Finite Group Databasebeta

← #13127871

Subgroups — #13127871

Order 1664.

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

normal subgroups only

This group has 350 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, complemented
2#11719247C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic
4#11718828C212yesmaximal
5#11718827C212yesmaximal
6#11718753C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic
8#11718510C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718454C212yesmaximal, complemented
11#11718450C212yesmaximal, complemented
12C2×C13×SD16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15Q8×Dic13C2212yes—
16#88198C2212yes—
17C2×#6107C2212yes—
18C2×#6107C2212yes—
19#88190C2212yes—
20C2×#6105C2211yescharacteristic
21#88180—21no—
22#88178—21no—
23C2×Dic52C2212yes—
24#88144—21no—
25#88143—22no—
26#88141—21no—
27#88141C2212yes—
28#88133—22no—
29#88123C2211yescharacteristic
30C4×Dic26C2211yescharacteristic
31C4×Dic26C2211yescharacteristic
32C13×C4⋊C8C2211yescharacteristic
33C13×#103C2212yes—
34#88072C2211yescharacteristic
35#88056C2212yes—
36#88055C2212yes—
37#88054C2212yes—
38#88050C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×Dic26D411yescharacteristic
45C2×Dic26C2311yescharacteristic
46C2×Dic26C2312yes—
47C13×SD16—42no—
48C2×C8×C13C2312yes—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2311yescharacteristic
52C13×C22⋊C4—21no—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56#6107—24no—
57#6107—42no—
58#6105—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13—21no—
61C4⋊Dic13—22no—
62C4⋊Dic13D411yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64#6101—21no—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—21no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13C2312yes—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75Dic52—42no—
76#3398—131nomaximal, Sylow
77C23×C13—21no—
78Q8×C13—22no—
79Q8×C13—22no—
80D4×C13—21no—
81D4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D412yes—
93Dic26—22no—
94Dic26—21no—
95Dic26—22no—
96Dic26—21no—
97Dic26—22no—
98C8×C13—22no—
99#1055—21no—
100#1055#4112yes—
101#557—131no—
102#556—131no—
103#497—132no—
104#494—131no—
105#464—132no—
106#462—131no—
107#462—132no—
108#461D1311yescharacteristic
109#446—131no—
110#441—132no—
111C4×SD16—131no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13—41no—
115C22×C13C22×D411yescharacteristic
116C4×C13—21no—
117C4×C13—42no—
118C4×C13—41no—
119C4×C13#13712yes—
120C4×C13C2×#4111yescharacteristic
121C4×C13H(5,𝔽2)11yescharacteristic
122Dic13—22no—
123Dic13—22no—
124Dic13—41no—
125Dic13—42no—
126Dic13—41no—
127C2×Q16—132no—
128C2×Q16—132no—
129C2×Q16—132no—
130C2×SD16—131no—
131C2×SD16C2×D1312yes—
132C4⋊Q8—132no—
133C4⋊Q8—131no—
134C4⋊Q8C2×D1311yescharacteristic
135#126—262no—
136#125—262no—
137#125—261no—
138#124—132no—
139C22⋊Q8—261no—
140C4×Q8—131no—
141C4×Q8—132no—
142C4×Q8—132no—
143C4×Q8—131no—
144C4×Q8—261no—
145C4×D4C2×D1311yescharacteristic
146#117—261no—
147#106—131no—
148C4⋊C8—132no—
149C4⋊C8C2×D1311yescharacteristic
150#103—132no—
151#103—131no—
152#103C2×D1312yes—
153#102—131no—
154#97—132no—
155C4×C8—131no—
156C2×C13—81no—
157C2×C13#55011yescharacteristic
158C2×C13C2×#13711yescharacteristic
159C2×C13#57811yescharacteristic
160C2×Q8—131no—
161C2×Q8—132no—
162C2×Q8—131no—
163C2×Q8C22×D1312yes—
164C2×D4C22×D1311yescharacteristic
165C22×C4—21no—
166Q16—264no—
167Q16—522no—
168Q16—522no—
169SD16—42no—
170SD16—262no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8C22×D1312yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—131no—
177C4⋊C4—132no—
178C4⋊C4—131no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4C22×D1311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—262no—
189C22⋊C4—262no—
190C42—132no—
191C42—262no—
192C42—262no—
193C42—261no—
194C42C22×D1311yescharacteristic
195C13#339811yescharacteristic, complemented, Sylow
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—262no—
200Q8—261no—
201Q8—262no—
202Q8—261no—
203Q8—262no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—132no—
210C2×C4—132no—
211C2×C4—261no—
212C2×C4—262no—
213C2×C4—261no—
214C2×C4D4×D1311yescharacteristic
215C2×C4D4×D1311yescharacteristic
216C2×C4C23×D1311yescharacteristic
217C8—22no—
218C8—132no—
219C8—261no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D1311yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—262no—
228C4—262no—
229C4—521no—
230C4—522no—
231C4—521no—
232C4#8816912yes—
233C4#8825111yescharacteristic
234C4#41×D1311yescharacteristic
235C2—81no—
236C2#1171930411yescharacteristic
237C2C2×#8816911yescharacteristic
238C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#461D13
hypocenterC13#3398
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
6. #11718753C2semidirect
8. #11718510C2semidirect
9. #11718492C2semidirect
10. #11718454C2semidirect
11. #11718450C2semidirect
195. C13#3398semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192472
C13×#4612
#117188282
#117188272
#117187532
C4×#61052
#117185102
#117184922
#117184542
#117184502
#339813