Finite Group Databasebeta

← #13125985

Subgroups — #13125985

Order 1664.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#11719327C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic
3C13×#484C211yesmaximal, characteristic
4#11718705C211yesmaximal, characteristic
5#11718631C211yesmaximal, characteristic
6#11718536C212yesmaximal, complemented
7#11718535C212yesmaximal, complemented
8#11718455C212yesmaximal, complemented
9#11718453C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic
11#11718379C211yesmaximal, characteristic
12C22×Dic26—21no—
13C13×C22⋊Q8C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15Q8×Dic13C2211yescharacteristic
16#88198C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18#88178C2211yescharacteristic
19C2×#6101—21no—
20C2×C4×Dic13C2211yescharacteristic
21#88143—21no—
22#88142—21no—
23#88142—21no—
24#88142C2212yes—
25#88142C2212yes—
26#88142C2211yescharacteristic
27#88141—21no—
28#88141C2211yescharacteristic
29#88132—21no—
30#88131—21no—
31C13×#107C2212yes—
32C13×#103C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88075C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88058C2212yes—
37#88056C2212yes—
38#88054C2212yes—
39C8×Dic13C2212yes—
40#88050C2212yes—
41#88047C2212yes—
42#88047C2212yes—
43C2×Q8×C13C2311yescharacteristic
44C22×C4×C13—21no—
45C22×C4×C13C2311yescharacteristic
46C22×Dic13—21no—
47C22×Dic13D411yescharacteristic
48C22×Dic13D411yescharacteristic
49C2×Dic26—21no—
50C2×Dic26—22no—
51C2×Dic26—22no—
52C2×Dic26—44no—
53C2×Dic26C2311yescharacteristic
54C2×C8×C13C2312yes—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C22⋊Dic13—21no—
61C4⋊Dic13—21no—
62C4⋊Dic13—21no—
63C4⋊Dic13C2312yes—
64C4⋊Dic13C2311yescharacteristic
65#6101—21no—
66#6101—21no—
67#6101—21no—
68#6101—21no—
69#6101—21no—
70#6101—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3230—131nomaximal, Sylow
80C23×C13C2×D411yescharacteristic
81Q8×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—42no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—42no—
94C2×Dic13Q1614yes—
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99Dic26—22no—
100Dic26—44no—
101Dic26—42no—
102Dic26—44no—
103C8×C13—22no—
104#1055—22no—
105#533—131no—
106C2×C4⋊Q8—131no—
107#500—132no—
108#487—132no—
109#484—131no—
110#484—131no—
111#484—131no—
112#484D1311yescharacteristic
113#477—132no—
114#477—132no—
115#431—131no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13C2×Q1612yes—
119C22×C13C22×D411yescharacteristic
120C4×C13—21no—
121C4×C13—41no—
122C4×C13—42no—
123C4×C13—41no—
124C4×C132−1+412yes—
125Dic13—21no—
126Dic13—41no—
127Dic13—42no—
128Dic13—41no—
129Dic13C2×Q1612yes—
130Dic13C2×Q1612yes—
131Dic13AGL(1,ℤ/8)12yes—
132C22×Q8—261no—
133C4⋊Q8—132no—
134C4⋊Q8—132no—
135C4⋊Q8—131no—
136C4⋊Q8—131no—
137C4⋊Q8—261no—
138C4⋊Q8—261no—
139#125—261no—
140C22⋊Q8—131no—
141C22⋊Q8—261no—
142C22⋊Q8C2×D1311yescharacteristic
143C4×Q8—131no—
144C4×Q8—131no—
145C4×Q8—261no—
146#117—261no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C42—131no—
151#107—132no—
152#107—132no—
153#107—132no—
154#107C2×D1312yes—
155C4⋊C8—132no—
156#103—132no—
157#103—132no—
158#103—132no—
159#103C2×D1312yes—
160C22⋊C8—131no—
161C22⋊C8C2×D1311yescharacteristic
162C4×C8—132no—
163C2×C13—22no—
164C2×C13#53611yescharacteristic
165C2×C13C22×Q1611yescharacteristic
166C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
167C2×Q8—131no—
168C2×Q8—261no—
169C2×Q8—262no—
170C2×Q8—262no—
171C2×Q8—524no—
172C2×Q8C22×D1311yescharacteristic
173C22×C4—21no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—261no—
177C22×C4C22×D1311yescharacteristic
178C2×C8—132no—
179C2×C8C22×D1312yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—132no—
183C4⋊C4—131no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4C22×D1312yes—
194C4⋊C4C22×D1311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—261no—
197C42—131no—
198C42—131no—
199C42—131no—
200C42—131no—
201C42—261no—
202C42—261no—
203C13#323011yescharacteristic, complemented, Sylow
204C23D4×D1311yescharacteristic
205Q8—22no—
206Q8—262no—
207Q8—522no—
208Q8—524no—
209Q8—524no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—134no—
216C2×C4—131no—
217C2×C4—131no—
218C2×C4—131no—
219C2×C4—131no—
220C2×C4—262no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—522no—
225C2×C4D4×D1311yescharacteristic
226C2×C4C23×D1311yescharacteristic
227C8—22no—
228C8—262no—
229C22—21no—
230C22—21no—
231C22Q16×D1312yes—
232C22C2×D4×D1311yescharacteristic
233C4—21no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—132no—
238C4—132no—
239C4—132no—
240C4—261no—
241C4—522no—
242C4—521no—
243C4—521no—
244C4#8825712yes—
245C2—22no—
246C2#1171935311yescharacteristic
247C2C2×Q16×D1311yescharacteristic
248C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#484C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#484D13
hypocenterC13#3230
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
6. #11718536C2semidirect
7. #11718535C2semidirect
8. #11718455C2semidirect
9. #11718453C2semidirect
203. C13#3230semidirect

Maximal subgroups

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

subgroupindex
#117193272
C2×#881422
C13×#4842
#117187052
#117186312
#117185362
#117185352
#117184552
#117184532
#117183832
#117183792
#323013