Finite Group Databasebeta

← #13119440

Subgroups — #13119440

Order 1664.

372 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 137 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×#382C211yesmaximal, characteristic
2#11718646C211yesmaximal, characteristic
3C4⋊C4×Dic13C211yesmaximal, characteristic
4#11718635C211yesmaximal, characteristic
5#11718635C211yesmaximal, characteristic
6C4×#6101C211yesmaximal, characteristic
7#11718590C211yesmaximal, characteristic
8C13⋊#401C212yesmaximal
9#11718321C212yesmaximal
10#11718315C212yesmaximal
11#11718312C212yesmaximal
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6101C2211yescharacteristic
19C2×#6101C2211yescharacteristic
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C2×C4×Dic13C2211yescharacteristic
23C13×#95C2212yes—
24C13×#95C2212yes—
25#88071C2211yescharacteristic
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2211yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2311yescharacteristic
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C42×C13—22no—
52C4⋊Dic13—22no—
53C4⋊Dic13—24no—
54#6101—22no—
55#6101—22no—
56C4×Dic13—22no—
57C4×Dic13—22no—
58C4×Dic13—24no—
59#2514—131nomaximal, Sylow
60C23×C13C2411yescharacteristic
61C2×C4×C13—22no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13#4112yes—
74C2×C4×C13#4112yes—
75C2×C4×C13#4112yes—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—22no—
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13#4112yes—
93C2×Dic13#4112yes—
94Dic26—44no—
95#401—132no—
96#400—132no—
97#391—131no—
98#391—131no—
99#391—131no—
100#389—131no—
101#387—132no—
102#383—132no—
103#382D1311yescharacteristic
104C4×C4⋊C4—131no—
105C4×C4⋊C4—131no—
106C22×C13C2×#4111yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C13C2×#4111yescharacteristic
109C22×C13C2×#4111yescharacteristic
110C22×C13C2×#4111yescharacteristic
111C22×C132−1+411yescharacteristic
112C22×C132−1+411yescharacteristic
113C4×C13—41no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13—42no—
117C4×C13#12614yes—
118Dic13—22no—
119Dic13—22no—
120Dic13—42no—
121Dic13—42no—
122Dic13—41no—
123Dic13—41no—
124C22×Q8—131no—
125C2×C4⋊C4—131no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C4⋊C4C2×D1311yescharacteristic
131C2×C42—131no—
132C2×C42—132no—
133C2×C42—131no—
134C2×C42C2×D1311yescharacteristic
135#95—131no—
136#95—132no—
137#95—131no—
138#95—132no—
139#95—132no—
140#95—132no—
141#95—132no—
142#95—132no—
143#95—132no—
144#95—132no—
145#95C2×D1312yes—
146#95C2×D1312yes—
147C2×C13C2×#12611yescharacteristic
148C2×C13#52911yescharacteristic
149C2×C13#54111yescharacteristic
150C2×C13#55211yescharacteristic
151C2×C13#55611yescharacteristic
152C2×C13#55611yescharacteristic
153C2×C13#55611yescharacteristic
154C2×Q8—262no—
155C2×Q8—262no—
156C2×Q8—262no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—132no—
161C22×C4—131no—
162C22×C4—132no—
163C22×C4C22×D1312yes—
164C22×C4C22×D1311yescharacteristic
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—264no—
173C4⋊C4—262no—
174C42—22no—
175C42—264no—
176C42—262no—
177C42—262no—
178C13#251411yescharacteristic, complemented, Sylow
179C23C23×D1311yescharacteristic
180Q8—524no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—261no—
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—262no—
205C2×C4—262no—
206C2×C4—261no—
207C2×C4—262no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4#612712yes—
212C2×C4#612912yes—
213C2×C4#613112yes—
214C22C2×#612711yescharacteristic
215C22C2×#612911yescharacteristic
216C22C2×#613111yescharacteristic
217C22#41×D1311yescharacteristic
218C22#41×D1311yescharacteristic
219C22#8825711yescharacteristic
220C22#8825711yescharacteristic
221C4—41no—
222C4—41no—
223C4—42no—
224C4—42no—
225C4—262no—
226C4—262no—
227C4—522no—
228C4—521no—
229C4—522no—
230C4—521no—
231C4#8815214yes—
232C2C2×#8815211yescharacteristic
233C2#1171923411yescharacteristic
234C2#1171923811yescharacteristic
235C2#1171937611yescharacteristic
236C2#1171937611yescharacteristic
237C2#1171939611yescharacteristic
238C2#1171940211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#382C2
hypercenter#382D13
hypocenterC13#2514
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
178. C13#2514semidirect

Maximal subgroups

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

subgroupindex
C13×#3822
#117186462
C4⋊C4×Dic132
#117186352
C4×#61012
#117185902
C13⋊#4012
#117183212
#117183152
#117183122
#251413