Finite Group Databasebeta

← #13130714

Subgroups — #13130714

Order 1664.

316 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×M16×D13C211yesmaximal, characteristic
2#11719136C212yesmaximal
3C2×#88102C211yesmaximal, characteristic, complemented
4C2×#88101C211yesmaximal, characteristic, complemented
5#11718265C212yesmaximal, complemented
6C22×C4×D13C2211yescharacteristic
7C2×C22⋊#261—22no—
8C2×C4⋊#261C2212yes—
9C2×C4⋊#261C2212yes—
10C2×C13×M16C411yescharacteristic, complemented
11C2×#6099C411yescharacteristic, complemented
12M16×D13—22no—
13M16×D13—22no—
14C2×#6094C411yescharacteristic, complemented
15C2×#6094C411yescharacteristic, complemented
16C2×C8×D13C2211yescharacteristic
17C2×C8×D13C2211yescharacteristic
18(C2×#261)⋊C4—22no—
19#88102—22no—
20#88101—22no—
21C23×D13D411yescharacteristic
22C22×#261—22no—
23C22×#261—22no—
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13Q811yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13—21no—
28C2×C4×D13—21no—
29C2×C4×D13—21no—
30C2×C4×D13C2×C411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13Q811yescharacteristic
33C2×C4×D13C2311yescharacteristic
34C22⋊#261—44no—
35C4⋊#261—22no—
36C4⋊#261—22no—
37C4⋊#261—22no—
38C4⋊#261—22no—
39C13×M16—22no—
40C2×C8×C13C2×C411yescharacteristic
41C2×C8×C13C2×C411yescharacteristic
42#6099—22no—
43C2×#1055C2×C411yescharacteristic
44C2×#1055C2×C411yescharacteristic
45#6094—22no—
46#6094—22no—
47C8×D13—21no—
48C8×D13—21no—
49C8×D13D412yes—
50C8×D13D412yes—
51#1809—131nomaximal, Sylow
52C23×C13C4⋊C411yescharacteristic
53C22×D13—21no—
54C22×D13—21no—
55C22×D13—22no—
56C22×D13—22no—
57C22×D13C4⋊C411yescharacteristic
58C22×D13C2×D411yescharacteristic
59C2×#261—42no—
60C2×#261—42no—
61C2×#261—42no—
62C2×#261—42no—
63C2×#261—42no—
64C2×#261—42no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13C4⋊C411yescharacteristic
68C2×C4×C13C22×C411yescharacteristic
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13C4⋊C411yescharacteristic
72C2×Dic13C2×Q811yescharacteristic
73C4×D13—21no—
74C4×D13—21no—
75C4×D13—21no—
76C4×D13—21no—
77C4×D13—21no—
78C4×D13—21no—
79C4×D13C2×D411yescharacteristic
80C4×D13C2×D411yescharacteristic
81C4×D13#4111yescharacteristic
82C4×D13#4111yescharacteristic
83C8×C13—21no—
84C8×C13C22⋊C412yescomplemented
85#1055—21no—
86#1055C22⋊C412yescomplemented
87C22×M16—131no—
88C2×#107—131no—
89C2×#106—131no—
90#380—132no—
91#340—132no—
92C22×C13—21no—
93C22×C13—22no—
94C22×C13C2×C4⋊C411yescharacteristic
95C2×D13—21no—
96C2×D13—22no—
97C2×D13—42no—
98C2×D13—41no—
99C2×D13—41no—
100C2×D13#12111yescharacteristic
101C2×D13#12111yescharacteristic
102C2×D13AGL(1,ℤ/8)12yes—
103C2×D13#13712yes—
104#261—82no—
105#261—82no—
106C4×C13—21no—
107C4×C13C2×C22⋊C411yescharacteristic
108C4×C13#11711yescharacteristic
109Dic13—21no—
110Dic13C22⋊Q811yescharacteristic
111Dic13C22⋊Q811yescharacteristic
112C23×C4—131no—
113C2×M16—131no—
114C2×M16—131no—
115C2×M16—131no—
116C2×M16—262no—
117C2×M16—262no—
118C2×M16#26111yescharacteristic, complemented
119C22×C8—131no—
120C22×C8—131no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—132no—
123C2×C22⋊C4—262no—
124#107—262no—
125#106—262no—
126#95—262no—
127C2×C13—41no—
128C2×C13#38011yescharacteristic
129C2×C13#42812yes—
130D13—41no—
131D13#46812yes—
132D13#46911yescharacteristic
133D13#47011yescharacteristic
134C24—131no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—131no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—261no—
141C22×C4—261no—
142C22×C4—261no—
143C22×C4—261no—
144C22×C4—262no—
145C22×C4—262no—
146C22×C4C2×#26111yescharacteristic
147M16—22no—
148M16—262no—
149M16—262no—
150M16—262no—
151C2×C8—131no—
152C2×C8—132no—
153C2×C8—132no—
154C2×C8—131no—
155C2×C8—261no—
156C2×C8—261no—
157C2×C8C2×#26111yescharacteristic
158C2×C8C2×#26111yescharacteristic
159C4⋊C4—262no—
160C4⋊C4—262no—
161C4⋊C4—262no—
162C4⋊C4—262no—
163C22⋊C4—524no—
164C13#180911yescharacteristic, complemented, Sylow
165C23—131no—
166C23—131no—
167C23—262no—
168C23—261no—
169C23—261no—
170C23—262no—
171C23C4⋊#26111yescharacteristic
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—131no—
175C2×C4—131no—
176C2×C4—131no—
177C2×C4—131no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4—261no—
187C2×C4—261no—
188C2×C4—522no—
189C2×C4—522no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4C4⋊#26111yescharacteristic
195C2×C4C22×#26111yescharacteristic
196C8—21no—
197C8—132no—
198C8—261no—
199C8C22⋊#26112yescomplemented
200C22—22no—
201C22—21no—
202C22—132no—
203C22—132no—
204C22—131no—
205C22—131no—
206C22—262no—
207C22—261no—
208C22—521no—
209C22—522no—
210C22—521no—
211C22C2×C4⋊#26111yescharacteristic
212C4—21no—
213C4—131no—
214C4—131no—
215C4—261no—
216C4—1042no—
217C4—1042no—
218C4#8823711yescharacteristic
219C4C2×C22⋊#26111yescharacteristic
220C2—41no—
221C2—131no—
222C2—132no—
223C2—131no—
224C2—521no—
225C2#1171909812yes—
226C2#1171913611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×M16C4
socleC22×C13C2×C4⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC2×M16#261
hypocenterC13#1809
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#88102C2semidirect
4. C2×#88101C2semidirect
5. #11718265C2semidirect
10. C2×C13×M16C4semidirect
11. C2×#6099C4semidirect
14. C2×#6094C4semidirect
15. C2×#6094C4semidirect
84. C8×C13C22⋊C4semidirect
86. #1055C22⋊C4semidirect
118. C2×M16#261semidirect
164. C13#1809semidirect
199. C8C22⋊#261semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D132
#117191362
C2×#881022
C2×#881012
#117182652
#180913