Finite Group Databasebeta

← #13126067

Subgroups — #13126067

Order 1664.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11719396C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718726C211yesmaximal, characteristic, complemented
6#11718551C212yesmaximal, complemented
7#11718545C212yesmaximal, complemented
8#11718524C212yesmaximal
9#11718515C212yesmaximal, complemented
10#11718375C211yesmaximal, characteristic, complemented
11#11718366C211yesmaximal, characteristic, complemented
12C2×Q8×D13—21no—
13C13×C4⋊Q8C2211yescharacteristic
14C13×#125C2211yescharacteristic
15#88198—21no—
16#88152—21no—
17#88151C2211yescharacteristic
18#88149C2211yescharacteristic
19#88148—21no—
20#88147—21no—
21#88147C2211yescharacteristic
22#88146—21no—
23C4⋊C4×D13—21no—
24C4⋊C4×D13C2212yes—
25#88142—21no—
26#88142C2212yes—
27#88141C2211yescharacteristic
28#88129C2211yescharacteristic
29C42×D13C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#107C2212yes—
32C13×#106C2212yes—
33C13×#97C2211yescharacteristic
34#88061C2212yes—
35#88060C2212yes—
36#88056C2212yes—
37#88054C2212yes—
38#88050C2212yes—
39#88049C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44Q8×D13—44no—
45C2×D52—21no—
46C2×D52C2311yescharacteristic
47C2×C4×D13—22no—
48C2×C4×D13—21no—
49C2×C4×D13D411yescharacteristic
50C2×C4×D13D411yescharacteristic
51C2×C4×D13C2311yescharacteristic
52C2×Dic26—21no—
53C2×Dic26—22no—
54C2×Dic26C2311yescharacteristic
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4C2311yescharacteristic
60C13×C4⋊C4C2312yes—
61C13×C4⋊C4C2311yescharacteristic
62C42×C13C2311yescharacteristic
63#6103—21no—
64#6103—21no—
65#6103—21no—
66#6103—21no—
67#6103—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13C2312yes—
71#6101—21no—
72#6101—22no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13D411yescharacteristic
76C4×Dic13D411yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3239—131nomaximal, Sylow
80C22×D13—21no—
81C22×D13C2×D411yescharacteristic
82Q8×C13—42no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13C2×D411yescharacteristic
92C2×Dic13C2×D411yescharacteristic
93C2×Dic13C2×D411yescharacteristic
94D52—22no—
95D52—42no—
96C4×D13—22no—
97C4×D13—22no—
98C4×D13—22no—
99C4×D13—44no—
100C4×D13—42no—
101Dic26—22no—
102Dic26—42no—
103Dic26—44no—
104C8×C13—22no—
105#1055—22no—
106C2×C4⋊Q8—131no—
107#529—131no—
108#501—131no—
109#501D1311yescharacteristic, complemented
110#489—131no—
111#489—131no—
112#484—132no—
113#481—132no—
114#475—132no—
115#474—132no—
116#432—131no—
117C22×C13C22×D411yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—41no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13#13712yes—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13—41no—
129C4×C132−1+412yes—
130Dic13—21no—
131Dic13—21no—
132Dic13—41no—
133Dic13—42no—
134Dic13AGL(1,ℤ/8)12yes—
135C22×Q8—261no—
136C4⋊Q8—132no—
137C4⋊Q8—131no—
138C4⋊Q8—261no—
139C4⋊Q8—261no—
140C4⋊Q8C2×D1311yescharacteristic
141#126—261no—
142#125C2×D1311yescharacteristic
143#124—131no—
144#123—261no—
145C22⋊Q8—131no—
146#121—131no—
147C4×Q8—131no—
148C4×D4—131no—
149C4×D4—261no—
150#117—261no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—261no—
153C2×C42—131no—
154#107—132no—
155#107C2×D1312yes—
156#106—132no—
157#106C2×D1312yes—
158C4⋊C8—132no—
159#103—132no—
160#103—132no—
161#102—132no—
162#102—132no—
163C22⋊C8—132no—
164#97—131no—
165#97C2×D1311yescharacteristic
166C2×C13#53611yescharacteristic
167C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C13C2×#13711yescharacteristic
169D13—22no—
170D13—81no—
171C2×Q8—21no—
172C2×Q8—131no—
173C2×Q8—262no—
174C2×Q8—261no—
175C2×Q8—524no—
176C2×D4—131no—
177C2×D4—261no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—131no—
181C22×C4—261no—
182C22×C4—262no—
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—132no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4C22×D1312yes—
195C4⋊C4C22×D1311yescharacteristic
196C4⋊C4C22×D1311yescharacteristic
197C22⋊C4—261no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C42—131no—
203C42—131no—
204C42—131no—
205C42—261no—
206C42C22×D1311yescharacteristic
207C13#323911yescharacteristic, complemented, Sylow
208C23—131no—
209C23—261no—
210Q8—42no—
211Q8—262no—
212Q8—522no—
213Q8—524no—
214D4—262no—
215D4—522no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—131no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—262no—
227C2×C4—522no—
228C2×C4—524no—
229C2×C4D4×D1311yescharacteristic
230C2×C4D4×D1311yescharacteristic
231C2×C4C23×D1311yescharacteristic
232C8—22no—
233C8—262no—
234C22—132no—
235C22—261no—
236C22—261no—
237C22—521no—
238C22—521no—
239C22—521no—
240C22C2×D4×D1311yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—42no—
245C4—41no—
246C4—132no—
247C4—261no—
248C4—261no—
249C4—521no—
250C4—522no—
251C4#8825412yes—
252C2—262no—
253C2—1041no—
254C2#1171942911yescharacteristic
255C2D13×AGL(1,ℤ/8)11yescharacteristic
256C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radical#88149C22
hypercenter#501D13
hypocenterC13#3239
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. D13×C4⋊Q8C2semidirect
3. C13×#501C2semidirect
4. #11718750C2semidirect
5. #11718726C2semidirect
6. #11718551C2semidirect
7. #11718545C2semidirect
9. #11718515C2semidirect
10. #11718375C2semidirect
11. #11718366C2semidirect
109. #501D13semidirect
207. C13#3239semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117193962
C13×#5012
#117187502
#117187262
#117185512
#117185452
#117185242
#117185152
#117183752
#117183662
#323913