Finite Group Databasebeta

← #13122789

Subgroups — #13122789

Order 1664.

368 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 141 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#11718647C212yesmaximal
4#11718646C212yesmaximal
5#11718642C212yesmaximal
6#11718590C211yesmaximal, characteristic
7#11718589C211yesmaximal, characteristic
8#11718317C212yesmaximal
9#11718316C212yesmaximal
10C22×Dic26C2211yescharacteristic
11C2×C13×C4⋊C4C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15C2×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2312yes—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C2×Dic26—22no—
41C2×Dic26—41no—
42C2×Dic26—41no—
43C13×C4⋊C4—24no—
44C13×C4⋊C4—41no—
45C13×C4⋊C4Q814yescomplemented
46C42×C13—41no—
47C4⋊Dic13—22no—
48C4⋊Dic13—41no—
49C4⋊Dic13—42no—
50C4⋊Dic13—41no—
51C4⋊Dic13—42no—
52#6101—24no—
53C4×Dic13—42no—
54#2805—131nomaximal, Sylow
55C23×C13C2411yescharacteristic
56C2×C4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13C2×Q812yes—
68C2×C4×C13C2×Q814yes—
69C2×C4×C13#4112yes—
70C2×C4×C13#4112yes—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83Dic26—44no—
84#400—132no—
85#400—132no—
86#395—132no—
87#391—131no—
88#389—132no—
89#389—131no—
90#389D1311yescharacteristic
91#387—132no—
92#387—132no—
93C22×C13C22×Q811yescharacteristic
94C22×C13C2×#4111yescharacteristic
95C22×C13C2×#4111yescharacteristic
96C22×C13H(5,𝔽2)11yescharacteristic
97C22×C13H(5,𝔽2)11yescharacteristic
98C22×C132−1+411yescharacteristic
99C22×C132−1+411yescharacteristic
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—22no—
103C4×C13—24no—
104C4×C13—42no—
105Dic13—42no—
106Dic13—42no—
107Dic13—42no—
108Dic13—42no—
109C22×Q8—131no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4—131no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—131no—
115C2×C4⋊C4—132no—
116C2×C4⋊C4C2×D1312yes—
117C2×C4⋊C4C2×D1311yescharacteristic
118C2×C4⋊C4C2×D1311yescharacteristic
119C2×C42—132no—
120C2×C42C2×D1311yescharacteristic
121#95—132no—
122#95—132no—
123#95—132no—
124#95—132no—
125#95—132no—
126#95—132no—
127#95—132no—
128#95—132no—
129#95C2×D1312yes—
130C2×C13#53811yescharacteristic
131C2×C13#53911yescharacteristic
132C2×C13#54411yescharacteristic
133C2×C13#55411yescharacteristic
134C2×C13#55611yescharacteristic
135C2×C13#55711yescharacteristic
136C2×C13#56311yescharacteristic
137C2×Q8—262no—
138C2×Q8—521no—
139C2×Q8—521no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4—132no—
143C22×C4—132no—
144C22×C4C22×D1312yes—
145C22×C4C22×D1311yescharacteristic
146C22×C4C22×D1312yes—
147C22×C4C22×D1311yescharacteristic
148C22×C4C22×D1311yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—41no—
151C4⋊C4—262no—
152C4⋊C4—264no—
153C4⋊C4—521no—
154C4⋊C4—522no—
155C4⋊C4—521no—
156C4⋊C4—522no—
157C4⋊C4Dic2614yescomplemented
158C42—41no—
159C42—522no—
160C13#280511yescharacteristic, complemented, Sylow
161C23C23×D1311yescharacteristic
162Q8—524no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—262no—
175C2×C4—262no—
176C2×C4—262no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4C2×Dic2612yes—
187C2×C4C2×Dic2614yes—
188C2×C4#612912yes—
189C2×C4#613112yes—
190C22C22×Dic2611yescharacteristic
191C22C2×#612911yescharacteristic
192C22#8825111yescharacteristic
193C22C2×#613111yescharacteristic
194C22#8825411yescharacteristic
195C22#8825611yescharacteristic
196C22#8825711yescharacteristic
197C4—22no—
198C4—24no—
199C4—22no—
200C4—22no—
201C4—42no—
202C4—522no—
203C4—522no—
204C4—522no—
205C4—522no—
206C2#1171920511yescharacteristic
207C2#1171924811yescharacteristic
208C2#1171927511yescharacteristic
209C2#1171930711yescharacteristic
210C2#1171934911yescharacteristic
211C2#1171940411yescharacteristic
212C2#1171943711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#389C2
hypercenter#389D13
hypocenterC13#2805
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
45. C13×C4⋊C4Q8semidirect
157. C4⋊C4Dic26semidirect
160. C13#2805semidirect

Maximal subgroups

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

subgroupindex
C13×#3892
#117186472
#117186462
#117186422
#117185902
#117185892
#117183172
#117183162
#280513