Finite Group Databasebeta

← #13131696

Subgroups — #13131696

Order 1664.

464 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C4×D4×D13C211yesmaximal, characteristic
2D4×#1057C212yesmaximal, complemented
3#11719127C212yesmaximal, complemented
4C2×#88111C212yesmaximal, complemented
5#11719076C212yesmaximal, complemented
6#11719064C214yesmaximal, complemented
7#11719054C211yesmaximal, characteristic, complemented
8#11719051C211yesmaximal, characteristic, complemented
9C2×D4×D13C411yescharacteristic
10C22×C4×D13C2212yes—
11C22×#1057C2214yescomplemented
12C2×#6118C2214yescomplemented
13C4×D4×C13C411yescharacteristic
14D4×Dic13C2211yescharacteristic
15C4×C22⋊D13C412yes—
16#88147C2211yescharacteristic
17C4⋊C4×D13C411yescharacteristic
18#88135C2212yes—
19C22⋊C4×D13C412yes—
20C4×D52C411yescharacteristic
21C42×D13C2211yescharacteristic
22C22⋊#1057C2214yescomplemented
23#88111C2211yescharacteristic
24#88111C2211yescharacteristic
25#88111C2212yes—
26#88111C2214yescomplemented
27#88110C2212yescomplemented
28C4⋊#1057C2212yescomplemented
29C4⋊#1057C2212yescomplemented
30C4×#1057C2212yescomplemented
31C23×D13C2×C412yes—
32C2×D4×C13C2×C411yescharacteristic
33C22×C4×C13C2×C412yes—
34C2×C22⋊D13C2×C412yes—
35C22×Dic13C2312yes—
36D4×D13—24no—
37C2×D52C2×C411yescharacteristic
38C2×C4×D13—44no—
39C2×C4×D13C2×C411yescharacteristic
40C2×C4×D13C2×C411yescharacteristic
41C2×C4×D13C2×C412yes—
42C2×C4×D13C2×C412yes—
43C2×C4×D13C2311yescharacteristic
44C2×C4×D13C2312yes—
45C2×#1057—44no—
46C2×#1057C2312yes—
47C2×#1057C2312yes—
48C2×#1057C2314yes—
49#6118—44no—
50C13×C4⋊C4C2×C411yescharacteristic
51C13×C22⋊C4C2×C412yes—
52C42×C13C2×C411yescharacteristic
53C22⋊Dic13C2×C412yes—
54#6103C2×C412yes—
55#6103C2×C412yes—
56C4⋊Dic13C2×C411yescharacteristic
57#6101C2×C412yes—
58C4×Dic13C2×C411yescharacteristic
59C4×Dic13C2311yescharacteristic
60C4×Dic13C2311yescharacteristic
61#2974—131nomaximal, Sylow
62C23×C13C22×C412yes—
63C22×D13—24no—
64C22×D13—24no—
65C22×D13—42no—
66C22×D13C22×C412yes—
67C22×D13C22×C411yescharacteristic
68D4×C13M1614yescomplemented
69C2×C4×C13—42no—
70C2×C4×C13C22×C411yescharacteristic
71C2×C4×C13C22×C411yescharacteristic
72C2×C4×C13C22×C412yes—
73C2×C4×C13C22×C411yescharacteristic
74C22⋊D13—24no—
75C2×Dic13—24no—
76C2×Dic13C22×C411yescharacteristic
77C2×Dic13C22×C411yescharacteristic
78C2×Dic13C22×C412yes—
79C2×Dic13C2411yescharacteristic
80D52—22no—
81C4×D13—22no—
82C4×D13—22no—
83C4×D13—24no—
84C4×D13—22no—
85C4×D13—42no—
86C4×D13—42no—
87#1057—22no—
88#1057—24no—
89#1057—22no—
90C2×C4×D4—131no—
91#436—132no—
92#435—134no—
93C8×D4—132no—
94#432—131no—
95#431—131no—
96#407—132no—
97C2×C22⋊C8—132no—
98C22×C13—22no—
99C22×C13—22no—
100C22×C13C2×M1614yes—
101C22×C13C23×C411yescharacteristic
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—22no—
105C2×D13—22no—
106C2×D13—22no—
107C2×D13—48no—
108C2×D13#13112yes—
109C4×C13—21no—
110C4×C13—22no—
111C4×C13—21no—
112C4×C13C2×M1612yes—
113Dic13—22no—
114Dic13—21no—
115Dic13—21no—
116Dic13H(5,𝔽2)12yes—
117C22×D4—131no—
118C23×C4—132no—
119C2×M16—134no—
120C22×C8—134no—
121C4×D4—131no—
122C4×D4—132no—
123C4×D4—131no—
124C4×D4—132no—
125C4×D4—131no—
126C4×D4#26111yescharacteristic
127C2×C4⋊C4—131no—
128C2×C22⋊C4—132no—
129C2×C42—131no—
130C4⋊C8—132no—
131C4⋊C8—132no—
132C22⋊C8—131no—
133C22⋊C8—132no—
134C22⋊C8—131no—
135C22⋊C8—134no—
136C22⋊C8—134no—
137#97—132no—
138C4×C8—132no—
139C2×C13—24no—
140C2×C13#51811yescharacteristic
141C2×C13C22×M1611yescharacteristic
142C2×C13C2×#13111yescharacteristic
143D13—22no—
144D13—42no—
145C24—132no—
146C2×D4—132no—
147C2×D4—131no—
148C2×D4—264no—
149C2×D4C2×#26111yescharacteristic
150C22×C4—132no—
151C22×C4—131no—
152C22×C4—132no—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—524no—
158C22×C4C2×#26112yes—
159M16—524no—
160C2×C8—132no—
161C2×C8—132no—
162C2×C8—134no—
163C2×C8—524no—
164C4⋊C4—132no—
165C4⋊C4—131no—
166C4⋊C4C2×#26111yescharacteristic
167C22⋊C4—132no—
168C22⋊C4—132no—
169C22⋊C4—132no—
170C22⋊C4C2×#26112yes—
171C42—131no—
172C42—131no—
173C42—131no—
174C42C2×#26111yescharacteristic
175C13#297411yescharacteristic, complemented, Sylow
176C23—131no—
177C23—132no—
178C23—264no—
179C23—264no—
180C23—522no—
181C23C22×#26112yes—
182D4—264no—
183D4—262no—
184D4#611814yescomplemented
185C2×C4—42no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—132no—
190C2×C4—264no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—264no—
194C2×C4—262no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4C22×#26111yescharacteristic
198C2×C4C22×#26111yescharacteristic
199C2×C4C22×#26112yes—
200C2×C4C22×#26111yescharacteristic
201C8—262no—
202C8—264no—
203C8—262no—
204C22—22no—
205C22—22no—
206C22—132no—
207C22—261no—
208C22—261no—
209C22—262no—
210C22—262no—
211C22—262no—
212C22—528no—
213C22C2×#611814yes—
214C22C23×#26111yescharacteristic
215C4—21no—
216C4—22no—
217C4—21no—
218C4—132no—
219C4—261no—
220C4—262no—
221C4—261no—
222C4C2×#611812yes—
223C2—24no—
224C2—262no—
225C2—522no—
226C2C22×#611811yescharacteristic
227C2#1171962311yescharacteristic
228C2D13⋊#13111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC4×D4×C13C4
prime radicalC2×D4×D13C4
cosocleC2×Dic13C24
hypercenterC4×D4#261
hypocenterC13#2974
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. D4×#1057C2semidirect
3. #11719127C2semidirect
4. C2×#88111C2semidirect
5. #11719076C2semidirect
6. #11719064C2semidirect
7. #11719054C2semidirect
8. #11719051C2semidirect
11. C22×#1057C22semidirect
12. C2×#6118C22semidirect
22. C22⋊#1057C22semidirect
26. #88111C22semidirect
27. #88110C22semidirect
28. C4⋊#1057C22semidirect
29. C4⋊#1057C22semidirect
30. C4×#1057C22semidirect
68. D4×C13M16semidirect
175. C13#2974semidirect
184. D4#6118semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D132
D4×#10572
#117191272
C2×#881112
#117190762
#117190642
#117190542
#117190512
#297413