Finite Group Databasebeta

← #13127581

Subgroups — #13127581

Order 1664.

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

normal subgroups only

This group has 338 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#11719437C211yesmaximal, characteristic
2#11719427C211yesmaximal, characteristic, complemented
3C13×#487C211yesmaximal, characteristic, complemented
4#11718751C211yesmaximal, characteristic, complemented
5#11718745C211yesmaximal, characteristic
6#11718459C212yesmaximal
7#11718456C212yesmaximal
8#11718452C212yesmaximal, complemented
9#11718450C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic
11#11718340C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88201C2212yes—
15Q8×Dic13C2212yes—
16#88198—22no—
17C2×#6107C2212yes—
18C2×#6095C2211yescharacteristic
19#88152—22no—
20#88151—21no—
21#88146—21no—
22#88142—21no—
23#88142C2212yes—
24#88141—21no—
25#88141C2212yes—
26C4×D52C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#103C2212yes—
30C13×#103C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88075C2212yes—
33#88061C2211yescharacteristic
34#88057C2211yescharacteristic
35#88056C2211yescharacteristic
36#88055C2212yes—
37#88054C2212yes—
38#88049C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13C2312yes—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×Dic26—22no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2311yescharacteristic
48C2×C8×C13C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C42×C13C2311yescharacteristic
55#6107—24no—
56#6103—21no—
57#6103—22no—
58#6103—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62C4⋊Dic13C2311yescharacteristic
63#6101—21no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2312yes—
72#6095—22no—
73#3369—131nomaximal, Sylow
74C22×D13—21no—
75Q8×C13—22no—
76Q8×C13—22no—
77Q8×C13—81no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13C2×D412yes—
87C2×Dic13C2×D412yes—
88D52—21no—
89D52—21no—
90C4×D13—42no—
91Dic26—22no—
92Dic26—21no—
93Dic26—82no—
94Dic26#4112yes—
95C8×C13—21no—
96C8×C13—21no—
97#1055—22no—
98Q82—131no—
99#556—131no—
100#489—132no—
101#487D1311yescharacteristic, complemented
102#476—131no—
103#475—132no—
104#464—132no—
105#462—131no—
106#446—131no—
107#441—132no—
108C4×SD16—131no—
109C22×C13C22×D411yescharacteristic
110C2×D13—41no—
111C2×D13—41no—
112C2×D13—41no—
113C4×C13—21no—
114C4×C13—42no—
115C4×C13—42no—
116C4×C13#13712yes—
117C4×C13C2×#4111yescharacteristic
118C4×C132−1+411yescharacteristic
119Dic13—22no—
120Dic13—22no—
121Dic13—22no—
122Dic13—41no—
123Dic13—41no—
124C2×Q16—132no—
125C2×SD16—131no—
126C4⋊Q8—132no—
127C4⋊Q8—261no—
128C4⋊Q8—262no—
129C4⋊Q8C2×D1311yescharacteristic
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#124—132no—
133C22⋊Q8—261no—
134C4×Q8—131no—
135C4×Q8—132no—
136C4×Q8—132no—
137C4×Q8—131no—
138C4×Q8—261no—
139C4×D4—131no—
140#117—261no—
141#106—131no—
142#106—132no—
143C4⋊C8—132no—
144C4⋊C8—131no—
145#103—132no—
146#103—131no—
147#103C2×D1312yes—
148#103C2×D1312yes—
149#102—131no—
150#102—132no—
151#97—132no—
152C4×C8C2×D1311yescharacteristic
153C2×C13#54811yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57711yescharacteristic
156D13—81no—
157C2×Q8—21no—
158C2×Q8—131no—
159C2×Q8—131no—
160C2×Q8—262no—
161C2×Q8C22×D1312yes—
162C2×D4—131no—
163C22×C4—261no—
164Q16—264no—
165SD16—262no—
166C2×C8—132no—
167C2×C8C22×D1311yescharacteristic
168C2×C8C22×D1311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—131no—
173C4⋊C4—132no—
174C4⋊C4—131no—
175C4⋊C4—131no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4C22×D1312yes—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C22⋊C4—261no—
184C42—132no—
185C42—262no—
186C42—262no—
187C42—261no—
188C42C22×D1311yescharacteristic
189C13#336911yescharacteristic, complemented, Sylow
190C23—261no—
191Q8—22no—
192Q8—22no—
193Q8—81no—
194Q8—132no—
195Q8—262no—
196Q8—261no—
197Q8—1042no—
198D4—261no—
199D4—261no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—522no—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—21no—
212C8—21no—
213C8—262no—
214C22—521no—
215C22—521no—
216C22—521no—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—42no—
220C4—42no—
221C4—262no—
222C4—262no—
223C4—262no—
224C4—521no—
225C4—521no—
226C4#8817212yes—
227C4#41×D1311yescharacteristic
228C4#8825711yescharacteristic
229C2—1041no—
230C2#1171938211yescharacteristic
231C2#1171946711yescharacteristic
232C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#487C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#487D13
hypocenterC13#3369
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
2. #11719427C2semidirect
3. C13×#487C2semidirect
4. #11718751C2semidirect
8. #11718452C2semidirect
9. #11718450C2semidirect
11. #11718340C2semidirect
101. #487D13semidirect
189. C13#3369semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117194272
C13×#4872
#117187512
#117187452
#117184592
#117184562
#117184522
#117184502
C4×#60952
#117183402
#336913