Finite Group Databasebeta

← #13125793

Subgroups — #13125793

Order 1664.

394 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719433C211yesmaximal, characteristic, complemented
2#11719421C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718737C211yesmaximal, characteristic, complemented
6#11718444C214yesmaximal, complemented
7#11718428C214yesmaximal, complemented
8#11718360C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6129C2212yes—
11C13×C4⋊Q8C2211yescharacteristic
12C13×#127C2211yescharacteristic
13#88200—21no—
14Q8×Dic13—21no—
15#88192—21no—
16#88192—21no—
17#88190C2212yes—
18D4×Dic13—21no—
19D4×Dic13—21no—
20C2×#6105C2214yes—
21C2×Dic52C2214yes—
22#88151C2212yes—
23#88146—21no—
24#88144—21no—
25#88141C2212yes—
26C42×D13C2211yescharacteristic
27#88123C2211yescharacteristic
28#88123C2211yescharacteristic
29C13×#102C2214yes—
30C4×C8×C13C2211yescharacteristic
31#88060C2212yes—
32#88054C2212yes—
33#88050C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C2×C22⋊D13—22no—
40C22×Dic13—22no—
41#6129—44no—
42C2×C4×D13D411yescharacteristic
43C2×C4×D13D411yescharacteristic
44C2×C4×D13C2311yescharacteristic
45C2×Dic26C2312yes—
46C2×Dic26C2312yes—
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51C22⋊Dic13—22no—
52C22⋊Dic13—22no—
53#6105—44no—
54#6103—22no—
55C4⋊Dic13—21no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—21no—
59C4⋊Dic13—22no—
60#6101—22no—
61C4×Dic13—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66Dic52—44no—
67#3210—131nomaximal, Sylow
68C23×C13—22no—
69C22×D13C2×D411yescharacteristic
70Q8×C13—42no—
71D4×C13—24no—
72D4×C13—42no—
73D4×C13—42no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2411yescharacteristic
78C22⋊D13—44no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—44no—
82C2×Dic13C2×D411yescharacteristic
83C2×Dic13C2×D411yescharacteristic
84C2×Dic13C2×D411yescharacteristic
85C4×D13—22no—
86C4×D13—22no—
87C4×D13—22no—
88Dic26—24no—
89Dic26—24no—
90C8×C13—22no—
91#1055—22no—
92#533—131no—
93#532—131no—
94#494—131no—
95#492—131no—
96#487—131no—
97#486D1311yescharacteristic, complemented
98#464—134no—
99#452—134no—
100#431—131no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13C22×D411yescharacteristic
105C2×D13—21no—
106C2×D13—21no—
107C2×D13—21no—
108C4×C13—42no—
109C4×C13#13512yes—
110C4×C13#13712yes—
111C4×C13H(5,𝔽2)12yes—
112Dic13—21no—
113Dic13—21no—
114Dic13—21no—
115Dic13—42no—
116Dic13—42no—
117C2×#41—132no—
118C2×Q16—134no—
119C2×SD16—134no—
120C4⋊Q8—131no—
121C4⋊Q8—131no—
122C4⋊Q8C2×D1311yescharacteristic
123#127C2×D1311yescharacteristic
124#125—261no—
125#124—132no—
126C22⋊Q8—132no—
127C22⋊Q8—261no—
128#121—261no—
129#121—261no—
130C4×Q8—132no—
131C4×Q8—261no—
132C4×D4—261no—
133C4×D4—261no—
134#117—261no—
135C2×C42—131no—
136C4⋊C8—132no—
137#103—134no—
138#102C2×D1314yes—
139C22⋊C8—132no—
140C4×C8—131no—
141C4×C8C2×D1311yescharacteristic
142C2×C13—82no—
143C2×C13#53511yescharacteristic
144C2×C13C2×#13511yescharacteristic
145C2×C13C2×#13711yescharacteristic
146D13—41no—
147#41—524no—
148C2×Q8—21no—
149C2×Q8—132no—
150C2×Q8—132no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—262no—
154C2×D4C22×D1312yes—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—262no—
159Q16—524no—
160SD16—524no—
161C2×C8—132no—
162C2×C8C22×D1312yes—
163C4⋊C4—21no—
164C4⋊C4—262no—
165C4⋊C4—262no—
166C4⋊C4—261no—
167C4⋊C4—261no—
168C4⋊C4—261no—
169C4⋊C4—261no—
170C4⋊C4C22×D1312yes—
171C22⋊C4—262no—
172C22⋊C4—262no—
173C22⋊C4—262no—
174C42—131no—
175C42—131no—
176C42—131no—
177C42—262no—
178C42C22×D1311yescharacteristic
179C13#321011yescharacteristic, complemented, Sylow
180C23—22no—
181C23—131no—
182Q8—42no—
183Q8—264no—
184Q8—264no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—524no—
189C2×C4—22no—
190C2×C4—131no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—524no—
199C2×C4D4×D1311yescharacteristic
200C2×C4D4×D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—22no—
203C8—262no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—261no—
208C22—261no—
209C22—261no—
210C22C2×D4×D1311yescharacteristic
211C4—42no—
212C4—261no—
213C4—261no—
214C4—261no—
215C4—522no—
216C4—522no—
217C4#8816612yes—
218C4#8816912yes—
219C4#8825612yes—
220C2—82no—
221C2—521no—
222C2#1171937911yescharacteristic
223C2C2×#8816611yescharacteristic
224C2C2×#8816911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719421C2
hypercenter#486D13
hypocenterC13#3210
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#486C2semidirect
4. #11718754C2semidirect
5. #11718737C2semidirect
6. #11718444C2semidirect
7. #11718428C2semidirect
8. #11718360C2semidirect
9. #11718346C2semidirect
97. #486D13semidirect
179. C13#3210semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117194212
C13×#4862
#117187542
#117187372
#117184442
#117184282
#117183602
#117183462
#321013