Finite Group Databasebeta

← #13127473

Subgroups — #13127473

Order 1664.

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

normal subgroups only

This group has 370 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, complemented
2D4×Dic26C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic
4#11718823C212yesmaximal
5SD16×Dic13C212yesmaximal
6#11718742C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic
8#11718512C211yesmaximal, characteristic, complemented
9#11718491C211yesmaximal, characteristic, complemented
10#11718453C212yesmaximal, complemented
11#11718452C212yesmaximal, complemented
12C22×Dic26—21no—
13C2×C13×SD16C2212yes—
14C13×C4⋊Q8C2211yescharacteristic
15C4×D4×C13C2211yescharacteristic
16Q8×Dic13C2212yes—
17#88198C2212yes—
18D4×Dic13C2212yes—
19C2×#6105C2211yescharacteristic
20#88178—21no—
21#88144—21no—
22#88143—22no—
23#88142C2212yes—
24#88141—21no—
25#88132—22no—
26#88123C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2211yescharacteristic
34#88057C2212yes—
35#88056C2212yes—
36#88054C2212yes—
37C8×Dic13C2212yes—
38#88050C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×Dic26—21no—
46C2×Dic26—22no—
47C2×Dic26—44no—
48C2×Dic26D411yescharacteristic
49C2×Dic26C2311yescharacteristic
50C13×SD16—24no—
51C2×C8×C13C2312yes—
52C13×C4⋊C4—21no—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2311yescharacteristic
55C13×C22⋊C4—21no—
56C42×C13C2311yescharacteristic
57C22⋊Dic13—22no—
58#6105—22no—
59C4⋊Dic13—21no—
60C4⋊Dic13—22no—
61C4⋊Dic13D411yescharacteristic
62C4⋊Dic13C2311yescharacteristic
63C4⋊Dic13C2312yes—
64#6101—21no—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—21no—
70C4×Dic13—22no—
71C4×Dic13C2312yes—
72C2×#1055C2311yescharacteristic
73C2×#1055C2311yescharacteristic
74#3359—131nomaximal, Sylow
75C23×C13—21no—
76Q8×C13—22no—
77Q8×C13—22no—
78D4×C13—21no—
79D4×C13#4112yes—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—42no—
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2411yescharacteristic
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—44no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92Dic26—21no—
93Dic26—21no—
94Dic26—42no—
95Dic26—44no—
96Dic26SD1614yescomplemented
97C8×C13—22no—
98#1055—21no—
99#1055—21no—
100#557—131no—
101D4×Q8—131no—
102#487—131no—
103#487—132no—
104#475—131no—
105#475—132no—
106#461—132no—
107#461D1311yescharacteristic
108C8×Q8—131no—
109C4×SD16—132no—
110C4×SD16—131no—
111C22×C13—22no—
112C22×C13—41no—
113C22×C13—41no—
114C22×C13C22×D411yescharacteristic
115C4×C13—21no—
116C4×C13—42no—
117C4×C13—41no—
118C4×C13C2×SD1612yes—
119C4×C13C2×#4111yescharacteristic
120C4×C132−1+411yescharacteristic
121Dic13—22no—
122Dic13—41no—
123Dic13—42no—
124Dic13—41no—
125Dic13C2×SD1614yes—
126C22×Q8—261no—
127C2×SD16—131no—
128C2×SD16C2×D1312yes—
129C4⋊Q8—132no—
130C4⋊Q8—132no—
131C4⋊Q8—131no—
132C4⋊Q8C2×D1311yescharacteristic
133#125—262no—
134#125—261no—
135C22⋊Q8—262no—
136C22⋊Q8—261no—
137C4×Q8—131no—
138C4×Q8—132no—
139C4×Q8—131no—
140C4×Q8—261no—
141C4×D4—132no—
142C4×D4C2×D1311yescharacteristic
143#106—132no—
144#106—131no—
145C4⋊C8—132no—
146C4⋊C8C2×D1311yescharacteristic
147#103—132no—
148#103—132no—
149#103—132no—
150#103—131no—
151#103C2×D1312yes—
152#102—131no—
153C4×C8—132no—
154C4×C8—131no—
155C2×C13—42no—
156C2×C13#54811yescharacteristic
157C2×C13C22×SD1611yescharacteristic
158C2×C13#57811yescharacteristic
159C2×Q8—131no—
160C2×Q8—131no—
161C2×Q8—262no—
162C2×Q8—261no—
163C2×Q8—524no—
164C2×Q8C22×D1312yes—
165C2×D4C22×D1311yescharacteristic
166C22×C4—21no—
167C22×C4—262no—
168SD16—24no—
169SD16—262no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8C22×D1312yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—132no—
176C4⋊C4—131no—
177C4⋊C4—131no—
178C4⋊C4—132no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4C22×D1311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—262no—
188C42—132no—
189C42—262no—
190C42—261no—
191C42C22×D1311yescharacteristic
192C13#335911yescharacteristic, complemented, Sylow
193C23—21no—
194Q8—22no—
195Q8—22no—
196Q8—134no—
197Q8—261no—
198Q8—261no—
199Q8—524no—
200Q8—522no—
201D4—21no—
202D4#612912yes—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—132no—
207C2×C4—132no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—262no—
211C2×C4—524no—
212C2×C4D4×D1311yescharacteristic
213C2×C4D4×D1311yescharacteristic
214C2×C4C23×D1311yescharacteristic
215C8—22no—
216C8—261no—
217C8—261no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22C2×D4×D1311yescharacteristic
222C4—21no—
223C4—41no—
224C4—42no—
225C4—134no—
226C4—262no—
227C4—522no—
228C4—521no—
229C4—521no—
230C4SD16×D1312yes—
231C4C2×#612911yescharacteristic
232C4#8825711yescharacteristic
233C2—42no—
234C2#1171930311yescharacteristic
235C2C2×SD16×D1311yescharacteristic
236C2#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#3359
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. #11718742C2semidirect
8. #11718512C2semidirect
9. #11718491C2semidirect
10. #11718453C2semidirect
11. #11718452C2semidirect
96. Dic26SD16semidirect
192. C13#3359semidirect

Maximal subgroups

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

subgroupindex
#117194262
D4×Dic262
C13×#4612
#117188232
SD16×Dic132
#117187422
C4×#61052
#117185122
#117184912
#117184532
#117184522
#335913