Finite Group Databasebeta

← #13131094

Subgroups — #13131094

Order 1664.

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719358C211yesmaximal, characteristic
2D13⋊#100C211yesmaximal, characteristic, complemented
3D13⋊#99C211yesmaximal, characteristic, complemented
4#11718288C212yesmaximal, complemented
5#11718236C212yesmaximal, complemented
6C2×D4×D13C2211yescharacteristic
7C22×D52C411yescharacteristic, complemented
8C2×C22⋊#261—21no—
9D13⋊M16—21no—
10C13×#123C411yescharacteristic, complemented
11#88191C411yescharacteristic, complemented
12#88183C2211yescharacteristic
13#88149—21no—
14#88148—21no—
15#88138—21no—
16#88136—21no—
17#88136C2211yescharacteristic
18C22⋊C4×D13C411yescharacteristic, complemented
19#88121—21no—
20#88121C2212yes—
21#88119C2212yes—
22#88107—21no—
23C23×D13C2×C411yescharacteristic
24C23×D13C2×C411yescharacteristic, complemented
25C23×D13D411yescharacteristic
26C22×#261—41no—
27C2×D4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic, complemented
29C2×C22⋊D13—21no—
30C2×C22⋊D13D411yescharacteristic
31C2×C22⋊D13C2311yescharacteristic
32D4×D13—41no—
33D4×D13—41no—
34C2×D52—21no—
35C2×D52—21no—
36C2×D52—21no—
37C2×D52—41no—
38C2×D52—41no—
39C2×D52D411yescharacteristic
40C2×C4×D13—21no—
41C2×C4×D13D411yescharacteristic
42C22⋊#261—22no—
43C22⋊#261—41no—
44#6122—22no—
45#6118—41no—
46D13⋊C8—41no—
47C13×C4⋊C4—21no—
48C13×C22⋊C4—21no—
49C13×C22⋊C4C2×C411yescharacteristic, complemented
50C22⋊Dic13C2×C411yescharacteristic, complemented
51#6103—21no—
52#6103—21no—
53#6103—21no—
54#6103—21no—
55#6101—21no—
56#2121—131nomaximal, Sylow
57C23×C13C22⋊C411yescharacteristic
58C23×C13C22×C411yescharacteristic
59C22×D13—21no—
60C22×D13—21no—
61C22×D13—21no—
62C22×D13—21no—
63C22×D13—21no—
64C22×D13—41no—
65C22×D13—81no—
66C22×D13—81no—
67C22×D13—81no—
68C22×D13C22⋊C411yescharacteristic
69C22×D13C22⋊C411yescharacteristic
70C22×D13C2×D411yescharacteristic
71C2×#261—42no—
72C2×#261—82no—
73D4×C13—41no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—41no—
77C2×C4×C13C22⋊C411yescharacteristic
78C22⋊D13—41no—
79C22⋊D13—41no—
80C22⋊D13—81no—
81C2×Dic13—21no—
82C2×Dic13C2×D411yescharacteristic
83D52—41no—
84D52—42no—
85D52—41no—
86D52—41no—
87D52—81no—
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—81no—
91#1057—42no—
92#534—131no—
93C2×#100—131no—
94C2×#99—131no—
95#352—132no—
96AΣL(1,𝔽16)—132no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13—41no—
100C22×C13—41no—
101C22×C13C2×C22⋊C411yescharacteristic
102C2×D13—21no—
103C2×D13—21no—
104C2×D13—41no—
105C2×D13—42no—
106C2×D13—41no—
107C2×D13—41no—
108C2×D13—41no—
109C2×D13—41no—
110C2×D13—41no—
111C2×D13—81no—
112C2×D13—81no—
113C2×D13—81no—
114C2×D13—82no—
115C2×D13#9911yescharacteristic
116C2×D13#9911yescharacteristic
117#261—82no—
118C4×C13—21no—
119C4×C13—41no—
120C4×C13—41no—
121Dic13—21no—
122Dic13—41no—
123C22×D4—131no—
124C22×D4—131no—
125C2×M16—261no—
126#123—131no—
127#123—261no—
128#123#26111yescharacteristic, complemented
129#121—261no—
130#121—261no—
131#120—131no—
132#120—131no—
133#120—261no—
134C2×C22⋊C4—131no—
135C2×C22⋊C4—261no—
136#100—132no—
137#100—261no—
138#99—132no—
139#99—261no—
140C2×C13—21no—
141C2×C13—41no—
142C2×C13—41no—
143C2×C13C2×#9911yescharacteristic
144D13—21no—
145D13—21no—
146D13—41no—
147D13—41no—
148D13—81no—
149C24—131no—
150C24—131no—
151C24—131no—
152C2×D4—131no—
153C2×D4—131no—
154C2×D4—131no—
155C2×D4—261no—
156C2×D4—261no—
157C2×D4—261no—
158C2×D4—261no—
159C2×D4—521no—
160C2×D4—521no—
161C2×D4—521no—
162C2×D4—521no—
163C2×D4C2×#26111yescharacteristic
164C22×C4—131no—
165C22×C4—261no—
166C22×C4—521no—
167C22×C4C2×#26111yescharacteristic, complemented
168M16—262no—
169M16—521no—
170C2×C8—521no—
171C4⋊C4—21no—
172C4⋊C4—261no—
173C22⋊C4—21no—
174C22⋊C4—131no—
175C22⋊C4—261no—
176C22⋊C4—261no—
177C22⋊C4—261no—
178C22⋊C4—261no—
179C22⋊C4—262no—
180C22⋊C4—521no—
181C22⋊C4C2×#26111yescharacteristic, complemented
182C13#212111yescharacteristic, complemented, Sylow
183C23—131no—
184C23—131no—
185C23—131no—
186C23—261no—
187C23—261no—
188C23—261no—
189C23—261no—
190C23—261no—
191C23—521no—
192C23—1041no—
193C23—1041no—
194C23—1041no—
195C23C22⋊#26111yescharacteristic
196C23C22×#26111yescharacteristic
197D4—41no—
198D4—521no—
199D4—521no—
200D4—521no—
201D4—522no—
202D4—521no—
203D4—521no—
204D4—1041no—
205D4—1041no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—131no—
210C2×C4—261no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—522no—
214C2×C4—1041no—
215C2×C4—1042no—
216C2×C4C22⋊#26111yescharacteristic
217C8—522no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—131no—
223C22—131no—
224C22—261no—
225C22—261no—
226C22—521no—
227C22—521no—
228C22—521no—
229C22—521no—
230C22—521no—
231C22—522no—
232C22—521no—
233C22—1041no—
234C22—1041no—
235C22—1041no—
236C22—1042no—
237C22C2×C22⋊#26111yescharacteristic
238C4—21no—
239C4—41no—
240C4—41no—
241C4—261no—
242C4—521no—
243C4—1042no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—261no—
248C2—261no—
249C2—521no—
250C2—521no—
251C2—1041no—
252C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#123C4
socleC2×C13C2×#99
prime radical#11719358C2
cosocleC2×C22⋊D13C23
hypercenter#123#261
hypocenterC13#2121
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
2. D13⋊#100C2semidirect
3. D13⋊#99C2semidirect
4. #11718288C2semidirect
5. #11718236C2semidirect
7. C22×D52C4semidirect
10. C13×#123C4semidirect
11. #88191C4semidirect
18. C22⋊C4×D13C4semidirect
24. C23×D13C2×C4semidirect
28. C22×C4×C13C2×C4semidirect
49. C13×C22⋊C4C2×C4semidirect
50. C22⋊Dic13C2×C4semidirect
128. #123#261semidirect
167. C22×C4C2×#261semidirect
181. C22⋊C4C2×#261semidirect
182. C13#2121semidirect

Maximal subgroups

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

subgroupindex
#117193582
D13⋊#1002
D13⋊#992
#117182882
#117182362
#212113