Finite Group Databasebeta

← #15751234

Subgroups — #15751234

Order 3328.

468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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#13114979C212yesmaximal, 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
14#11718116—22no—
15#11718116—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—
39#7649—131nomaximal, Sylow
40C24×C13—21no—
41C2×Q8×C13—21no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C2×Q8×C13M1612yes—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13M1612yes—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—44no—
53C22×C4×C13—42no—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D412yes—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C22⋊C4—28no—
63C13×C22⋊C4—42no—
64C13×C22⋊C4—44no—
65C42×C13—22no—
66C42×C13—21no—
67C42×C13—21no—
68C42×C13—24no—
69C42×C13—42no—
70C42×C13—41no—
71C42×C13—42no—
72C2×#1055—44no—
73C2×#1055—44no—
74C2×#1055—44no—
75C4×#124D1311yescharacteristic
76#1839—132no—
77#1272—132no—
78#1270—132no—
79C23×C13—22no—
80C23×C13—41no—
81C23×C13—41no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87D4×C13—42no—
88D4×C13—42no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—84no—
107C2×C4×C13#10012yes—
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C2×C4×C13#13514yes—
111#1055—84no—
112C2×#124Dic1311yescharacteristic
113C2×C4×Q8Dic1311yescharacteristic
114C2×C4×D4Dic1311yescharacteristic
115#391C2×D1311yescharacteristic
116#390C2×D1311yescharacteristic
117#388—22no—
118#382Dic1311yescharacteristic
119C4×C22⋊C4—22no—
120C43C2×D1311yescharacteristic
121#336—134no—
122#336—262no—
123#336—262no—
124C22×C13—42no—
125C22×C13—44no—
126C22×C13—81no—
127C22×C13—82no—
128C22×C13—81no—
129C22×C13#40711yescharacteristic
130C22×C13#41011yescharacteristic
131C22×C13C2×#10011yescharacteristic
132C22×C13#41612yes—
133C22×C13#42112yes—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—24no—
137C4×C13—22no—
138C4×C13—41no—
139C4×C13—42no—
140C4×C13—42no—
141C4×C13—81no—
142C4×C13—81no—
143C22×Q8C2×Dic1311yescharacteristic
144C22×D4C2×Dic1311yescharacteristic
145C23×C4—21no—
146C22×C8—264no—
147#124—22no—
148#124—22no—
149C4×Q8—42no—
150C4×D4—42no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4C2×Dic1311yescharacteristic
153C2×C4⋊C4C2×Dic1311yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—22no—
157C2×C42—21no—
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C2×Dic1311yescharacteristic
160C2×C42C22⋊D1312yes—
161C2×C42C22⋊D1312yes—
162C2×C42C22×D1311yescharacteristic
163#95—22no—
164#95—22no—
165C2×C13—82no—
166C2×C13#146611yescharacteristic
167C2×C13#148812yes—
168C2×C13#152112yes—
169C2×C13#153311yescharacteristic
170C2×C13#154311yescharacteristic
171C24—21no—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8#609912yes—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#609912yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—44no—
184C22×C4—42no—
185C22×C4C22⋊Dic1312yes—
186C22×C4C22⋊Dic1311yescharacteristic
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22×Dic1311yescharacteristic
189C22×C4C2×C22⋊D1312yes—
190C2×C8—524no—
191C2×C8—524no—
192C2×C8—524no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C22⋊C4—28no—
197C22⋊C4—42no—
198C22⋊C4—44no—
199C42—22no—
200C42—21no—
201C42—21no—
202C42—24no—
203C42—42no—
204C42—41no—
205C42—42no—
206C13#764911yescharacteristic, complemented, Sylow
207C23—22no—
208C23—41no—
209C23—42no—
210C23—42no—
211C23—41no—
212C23C2×C22⋊Dic1311yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4#8807312yes—
236C2×C4C2×#609911yescharacteristic
237C2×C4C2×#609911yescharacteristic
238C2×C4#8820414yes—
239C8—1044no—
240C22—42no—
241C22—44no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22#1171886811yescharacteristic
246C22C2×#8807311yescharacteristic
247C22#1171889412yes—
248C22#1171889712yes—
249C22#1171890111yescharacteristic
250C4—24no—
251C4—21no—
252C4—21no—
253C4—22no—
254C4—42no—
255C4—41no—
256C4—42no—
257C4—81no—
258C4—81no—
259C2—82no—
260C2#1311317711yescharacteristic
261C2#1311327012yes—
262C2#1311341312yes—
263C2#1311346011yescharacteristic
264C2#1311349811yescharacteristic
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#7649
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. #13114979C2semidirect
2. #13112662C2semidirect
206. C13#7649semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131126622
#131126572
C4×C13×#1242
#764913