Finite Group Databasebeta

← #13126064

Subgroups — #13126064

Order 1664.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719305C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic
4#11718695C211yesmaximal, characteristic
5#11718631C211yesmaximal, characteristic, complemented
6#11718517C212yesmaximal, complemented
7#11718515C212yesmaximal, complemented
8#11718426C212yesmaximal, complemented
9#11718420C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×Dic26—21no—
13C13×#121C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15#88190C2211yescharacteristic
16#88189—21no—
17D4×Dic13—21no—
18D4×Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×#6101—21no—
22C2×C4×Dic13C2211yescharacteristic
23#88144C2211yescharacteristic
24#88142—21no—
25#88142—21no—
26#88142C2212yes—
27#88142C2212yes—
28#88141C2211yescharacteristic
29#88133—21no—
30#88131—21no—
31C13×#106C2212yes—
32C13×#102C2212yes—
33C13×C22⋊C8C2211yescharacteristic
34#88072C2212yes—
35C22⋊#1055C2211yescharacteristic
36#88058C2212yes—
37#88056C2212yes—
38#88055C2212yes—
39#88054C2212yes—
40#88050C2212yes—
41#88048C2212yes—
42#88047C2212yes—
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C22×Dic13—21no—
48C22×Dic13—21no—
49C22×Dic13D411yescharacteristic
50C22×Dic13D411yescharacteristic
51C2×Dic26—22no—
52C2×Dic26—22no—
53C2×Dic26—44no—
54C2×Dic26C2311yescharacteristic
55C2×C8×C13C2312yes—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60C22⋊Dic13—21no—
61C22⋊Dic13—21no—
62C22⋊Dic13—21no—
63C22⋊Dic13—21no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13C2312yes—
67C4⋊Dic13C2311yescharacteristic
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—22no—
72#6101—22no—
73C4×Dic13—21no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C4×Dic13C2311yescharacteristic
78C2×#1055C2312yes—
79#3239—131nomaximal, Sylow
80C23×C13—21no—
81C23×C13C2×D411yescharacteristic
82D4×C13—22no—
83D4×C13—42no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—42no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2411yescharacteristic
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13C2×D411yescharacteristic
98C2×Dic13C2×D411yescharacteristic
99C2×Dic13C2×D411yescharacteristic
100C2×Dic13C2×D411yescharacteristic
101Dic26—22no—
102Dic26—44no—
103Dic26—44no—
104C8×C13—22no—
105#1055—22no—
106C2×C4⋊Q8—131no—
107#529—131no—
108#501—132no—
109#489—132no—
110#484—131no—
111#484—131no—
112#481—131no—
113#481D1311yescharacteristic
114#475—132no—
115#474—132no—
116#432—131no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13—41no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13#13712yes—
123C22×C13C22×D411yescharacteristic
124C4×C13—21no—
125C4×C13—42no—
126C4×C13—41no—
127C4×C132−1+412yes—
128Dic13—21no—
129Dic13—21no—
130Dic13—21no—
131Dic13—41no—
132Dic13—42no—
133Dic13—41no—
134Dic13AGL(1,ℤ/8)12yes—
135C22×Q8—261no—
136C4⋊Q8—132no—
137C4⋊Q8—132no—
138C4⋊Q8—261no—
139C4⋊Q8—261no—
140#126—261no—
141#125—131no—
142#124—131no—
143#123—261no—
144C22⋊Q8—131no—
145#121C2×D1311yescharacteristic
146C4×Q8—131no—
147C4×D4—131no—
148C4×D4—261no—
149#117—261no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C2×D1311yescharacteristic
153C2×C42—131no—
154#107—132no—
155#107—132no—
156#106—132no—
157#106C2×D1312yes—
158C4⋊C8—132no—
159#103—132no—
160#103—132no—
161#102—132no—
162#102C2×D1312yes—
163C22⋊C8—131no—
164C22⋊C8C2×D1311yescharacteristic
165#97—132no—
166C2×C13—22no—
167C2×C13—81no—
168C2×C13#53611yescharacteristic
169C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C13C2×#13711yescharacteristic
171C2×Q8—131no—
172C2×Q8—262no—
173C2×Q8—262no—
174C2×Q8—524no—
175C2×D4—21no—
176C2×D4C22×D1311yescharacteristic
177C22×C4—21no—
178C22×C4—131no—
179C22×C4—131no—
180C22×C4—261no—
181C22×C4—261no—
182C22×C4C22×D1311yescharacteristic
183C2×C8—132no—
184C2×C8C22×D1312yes—
185C4⋊C4—21no—
186C4⋊C4—132no—
187C4⋊C4—131no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C4⋊C4—261no—
195C4⋊C4C22×D1312yes—
196C4⋊C4C22×D1311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C42—131no—
203C42—131no—
204C42—131no—
205C42—131no—
206C42—261no—
207C13#323911yescharacteristic, complemented, Sylow
208C23—21no—
209C23D4×D1311yescharacteristic
210Q8—262no—
211Q8—524no—
212Q8—524no—
213D4—22no—
214D4—42no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—131no—
220C2×C4—131no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4D4×D1311yescharacteristic
231C2×C4C23×D1311yescharacteristic
232C8—22no—
233C8—262no—
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22#8816912yes—
240C22C2×D4×D1311yescharacteristic
241C4—21no—
242C4—41no—
243C4—42no—
244C4—132no—
245C4—261no—
246C4—261no—
247C4—261no—
248C4—521no—
249C4—522no—
250C4—521no—
251C4#8825712yes—
252C2—22no—
253C2—81no—
254C2#1171935311yescharacteristic
255C2C2×#8816911yescharacteristic
256C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#481D13
hypocenterC13#3239
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
5. #11718631C2semidirect
6. #11718517C2semidirect
7. #11718515C2semidirect
8. #11718426C2semidirect
9. #11718420C2semidirect
10. #11718383C2semidirect
11. #11718380C2semidirect
207. C13#3239semidirect

Maximal subgroups

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

subgroupindex
#117193052
C2×#881422
C13×#4812
#117186952
#117186312
#117185172
#117185152
#117184262
#117184202
#117183832
#117183802
#323913