Finite Group Databasebeta

← #15772218

Subgroups — #15772218

Order 3328.

382 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 83 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#13123526C211yesmaximal, characteristic
2#13116455C212yesmaximal, complemented
3#13112788C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic, complemented
5C13×#1320C211yesmaximal, characteristic, complemented
6#11719496C411yescharacteristic
7C23×#1055C411yescharacteristic
8C2×#88161C2211yescharacteristic
9C13×#407C2211yescharacteristic
10#11718790C411yescharacteristic
11#11718783C411yescharacteristic
12#11718780C2211yescharacteristic
13D13×M32—22no—
14#11718391—22no—
15#11718386—22no—
16C13×#349C2212yes—
17#11718145C2212yes—
18#11718106—22no—
19C23×C4×C13C2×C411yescharacteristic
20C2×#6127C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23#88207C812yes—
24#88184—21no—
25#88183C812yes—
26C4×C22⋊D13—22no—
27#88180C2×C411yescharacteristic
28#88178—21no—
29C22×#1055—21no—
30C22×#1055—21no—
31C22×#1055—41no—
32C22×#1055—41no—
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35#88161—41no—
36#88161—41no—
37C2×#6094D412yes—
38C2×C8×D13D412yes—
39C13×M32—22no—
40C13×C22⋊C8—22no—
41#88060—22no—
42#88055—21no—
43#88054—22no—
44C8×Dic13—21no—
45#88052—22no—
46#88038—42no—
47C16×D13—42no—
48#11483—131nomaximal, Sylow
49C24×C13C2×C811yescharacteristic
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13C2×C811yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C2×C22⋊D13—22no—
57C2×C22⋊D13C2×C812yes—
58#6127—41no—
59#6127—41no—
60C2×D52M1611yescharacteristic
61C2×C4×D13C22⋊C412yes—
62C2×Dic26M1611yescharacteristic
63C13×M16—41no—
64C13×M16—41no—
65C2×C8×C13—21no—
66C2×C8×C13C2×D412yes—
67C22⋊Dic13—22no—
68C22⋊Dic13C2×C812yes—
69#6103—22no—
70C4⋊Dic13—21no—
71#6101—22no—
72C4×Dic13—21no—
73C2×#1055—21no—
74C2×#1055—21no—
75C2×#1055—21no—
76C2×#1055—42no—
77C2×#1055—41no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055C22⋊C411yescharacteristic
81C2×#1055C22⋊C411yescharacteristic
82#6094—42no—
83C8×D13—22no—
84C8×D13—22no—
85C13×C16—42no—
86#6090—42no—
87#2929—131no—
88#2115—132no—
89#1328—132no—
90#1320—131no—
91#1320D1311yescharacteristic, complemented
92C23×C13—21no—
93C23×C13—41no—
94C23×C13—42no—
95C23×C13C22×C811yescharacteristic
96C22×D13C22⋊C812yes—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13C2×M1611yescharacteristic
106C22⋊D13—42no—
107C22⋊D13—44no—
108C2×Dic13—22no—
109C2×Dic13C22⋊C812yes—
110D52—41no—
111C4×D13—22no—
112C4×D13—22no—
113Dic26—41no—
114C8×C13—22no—
115C8×C13—41no—
116#1055—21no—
117#1055—41no—
118#1055#9911yescharacteristic
119#1055#9911yescharacteristic
120C2×#131—131no—
121C23×C8—131no—
122#525—131no—
123C2×M32—262no—
124#435—262no—
125C8×D4—262no—
126#424—131no—
127#408—131no—
128#407C2×D1311yescharacteristic
129#405—131no—
130#349—132no—
131#349—262no—
132#349C2×D1312yes—
133C22×C13—22no—
134C22×C13—21no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—41no—
140C22×C13C2×C22⋊C811yescharacteristic
141C2×D13—22no—
142C2×D13—42no—
143C4×C13—21no—
144C4×C13—41no—
145C4×C13C2×#9911yescharacteristic
146C4×C13#41311yescharacteristic
147Dic13—22no—
148Dic13—42no—
149C2×#41—131no—
150C23×C4C4×D1311yescharacteristic
151#131—521no—
152#131—521no—
153C2×M16—132no—
154C2×M16C4×D1311yescharacteristic
155C2×M16C22×D1311yescharacteristic
156C22×C8—131no—
157C22×C8—132no—
158C22×C8—131no—
159C22×C8—261no—
160C22×C8—261no—
161C22×C8—521no—
162C22×C8—521no—
163#123—132no—
164C22⋊Q8—261no—
165#121—261no—
166#120—132no—
167C4×D4—262no—
168#117—131no—
169M32—22no—
170M32—262no—
171M32—522no—
172C2×C16—522no—
173C4⋊C8—262no—
174C22⋊C8—22no—
175C22⋊C8—262no—
176#97—261no—
177C4×C8—261no—
178C2×C13—21no—
179C2×C13—42no—
180C2×C13—41no—
181C2×C13#145911yescharacteristic
182D13—42no—
183C24C8×D1311yescharacteristic
184#41—521no—
185#41—521no—
186C2×Q8—131no—
187C2×D4—132no—
188C2×D4—131no—
189C2×D4—262no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—132no—
195C22×C4C8×D1311yescharacteristic
196C22×C4C2×C4×D1311yescharacteristic
197M16—41no—
198M16—41no—
199M16—522no—
200C2×C8—21no—
201C2×C8—131no—
202C2×C8—131no—
203C2×C8—262no—
204C2×C8—262no—
205C2×C8—261no—
206C2×C8—261no—
207C2×C8—261no—
208C2×C8—521no—
209C2×C8—521no—
210C2×C8—522no—
211C2×C8—521no—
212C2×C8D4×D1312yes—
213C4⋊C4—262no—
214C4⋊C4—261no—
215C22⋊C4—132no—
216C22⋊C4—262no—
217C22⋊C4—262no—
218C42—261no—
219C16—42no—
220C16—522no—
221C13#1148311yescharacteristic, complemented, Sylow
222C23—21no—
223C23—41no—
224C23—42no—
225C23—132no—
226C23C2×C8×D1311yescharacteristic
227Q8—521no—
228D4—521no—
229D4—522no—
230D4—524no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—132no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4C22⋊C4×D1311yescharacteristic
243C2×C4M16×D1311yescharacteristic
244C8—22no—
245C8—41no—
246C8—131no—
247C8—131no—
248C8—261no—
249C8—521no—
250C22—22no—
251C22—21no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—262no—
258C22—522no—
259C22D13×C22⋊C811yescharacteristic
260C4—21no—
261C4—41no—
262C4—262no—
263C4—522no—
264C4D13×#9911yescharacteristic
265C4#1171840611yescharacteristic
266C2—21no—
267C2—42no—
268C2—41no—
269C2—522no—
270C2#1311315111yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC23×C13C22×C8
FrattiniC2×M16C22×D13
FittingC13×#1320C2
socleC2×C13#1459
prime radical#11719496C4
cosocleC2×C13×M16C23
hypercenter#1320D13
hypocenterC13#11483
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13116455C2semidirect
3. #13112788C2semidirect
4. #13112772C2semidirect
5. C13×#1320C2semidirect
91. #1320D13semidirect
221. C13#11483semidirect

Maximal subgroups

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

subgroupindex
#131235262
#131164552
#131127882
#131127722
C13×#13202
#1148313