Finite Group Databasebeta

← #13127726

Subgroups — #13127726

Order 1664.

324 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719426C211yesmaximal, characteristic
2#11719275C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic
4#11718739C211yesmaximal, characteristic
5C4×#6107C211yesmaximal, characteristic
6#11718519C212yesmaximal
7#11718518C212yesmaximal
8#11718512C211yesmaximal, characteristic
9#11718491C211yesmaximal, characteristic
10#11718460C212yesmaximal
11#11718451C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×Q8×C13C2211yescharacteristic
14Q8×Dic13—21no—
15Q8×Dic13C2212yes—
16#88198—21no—
17C2×#6107C2211yescharacteristic
18#88144—22no—
19#88144C2212yes—
20#88144C2212yes—
21#88143—22no—
22#88141C2212yes—
23#88123—21no—
24#88123C2211yescharacteristic
25C4×Dic26—21no—
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#106C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2211yescharacteristic
32#88057C2212yes—
33#88056C2212yes—
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2211yescharacteristic
37#88047C2211yescharacteristic
38#88047C2212yes—
39#88047C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2311yescharacteristic
43C2×Dic26—21no—
44C2×Dic26D411yescharacteristic
45C2×Dic26C2311yescharacteristic
46C2×C8×C13C2312yes—
47C13×C4⋊C4—21no—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C13×C4⋊C4C2311yescharacteristic
51C42×C13—21no—
52C42×C13C2311yescharacteristic
53#6107Q814yescomplemented
54C4⋊Dic13—21no—
55C4⋊Dic13—22no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13D411yescharacteristic
59C4⋊Dic13C2311yescharacteristic
60C4⋊Dic13C2312yes—
61#6101—21no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101D412yes—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#3383—131nomaximal, Sylow
73Q8×C13—21no—
74Q8×C13—42no—
75Q8×C13C2×Q812yes—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2411yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13C2×D412yes—
86C2×Dic13C2×D412yes—
87Dic26—22no—
88Dic26—21no—
89Dic26—42no—
90Dic26C2×Q812yes—
91C8×C13—22no—
92#1055—21no—
93#1055C2×Q812yes—
94#557—131no—
95#557—131no—
96#500—131no—
97#499—132no—
98#479—132no—
99#479—132no—
100#475—131no—
101#475D1311yescharacteristic
102C8×Q8—131no—
103C4×Q16—131no—
104C4×Q16—132no—
105C22×C13C22×D411yescharacteristic
106C4×C13—22no—
107C4×C13—21no—
108C4×C13—42no—
109C4×C13—41no—
110C4×C13#13512yes—
111C4×C13C22×Q811yescharacteristic
112C4×C132−1+411yescharacteristic
113Dic13—22no—
114Dic13—22no—
115Dic13—22no—
116Dic13—42no—
117Dic13—41no—
118C2×Q16—131no—
119C4⋊Q8—131no—
120C4⋊Q8—261no—
121C4⋊Q8—261no—
122C4⋊Q8C2×D1311yescharacteristic
123#125—132no—
124#125—132no—
125#125—262no—
126#125—262no—
127C4×Q8—131no—
128C4×Q8—132no—
129C4×Q8—132no—
130C4×Q8—131no—
131C4×Q8—261no—
132C4×Q8—261no—
133C4×Q8C2×D1311yescharacteristic
134#107—131no—
135#107—132no—
136#107—132no—
137#106—132no—
138#106C2×D1312yes—
139C4⋊C8—132no—
140C4⋊C8C2×D1311yescharacteristic
141#103—131no—
142#103—132no—
143#103—131no—
144#103C2×D1312yes—
145C4×C8—132no—
146C4×C8—131no—
147C2×C13D4×Q811yescharacteristic
148C2×C13C2×#13511yescharacteristic
149C2×C13#57811yescharacteristic
150C2×Q8—21no—
151C2×Q8—131no—
152C2×Q8—131no—
153C2×Q8—261no—
154C2×Q8C22×D1311yescharacteristic
155Q16—134no—
156C2×C8—131no—
157C2×C8—131no—
158C2×C8C22×D1312yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—131no—
162C4⋊C4—132no—
163C4⋊C4—131no—
164C4⋊C4—132no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4C22×D1311yescharacteristic
174C4⋊C4C22×D1312yes—
175C42—21no—
176C42—132no—
177C42—262no—
178C42—262no—
179C42—261no—
180C42C22×D1311yescharacteristic
181C13#338311yescharacteristic, complemented, Sylow
182Q8—21no—
183Q8—42no—
184Q8—132no—
185Q8—262no—
186Q8—261no—
187Q8—522no—
188Q8Q8×D1312yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—132no—
193C2×C4—132no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—262no—
197C2×C4D4×D1311yescharacteristic
198C2×C4D4×D1311yescharacteristic
199C2×C4C23×D1311yescharacteristic
200C8—22no—
201C8—132no—
202C8—261no—
203C22C2×D4×D1311yescharacteristic
204C4—21no—
205C4—22no—
206C4—42no—
207C4—41no—
208C4—262no—
209C4—262no—
210C4—262no—
211C4—522no—
212C4—521no—
213C4#8817012yes—
214C4C2×Q8×D1311yescharacteristic
215C4#8825711yescharacteristic
216C2#1171933711yescharacteristic
217C2C2×#8817011yescharacteristic
218C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socle, prime radicalC22×C13C22×D4
hypercenter#475D13
hypocenterC13#3383
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
53. #6107Q8semidirect
181. C13#3383semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192752
C13×#4752
#117187392
C4×#61072
#117185192
#117185182
#117185122
#117184912
#117184602
#117184512
#338313