Finite Group Databasebeta

← #13130212

Subgroups — #13130212

Order 1664.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719311C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic, complemented
3C2×#88111C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718241C212yesmaximal, complemented
6C2×#6129C411yescharacteristic, complemented
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C22×#1057—21no—
10C2×C4×#261—21no—
11C13×#121C411yescharacteristic, complemented
12#88192C2211yescharacteristic
13#88191—21no—
14D4×Dic13—21no—
15#88178C411yescharacteristic, complemented
16#88151C2211yescharacteristic
17#88146C411yescharacteristic, complemented
18#88137—21no—
19#88135—21no—
20(C2×#261)⋊C4C2212yes—
21#88111—21no—
22#88111C2212yes—
23C23×D13D411yescharacteristic
24C22×#261—22no—
25C2×D4×C13—21no—
26C2×D4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C2×C22⋊D13—21no—
29C2×C22⋊D13—21no—
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32#6129—42no—
33C2×C4×D13—42no—
34C2×C4×D13C2×C411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×C4×D13C2311yescharacteristic
38C2×Dic26C2×C411yescharacteristic
39C22⋊#261—24no—
40C2×#1057—22no—
41C2×#1057—42no—
42C4×#261—42no—
43C13×C4⋊C4C2×C411yescharacteristic
44C13×C22⋊C4—21no—
45C22⋊Dic13—21no—
46C22⋊Dic13—21no—
47#6103—21no—
48#6103—21no—
49C4⋊Dic13—21no—
50C4⋊Dic13C2×C411yescharacteristic
51#6101—21no—
52C4×Dic13—21no—
53#1501—131nomaximal, Sylow
54C23×C13—21no—
55C23×C13C22⋊C411yescharacteristic
56C22×D13—22no—
57C22×D13—22no—
58C22×D13—41no—
59C22×D13C22⋊C411yescharacteristic
60C22×D13C2×D411yescharacteristic
61C2×#261—24no—
62C2×#261—42no—
63C2×#261—42no—
64D4×C13—41no—
65D4×C13—42no—
66C2×C4×C13—21no—
67C2×C4×C13—41no—
68C2×C4×C13C22⋊C411yescharacteristic
69C2×C4×C13C22×C411yescharacteristic
70C22⋊D13—42no—
71C22⋊D13—42no—
72C2×Dic13—22no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—42no—
76C2×Dic13C22⋊C411yescharacteristic
77C2×Dic13C2×D411yescharacteristic
78C4×D13—22no—
79C4×D13—22no—
80C4×D13—41no—
81C4×D13—41no—
82Dic26—41no—
83#1057—42no—
84#525—131no—
85C2×C22⋊C8—131no—
86C4×C22⋊C4—131no—
87#328—132no—
88#327—132no—
89C22×C13—21no—
90C22×C13—21no—
91C22×C13—41no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13#10412yes—
95C22×C13C2×C22⋊C411yescharacteristic
96C2×D13—21no—
97C2×D13—21no—
98C2×D13—21no—
99C2×D13—21no—
100C2×D13—21no—
101C2×D13—44no—
102C2×D13#13512yes—
103#261—44no—
104C4×C13—21no—
105C4×C13—21no—
106C4×C13—41no—
107Dic13—21no—
108Dic13—41no—
109Dic13—41no—
110Dic13#9912yes—
111C2×#41—131no—
112C23×C4—131no—
113C22×C8—261no—
114#123—261no—
115C22⋊Q8—131no—
116C22⋊Q8—131no—
117#121—131no—
118#121#26111yescharacteristic, complemented
119#120—261no—
120C4×D4—261no—
121C4×D4—261no—
122#117—131no—
123C2×C22⋊C4—261no—
124C2×C42—261no—
125C22⋊C8—132no—
126C22⋊C8—261no—
127#95—132no—
128C2×C13—22no—
129C2×C13—81no—
130C2×C13C2×#9911yescharacteristic
131C2×C13#41611yescharacteristic
132C2×C13C2×#10411yescharacteristic
133D13—22no—
134D13—41no—
135C24—131no—
136#41—522no—
137C2×Q8—131no—
138C2×D4—21no—
139C2×D4—261no—
140C2×D4—261no—
141C2×D4C2×#26111yescharacteristic
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4—261no—
148C22×C4—262no—
149C22×C4—522no—
150C22×C4C2×#26111yescharacteristic
151C2×C8—262no—
152C2×C8—522no—
153C4⋊C4—131no—
154C4⋊C4—261no—
155C4⋊C4—261no—
156C4⋊C4C2×#26111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—261no—
159C22⋊C4—261no—
160C22⋊C4—261no—
161C22⋊C4—264no—
162C22⋊C4—261no—
163C42—261no—
164C42—522no—
165C13#150111yescharacteristic, complemented, Sylow
166C23—21no—
167C23—131no—
168C23—131no—
169C23—262no—
170C23—262no—
171C23—521no—
172C23C22⋊#26111yescharacteristic
173Q8—521no—
174D4—41no—
175D4—42no—
176D4—522no—
177D4—522no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—131no—
181C2×C4—131no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—264no—
186C2×C4—261no—
187C2×C4—261no—
188C2×C4—521no—
189C2×C4—521no—
190C2×C4—522no—
191C2×C4—522no—
192C2×C4—522no—
193C2×C4C22⋊#26111yescharacteristic
194C2×C4C22×#26111yescharacteristic
195C8—522no—
196C22—21no—
197C22—21no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—132no—
202C22—261no—
203C22—261no—
204C22—261no—
205C22—261no—
206C22—261no—
207C22—524no—
208C22#8811612yes—
209C22C2×C22⋊#26111yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—132no—
214C4—261no—
215C4—524no—
216C4—521no—
217C4—521no—
218C2—22no—
219C2—81no—
220C2—262no—
221C2—521no—
222C2C2×#8811611yescharacteristic
223C2D13⋊#9911yescharacteristic
224C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radical#11719311C2
cosocleC2×C4×D13C23
hypercenter#121#261
hypocenterC13#1501
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#261C2semidirect
3. C2×#88111C2semidirect
4. #11718292C2semidirect
5. #11718241C2semidirect
6. C2×#6129C4semidirect
11. C13×#121C4semidirect
15. #88178C4semidirect
17. #88146C4semidirect
118. #121#261semidirect
165. C13#1501semidirect

Maximal subgroups

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

subgroupindex
#117193112
C4×C22⋊#2612
C2×#881112
#117182922
#117182412
#150113