Finite Group Databasebeta

← #13126057

Subgroups — #13126057

Order 1664.

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

normal subgroups only

This group has 362 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
1C2×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic
3#11718752C212yesmaximal, complemented
4#11718750C212yesmaximal, complemented
5#11718745C212yesmaximal, complemented
6#11718741C212yesmaximal, complemented
7#11718632C212yesmaximal, complemented
8#11718628C212yesmaximal
9#11718587C211yesmaximal, characteristic, complemented
10C22×Q8×C13—21no—
11C13×C4⋊Q8—21no—
12C13×C4⋊Q8—21no—
13C13×C4⋊Q8C2212yes—
14C13×C4⋊Q8C2212yes—
15C2×C13×C4⋊C4—21no—
16C2×C13×C4⋊C4C2212yes—
17C2×C42×C13C2211yescharacteristic
18#88184C2211yescharacteristic
19#88183—21no—
20C4×C22⋊D13—21no—
21#88178C2211yescharacteristic
22#88130—21no—
23#88129C2211yescharacteristic
24C4×D52C2211yescharacteristic
25#88126—21no—
26#88124C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C22⋊#1055C2212yes—
29#88050C2214yes—
30#88049C2214yes—
31#88048C2214yes—
32#88047C2214yes—
33C4⋊#1055C2212yes—
34#88043C2212yes—
35C2×Q8×C13—22no—
36C2×Q8×C13—22no—
37C2×Q8×C13—44no—
38C22×C4×C13—22no—
39C22×C4×C13D411yescharacteristic
40C22×C4×C13D411yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C2×C22⋊D13—21no—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×Dic26C2311yescharacteristic
46C13×C4⋊C4—22no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4C2314yes—
50C42×C13D411yescharacteristic
51C42×C13D411yescharacteristic
52C42×C13C2311yescharacteristic
53C42×C13C2311yescharacteristic
54C22⋊Dic13—21no—
55#6103—21no—
56#6103—21no—
57#6103—21no—
58#6103—21no—
59C4⋊Dic13C2311yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61#6101—21no—
62#6101—21no—
63#6101—21no—
64#6101—21no—
65C4×Dic13—21no—
66C2×#1055C2314yes—
67#3238—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—21no—
70Q8×C13—44no—
71Q8×C13—44no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—24no—
76C2×C4×C13—44no—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C22⋊D13—42no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87D52—22no—
88C4×D13—42no—
89Dic26—22no—
90#1055—24no—
91C2×C4⋊Q8D1311yescharacteristic, complemented
92#529—131no—
93#501—132no—
94#489—132no—
95#483—132no—
96#480—132no—
97#477—132no—
98#476—132no—
99#432—131no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13AGL(1,ℤ/8)12yes—
103C22×C13C22×D411yescharacteristic
104C2×D13—41no—
105C2×D13—41no—
106C2×D13—41no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—44no—
112C4×C13#13712yes—
113C4×C132−1+412yes—
114Dic13—41no—
115Dic13—41no—
116Dic13—41no—
117C22×Q8—21no—
118C4⋊Q8—21no—
119C4⋊Q8—21no—
120C4⋊Q8C2×D1312yes—
121C4⋊Q8C2×D1312yes—
122#126—261no—
123#125—131no—
124#124—131no—
125#123—261no—
126C22⋊Q8—131no—
127#121—131no—
128C4×Q8—131no—
129C4×D4—131no—
130C4×D4—261no—
131#117—261no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4C2×D1312yes—
134C2×C42C2×D1311yescharacteristic
135#107—134no—
136#106—134no—
137C4⋊C8—132no—
138#103—134no—
139#102—134no—
140C22⋊C8—132no—
141#97—132no—
142C2×C13—22no—
143C2×C13#53611yescharacteristic
144C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C13C2×#13711yescharacteristic
146D13—81no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—44no—
150C2×Q8—131no—
151C2×D4—131no—
152C2×D4—261no—
153C22×C4—22no—
154C22×C4—261no—
155C22×C4C22⋊D1311yescharacteristic
156C22×C4C22⋊D1311yescharacteristic
157C22×C4C22×D1311yescharacteristic
158C2×C8—134no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—131no—
163C4⋊C4—131no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C4⋊C4—261no—
167C4⋊C4—261no—
168C4⋊C4C22×D1314yes—
169C22⋊C4—261no—
170C22⋊C4—261no—
171C22⋊C4—261no—
172C22⋊C4—261no—
173C22⋊C4—261no—
174C42—261no—
175C42C22⋊D1311yescharacteristic
176C42C22⋊D1311yescharacteristic
177C42C22×D1311yescharacteristic
178C42C22×D1311yescharacteristic
179C13#323811yescharacteristic, complemented, Sylow
180C23—261no—
181C23C2×C22⋊D1311yescharacteristic
182Q8—44no—
183Q8—44no—
184Q8—262no—
185D4—262no—
186D4—522no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—44no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—261no—
195C2×C4—522no—
196C2×C4C2×C22⋊D1311yescharacteristic
197C2×C4C2×C22⋊D1311yescharacteristic
198C2×C4C2×C22⋊D1311yescharacteristic
199C2×C4C2×C22⋊D1311yescharacteristic
200C2×C4C2×C22⋊D1311yescharacteristic
201C2×C4C23×D1311yescharacteristic
202C8—264no—
203C22—21no—
204C22—21no—
205C22—521no—
206C22—521no—
207C22—521no—
208C22#8818612yes—
209C22C22×C22⋊D1311yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—44no—
215C4—521no—
216C4—521no—
217C4—521no—
218C4#8819612yes—
219C4#8825412yes—
220C2—22no—
221C2—1041no—
222C2C2×#8818611yescharacteristic
223C2C2×#8819611yescharacteristic
224C2#1171952111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C4⋊Q8C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenterC2×C4⋊Q8D13
hypocenterC13#3238
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C4⋊Q8C2semidirect
3. #11718752C2semidirect
4. #11718750C2semidirect
5. #11718745C2semidirect
6. #11718741C2semidirect
7. #11718632C2semidirect
9. #11718587C2semidirect
91. C2×C4⋊Q8D13semidirect
179. C13#3238semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C4⋊Q82
#117191842
#117187522
#117187502
#117187452
#117187412
#117186322
#117186282
#117185872
#323813