Finite Group Databasebeta

← #13120042

Subgroups — #13120042

Order 1664.

500 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 177 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×#88142C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#384C211yesmaximal, characteristic
4#11718640C214yesmaximal
5#11718637C211yesmaximal, characteristic
6#11718635C211yesmaximal, characteristic
7#11718633C214yesmaximal
8C4×#6101C211yesmaximal, characteristic
9#11718590C211yesmaximal, characteristic
10C22×Dic26C2211yescharacteristic
11C22×Dic26C2212yes—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2214yes—
15C2×C42×C13C2211yescharacteristic
16C2×C4⋊Dic13C2211yescharacteristic
17C2×#6101C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2214yes—
20C2×#6101C2212yes—
21C2×C4×Dic13C2212yes—
22C2×C4×Dic13C2211yescharacteristic
23C2×C4×Dic13C2211yescharacteristic
24#88142—24no—
25#88141—24no—
26#88071C2214yes—
27#88071C2212yes—
28#88071C2214yes—
29C22×C4×C13C2312yes—
30C22×C4×C13C2312yes—
31C22×C4×C13C2312yes—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2312yes—
34C22×Dic13C2311yescharacteristic
35C22×Dic13C2312yes—
36C22×Dic13C2312yes—
37C22×Dic13C2311yescharacteristic
38C2×Dic26—22no—
39C2×Dic26—22no—
40C2×Dic26—24no—
41C2×Dic26—44no—
42C2×Dic26Q814yescomplemented
43C13×C4⋊C4—22no—
44C13×C4⋊C4—22no—
45C13×C4⋊C4—44no—
46C42×C13—22no—
47C4⋊Dic13—22no—
48#6101—24no—
49#6101—24no—
50#6101—44no—
51#6101Q818yescomplemented
52C4×Dic13—22no—
53C4×Dic13—24no—
54C4×Dic13D414yes—
55#2567—131nomaximal, Sylow
56C23×C13C2411yescharacteristic
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—24no—
62C2×C4×C13—24no—
63C2×C4×C13C2×D412yes—
64C2×C4×C13C2×Q814yes—
65C2×C4×C13C2×Q812yes—
66C2×C4×C13#4112yes—
67C2×Dic13—22no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—22no—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—24no—
74C2×Dic13C2×D412yes—
75C2×Dic13C2×D412yes—
76C2×Dic13C2×Q814yes—
77C2×Dic13C2×Q814yes—
78C2×Dic13C2×Q814yes—
79Dic26—28no—
80Dic26—48no—
81C2×C4⋊Q8—131no—
82C2×C4×Q8—131no—
83#395—134no—
84#391—131no—
85#391—131no—
86#389—134no—
87#384—131no—
88#384D1311yescharacteristic
89C4×C4⋊C4—131no—
90C22×C13C22×D411yescharacteristic
91C22×C13C22×Q811yescharacteristic
92C22×C13C22×Q812yes—
93C22×C13C2×#4111yescharacteristic
94C22×C13H(5,𝔽2)12yes—
95C4×C13—24no—
96C4×C13—42no—
97C4×C13—42no—
98C4×C13C22⋊Q814yes—
99Dic13—24no—
100Dic13—22no—
101Dic13—24no—
102Dic13—42no—
103Dic13C4⋊Q814yes—
104C22×Q8—131no—
105C22×Q8—132no—
106C4⋊Q8—264no—
107C4×Q8—264no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—131no—
112C2×C4⋊C4—134no—
113C2×C4⋊C4C2×D1311yescharacteristic
114C2×C4⋊C4C2×D1311yescharacteristic
115C2×C4⋊C4C2×D1314yes—
116C2×C42—131no—
117C2×C42—132no—
118C2×C42—131no—
119C2×C42C2×D1311yescharacteristic
120#95—132no—
121#95—134no—
122#95—134no—
123C2×C13C2×C22⋊Q811yescharacteristic
124C2×C13C2×C4⋊Q811yescharacteristic
125C2×C13#53511yescharacteristic
126C2×C13#55412yes—
127C2×C13Q8212yes—
128C2×Q8—134no—
129C2×Q8—264no—
130C2×Q8—262no—
131C2×Q8—262no—
132C2×Q8—524no—
133C22×C4—131no—
134C22×C4—132no—
135C22×C4—132no—
136C22×C4—131no—
137C22×C4—132no—
138C22×C4C22×D1312yes—
139C22×C4C22×D1312yes—
140C22×C4C22×D1312yes—
141C22×C4C22×D1311yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—44no—
145C4⋊C4—138no—
146C4⋊C4—264no—
147C4⋊C4—264no—
148C4⋊C4—262no—
149C4⋊C4—524no—
150C42—22no—
151C42—134no—
152C42—264no—
153C42—262no—
154C13#256711yescharacteristic, complemented, Sylow
155C23C23×D1311yescharacteristic
156Q8—268no—
157Q8—528no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—132no—
165C2×C4—134no—
166C2×C4—132no—
167C2×C4—134no—
168C2×C4—134no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4—262no—
172C2×C4—262no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—264no—
176C2×C4#612712yes—
177C2×C4D4×D1312yes—
178C2×C4Q8×D1314yes—
179C2×C4Q8×D1312yes—
180C22C2×#612711yescharacteristic
181C22C2×D4×D1311yescharacteristic
182C22#8825112yes—
183C22C2×Q8×D1311yescharacteristic
184C22C2×Q8×D1312yes—
185C4—24no—
186C4—42no—
187C4—42no—
188C4—134no—
189C4—264no—
190C4—264no—
191C4—262no—
192C4—522no—
193C4#8815014yes—
194C2C2×#8815011yescharacteristic
195C2#1171921612yes—
196C2#1171942011yescharacteristic
197C2#1171942712yes—
198C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#384C2
hypercenter#384D13
hypocenterC13#2567
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
42. C2×Dic26Q8semidirect
51. #6101Q8semidirect
154. C13#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881412
C13×#3842
#117186402
#117186372
#117186352
#117186332
C4×#61012
#117185902
#256713