Finite Group Databasebeta

← #13127580

Subgroups — #13127580

Order 1664.

338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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
2Q8×Dic26C211yesmaximal, characteristic, complemented
3C13×#462C211yesmaximal, characteristic, complemented
4#11718846C212yesmaximal
5#11718845C212yesmaximal, complemented
6#11718742C211yesmaximal, characteristic, complemented
7C4×#6106C211yesmaximal, characteristic
8#11718503C211yesmaximal, characteristic
9#11718492C211yesmaximal, characteristic, complemented
10#11718456C212yesmaximal
11#11718452C212yesmaximal, complemented
12C2×C13×Q16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×Q8×C13C2211yescharacteristic
15#88201C2212yes—
16Q8×Dic13C2212yes—
17Q8×Dic13C2212yes—
18C2×#6106C2211yescharacteristic
19#88152—22no—
20#88151—21no—
21#88146—21no—
22#88142—22no—
23#88142C2212yes—
24C4×D52C2211yescharacteristic
25#88123—21no—
26#88123C2211yescharacteristic
27C4×Dic26—21no—
28C4×Dic26C2211yescharacteristic
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2211yescharacteristic
32#88075C2212yes—
33#88075C2212yes—
34#88061C2212yes—
35#88057C2212yes—
36#88055C2212yes—
37#88054C2212yes—
38#88049C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×Q8×C13C2311yescharacteristic
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×Dic26—21no—
46C2×Dic26—22no—
47C2×Dic26D411yescharacteristic
48C13×Q16—24no—
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2311yescharacteristic
54C42×C13—21no—
55C42×C13C2311yescharacteristic
56#6106—22no—
57#6103—21no—
58#6103—22no—
59#6103—22no—
60C4⋊Dic13—21no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13D411yescharacteristic
64C4⋊Dic13C2312yes—
65C4⋊Dic13C2311yescharacteristic
66#6101—22no—
67#6101D412yes—
68C4×Dic13—22no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#3369—131nomaximal, Sylow
74C22×D13—21no—
75Q8×C13—21no—
76Q8×C13—22no—
77Q8×C13—22no—
78Q8×C13#4112yes—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2411yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89D52—21no—
90D52—21no—
91C4×D13—42no—
92Dic26—22no—
93Dic26—82no—
94Dic26—81no—
95C8×C13—22no—
96#1055—21no—
97#1055—21no—
98Q82—131no—
99#556—131no—
100#489—132no—
101#487—131no—
102#476—131no—
103#475—132no—
104#464—132no—
105#462D1311yescharacteristic, complemented
106#446—131no—
107#441—132no—
108C4×SD16—131no—
109C22×C13C22×D411yescharacteristic
110C2×D13—41no—
111C2×D13—41no—
112C2×D13—41no—
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—42no—
116C4×C13—41no—
117C4×C13#13712yes—
118C4×C13C2×#4111yescharacteristic
119C4×C132−1+411yescharacteristic
120Dic13—22no—
121Dic13—22no—
122Dic13—41no—
123Dic13—42no—
124C2×Q16C2×D1312yes—
125C2×SD16—131no—
126C4⋊Q8—132no—
127C4⋊Q8—131no—
128C4⋊Q8—261no—
129C4⋊Q8—262no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#124—132no—
133C22⋊Q8—261no—
134C4×Q8—131no—
135C4×Q8—132no—
136C4×Q8—132no—
137C4×Q8—261no—
138C4×Q8C2×D1311yescharacteristic
139C4×D4—131no—
140#117—261no—
141#106—132no—
142#106—131no—
143C4⋊C8—132no—
144C4⋊C8C2×D1311yescharacteristic
145#103—131no—
146#103—132no—
147#103—132no—
148#103C2×D1312yes—
149#102—132no—
150#102—131no—
151#97—132no—
152C4×C8—131no—
153C2×C13#54811yescharacteristic
154C2×C13C2×#13711yescharacteristic
155C2×C13#57711yescharacteristic
156D13—81no—
157C2×Q8—131no—
158C2×Q8—262no—
159C2×Q8—261no—
160C2×Q8C22×D1312yes—
161C2×Q8C22×D1311yescharacteristic
162C2×D4—131no—
163C22×C4—261no—
164Q16—24no—
165SD16—262no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8C22×D1312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—131no—
173C4⋊C4—132no—
174C4⋊C4—132no—
175C4⋊C4—131no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4C22×D1311yescharacteristic
181C22⋊C4—262no—
182C22⋊C4—262no—
183C22⋊C4—261no—
184C42—21no—
185C42—132no—
186C42—262no—
187C42—262no—
188C42C22×D1311yescharacteristic
189C13#336911yescharacteristic, complemented, Sylow
190C23—261no—
191Q8—21no—
192Q8—22no—
193Q8—22no—
194Q8—262no—
195Q8—1041no—
196Q8—1042no—
197Q8#612912yes—
198D4—261no—
199D4—261no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—522no—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—261no—
213C8—261no—
214C22—521no—
215C22—521no—
216C22—521no—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—22no—
220C4—41no—
221C4—42no—
222C4—262no—
223C4—262no—
224C4—521no—
225C4—522no—
226C4#8817212yes—
227C4C2×#612911yescharacteristic
228C4#8825711yescharacteristic
229C2—1041no—
230C2#1171930311yescharacteristic
231C2C2×#8817211yescharacteristic
232C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#462D13
hypocenterC13#3369
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. Q8×Dic26C2semidirect
3. C13×#462C2semidirect
5. #11718845C2semidirect
6. #11718742C2semidirect
9. #11718492C2semidirect
11. #11718452C2semidirect
105. #462D13semidirect
189. C13#3369semidirect

Maximal subgroups

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

subgroupindex
#117194372
Q8×Dic262
C13×#4622
#117188462
#117188452
#117187422
C4×#61062
#117185032
#117184922
#117184562
#117184522
#336913