Finite Group Databasebeta

← #13127761

Subgroups — #13127761

Order 1664.

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

normal subgroups only

This group has 360 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×#474C211yesmaximal, characteristic
4#11718739C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic
6#11718537C212yesmaximal, complemented
7#11718536C212yesmaximal, complemented
8#11718512C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718424C212yesmaximal
11#11718418C212yesmaximal
12C22×Dic26—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15Q8×Dic13—21no—
16#88198—21no—
17D4×Dic13C2212yes—
18C2×#6105C2211yescharacteristic
19#88178—21no—
20#88144C2212yes—
21#88143—22no—
22#88142C2212yes—
23#88141C2212yes—
24#88132—22no—
25#88123C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#107C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#102C2212yes—
31#88072C2211yescharacteristic
32#88057C2212yes—
33#88056C2212yes—
34#88055C2212yes—
35#88054C2212yes—
36#88050C2211yescharacteristic
37#88048C2211yescharacteristic
38#88047C2212yes—
39#88047C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×Dic26—21no—
46C2×Dic26—22no—
47C2×Dic26—44no—
48C2×Dic26D411yescharacteristic
49C2×Dic26C2311yescharacteristic
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2312yes—
53C13×C4⋊C4C2311yescharacteristic
54C13×C22⋊C4—21no—
55C42×C13C2311yescharacteristic
56C22⋊Dic13—22no—
57#6105Q814yescomplemented
58C4⋊Dic13—21no—
59C4⋊Dic13—22no—
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62C4⋊Dic13C2312yes—
63#6101—21no—
64#6101—22no—
65#6101—22no—
66#6101—22no—
67#6101D412yes—
68C4×Dic13—21no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#3386—131nomaximal, Sylow
74C23×C13—21no—
75Q8×C13—42no—
76D4×C13—21no—
77D4×C13C2×Q812yes—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—44no—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D412yes—
90Dic26—22no—
91Dic26—21no—
92Dic26—44no—
93Dic26—42no—
94Dic26C2×Q812yescomplemented
95C8×C13—22no—
96#1055—21no—
97#1055C2×Q812yescomplemented
98#557—131no—
99D4×Q8—131no—
100#501—132no—
101#500—131no—
102#478—132no—
103#477—132no—
104#475—131no—
105#474D1311yescharacteristic
106#446—131no—
107#440—132no—
108C4×SD16—131no—
109C22×C13—22no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13C22×D411yescharacteristic
113C4×C13—21no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13AGL(1,ℤ/8)12yes—
117C4×C13C22×Q811yescharacteristic
118C4×C132−1+411yescharacteristic
119Dic13—22no—
120Dic13—22no—
121Dic13—22no—
122Dic13—42no—
123Dic13—41no—
124C22×Q8—261no—
125C2×SD16—131no—
126C4⋊Q8—132no—
127C4⋊Q8—131no—
128C4⋊Q8—261no—
129C4⋊Q8C2×D1311yescharacteristic
130#125—132no—
131#125—262no—
132C22⋊Q8—262no—
133C22⋊Q8—261no—
134C4×Q8—131no—
135C4×Q8—132no—
136C4×Q8—131no—
137C4×Q8—261no—
138C4×D4—132no—
139C4×D4C2×D1311yescharacteristic
140#107—132no—
141#107—132no—
142#107C2×D1312yes—
143#106—132no—
144#106—131no—
145C4⋊C8—132no—
146C4⋊C8C2×D1311yescharacteristic
147#103—132no—
148#103—131no—
149#102—131no—
150#102C2×D1312yes—
151#97—132no—
152C4×C8—131no—
153C2×C13—42no—
154C2×C13D4×Q811yescharacteristic
155C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C13#57811yescharacteristic
157C2×Q8—21no—
158C2×Q8—131no—
159C2×Q8—131no—
160C2×Q8—262no—
161C2×Q8—261no—
162C2×Q8—524no—
163C2×D4C22×D1311yescharacteristic
164C22×C4—21no—
165C22×C4—262no—
166SD16—134no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8C22×D1312yes—
170C4⋊C4—21no—
171C4⋊C4—131no—
172C4⋊C4—132no—
173C4⋊C4—131no—
174C4⋊C4—132no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4C22×D1312yes—
182C4⋊C4C22×D1311yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—262no—
185C42—132no—
186C42—262no—
187C42—261no—
188C42C22×D1311yescharacteristic
189C13#338611yescharacteristic, complemented, Sylow
190C23—21no—
191Q8—42no—
192Q8—132no—
193Q8—262no—
194Q8—261no—
195Q8—524no—
196Q8—522no—
197D4—21no—
198D4Q8×D1312yes—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—524no—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—132no—
213C8—261no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—262no—
222C4—262no—
223C4—262no—
224C4—522no—
225C4—521no—
226C4#8816512yes—
227C4C2×Q8×D1311yescharacteristic
228C4#8825711yescharacteristic
229C2—42no—
230C2#1171933711yescharacteristic
231C2C2×#8816511yescharacteristic
232C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#474D13
hypocenterC13#3386
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
4. #11718739C2semidirect
6. #11718537C2semidirect
7. #11718536C2semidirect
8. #11718512C2semidirect
9. #11718492C2semidirect
57. #6105Q8semidirect
94. Dic26C2×Q8semidirect
97. #1055C2×Q8semidirect
189. C13#3386semidirect

Maximal subgroups

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

subgroupindex
#117194262
D4×Dic262
C13×#4742
#117187392
C4×#61052
#117185372
#117185362
#117185122
#117184922
#117184242
#117184182
#338613