Finite Group Databasebeta

← #13126231

Subgroups — #13126231

Order 1664.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#11719305C212yesmaximal, complemented
2C13×#469C211yesmaximal, characteristic
3#11718814C212yesmaximal, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718779C211yesmaximal, characteristic, complemented
6#11718703C212yesmaximal, complemented
7#11718518C212yesmaximal, complemented
8#11718428C212yesmaximal, complemented
9#11718424C212yesmaximal, complemented
10C2×C13×D8C2211yescharacteristic
11C2×C13×M16C2211yescharacteristic
12C13×#121C2212yes—
13#88190C2212yes—
14#88189—22no—
15D4×Dic13—22no—
16D4×Dic13C2212yes—
17C2×#6105C2212yes—
18#88178C2212yes—
19C2×C4×Dic13C2211yescharacteristic
20C2×#6099C2211yescharacteristic
21C2×Dic52C2211yescharacteristic
22#88144C2212yes—
23#88141C2212yes—
24#88133—22no—
25#88131—22no—
26C13×#106C2211yescharacteristic
27C13×#102C2212yes—
28#88072C2212yes—
29#88057C2211yescharacteristic
30#88056C2212yes—
31#88054C2212yes—
32#88054C2212yes—
33#88050C2212yes—
34#88047C2212yes—
35C2×D4×C13—22no—
36C2×D4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13—22no—
39C22×Dic13D412yes—
40C2×Dic26C2312yes—
41C13×D8—41no—
42C13×M16—41no—
43C2×C8×C13C2311yescharacteristic
44C2×C8×C13C2311yescharacteristic
45C13×C4⋊C4C2312yes—
46C13×C22⋊C4—22no—
47C22⋊Dic13—22no—
48C22⋊Dic13—22no—
49C22⋊Dic13—22no—
50C22⋊Dic13—22no—
51#6105—42no—
52C4⋊Dic13—22no—
53C4⋊Dic13C2312yes—
54#6101—22no—
55#6101—22no—
56#6101—22no—
57C4×Dic13—22no—
58C4×Dic13D411yescharacteristic
59C4×Dic13D411yescharacteristic
60C4×Dic13C2312yes—
61#6099—41no—
62C2×#1055C2312yes—
63Dic52—41no—
64#3256—131nomaximal, Sylow
65C23×C13—22no—
66C23×C13C2×D411yescharacteristic
67D4×C13—22no—
68D4×C13—22no—
69D4×C13—44no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2411yescharacteristic
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—42no—
78C2×Dic13—44no—
79C2×Dic13C2×D412yes—
80C2×Dic13C2×D412yes—
81Dic26—22no—
82Dic26—22no—
83C8×C13—21no—
84C8×C13—21no—
85#1055—22no—
86#529—132no—
87#479—132no—
88#478—132no—
89#470—131no—
90#469D1311yescharacteristic
91#468—132no—
92#464—132no—
93#463—132no—
94#423—131no—
95C22×C13—21no—
96C22×C13—22no—
97C22×C13—42no—
98C22×C13—42no—
99C22×C13—42no—
100C22×C13C22×D411yescharacteristic
101C4×C13—21no—
102C4×C13—42no—
103C4×C13H(5,𝔽2)11yescharacteristic
104C4×C132−1+411yescharacteristic
105Dic13—22no—
106Dic13—22no—
107Dic13—42no—
108Dic13—42no—
109C2×Q16—131no—
110C2×SD16—132no—
111C2×D8C2×D1311yescharacteristic
112C2×M16—131no—
113C2×M16C2×D1311yescharacteristic
114#126—262no—
115#125—132no—
116#124—132no—
117#123—262no—
118C22⋊Q8—132no—
119#121C2×D1312yes—
120C4×Q8—132no—
121C4×D4—132no—
122C4×D4—262no—
123#117—262no—
124C2×C42—131no—
125#107—132no—
126#106—131no—
127#106C2×D1311yescharacteristic
128C4⋊C8—132no—
129C4⋊C8—132no—
130#103—132no—
131#103—132no—
132#102—132no—
133#102C2×D1312yes—
134C2×C13—41no—
135C2×C13—82no—
136C2×C13#53711yescharacteristic
137C2×C13#57512yes—
138C2×Q8—132no—
139C2×D4—22no—
140C2×D4C22×D1312yes—
141C22×C4—132no—
142C22×C4—262no—
143C22×C4C22×D1311yescharacteristic
144Q16—521no—
145SD16—522no—
146D8—41no—
147M16—41no—
148M16—521no—
149C2×C8—132no—
150C2×C8C22×D1311yescharacteristic
151C2×C8C22×D1311yescharacteristic
152C4⋊C4—132no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4—262no—
156C4⋊C4—262no—
157C4⋊C4C22×D1312yes—
158C22⋊C4—22no—
159C22⋊C4—262no—
160C22⋊C4—262no—
161C22⋊C4—262no—
162C22⋊C4—262no—
163C42—131no—
164C42—131no—
165C42—132no—
166C42—262no—
167C13#325611yescharacteristic, complemented, Sylow
168C23—22no—
169C23D4×D1311yescharacteristic
170Q8—262no—
171Q8—262no—
172D4—22no—
173D4—22no—
174D4—44no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—132no—
179C2×C4—132no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—522no—
183C2×C4—524no—
184C2×C4D4×D1311yescharacteristic
185C2×C4C23×D1311yescharacteristic
186C8—21no—
187C8—21no—
188C8—262no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D1311yescharacteristic
195C4—21no—
196C4—42no—
197C4—262no—
198C4—262no—
199C4—522no—
200C4—522no—
201C4#8825111yescharacteristic
202C4#8825711yescharacteristic
203C2—41no—
204C2—82no—
205C2#1171930211yescharacteristic
206C2#1171947812yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3256
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719305C2semidirect
3. #11718814C2semidirect
4. #11718798C2semidirect
5. #11718779C2semidirect
6. #11718703C2semidirect
7. #11718518C2semidirect
8. #11718428C2semidirect
9. #11718424C2semidirect
167. C13#3256semidirect

Maximal subgroups

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

subgroupindex
#117193052
C13×#4692
#117188142
#117187982
#117187792
#117187032
#117185182
#117184282
#117184242
#325613