Finite Group Databasebeta

← #15772349

Subgroups — #15772349

Order 3328.

330 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 75 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#13123467C211yesmaximal, characteristic
2#13116648C211yesmaximal, characteristic, complemented
3#13112786C212yesmaximal, complemented
4#13112771C212yesmaximal
5C13×#2165C211yesmaximal, characteristic, complemented
6C2×C42×D13C411yescharacteristic
7C4×C13×M16C2211yescharacteristic
8#11718787C411yescharacteristic
9#11718787C2211yescharacteristic
10#11718779C411yescharacteristic
11#11718779C2211yescharacteristic
12C4×#6099C411yescharacteristic
13#11718366—21no—
14#11718366—21no—
15#11718346—21no—
16#11718346—21no—
17C13×#364—21no—
18C13×#349C2212yes—
19C13×#347—21no—
20#11718145C2212yes—
21#11718058—21no—
22#11718055—21no—
23C22×C4×D13—21no—
24C22×C4×D13C2×C411yescharacteristic
25C2×C13×M16C2×C411yescharacteristic
26C2×C13×M16C2311yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C4×Dic13—21no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C2×#6099C2×C411yescharacteristic
32C42×D13—21no—
33C42×D13—21no—
34C42×D13—21no—
35C42×D13—21no—
36C13×M32—22no—
37C13×#97D411yescharacteristic
38C13×#97D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13D411yescharacteristic
41#88060—21no—
42#88060—21no—
43#88060—21no—
44#88060—21no—
45#88054—21no—
46#88054—21no—
47#88054—21no—
48#88054—21no—
49#88052—22no—
50#88043—21no—
51C4×#1055—21no—
52#11521—131nomaximal, Sylow
53C23×D13M1611yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13M1611yescharacteristic
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13—44no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C13×M16—41no—
68C13×M16—41no—
69C2×C8×C13C22⋊C411yescharacteristic
70C2×C8×C13C22⋊C411yescharacteristic
71C2×C8×C13C2×D411yescharacteristic
72C2×C8×C13C2×D411yescharacteristic
73C42×C13—21no—
74C42×C13C22⋊C411yescharacteristic
75C42×C13C22⋊C411yescharacteristic
76C4×Dic13—21no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13M1611yescharacteristic
82C4×Dic13M1611yescharacteristic
83#6099—41no—
84#6099—41no—
85C2×#1055—21no—
86C2×#1055—21no—
87C13×C16—42no—
88#6090—42no—
89#2920—131no—
90#2165—131no—
91#2165D1311yescharacteristic, complemented
92#1327—132no—
93#1320—132no—
94C23×C13C2×M1611yescharacteristic
95C22×D13—21no—
96C22×D13—42no—
97C22×D13—41no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C4×D13—24no—
111C4×D13—42no—
112C4×D13—42no—
113C4×D13—42no—
114C4×D13—42no—
115C4×D13—41no—
116C4×D13—41no—
117C8×C13—21no—
118C8×C13—21no—
119C8×C13—21no—
120C8×C13—21no—
121#1055—41no—
122#1055—41no—
123C22×C42—131no—
124#432—261no—
125#432—261no—
126#431—261no—
127#431—261no—
128#423—131no—
129#423—131no—
130#407—131no—
131#407—131no—
132C4×M16—131no—
133C4×M16C2×D1311yescharacteristic
134#364—21no—
135#364—261no—
136#349—132no—
137#349C2×D1312yes—
138#347—21no—
139#347—261no—
140C22×C13—21no—
141C22×C13—41no—
142C22×C13#40711yescharacteristic
143C2×D13—22no—
144C2×D13—41no—
145C2×D13—42no—
146C2×D13—41no—
147C2×D13—42no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13#41011yescharacteristic
152C4×C13#41311yescharacteristic
153Dic13—22no—
154Dic13—41no—
155Dic13—41no—
156C23×C4—131no—
157C23×C4—261no—
158C2×M16—131no—
159C2×M16—131no—
160C2×M16C4×D1311yescharacteristic
161C2×M16C22×D1311yescharacteristic
162C2×C42—131no—
163C2×C42—261no—
164C2×C42—261no—
165C2×C42—261no—
166C2×C42—261no—
167C2×C42—261no—
168C2×C42C4×D1311yescharacteristic
169M32—22no—
170M32—262no—
171C4⋊C8—261no—
172C4⋊C8—261no—
173C4⋊C8—261no—
174C4⋊C8—261no—
175C22⋊C8—261no—
176C22⋊C8—261no—
177C22⋊C8—261no—
178C22⋊C8—261no—
179#97—261no—
180#97D5211yescharacteristic
181#97C22⋊D1311yescharacteristic
182C4×C8—261no—
183C4×C8D5211yescharacteristic
184C4×C8C22⋊D1311yescharacteristic
185C2×C13—21no—
186C2×C13—41no—
187C2×C13#146411yescharacteristic
188D13—42no—
189C24—131no—
190C22×C4—21no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—261no—
199C22×C4—521no—
200C22×C4—521no—
201C22×C4—524no—
202C22×C4C2×C4×D1311yescharacteristic
203M16—41no—
204M16—41no—
205M16—521no—
206M16—521no—
207C2×C8—261no—
208C2×C8—261no—
209C2×C8#610311yescharacteristic
210C2×C8#610311yescharacteristic
211C2×C8C2×D5211yescharacteristic
212C2×C8C2×C22⋊D1311yescharacteristic
213C42—21no—
214C42—131no—
215C42—131no—
216C42—261no—
217C42—261no—
218C42—261no—
219C42—261no—
220C42—261no—
221C42#610311yescharacteristic
222C42#610311yescharacteristic
223C16—42no—
224C16—522no—
225C13#1152111yescharacteristic, complemented, Sylow
226C23—261no—
227C23—521no—
228C23—522no—
229C23M16×D1311yescharacteristic
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—264no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—261no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4M16×D1311yescharacteristic
248C2×C4C2×#610311yescharacteristic
249C8—21no—
250C8—21no—
251C8—21no—
252C8—21no—
253C8—521no—
254C8—521no—
255C22—21no—
256C22—41no—
257C22—262no—
258C22—521no—
259C22—522no—
260C22—522no—
261C22—521no—
262C22#1171878711yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—262no—
267C4—521no—
268C4—521no—
269C4#1171866711yescharacteristic
270C4#1171879311yescharacteristic
271C2—21no—
272C2—41no—
273C2—522no—
274C2#1311316811yescharacteristic
subgroupG/H
centerC4#11718667
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2165C2
socleC2×C13#1464
prime radicalC23×D13M16
cosocleC2×C13×M16C23
hypercenter#2165D13
hypocenterC13#11521
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #13116648C2semidirect
3. #13112786C2semidirect
5. C13×#2165C2semidirect
91. #2165D13semidirect
225. C13#11521semidirect

Maximal subgroups

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

subgroupindex
#131234672
#131166482
#131127862
#131127712
C13×#21652
#1152113