Finite Group Databasebeta

← #13120804

Subgroups — #13120804

Order 1664.

352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C13×#389C211yesmaximal, characteristic
2#11718647C212yesmaximal
3#11718646C211yesmaximal, characteristic
4#11718643C212yesmaximal
5#11718635C211yesmaximal, characteristic
6#11718635C211yesmaximal, characteristic
7#11718634C211yesmaximal, characteristic
8#11718593C211yesmaximal, characteristic
9#11718590C211yesmaximal, characteristic
10C13⋊#401C212yesmaximal
11#11718321C212yesmaximal
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C42×C13C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2211yescharacteristic
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2212yes—
23#88071C2211yescharacteristic
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2211yescharacteristic
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2211yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2311yescharacteristic
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—42no—
52C42×C13—22no—
53C4⋊Dic13—22no—
54C4⋊Dic13—42no—
55#6101—42no—
56C4×Dic13—22no—
57C4×Dic13—22no—
58#2645—131nomaximal, Sylow
59C23×C13C2411yescharacteristic
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—22no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13#4112yes—
73C2×C4×C13#4112yes—
74C2×C4×C13#4112yes—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93Dic26—44no—
94#401—132no—
95#400—132no—
96#400—132no—
97#400—132no—
98#391—131no—
99#391—131no—
100#391—131no—
101#389—131no—
102#389—131no—
103#389D1311yescharacteristic
104#376—131no—
105C22×C13C2×#4111yescharacteristic
106C22×C13C2×#4111yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C13H(5,𝔽2)11yescharacteristic
109C22×C132−1+411yescharacteristic
110C22×C132−1+411yescharacteristic
111C22×C132−1+411yescharacteristic
112C4×C13—41no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13#12614yes—
117Dic13—42no—
118Dic13—41no—
119Dic13—41no—
120Dic13—41no—
121Dic13—42no—
122Dic13—41no—
123C22×Q8—131no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4C2×D1311yescharacteristic
128C2×C4⋊C4C2×D1311yescharacteristic
129C2×C4⋊C4C2×D1312yes—
130C2×C42—131no—
131C2×C42—131no—
132C2×C42C2×D1311yescharacteristic
133#95—131no—
134#95—131no—
135#95—131no—
136#95—131no—
137#95—132no—
138#95—132no—
139#95—132no—
140#95—132no—
141#95—132no—
142#95—132no—
143#95—132no—
144#95—132no—
145#95C2×D1312yes—
146C2×C13C2×#12611yescharacteristic
147C2×C13#54111yescharacteristic
148C2×C13#54111yescharacteristic
149C2×C13#54111yescharacteristic
150C2×C13#54211yescharacteristic
151C2×C13#54211yescharacteristic
152C2×C13#54211yescharacteristic
153C2×Q8—262no—
154C2×Q8—262no—
155C2×Q8—262no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—132no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—132no—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1312yes—
165C22×C4C22×D1312yes—
166C22×C4C22×D1311yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4—262no—
171C4⋊C4—522no—
172C4⋊C4—522no—
173C42—22no—
174C42—262no—
175C42—262no—
176C13#264511yescharacteristic, complemented, Sylow
177C23C23×D1311yescharacteristic
178Q8—524no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—261no—
203C2×C4—262no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4#612712yes—
210C2×C4#612912yes—
211C2×C4#613112yes—
212C22C2×#612711yescharacteristic
213C22C2×#612911yescharacteristic
214C22#8825111yescharacteristic
215C22C2×#613111yescharacteristic
216C22#8825411yescharacteristic
217C22#8825711yescharacteristic
218C22#8825711yescharacteristic
219C4—42no—
220C4—41no—
221C4—42no—
222C4—41no—
223C4—521no—
224C4—522no—
225C4—522no—
226C4—521no—
227C4—521no—
228C4—521no—
229C4#8815214yes—
230C2C2×#8815211yescharacteristic
231C2#1171926611yescharacteristic
232C2#1171928811yescharacteristic
233C2#1171930811yescharacteristic
234C2#1171933011yescharacteristic
235C2#1171940211yescharacteristic
236C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#389C2
hypercenter#389D13
hypocenterC13#2645
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
176. C13#2645semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186472
#117186462
#117186432
#117186352
#117186342
#117185932
#117185902
C13⋊#4012
#117183212
#264513