Finite Group Databasebeta

← #13125965

Subgroups — #13125965

Order 1664.

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

normal subgroups only

This group has 404 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#11719430C211yesmaximal, characteristic
2D13×C4⋊Q8C211yesmaximal, characteristic, complemented
3C13×#498C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718740C211yesmaximal, characteristic, complemented
6#11718531C214yesmaximal, complemented
7#11718524C214yesmaximal, complemented
8#11718355C211yesmaximal, characteristic, complemented
9#11718346C211yesmaximal, characteristic, complemented
10C2×#6131—21no—
11C2×Q8×D13—21no—
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88201—21no—
15#88198—21no—
16#88149—21no—
17#88149C2212yes—
18#88147—21no—
19#88147C2212yes—
20C4⋊C4×D13—21no—
21C4⋊C4×D13C2212yes—
22#88142—21no—
23#88142C2212yes—
24#88128C2211yescharacteristic
25C42×D13C2211yescharacteristic
26#88123C2211yescharacteristic
27C13×#106C2214yes—
28C4×C8×C13C2211yescharacteristic
29#88061C2214yes—
30#88060C2212yes—
31#88054C2212yes—
32#88049C2214yes—
33#88048C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13—21no—
37#6131—44no—
38Q8×D13—44no—
39C2×D52—22no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52C2312yes—
43C2×C4×D13—22no—
44C2×C4×D13—22no—
45C2×C4×D13D411yescharacteristic
46C2×C4×D13D411yescharacteristic
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26—22no—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56#6103—22no—
57#6103—22no—
58C4⋊Dic13—21no—
59C4⋊Dic13C2312yes—
60#6101—22no—
61#6101—22no—
62C4×Dic13D411yescharacteristic
63C4×Dic13D411yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055C2312yes—
66#3227—131nomaximal, Sylow
67C22×D13—22no—
68C22×D13C2×D411yescharacteristic
69Q8×C13—42no—
70Q8×C13—42no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2411yescharacteristic
76C2×Dic13—22no—
77C2×Dic13C2×D411yescharacteristic
78C2×Dic13C2×D411yescharacteristic
79C2×Dic13C2×D411yescharacteristic
80D52—24no—
81D52—44no—
82D52—42no—
83D52—42no—
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—44no—
87C4×D13—44no—
88C4×D13SD1614yes—
89Dic26—44no—
90Dic26—42no—
91C8×C13—22no—
92#1055—22no—
93#532—131no—
94C2×C4⋊Q8—131no—
95#498—131no—
96#498D1311yescharacteristic, complemented
97#486—131no—
98#486—131no—
99#481—134no—
100#476—134no—
101#431—131no—
102C22×C13C22×D411yescharacteristic
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—42no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13C2×SD1612yes—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13C2×SD1612yes—
112C4×C13AGL(1,ℤ/8)12yes—
113C4×C132−1+412yes—
114Dic13—21no—
115Dic13—21no—
116Dic13—42no—
117Dic13C2×SD1612yes—
118C2×#41—261no—
119C22×Q8—261no—
120C4⋊Q8—132no—
121C4⋊Q8—131no—
122C4⋊Q8—261no—
123C4⋊Q8—261no—
124C4⋊Q8C2×D1311yescharacteristic
125C4⋊Q8C2×D1311yescharacteristic
126#127—131no—
127#124—261no—
128#121—132no—
129#121—261no—
130C4×D4—132no—
131C4×D4—261no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—261no—
134C2×C42—131no—
135#106—134no—
136#106C2×D1314yes—
137C4⋊C8—132no—
138#102—134no—
139#102—134no—
140C22⋊C8—132no—
141C4×C8—131no—
142C4×C8C2×D1311yescharacteristic
143C2×C13#53611yescharacteristic
144C2×C13C22×SD1611yescharacteristic
145C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
146D13—22no—
147D13—82no—
148#41—524no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—262no—
152C2×Q8—261no—
153C2×Q8—524no—
154C2×D4—132no—
155C2×D4—262no—
156C2×D4—261no—
157C2×D4—261no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—262no—
162C22×C4—262no—
163C2×C8—132no—
164C2×C8C22×D1312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—132no—
168C4⋊C4—262no—
169C4⋊C4—262no—
170C4⋊C4—261no—
171C4⋊C4C22×D1312yes—
172C4⋊C4C22×D1312yes—
173C22⋊C4—262no—
174C22⋊C4—262no—
175C42—131no—
176C42—131no—
177C42—131no—
178C42C22×D1311yescharacteristic
179C13#322711yescharacteristic, complemented, Sylow
180C23—131no—
181C23—262no—
182Q8—42no—
183Q8—42no—
184Q8—524no—
185Q8—522no—
186D4—264no—
187D4—524no—
188D4—522no—
189D4—522no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—131no—
193C2×C4—134no—
194C2×C4—131no—
195C2×C4—131no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—524no—
200C2×C4—524no—
201C2×C4D4×D1311yescharacteristic
202C2×C4D4×D1311yescharacteristic
203C2×C4C23×D1311yescharacteristic
204C8—22no—
205C8—262no—
206C22—132no—
207C22—261no—
208C22—261no—
209C22—522no—
210C22—522no—
211C22—522no—
212C22C2×D4×D1311yescharacteristic
213C4—42no—
214C4—42no—
215C4—132no—
216C4—261no—
217C4—261no—
218C4—522no—
219C4SD16×D1312yes—
220C4#8816812yes—
221C4#8825412yes—
222C2—262no—
223C2—1042no—
224C2#1171942911yescharacteristic
225C2C2×SD16×D1311yescharacteristic
226C2C2×#8816811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#498C2
socleC22×C13C22×D4
prime radical#11719430C2
hypercenter#498D13
hypocenterC13#3227
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. D13×C4⋊Q8C2semidirect
3. C13×#498C2semidirect
4. #11718749C2semidirect
5. #11718740C2semidirect
6. #11718531C2semidirect
7. #11718524C2semidirect
8. #11718355C2semidirect
9. #11718346C2semidirect
96. #498D13semidirect
179. C13#3227semidirect

Maximal subgroups

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

subgroupindex
#117194302
D13×C4⋊Q82
C13×#4982
#117187492
#117187402
#117185312
#117185242
#117183552
#117183462
#322713