Finite Group Databasebeta

← #35224780

Subgroups — #35224780

Order 20864.

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#23782270C211yesmaximal, characteristic, complemented
2#23782139C211yesmaximal, characteristic, complemented
3#23781990C212yesmaximal, complemented
4#23781966C212yesmaximal, complemented
5#23781861C212yesmaximal, complemented
6#23781801C212yesmaximal, complemented
7#23781778C212yesmaximal, complemented
8C4×D1304C212yesmaximal, complemented
9#433×C163C211yesmaximal, characteristic, complemented
10C22×D652C2211yescharacteristic
11C2×D1304C2212yes—
12C2×D1304C2212yes—
13#19104732C2211yescharacteristic, complemented
14#19104727C2211yescharacteristic, complemented
15#19104720—22no—
16#19104709C2212yes—
17#19104708—22no—
18C4×D652C2212yes—
19C4×D652C2212yes—
20C4×D652C2212yescomplemented
21#19104697—22no—
22#19104694C2211yescharacteristic
23C22⋊C4×D163—22no—
24#19104669C2212yescomplemented
25#19104667C2212yescomplemented
26#19104657C2212yes—
27#19104657C2212yes—
28#19104657C2212yescomplemented
29#19104657C2212yescomplemented
30#117×C163C2211yescharacteristic
31C4⋊C8×C163C2212yescomplemented
32C22⋊C8×C163C2212yes—
33#97×C163C2211yescharacteristic, complemented
34C4×C8×C163C2211yescharacteristic, complemented
35C23×D163—21no—
36C2×D652—24no—
37C2×D652—21no—
38C2×D652—22no—
39C2×D652C2312yes—
40C2×D652C2312yes—
41C2×C22⋊D163—22no—
42C2×C4×D163—22no—
43C2×C4×D163—22no—
44C2×C4×D163—22no—
45D1304—24no—
46D1304—24no—
47C4⋊Dic163C2312yes—
48C4⋊Dic163C2312yes—
49Dic163⋊C4—22no—
50C22⋊Dic163—21no—
51(C2×D163)⋊C4—22no—
52(C2×D163)⋊C4—22no—
53(C2×D163)⋊C4—22no—
54(C2×D163)⋊C4—22no—
55C4×Dic163—21no—
56C22×C4×C163C2311yescharacteristic
57C2×C8×C163C2312yes—
58C2×C8×C163C2312yes—
59C4⋊C4×C163D412yes—
60C22⋊C4×C163D412yes—
61C42×C163C2311yescharacteristic
62C42×C163C2311yescharacteristic
63C22×D163—22no—
64C22×D163—24no—
65C22×D163—22no—
66C22×D163—82no—
67D652—24no—
68D652—22no—
69D652—22no—
70D652—22no—
71D652—82no—
72D652#4114yes—
73C22⋊D163—82no—
74C2×Dic163—22no—
75C2×Dic163—22no—
76C4×D163—82no—
77C4×D163—82no—
78C4×D163—82no—
79C23×C163C2×D411yescharacteristic
80C2×C4×C163—22no—
81C2×C4×C163C2×D412yes—
82C2×C4×C163C2×D412yes—
83C2×C4×C163C2×D411yescharacteristic
84C2×C4×C163C2411yescharacteristic
85C8×C163—22no—
86C8×C163—22no—
87C22×C163—21no—
88C22×C163—22no—
89C22×C163C22×D411yescharacteristic
90C2×D163—24no—
91C2×D163—42no—
92C2×D163—42no—
93C2×D163—42no—
94C2×D163—42no—
95C2×D163—42no—
96C2×D163—84no—
97C4×C163—21no—
98C4×C163—22no—
99C4×C163—22no—
100C4×C163C2×#4112yes—
101Dic163—42no—
102Dic163—42no—
103C2×C163—41no—
104C2×C163#52511yescharacteristic
105C2×C163#57612yes—
106D163—44no—
107D163—82no—
108C163#312211yescharacteristic, complemented, Sylow
109#3122—1631nomaximal, Sylow
110#540—1631no—
111#518—1631no—
112#482—1632no—
113#478—1632no—
114#459—1632no—
115#447—1632no—
116#442—1632no—
117C4×D8—1632no—
118#433D16311yescharacteristic, complemented
119C22×D4—1631no—
120C2×D8—1632no—
121C2×D8—1632no—
122#127—1631no—
123#125—1631no—
124#123—3262no—
125#121—3262no—
126#121—1632no—
127C4×D4—3262no—
128C4×D4—1632no—
129C4×D4—1632no—
130C4×D4—1632no—
131#117—1631no—
132#117C2×D16311yescharacteristic
133C2×C22⋊C4—3262no—
134#107—1632no—
135#106—1632no—
136C4⋊C8C2×D16312yescomplemented
137#102—1632no—
138#102—1632no—
139#102—1632no—
140#102—1632no—
141C22⋊C8C2×D16312yes—
142#97C2×D16311yescharacteristic, complemented
143C4×C8C2×D16311yescharacteristic, complemented
144C24—3261no—
145C2×D4—3264no—
146C2×D4—3262no—
147C2×D4—3262no—
148C2×D4—3261no—
149C2×D4—1632no—
150C2×D4—1632no—
151C22×C4—3262no—
152C22×C4—3262no—
153C22×C4—3262no—
154C22×C4C22×D16311yescharacteristic
155D8—3264no—
156D8—3264no—
157C2×C8C22×D16312yes—
158C2×C8C22×D16312yes—
159C4⋊C4—3262no—
160C4⋊C4—1632no—
161C4⋊C4—1632no—
162C4⋊C4D65212yes—
163C22⋊C4—3261no—
164C22⋊C4—3262no—
165C22⋊C4—3262no—
166C22⋊C4—3262no—
167C22⋊C4—3262no—
168C22⋊C4D65212yes—
169C42—3261no—
170C42C22×D16311yescharacteristic
171C42C22×D16311yescharacteristic
172C23—13042no—
173C23—3264no—
174C23—3262no—
175C23—3262no—
176C23C2×D65211yescharacteristic
177D4—13042no—
178D4—13042no—
179D4—3264no—
180D4—3262no—
181D4—3262no—
182D4—3262no—
183D4—1634no—
184C2×C4—22no—
185C2×C4—13042no—
186C2×C4—13042no—
187C2×C4—13042no—
188C2×C4—3262no—
189C2×C4—3262no—
190C2×C4C2×D65211yescharacteristic
191C2×C4C2×D65212yes—
192C2×C4C2×D65212yes—
193C2×C4C23×D16311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—13044no—
199C22—3264no—
200C22—6522no—
201C22—6522no—
202C22—6522no—
203C22—6522no—
204C22—6522no—
205C22C22×D65211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—6522no—
210C4—6522no—
211C4#41×D16312yes—
212C2—41no—
213C2—13042no—
214C2—6524no—
215C2#2378217711yescharacteristic
216C2#2378247012yes—
subgroupG/H
centerC22C22×D652
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
Fitting#433×C163C2
socleC22×C163C22×D4
hypercenter#433D163
hypocenterC163#3122
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23782270C2semidirect
2. #23782139C2semidirect
3. #23781990C2semidirect
4. #23781966C2semidirect
5. #23781861C2semidirect
6. #23781801C2semidirect
7. #23781778C2semidirect
8. C4×D1304C2semidirect
9. #433×C163C2semidirect
13. #19104732C22semidirect
14. #19104727C22semidirect
20. C4×D652C22semidirect
24. #19104669C22semidirect
25. #19104667C22semidirect
28. #19104657C22semidirect
29. #19104657C22semidirect
31. C4⋊C8×C163C22semidirect
33. #97×C163C22semidirect
34. C4×C8×C163C22semidirect
108. C163#3122semidirect
118. #433D163semidirect
136. C4⋊C8C2×D163semidirect
142. #97C2×D163semidirect
143. C4×C8C2×D163semidirect

Maximal subgroups

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

subgroupindex
#237822702
#237821392
#237819902
#237819662
#237818612
#237818012
#237817782
C4×D13042
#433×C1632
#3122163