Finite Group Databasebeta

← #13127644

Subgroups — #13127644

Order 1664.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719426C211yesmaximal, characteristic
3C13×#487C211yesmaximal, characteristic
4#11718755C211yesmaximal, characteristic
5#11718751C211yesmaximal, characteristic
6#11718458C212yesmaximal
7#11718457C212yesmaximal
8#11718454C212yesmaximal
9#11718450C212yesmaximal
10C4×Dic52C211yesmaximal, characteristic
11#11718340C211yesmaximal, characteristic
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14Q8×Dic13—21no—
15Q8×Dic13C2212yes—
16#88198—21no—
17#88198C2212yes—
18C2×#6107C2212yes—
19C2×Dic52C2211yescharacteristic
20#88144—21no—
21#88144C2212yes—
22#88143—22no—
23#88143—22no—
24#88141—21no—
25#88141C2212yes—
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#103C2212yes—
30C13×#103C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88075C2212yes—
33#88058C2211yescharacteristic
34#88056C2211yescharacteristic
35#88056C2211yescharacteristic
36#88055C2212yes—
37#88054C2212yes—
38#88050C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43C2×Dic26D411yescharacteristic
44C2×Dic26C2311yescharacteristic
45C2×Dic26C2311yescharacteristic
46C2×C8×C13C2311yescharacteristic
47C2×C8×C13C2311yescharacteristic
48C13×C4⋊C4—21no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C42×C13C2311yescharacteristic
53#6107—24no—
54C4⋊Dic13—22no—
55C4⋊Dic13—22no—
56C4⋊Dic13D411yescharacteristic
57C4⋊Dic13C2311yescharacteristic
58C4⋊Dic13C2311yescharacteristic
59#6101—21no—
60#6101—21no—
61#6101—22no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101D412yes—
66C4×Dic13—21no—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2312yes—
72Dic52—22no—
73#3374—131nomaximal, Sylow
74Q8×C13—22no—
75Q8×C13—22no—
76Q8×C13—42no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2411yescharacteristic
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13C2×D412yes—
87C2×Dic13C2×D412yes—
88Dic26—22no—
89Dic26—21no—
90Dic26—21no—
91Dic26—21no—
92Dic26#4112yes—
93C8×C13—21no—
94C8×C13—21no—
95#1055—22no—
96#557—131no—
97#557—131no—
98#491—132no—
99#487D1311yescharacteristic
100#479—132no—
101#475—131no—
102#462—131no—
103#462—132no—
104#446—131no—
105#441—132no—
106C4×Q16—131no—
107C22×C13C22×D411yescharacteristic
108C4×C13—21no—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13#13712yes—
112C4×C13C2×#4111yescharacteristic
113C4×C132−1+411yescharacteristic
114Dic13—22no—
115Dic13—22no—
116Dic13—22no—
117Dic13—41no—
118Dic13—41no—
119Dic13—41no—
120C2×Q16—132no—
121C2×Q16—131no—
122C4⋊Q8—132no—
123C4⋊Q8—261no—
124C4⋊Q8C2×D1311yescharacteristic
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—262no—
128#125—262no—
129#125—261no—
130C4×Q8—131no—
131C4×Q8—132no—
132C4×Q8—132no—
133C4×Q8—131no—
134C4×Q8—131no—
135C4×Q8—261no—
136C4×Q8—261no—
137#107—131no—
138#106—132no—
139C4⋊C8—132no—
140C4⋊C8—131no—
141#103—132no—
142#103—131no—
143#103—131no—
144#103—132no—
145#103C2×D1312yes—
146#103C2×D1312yes—
147#97—132no—
148C4×C8C2×D1311yescharacteristic
149C2×C13#54811yescharacteristic
150C2×C13C2×#13711yescharacteristic
151C2×C13#57811yescharacteristic
152C2×Q8—21no—
153C2×Q8—131no—
154C2×Q8—131no—
155C2×Q8—131no—
156C2×Q8C22×D1312yes—
157Q16—262no—
158Q16—264no—
159C2×C8—132no—
160C2×C8C22×D1311yescharacteristic
161C2×C8C22×D1311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—131no—
166C4⋊C4—132no—
167C4⋊C4—131no—
168C4⋊C4—131no—
169C4⋊C4—262no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4C22×D1312yes—
178C42—132no—
179C42—262no—
180C42—262no—
181C42—261no—
182C42—261no—
183C42C22×D1311yescharacteristic
184C13#337411yescharacteristic, complemented, Sylow
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—132no—
189Q8—262no—
190Q8—261no—
191Q8—261no—
192Q8—261no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—132no—
196C2×C4—132no—
197C2×C4—261no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4D4×D1311yescharacteristic
202C2×C4D4×D1311yescharacteristic
203C2×C4C23×D1311yescharacteristic
204C8—21no—
205C8—21no—
206C8—262no—
207C22C2×D4×D1311yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—262no—
212C4—262no—
213C4—262no—
214C4—521no—
215C4—521no—
216C4—521no—
217C4#8816912yes—
218C4#41×D1311yescharacteristic
219C4#8825711yescharacteristic
220C2#1171938211yescharacteristic
221C2C2×#8816911yescharacteristic
222C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socle, prime radicalC22×C13C22×D4
hypercenter#487D13
hypocenterC13#3374
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
184. C13#3374semidirect

Maximal subgroups

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

subgroupindex
#117194262
C13×#4872
#117187552
#117187512
#117184582
#117184572
#117184542
#117184502
C4×Dic522
#117183402
#337413