Finite Group Databasebeta

← #15751180

Subgroups — #15751180

Order 3328.

520 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 135 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#13114689C212yesmaximal, complemented
2#13112662C212yesmaximal, complemented
3#13112657C212yesmaximal
4C4×C13×#124C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#382C411yescharacteristic
12C4×C13×C22⋊C4—22no—
13C43×C13C2211yescharacteristic
14C2×C4⋊#1055—22no—
15C2×#88043—22no—
16#11718116C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C13×#124—22no—
21C13×#124—22no—
22C4×Q8×C13—42no—
23C4×D4×C13—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—22no—
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D412yes—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C22×#1055—24no—
37C13×#95—22no—
38C13×#95—22no—
39C4⋊#1055—28no—
40#88043—44no—
41#7635—131nomaximal, Sylow
42C24×C13—21no—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13M1612yes—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13M1612yes—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—42no—
55C22×C4×C13—44no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—28no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C42×C13—22no—
69C42×C13—24no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—41no—
75C42×C13—42no—
76C2×#1055—28no—
77C2×#1055—44no—
78C2×#1055—44no—
79C4×#124D1311yescharacteristic
80#1767—132no—
81#1272—132no—
82#1270—132no—
83C23×C13—22no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—42no—
90Q8×C13—42no—
91D4×C13—42no—
92D4×C13—42no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—84no—
110C2×C4×C13#10012yes—
111C2×C4×C13#10414yes—
112C2×C4×C13C2×M1611yescharacteristic
113C2×C4×C13C2×M1611yescharacteristic
114C2×C4×C13AGL(1,ℤ/8)12yes—
115C2×C4×C13#13712yes—
116#1055—48no—
117C2×#124Dic1311yescharacteristic
118C2×C4×Q8Dic1311yescharacteristic
119C2×C4×D4Dic1311yescharacteristic
120C2×C4⋊C8—262no—
121C2×#97—262no—
122#391C2×D1311yescharacteristic
123#390C2×D1311yescharacteristic
124#388—22no—
125#382Dic1311yescharacteristic
126C4×C22⋊C4—22no—
127C43C2×D1311yescharacteristic
128#336—134no—
129C22×C13—42no—
130C22×C13—44no—
131C22×C13—81no—
132C22×C13—82no—
133C22×C13—81no—
134C22×C13#40711yescharacteristic
135C22×C13#41011yescharacteristic
136C22×C13C2×#10011yescharacteristic
137C22×C13#41712yes—
138C22×C13C2×#10412yes—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—41no—
144C4×C13—42no—
145C4×C13—42no—
146C4×C13—81no—
147C4×C13—81no—
148C4×C13#32914yes—
149C22×Q8C2×Dic1311yescharacteristic
150C22×D4C2×Dic1311yescharacteristic
151C23×C4—21no—
152C22×C8—264no—
153#124—22no—
154#124—22no—
155C4×Q8—42no—
156C4×D4—42no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C2×Dic1311yescharacteristic
159C2×C4⋊C4C2×Dic1311yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—22no—
163C2×C42—21no—
164C2×C42C2×Dic1311yescharacteristic
165C2×C42C2×Dic1311yescharacteristic
166C2×C42C22⋊D1312yes—
167C2×C42C22⋊D1312yes—
168C2×C42C22×D1311yescharacteristic
169C4⋊C8—268no—
170#97—524no—
171#95—22no—
172#95—22no—
173C2×C13—82no—
174C2×C13#146611yescharacteristic
175C2×C13#148912yes—
176C2×C13#150912yes—
177C2×C13C2×#32911yescharacteristic
178C2×C13#156011yescharacteristic
179C24—21no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8#609912yes—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4#609912yes—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4—44no—
193C22×C4C22⋊Dic1312yes—
194C22×C4C22⋊Dic1311yescharacteristic
195C22×C4C22⋊Dic1311yescharacteristic
196C22×C4C22×Dic1311yescharacteristic
197C22×C4C2×C22⋊D1312yes—
198C2×C8—268no—
199C2×C8—524no—
200C2×C8—524no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C22⋊C4—28no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—22no—
209C42—24no—
210C42—21no—
211C42—21no—
212C42—22no—
213C42—22no—
214C42—41no—
215C42—42no—
216C13#763511yescharacteristic, complemented, Sylow
217C23—22no—
218C23—41no—
219C23—42no—
220C23—42no—
221C23—41no—
222C23C2×C22⋊Dic1311yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—84no—
244C2×C4#8807312yes—
245C2×C4#8807714yes—
246C2×C4C2×#609911yescharacteristic
247C2×C4C2×#609911yescharacteristic
248C2×C4#8820312yes—
249C2×C4#8820512yes—
250C8—528no—
251C22—42no—
252C22—44no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1171886811yescharacteristic
257C22C2×#8807311yescharacteristic
258C22#1171889312yes—
259C22C2×#8807712yes—
260C22#1171890111yescharacteristic
261C4—22no—
262C4—22no—
263C4—21no—
264C4—21no—
265C4—42no—
266C4—42no—
267C4—41no—
268C4—81no—
269C4—81no—
270C4#1171813214yes—
271C2—82no—
272C2#1311317711yescharacteristic
273C2#1311327512yes—
274C2#1311336112yes—
275C2C2×#1171813211yescharacteristic
276C2#1311357111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#124C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenterC4×#124D13
hypocenterC13#7635
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #13114689C2semidirect
2. #13112662C2semidirect
216. C13#7635semidirect

Maximal subgroups

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

subgroupindex
#131146892
#131126622
#131126572
C4×C13×#1242
#763513