Finite Group Databasebeta

← #13130176

Subgroups — #13130176

Order 1664.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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
2#11719054C211yesmaximal, characteristic, complemented
3C4×#6118C211yesmaximal, characteristic, complemented
4D4⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×D4×D13C411yescharacteristic
7C22×C4×D13—21no—
8C2×#6118—21no—
9C4×D4×C13C411yescharacteristic
10D4×Dic13C2211yescharacteristic
11C4×C22⋊D13—21no—
12#88147C2211yescharacteristic
13C4⋊C4×D13C411yescharacteristic
14#88135—21no—
15C22⋊C4×D13—21no—
16C4×D52C411yescharacteristic
17C42×D13C2211yescharacteristic
18#88111—21no—
19#88110—21no—
20#88110—21no—
21C4⋊#1057C2212yescomplemented
22C4×#1057C2212yescomplemented
23C23×D13—21no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13—21no—
26C2×C22⋊D13—21no—
27C22×Dic13—21no—
28D4×D13—22no—
29D4×D13—22no—
30C2×D52C2×C411yescharacteristic
31C2×C4×D13—21no—
32C2×C4×D13—21no—
33C2×C4×D13—21no—
34C2×C4×D13—44no—
35C2×C4×D13C2×C411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×#1057—22no—
39C2×#1057—22no—
40#6118—24no—
41C13×C4⋊C4C2×C411yescharacteristic
42C13×C22⋊C4—21no—
43C42×C13C2×C411yescharacteristic
44C22⋊Dic13—21no—
45#6103—21no—
46#6103—21no—
47C4⋊Dic13C2×C411yescharacteristic
48#6101—21no—
49C4×Dic13D411yescharacteristic
50C4×Dic13D411yescharacteristic
51C4×Dic13C2311yescharacteristic
52#1490—131nomaximal, Sylow
53C23×C13—21no—
54C22×D13—24no—
55C22×D13—21no—
56C22×D13—42no—
57C22×D13—42no—
58C22×D13C22⋊C411yescharacteristic
59D4×C13—21no—
60D4×C13M1612yescomplemented
61C2×C4×C13—21no—
62C2×C4×C13—42no—
63C2×C4×C13C22⋊C411yescharacteristic
64C2×C4×C13C22⋊C411yescharacteristic
65C2×C4×C13C22×C411yescharacteristic
66C22⋊D13—24no—
67C2×Dic13—21no—
68C2×Dic13—42no—
69C2×Dic13C22⋊C411yescharacteristic
70C2×Dic13C2×D411yescharacteristic
71C2×Dic13C2×D411yescharacteristic
72D52—21no—
73D52M1612yescomplemented
74C4×D13—22no—
75C4×D13—21no—
76C4×D13—21no—
77C4×D13—22no—
78C4×D13—42no—
79C4×D13—42no—
80C4×D13—42no—
81#1057—24no—
82#1057—42no—
83C2×C4×D4—131no—
84#432—131no—
85C4×M16—131no—
86D4⋊C8—132no—
87D4⋊C8—132no—
88C22×C13—22no—
89C22×C13—41no—
90C22×C13—41no—
91C22×C13C2×C22⋊C411yescharacteristic
92C2×D13—21no—
93C2×D13—21no—
94C2×D13—22no—
95C2×D13—48no—
96C2×D13—41no—
97C2×D13—41no—
98C2×D13#10412yes—
99C4×C13—21no—
100C4×C13—21no—
101C4×C13—41no—
102C4×C13C2×M1611yescharacteristic
103C4×C13C2×M1611yescharacteristic
104Dic13—21no—
105Dic13—21no—
106Dic13—41no—
107Dic13AGL(1,ℤ/8)12yes—
108C22×D4—131no—
109C23×C4—261no—
110C2×M16—261no—
111C4×D4—131no—
112C4×D4—131no—
113C4×D4—131no—
114C4×D4—261no—
115C4×D4—261no—
116C4×D4#26111yescharacteristic
117C2×C4⋊C4—131no—
118C2×C22⋊C4—261no—
119C2×C42—131no—
120C4⋊C8—132no—
121C22⋊C8—261no—
122#97—261no—
123#97—261no—
124C4×C8—132no—
125C2×C13—42no—
126C2×C13#40711yescharacteristic
127C2×C13#41811yescharacteristic
128C2×C13C2×#10411yescharacteristic
129D13—22no—
130D13—42no—
131C24—261no—
132C2×D4—131no—
133C2×D4—261no—
134C2×D4—262no—
135C2×D4—262no—
136C2×D4C2×#26111yescharacteristic
137C22×C4—21no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—131no—
141C22×C4—261no—
142C22×C4—261no—
143C22×C4—261no—
144C22×C4—261no—
145C22×C4—524no—
146M16—264no—
147C2×C8—262no—
148C2×C8—262no—
149C4⋊C4—131no—
150C4⋊C4—261no—
151C4⋊C4C2×#26111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—261no—
154C22⋊C4—261no—
155C22⋊C4—261no—
156C42—131no—
157C42—131no—
158C42—131no—
159C42C2×#26111yescharacteristic
160C13#149011yescharacteristic, complemented, Sylow
161C23—21no—
162C23—131no—
163C23—264no—
164C23—261no—
165C23—522no—
166C23—522no—
167D4—21no—
168D4—132no—
169D4—264no—
170D4—261no—
171D4#611812yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—131no—
175C2×C4—131no—
176C2×C4—131no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—522no—
183C2×C4—522no—
184C2×C4—522no—
185C2×C4—522no—
186C2×C4C22⋊#26111yescharacteristic
187C2×C4C22⋊#26111yescharacteristic
188C2×C4C22×#26111yescharacteristic
189C8—264no—
190C8—522no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—132no—
195C22—261no—
196C22—261no—
197C22—262no—
198C22—528no—
199C22—521no—
200C22—521no—
201C22C2×C22⋊#26111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—132no—
206C4—261no—
207C4—261no—
208C4—521no—
209C4C2×#611811yescharacteristic
210C4D13⋊M1611yescharacteristic
211C2—42no—
212C2—262no—
213C2—522no—
214C2#1171912711yescharacteristic
215C2#1171913811yescharacteristic
216C2D13⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC2×D4×D13C4
cosocleC4×Dic13C23
hypercenterC4×D4#261
hypocenterC13#1490
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11719054C2semidirect
3. C4×#6118C2semidirect
4. D4⋊#1057C2semidirect
5. #11718243C2semidirect
21. C4⋊#1057C22semidirect
22. C4×#1057C22semidirect
60. D4×C13M16semidirect
73. D52M16semidirect
160. C13#1490semidirect
171. 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
#117190542
C4×#61182
D4⋊#10572
#117182432
#149013