Finite Group Databasebeta

← #13126492

Subgroups — #13126492

Order 1664.

476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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×#88172C212yesmaximal, complemented
2#11719281C212yesmaximal, complemented
3C4×C13×Q16C211yesmaximal, characteristic, complemented
4#11718689C212yesmaximal, complemented
5#11718547C212yesmaximal, complemented
6#11718472C212yesmaximal, complemented
7#11718469C212yesmaximal, complemented
8#11718357C211yesmaximal, characteristic, complemented
9#11718349C211yesmaximal, characteristic, complemented
10C2×#6131C2212yes—
11C2×Q8×D13C2212yes—
12C2×C13×Q16C2211yescharacteristic
13C4×Q8×C13C2212yes—
14C2×#6107C2212yes—
15C2×#6106C2212yes—
16#88172—28no—
17C2×Dic52C2211yescharacteristic
18C2×D104C2211yescharacteristic
19C2×#6095C2212yes—
20C2×#6094C2212yes—
21#88151—22no—
22#88151C2212yes—
23#88149—22no—
24#88149C2212yes—
25#88129—22no—
26#88129C2212yes—
27C4×D52—22no—
28C4×D52C2211yescharacteristic
29C13×#107C2211yescharacteristic
30C13×#103C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88060C2212yes—
33#88050C2212yes—
34#88049C2212yes—
35C4⋊#1055C2211yescharacteristic
36C2×Q8×C13C2312yes—
37#6131—24no—
38#6131—42no—
39Q8×D13—24no—
40Q8×D13—42no—
41C2×D52—22no—
42C2×D52—22no—
43C2×D52D411yescharacteristic
44C2×D52C2312yes—
45C2×C4×D13—22no—
46C2×C4×D13—22no—
47C2×C4×D13C2312yes—
48C2×Dic26—22no—
49C2×Dic26C2312yes—
50C13×Q16D414yescomplemented
51C2×C8×C13C2311yescharacteristic
52C2×C8×C13C2311yescharacteristic
53C13×C4⋊C4—22no—
54C13×C4⋊C4C2312yes—
55C42×C13—22no—
56C42×C13C2311yescharacteristic
57#6107—24no—
58#6106—24no—
59#6103—22no—
60#6103—22no—
61#6103—22no—
62#6103—22no—
63#6103D412yes—
64C4⋊Dic13—22no—
65C4⋊Dic13D411yescharacteristic
66C2×#1055C2312yes—
67Dic52—41no—
68D104—41no—
69#6095—24no—
70#6094—24no—
71#3277—131nomaximal, Sylow
72C22×D13—22no—
73C22×D13C2×D412yes—
74Q8×C13—22no—
75Q8×C13C2×D414yes—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C2×Dic13—22no—
82C2×Dic13C2×D412yes—
83D52—22no—
84D52—22no—
85D52—41no—
86D52—44no—
87D52—44no—
88C4×D13—22no—
89C4×D13—22no—
90C4×D13—44no—
91C4×D13—44no—
92Dic26—22no—
93Dic26—22no—
94Dic26—44no—
95C8×C13—21no—
96C8×C13C2×D412yes—
97#1055—22no—
98C2×#137—132no—
99#548—132no—
100#495—131no—
101#468—132no—
102#464—132no—
103#451—132no—
104#449—132no—
105C4×Q16D1311yescharacteristic, complemented
106#436—131no—
107C22×C13C22×D411yescharacteristic
108C2×D13—22no—
109C2×D13—22no—
110C2×D13—22no—
111C2×D13—42no—
112C2×D13—42no—
113C2×D13—42no—
114C4×C13—24no—
115C4×C13—21no—
116C4×C13—21no—
117C4×C13—42no—
118C4×C13C22×D411yescharacteristic
119C4×C13H(5,𝔽2)11yescharacteristic
120Dic13—22no—
121Dic13—42no—
122C2×#41—132no—
123C22×Q8—132no—
124#137—268no—
125C2×Q16—132no—
126C2×Q16—131no—
127C2×Q16C2×D1311yescharacteristic
128C2×SD16—132no—
129C2×SD16—132no—
130C2×D8—131no—
131C2×M16—132no—
132#124—132no—
133#124—262no—
134C22⋊Q8—132no—
135C22⋊Q8—262no—
136#121—132no—
137#121—262no—
138C4×Q8C2×D1312yes—
139C4×D4—131no—
140C4×D4—262no—
141#107C2×D1311yescharacteristic
142C4⋊C8—131no—
143#103—132no—
144#103C2×D1312yes—
145#102—132no—
146C22⋊C8—132no—
147C4×C8C2×D1311yescharacteristic
148C2×C13D4211yescharacteristic
149C2×C13#57511yescharacteristic
150C2×C13#57811yescharacteristic
151D13—42no—
152D13—82no—
153#41—264no—
154#41—522no—
155C2×Q8—132no—
156C2×Q8—262no—
157C2×Q8—264no—
158C2×Q8—522no—
159C2×Q8C22×D1312yes—
160C2×D4—131no—
161C2×D4—132no—
162C2×D4—262no—
163C2×D4—262no—
164C22×C4—132no—
165C22×C4—262no—
166C22×C4—262no—
167Q16—264no—
168Q16—521no—
169Q16D5214yescomplemented
170SD16—264no—
171SD16—264no—
172D8—521no—
173M16—264no—
174C2×C8—132no—
175C2×C8C22×D1311yescharacteristic
176C2×C8C22×D1311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—131no—
179C4⋊C4—262no—
180C4⋊C4C22×D1312yes—
181C22⋊C4—132no—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C22⋊C4—262no—
186C42—22no—
187C42C22×D1311yescharacteristic
188C13#327711yescharacteristic, complemented, Sylow
189C23—132no—
190C23—262no—
191Q8—22no—
192Q8—262no—
193Q8—262no—
194Q8—524no—
195Q8C2×D5214yes—
196D4—262no—
197D4—262no—
198D4—521no—
199D4—524no—
200D4—524no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—132no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—524no—
208C2×C4—524no—
209C2×C4D4×D1311yescharacteristic
210C2×C4D4×D1311yescharacteristic
211C2×C4C23×D1311yescharacteristic
212C8—21no—
213C8—262no—
214C8C2×D5212yes—
215C22—262no—
216C22—262no—
217C22—262no—
218C22—522no—
219C22—522no—
220C22—522no—
221C22C2×D4×D1311yescharacteristic
222C4—21no—
223C4—21no—
224C4—24no—
225C4—42no—
226C4—262no—
227C4—522no—
228C4C22×D5211yescharacteristic
229C4#8825611yescharacteristic
230C2—522no—
231C2—1042no—
232C2D4×D5211yescharacteristic
233C2#1171947111yescharacteristic
234C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×Q16C2
socleC22×C13C22×D4
hypercenterC4×Q16D13
hypocenterC13#3277
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#88172C2semidirect
2. #11719281C2semidirect
3. C4×C13×Q16C2semidirect
4. #11718689C2semidirect
5. #11718547C2semidirect
6. #11718472C2semidirect
7. #11718469C2semidirect
8. #11718357C2semidirect
9. #11718349C2semidirect
50. C13×Q16D4semidirect
105. C4×Q16D13semidirect
169. Q16D52semidirect
188. C13#3277semidirect

Maximal subgroups

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

subgroupindex
C2×#881722
#117192812
C4×C13×Q162
#117186892
#117185472
#117184722
#117184692
#117183572
#117183492
#327713