Finite Group Databasebeta

← #34110380

Subgroups — #34110380

Order 20096.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#23757878C211yesmaximal, characteristic, complemented
2#23757747C211yesmaximal, characteristic, complemented
3#23757598C212yesmaximal, complemented
4#23757574C212yesmaximal, complemented
5#23757469C212yesmaximal, complemented
6#23757409C212yesmaximal, complemented
7#23757386C212yesmaximal, complemented
8C4×D1256C212yesmaximal, complemented
9#433×C157C211yesmaximal, characteristic, complemented
10C22×D628C2211yescharacteristic
11C2×D1256C2212yes—
12C2×D1256C2212yes—
13#19097768C2211yescharacteristic, complemented
14#19097763C2211yescharacteristic, complemented
15#19097756—22no—
16#19097745C2212yes—
17#19097744—22no—
18C4×D628C2212yes—
19C4×D628C2212yes—
20C4×D628C2212yescomplemented
21#19097733—22no—
22#19097730C2211yescharacteristic
23C22⋊C4×D157—22no—
24#19097705C2212yescomplemented
25#19097703C2212yescomplemented
26#19097693C2212yes—
27#19097693C2212yes—
28#19097693C2212yescomplemented
29#19097693C2212yescomplemented
30#117×C157C2211yescharacteristic
31C4⋊C8×C157C2212yescomplemented
32C22⋊C8×C157C2212yes—
33#97×C157C2211yescharacteristic, complemented
34C4×C8×C157C2211yescharacteristic, complemented
35C23×D157—21no—
36C2×D628—24no—
37C2×D628—21no—
38C2×D628—22no—
39C2×D628C2312yes—
40C2×D628C2312yes—
41C2×C22⋊D157—22no—
42C2×C4×D157—22no—
43C2×C4×D157—22no—
44C2×C4×D157—22no—
45D1256—24no—
46D1256—24no—
47C4⋊Dic157C2312yes—
48C4⋊Dic157C2312yes—
49#14578933—22no—
50C22⋊Dic157—21no—
51#14578931—22no—
52#14578931—22no—
53#14578931—22no—
54#14578931—22no—
55C4×Dic157—21no—
56C22×C4×C157C2311yescharacteristic
57C2×C8×C157C2312yes—
58C2×C8×C157C2312yes—
59C4⋊C4×C157D412yes—
60C22⋊C4×C157D412yes—
61C42×C157C2311yescharacteristic
62C42×C157C2311yescharacteristic
63C22×D157—22no—
64C22×D157—24no—
65C22×D157—22no—
66C22×D157—82no—
67D628—24no—
68D628—22no—
69D628—22no—
70D628—22no—
71D628—82no—
72D628#4114yes—
73C22⋊D157—82no—
74C2×Dic157—22no—
75C2×Dic157—22no—
76C4×D157—82no—
77C4×D157—82no—
78C4×D157—82no—
79C23×C157C2×D411yescharacteristic
80C2×C4×C157—22no—
81C2×C4×C157C2×D412yes—
82C2×C4×C157C2×D412yes—
83C2×C4×C157C2×D411yescharacteristic
84C2×C4×C157C2411yescharacteristic
85C8×C157—22no—
86C8×C157—22no—
87C22×C157—21no—
88C22×C157—22no—
89C22×C157C22×D411yescharacteristic
90C2×D157—24no—
91C2×D157—42no—
92C2×D157—42no—
93C2×D157—42no—
94C2×D157—42no—
95C2×D157—42no—
96C2×D157—84no—
97C4×C157—21no—
98C4×C157—22no—
99C4×C157—22no—
100C4×C157C2×#4112yes—
101Dic157—42no—
102Dic157—42no—
103C2×C157—41no—
104C2×C157#52511yescharacteristic
105C2×C157#57612yes—
106D157—44no—
107D157—82no—
108C157#312211yescharacteristic, complemented, Sylow
109#3122—1571nomaximal, Sylow
110#540—1571no—
111#518—1571no—
112#482—1572no—
113#478—1572no—
114#459—1572no—
115#447—1572no—
116#442—1572no—
117C4×D8—1572no—
118#433D15711yescharacteristic, complemented
119C22×D4—1571no—
120C2×D8—1572no—
121C2×D8—1572no—
122#127—1571no—
123#125—1571no—
124#123—3142no—
125#121—3142no—
126#121—1572no—
127C4×D4—3142no—
128C4×D4—1572no—
129C4×D4—1572no—
130C4×D4—1572no—
131#117—1571no—
132#117C2×D15711yescharacteristic
133C2×C22⋊C4—3142no—
134#107—1572no—
135#106—1572no—
136C4⋊C8C2×D15712yescomplemented
137#102—1572no—
138#102—1572no—
139#102—1572no—
140#102—1572no—
141C22⋊C8C2×D15712yes—
142#97C2×D15711yescharacteristic, complemented
143C4×C8C2×D15711yescharacteristic, complemented
144C24—3141no—
145C2×D4—3144no—
146C2×D4—3142no—
147C2×D4—3141no—
148C2×D4—3142no—
149C2×D4—1572no—
150C2×D4—1572no—
151C22×C4—3142no—
152C22×C4—3142no—
153C22×C4—3142no—
154C22×C4C22×D15711yescharacteristic
155D8—3144no—
156D8—3144no—
157C2×C8C22×D15712yes—
158C2×C8C22×D15712yes—
159C4⋊C4—3142no—
160C4⋊C4—1572no—
161C4⋊C4—1572no—
162C4⋊C4D62812yes—
163C22⋊C4—3141no—
164C22⋊C4—3142no—
165C22⋊C4—3142no—
166C22⋊C4—3142no—
167C22⋊C4—3142no—
168C22⋊C4D62812yes—
169C42—3141no—
170C42C22×D15711yescharacteristic
171C42C22×D15711yescharacteristic
172C23—3144no—
173C23—3142no—
174C23—3142no—
175C23—12562no—
176C23C2×D62811yescharacteristic
177D4—3144no—
178D4—3142no—
179D4—3142no—
180D4—3142no—
181D4—1574no—
182D4—12562no—
183D4—12562no—
184C2×C4—22no—
185C2×C4—3142no—
186C2×C4—3142no—
187C2×C4—12562no—
188C2×C4—12562no—
189C2×C4—12562no—
190C2×C4C2×D62811yescharacteristic
191C2×C4C2×D62812yes—
192C2×C4C2×D62812yes—
193C2×C4C23×D15711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—3144no—
199C22—6282no—
200C22—6282no—
201C22—6282no—
202C22—6282no—
203C22—6282no—
204C22—12564no—
205C22C22×D62811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—6282no—
210C4—6282no—
211C4#41×D15712yes—
212C2—41no—
213C2—6284no—
214C2—12562no—
215C2#2375778511yescharacteristic
216C2#2375807812yes—
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#433×C157C2
socleC22×C157C22×D4
hypercenter#433D157
hypocenterC157#3122
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23757878C2semidirect
2. #23757747C2semidirect
3. #23757598C2semidirect
4. #23757574C2semidirect
5. #23757469C2semidirect
6. #23757409C2semidirect
7. #23757386C2semidirect
8. C4×D1256C2semidirect
9. #433×C157C2semidirect
13. #19097768C22semidirect
14. #19097763C22semidirect
20. C4×D628C22semidirect
24. #19097705C22semidirect
25. #19097703C22semidirect
28. #19097693C22semidirect
29. #19097693C22semidirect
31. C4⋊C8×C157C22semidirect
33. #97×C157C22semidirect
34. C4×C8×C157C22semidirect
108. C157#3122semidirect
118. #433D157semidirect
136. C4⋊C8C2×D157semidirect
142. #97C2×D157semidirect
143. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578782
#237577472
#237575982
#237575742
#237574692
#237574092
#237573862
C4×D12562
#433×C1572
#3122157