristic
106C8×C157—22no—
107C22×C157—21no—
108C22×C157—21no—
109C22×C157#13712yes—
110C22×C157C22×D411yescharacteristic
111C4×C157—21no—
112C4×C157—41no—
113C4×C157—42no—
114C4×C157—41no—
115C4×C157C2×#4112yes—
116Dic157—24no—
117Dic157—21no—
118Dic157—21no—
119Dic157—21no—
120Dic157—41no—
121Dic157—41no—
122Dic157#13712yes—
123C2×C157—22no—
124C2×C157#52511yescharacteristic
125C2×C157C2×#13711yescharacteristic
126C2×C157C2×#13711yescharacteristic
127C157#311311yescharacteristic, complemented, Sylow
128#3113—1571nomaximal, Sylow
129#533—1571no—
130C2×C4×Q8—1571no—
131#483—1571no—
132#483D15711yescharacteristic
133#475—1572no—
134#462—1572no—
135#451—1571no—
136#451—1571no—
137#441—1572no—
138#441—1572no—
139#432—1571no—
140C22×Q8—1571no—
141C2×Q16—1572no—
142C2×Q16—1572no—
143C4⋊Q8—1571no—
144C4⋊Q8—1571no—
145#125—3141no—
146C22⋊Q8—3141no—
147C22⋊Q8—1571no—
148C22⋊Q8C2×D15711yescharacteristic
149C4×Q8—3141no—
150C4×Q8—3141no—
151C4×Q8—3141no—
152C4×Q8—1571no—
153C4×Q8—1572no—
154C4×Q8—1572no—
155C4×Q8—1571no—
156#117—3141no—
157C2×C4⋊C4—3141no—
158C2×C4⋊C4C2×D15711yescharacteristic
159C2×C42—3141no—
160C2×C42—1571no—
161#106—1572no—
162#106C2×D15712yes—
163C4⋊C8—1572no—
164#103—1572no—
165#103—1572no—
166#103—1572no—
167#103C2×D15712yes—
168C22⋊C8—1571no—
169C22⋊C8C2×D15711yescharacteristic
170#97—1572no—
171C2×Q8—3144no—
172C2×Q8—3141no—
173C2×Q8—3141no—
174C2×Q8—1571no—
175C2×Q8—1572no—
176C2×Q8C22×D15711yescharacteristic
177C22×C4—21no—
178C22×C4—3141no—
179C22×C4—1571no—
180C22×C4—1571no—
181C22×C4C22×D15711yescharacteristic
182Q16—3144no—
183Q16—3144no—
184C2×C8—1572no—
185C2×C8C22×D15712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—3142no—
189C4⋊C4—3142no—
190C4⋊C4—3141no—
191C4⋊C4—3141no—
192C4⋊C4—3141no—
193C4⋊C4—3141no—
194C4⋊C4—3141no—
195C4⋊C4—3141no—
196C4⋊C4—1571no—
197C4⋊C4C22×D15711yescharacteristic
198C4⋊C4C22×D15712yes—
199C22⋊C4—21no—
200C22⋊C4—3141no—
201C42—3142no—
202C42—3142no—
203C42—3141no—
204C42—3141no—
205C42—1571no—
206C42—1571no—
207C42—1571no—
208C42—1571no—
209C23D4×D15711yescharacteristic
210Q8—22no—
211Q8—3144no—
212Q8—3142no—
213Q8—3142no—
214Q8—6282no—
215Q8—1574no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—3144no—
222C2×C4—3142no—
223C2×C4—3142no—
224C2×C4—3142no—
225C2×C4—3141no—
226C2×C4—3141no—
227C2×C4—1571no—
228C2×C4—1571no—
229C2×C4—1571no—
230C2×C4—1571no—
231C2×C4D4×D15711yescharacteristic
232C2×C4C23×D15711yescharacteristic
233C8—22no—
234C8—3142no—
235C22—21no—
236C22—21no—
237C22#1909780012yes—
238C22C2×D4×D15711yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—3144no—
244C4—3141no—
245C4—3141no—
246C4—3141no—
247C4—6281no—
248C4—6281no—
249C4—1572no—
250C4#41×D15712yes—
251C2—22no—
252C2#2375778111yescharacteristic
253C2#137×D15711yescharacteristic
254C2C2×#1909780011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#483×C157C2
socleC22×C157C22×D4
prime radicalC23×C157C2×D4
hypercenter#483D157
hypocenterC157#3113
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
4. #23757557C2semidirect
5. #23757482C2semidirect
8. #23757379C2semidirect
9. #23757377C2semidirect
127. C157#3113semidirect

Maximal subgroups

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

subgroupindex
#237578252
C2×#190977362
#237576032
#237575572
#237574822
#237574312
#237574282
#237573792
#237573772
#237573272
#483×C1572
#3113157