Finite Group Databasebeta

← #13131093

Subgroups — #13131093

Order 1664.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719198C211yesmaximal, characteristic
2C2×#88121C211yesmaximal, characteristic, complemented
3C2×#88119C211yesmaximal, characteristic, complemented
4#11718237C212yesmaximal, complemented
5#11718236C212yesmaximal, complemented
6C22×C22⋊D13C411yescharacteristic, complemented
7C22×C22⋊D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×#6122—21no—
10C2×C13×C22⋊C4C411yescharacteristic, complemented
11#88184—21no—
12#88184—21no—
13#88140—21no—
14#88140C411yescharacteristic, complemented
15#88140C2211yescharacteristic
16#88136—21no—
17#88136C411yescharacteristic, complemented
18#88136C2211yescharacteristic
19#88121—21no—
20#88121C2212yes—
21#88119—21no—
22#88119C2212yes—
23C24×C13C2×C411yescharacteristic
24C23×D13C2×C411yescharacteristic, complemented
25C23×D13D411yescharacteristic
26C22×#261—41no—
27C22×C4×C13—21no—
28C2×C22⋊D13—21no—
29C2×C22⋊D13—21no—
30C2×C22⋊D13—41no—
31C2×C22⋊D13—41no—
32C2×C22⋊D13—41no—
33C2×C22⋊D13—41no—
34C2×C22⋊D13C2×C411yescharacteristic
35C2×C22⋊D13D411yescharacteristic
36C2×C22⋊D13D411yescharacteristic
37C2×C22⋊D13C2311yescharacteristic
38C22×Dic13C2×C411yescharacteristic, complemented
39C22×Dic13D411yescharacteristic
40C2×D52—21no—
41C2×D52—21no—
42C22⋊#261—22no—
43C22⋊#261—41no—
44#6122—22no—
45#6122—41no—
46C2×#1057—41no—
47C13×C22⋊C4—21no—
48C13×C22⋊C4C2×C411yescharacteristic, complemented
49C13×C22⋊C4C2×C411yescharacteristic, complemented
50#6103—21no—
51#6103—21no—
52#6103—21no—
53#6103—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56#2121—131nomaximal, Sylow
57C23×C13—21no—
58C23×C13—21no—
59C23×C13—81no—
60C23×C13C22⋊C411yescharacteristic
61C23×C13C22⋊C411yescharacteristic
62C23×C13C22×C411yescharacteristic
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—21no—
66C22×D13—41no—
67C22×D13—81no—
68C22×D13—81no—
69C22×D13C22⋊C411yescharacteristic
70C22×D13C2×D411yescharacteristic
71C2×#261—42no—
72C2×#261—82no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—81no—
76C22⋊D13—41no—
77C22⋊D13—41no—
78C22⋊D13—41no—
79C22⋊D13—41no—
80C22⋊D13—42no—
81C22⋊D13—41no—
82C22⋊D13—41no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—41no—
87C2×Dic13C22⋊C411yescharacteristic
88C2×Dic13C2×D411yescharacteristic
89D52—81no—
90D52—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×C13—41no—
102C22×C13—81no—
103C22×C13—81no—
104C22×C13#9911yescharacteristic
105C22×C13#9911yescharacteristic
106C22×C13C2×C22⋊C411yescharacteristic
107C2×D13—21no—
108C2×D13—21no—
109C2×D13—42no—
110C2×D13—41no—
111C2×D13—41no—
112C2×D13—41no—
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—81no—
116C2×D13—82no—
117#261—82no—
118C4×C13—41no—
119C4×C13—41no—
120Dic13—21no—
121Dic13—21no—
122Dic13—41no—
123C22×D4—131no—
124C22×D4—131no—
125C2×M16—261no—
126#123—131no—
127#123—131no—
128#123—261no—
129#121—261no—
130#121—261no—
131#120—131no—
132#120—131no—
133#120—261no—
134C2×C22⋊C4—261no—
135C2×C22⋊C4#26111yescharacteristic, complemented
136#100—132no—
137#100—261no—
138#99—132no—
139#99—261no—
140C2×C13—21no—
141C2×C13—21no—
142C2×C13—21no—
143C2×C13—41no—
144C2×C13—41no—
145C2×C13C2×#9911yescharacteristic
146D13—41no—
147D13—41no—
148D13—81no—
149C24—131no—
150C24—131no—
151C24C2×#26111yescharacteristic
152C2×D4—131no—
153C2×D4—131no—
154C2×D4—131no—
155C2×D4—131no—
156C2×D4—261no—
157C2×D4—261no—
158C2×D4—261no—
159C2×D4—261no—
160C2×D4—521no—
161C2×D4—521no—
162C2×D4—521no—
163C2×D4—521no—
164C22×C4—21no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—521no—
168M16—262no—
169M16—521no—
170C2×C8—521no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C22⋊C4—21no—
174C22⋊C4—261no—
175C22⋊C4—261no—
176C22⋊C4—261no—
177C22⋊C4—261no—
178C22⋊C4—262no—
179C22⋊C4—521no—
180C22⋊C4C2×#26111yescharacteristic, complemented
181C22⋊C4C2×#26111yescharacteristic, complemented
182C13#212111yescharacteristic, complemented, Sylow
183C23—21no—
184C23—21no—
185C23—81no—
186C23—131no—
187C23—131no—
188C23—261no—
189C23—261no—
190C23—261no—
191C23—521no—
192C23—1041no—
193C23—1041no—
194C23C22⋊#26111yescharacteristic
195C23C22⋊#26111yescharacteristic
196C23C22×#26111yescharacteristic
197D4—521no—
198D4—521no—
199D4—521no—
200D4—521no—
201D4—522no—
202D4—521no—
203D4—521no—
204D4—1041no—
205D4—1041no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—81no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—261no—
214C2×C4—521no—
215C2×C4—522no—
216C2×C4—1042no—
217C8—522no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—261no—
226C22—261no—
227C22—521no—
228C22—521no—
229C22—522no—
230C22—521no—
231C22—521no—
232C22—521no—
233C22—1041no—
234C22—1042no—
235C22#8810711yescharacteristic
236C22#8810711yescharacteristic
237C22C2×C22⋊#26111yescharacteristic
238C4—41no—
239C4—41no—
240C4—261no—
241C4—261no—
242C4—521no—
243C4—1042no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—521no—
250C2—521no—
251C2—1041no—
252C2C2×#8810711yescharacteristic
subgroupG/H
centerC2C2×#88107
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C22⋊C4C4
socleC2×C13C2×#99
prime radical#11719198C2
cosocleC2×C22⋊D13C23
hypercenterC2×C22⋊C4#261
hypocenterC13#2121
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#88121C2semidirect
3. C2×#88119C2semidirect
4. #11718237C2semidirect
5. #11718236C2semidirect
6. C22×C22⋊D13C4semidirect
10. C2×C13×C22⋊C4C4semidirect
14. #88140C4semidirect
17. #88136C4semidirect
24. C23×D13C2×C4semidirect
38. C22×Dic13C2×C4semidirect
48. C13×C22⋊C4C2×C4semidirect
49. C13×C22⋊C4C2×C4semidirect
135. C2×C22⋊C4#261semidirect
180. 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
#117191982
C2×#881212
C2×#881192
#117182372
#117182362
#212113