Finite Group Databasebeta

← #13119861

Subgroups — #13119861

Order 1664.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#88198C212yesmaximal
2C2×#88142C212yesmaximal
3C13×#395C211yesmaximal, characteristic
4#11718640C211yesmaximal, characteristic
5#11718637C211yesmaximal, characteristic
6#11718633C212yesmaximal
7#11718317C212yesmaximal
8#11718310C212yesmaximal
9#11718308C212yesmaximal
10C22×Q8×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C22×Dic26C2212yes—
13C2×C13×C4⋊C4C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15#88198—28no—
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27#88142—28no—
28C13×#95C2211yescharacteristic
29C13×#95C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2211yescharacteristic
33C2×Q8×C13—24no—
34C2×Q8×C13—41no—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C2×Dic26—24no—
45C2×Dic26—24no—
46C2×Dic26—24no—
47C2×Dic26—41no—
48C2×Dic26—42no—
49C13×C4⋊C4—24no—
50C13×C4⋊C4—41no—
51C4⋊Dic13—24no—
52C4⋊Dic13—41no—
53#6101—24no—
54#6101—24no—
55#6101—24no—
56#6101—24no—
57#6101D418yes—
58#6101Q818yescomplemented
59C4×Dic13—24no—
60C4×Dic13—24no—
61C4×Dic13Q814yescomplemented
62#2551—131nomaximal, Sylow
63C23×C13C2411yescharacteristic
64Q8×C13—44no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—21no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13C2×D414yes—
76C2×C4×C13C2×Q812yes—
77C2×C4×C13C2×Q814yes—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13C2×D414yes—
86C2×Dic13C2×D414yes—
87C2×Dic13C2×Q814yes—
88C2×Dic13C2×Q814yes—
89C2×Dic13C2×Q814yes—
90Dic26—44no—
91Dic26—48no—
92C2×C4⋊Q8—132no—
93C2×C4⋊Q8—132no—
94#395—131no—
95#395—132no—
96#395D1311yescharacteristic
97#389—132no—
98#389—132no—
99#384—131no—
100C4×C4⋊C4—132no—
101C22×C13C22×D412yes—
102C22×C13C22×Q811yescharacteristic
103C22×C13C22×Q812yes—
104C22×C13H(5,𝔽2)11yescharacteristic
105C22×C132−1+411yescharacteristic
106C4×C13—22no—
107C4×C13—24no—
108C4×C13—24no—
109C4×C13—41no—
110C4×C13—41no—
111Dic13—24no—
112Dic13—24no—
113Dic13—42no—
114Dic13C4⋊Q818yescomplemented
115C22×Q8—131no—
116C22×Q8—132no—
117C22×Q8C2×D1311yescharacteristic
118C4⋊Q8—268no—
119C4⋊Q8—268no—
120C2×C4⋊C4—132no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—132no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—131no—
128C2×C4⋊C4C2×D1312yes—
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C42—131no—
131C2×C42—132no—
132C2×C42—132no—
133#95—132no—
134#95—131no—
135#95—132no—
136#95C2×D1312yes—
137#95C2×D1311yescharacteristic
138C2×C13C2×C4⋊Q812yes—
139C2×C13#54411yescharacteristic
140C2×C13D4211yescharacteristic
141C2×C13D4×Q812yes—
142C2×C13Q8211yescharacteristic
143C2×Q8—24no—
144C2×Q8—41no—
145C2×Q8—264no—
146C2×Q8—264no—
147C2×Q8—264no—
148C2×Q8—522no—
149C2×Q8—521no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4C22×D1311yescharacteristic
155C22×C4C22×D1311yescharacteristic
156C22×C4C22×D1312yes—
157C22×C4C22×D1311yescharacteristic
158C22×C4C22×D1312yes—
159C4⋊C4—24no—
160C4⋊C4—41no—
161C4⋊C4—138no—
162C4⋊C4—138no—
163C4⋊C4—264no—
164C4⋊C4—264no—
165C4⋊C4—264no—
166C4⋊C4—264no—
167C4⋊C4—264no—
168C4⋊C4—521no—
169C42—134no—
170C42—264no—
171C42—264no—
172C13#255111yescharacteristic, complemented, Sylow
173C23C23×D1311yescharacteristic
174Q8—44no—
175Q8—528no—
176Q8—524no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—134no—
188C2×C4—134no—
189C2×C4—134no—
190C2×C4—134no—
191C2×C4—134no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4D4×D1314yes—
200C2×C4Q8×D1312yes—
201C2×C4Q8×D1314yes—
202C22C2×D4×D1312yes—
203C22#8825111yescharacteristic
204C22C2×Q8×D1312yes—
205C22C2×Q8×D1311yescharacteristic
206C22#8825711yescharacteristic
207C4—24no—
208C4—22no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—138no—
213C4—264no—
214C4—264no—
215C4—522no—
216C2#1171929511yescharacteristic
217C2#1171932811yescharacteristic
218C2#1171933712yes—
219C2#1171942711yescharacteristic
220C2D13×C4⋊Q812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2551
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. #6101Q8semidirect
61. C4×Dic13Q8semidirect
114. Dic13C4⋊Q8semidirect
172. C13#2551semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881422
C13×#3952
#117186402
#117186372
#117186332
#117183172
#117183102
#117183082
#255113