Finite Group Databasebeta

← #13130915

Subgroups — #13130915

Order 1664.

254 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 70 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(C2×#261)⋊Q8C211yesmaximal, characteristic
2C2×#88117C211yesmaximal, characteristic
3C2×#88101C211yesmaximal, characteristic
4C4⋊C4×#261C211yesmaximal, characteristic
5D13×#103C211yesmaximal, characteristic
6(C2×#261)⋊C8C211yesmaximal, characteristic
7#11718246C211yesmaximal, characteristic
8C2×Q8×D13C2211yescharacteristic
9C2×C4⋊#261C2211yescharacteristic
10C2×C4⋊#261C2211yescharacteristic
11C2×C4×#261—21no—
12C2×C4×#261C2211yescharacteristic
13C2×D13⋊C8C2211yescharacteristic
14C2×C8×D13C2211yescharacteristic
15C4⋊C4×D13C2211yescharacteristic
16#88117—22no—
17(C2×#261)⋊C4—21no—
18(C2×#261)⋊C4—21no—
19(C2×#261)⋊C4—21no—
20#88101—22no—
21C13×#103C411yescharacteristic, complemented
22#88075C411yescharacteristic, complemented
23#88056C411yescharacteristic, complemented
24#88050C411yescharacteristic, complemented
25C22×#261—21no—
26C22×#261—21no—
27C22×#261D411yescharacteristic
28C22×#261D411yescharacteristic
29C2×Q8×C13C2×C411yescharacteristic
30Q8×D13—21no—
31Q8×D13—21no—
32Q8×D13—21no—
33Q8×D13—21no—
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13C2311yescharacteristic
37C2×Dic26—21no—
38C2×Dic26C2×C411yescharacteristic
39C2×#1057—21no—
40C4⋊#261—21no—
41C4⋊#261—21no—
42C4⋊#261—21no—
43C4⋊#261D412yes—
44C4×#261—21no—
45C4×#261—21no—
46C4×#261—42no—
47D13⋊C8—21no—
48D13⋊C8—21no—
49C2×C8×C13C2×C411yescharacteristic
50C13×C4⋊C4C2×C411yescharacteristic
51C4⋊Dic13C2×C411yescharacteristic
52#6101—21no—
53C2×#1055C2×C411yescharacteristic
54C8×D13—21no—
55C8×D13—21no—
56#1927—131nomaximal, Sylow
57C22×D13C2×D411yescharacteristic
58C2×#261—21no—
59C2×#261—21no—
60C2×#261—22no—
61C2×#261—21no—
62C2×#261—21no—
63C2×#261—21no—
64C2×#261—41no—
65C2×#261—41no—
66C2×#261—41no—
67C2×#261—41no—
68C2×#261—41no—
69C2×#261SD1612yes—
70Q8×C13—21no—
71Q8×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13C22×C411yescharacteristic
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13#4111yescharacteristic
78C4×D13—41no—
79C4×D13—41no—
80C4×D13—41no—
81C4×D13—41no—
82C4×D13C2×D411yescharacteristic
83C4×D13#4111yescharacteristic
84C4×D13#4111yescharacteristic
85C4×D13#4111yescharacteristic
86Dic26—21no—
87Dic26—21no—
88Dic26—41no—
89Dic26—41no—
90#1057—41no—
91C8×C13—21no—
92#1055—21no—
93C2×#106—131no—
94C2×#103—131no—
95C2×#103—131no—
96#391—131no—
97C4×C4⋊C4—131no—
98#340—131no—
99#336—131no—
100C22×C13C4×D411yescharacteristic
101C2×D13#12111yescharacteristic
102C2×D13#12311yescharacteristic
103C2×D13C2×SD1611yescharacteristic
104C2×D13#13511yescharacteristic
105C2×D13#13711yescharacteristic
106C2×D13#13711yescharacteristic
107#261—22no—
108#261—42no—
109#261—41no—
110#261—81no—
111C4×C13—41no—
112C4×C13—41no—
113C4×C13#11711yescharacteristic
114C4×C13C4×D411yescharacteristic
115Dic13—41no—
116Dic13—41no—
117Dic13#12411yescharacteristic
118Dic13#12611yescharacteristic
119C22×Q8—131no—
120C22×C8—131no—
121C22×C8—131no—
122C2×C4⋊C4—131no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4—131no—
125C2×C42—131no—
126C2×C42—261no—
127#106—262no—
128#103—131no—
129#103—131no—
130#103—131no—
131#103—262no—
132#103#26111yescharacteristic, complemented
133#95—261no—
134#95—261no—
135#95—261no—
136C2×C13#38811yescharacteristic
137C2×C13C4×SD1611yescharacteristic
138C2×C13#44111yescharacteristic
139D13#46111yescharacteristic
140D13#46411yescharacteristic
141D13#48311yescharacteristic
142D13#48511yescharacteristic
143C2×Q8—131no—
144C2×Q8—261no—
145C2×Q8—261no—
146C2×Q8—261no—
147C2×Q8—261no—
148C2×Q8—261no—
149C2×Q8C2×#26111yescharacteristic
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—261no—
154C22×C4—261no—
155C22×C4—261no—
156C22×C4—261no—
157C2×C8—131no—
158C2×C8—261no—
159C2×C8—261no—
160C2×C8—261no—
161C2×C8—261no—
162C2×C8—261no—
163C2×C8C2×#26111yescharacteristic
164C4⋊C4—132no—
165C4⋊C4—131no—
166C4⋊C4—261no—
167C4⋊C4—261no—
168C4⋊C4—261no—
169C4⋊C4—261no—
170C4⋊C4C2×#26111yescharacteristic
171C42—261no—
172C42—261no—
173C42—522no—
174C13#192711yescharacteristic, complemented, Sylow
175C23—131no—
176Q8—21no—
177Q8—21no—
178Q8—261no—
179Q8—261no—
180Q8—521no—
181Q8—521no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—131no—
185C2×C4—131no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—132no—
190C2×C4—261no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—262no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—521no—
199C2×C4—521no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4—521no—
206C2×C4—521no—
207C2×C4C22×#26111yescharacteristic
208C8—21no—
209C8—261no—
210C8—521no—
211C22—131no—
212C22—131no—
213C22—131no—
214C22—131no—
215C22—131no—
216C22—131no—
217C22D4×#26111yescharacteristic
218C4—41no—
219C4—41no—
220C4—131no—
221C4—131no—
222C4—262no—
223C4—521no—
224C4—522no—
225C4—521no—
226C4—521no—
227C4—1041no—
228C4#8823711yescharacteristic
229C4D4×#26111yescharacteristic
230C2—131no—
231C2—131no—
232C2—131no—
233C2—131no—
234C2#1171907111yescharacteristic
235C2SD16×#26111yescharacteristic
236C2#1171911011yescharacteristic
subgroupG/H
centerC22D4×#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#103C4
socleC22×C13C4×D4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenter#103#261
hypocenterC13#1927
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
21. C13×#103C4semidirect
22. #88075C4semidirect
23. #88056C4semidirect
24. #88050C4semidirect
132. #103#261semidirect
174. C13#1927semidirect

Maximal subgroups

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

subgroupindex
(C2×#261)⋊Q82
C2×#881172
C2×#881012
C4⋊C4×#2612
D13×#1032
(C2×#261)⋊C82
#117182462
#192713