Finite Group Databasebeta

← #14652011

Subgroups — #14652011

Order 2816.

378 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13067368C211yesmaximal, characteristic, complemented
2#13067007C211yesmaximal, characteristic
3C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
4M16×C11⋊C8C211yesmaximal, characteristic, complemented
5#13066467C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C4×C11×#100C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×C11×#100C411yescharacteristic
10C2×C11×#100C411yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622538C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C11×#343C411yescharacteristic
18C11×#343C411yescharacteristic
19D4⋊(C11⋊C8)—21no—
20D4⋊(C11⋊C8)—21no—
21D4⋊(C11⋊C8)—21no—
22D4⋊(C11⋊C8)—21no—
23#10622096—21no—
24#10622095—21no—
25#10622093—21no—
26C8×C11⋊C8—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11—21no—
29C2×C11×M16C2×C411yescharacteristic
30C2×C11×M16C2×C411yescharacteristic
31C2×C11×M16C2×C411yescharacteristic
32C2×C11×M16C2×C411yescharacteristic
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C22×C11⋊C8—21no—
41C22×C11⋊C8—21no—
42C11×#100—22no—
43C11×#100C814yescomplemented
44C11×#97—21no—
45C11×#97—21no—
46C4×C8×C11—21no—
47C4×C8×C11—21no—
48C22⋊(C11⋊C8)—21no—
49C22⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54C4⋊(C11⋊C8)D411yescharacteristic
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8D411yescharacteristic
59C4×C11⋊C8D411yescharacteristic
60#9550—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11C2×C812yes—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—81no—
72C22×C4×C11—81no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C11×M16—21no—
77C11×M16—21no—
78C11×M16—21no—
79C11×M16—21no—
80C11×M16—21no—
81C11×M16C2×C812yes—
82C11×M16C2×C812yes—
83C11×M16M1612yes—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—81no—
104C4×#100D1111yescharacteristic
105#1565—111no—
106#1478—111no—
107C2×D4⋊C8—111no—
108C8×M16—111no—
109#1283—111no—
110#1278—111no—
111C23×C11—22no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—81no—
115C23×C11—81no—
116C23×C11#11711yescharacteristic
117D4×C11—22no—
118D4×C11—22no—
119D4×C11—41no—
120D4×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—82no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12611yescharacteristic
135C2×C4×C11C22×C811yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11#13111yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C8×C11—22no—
140C8×C11—22no—
141C8×C11—22no—
142C8×C11—41no—
143C11⋊C8—22no—
144C11⋊C8—41no—
145C11⋊C8—41no—
146C11⋊C8—41no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149C2×C4×D4C2×D1111yescharacteristic
150#431—111no—
151#431—111no—
152C2×C4⋊C8—111no—
153C2×#100Dic1111yescharacteristic
154C2×#100Dic1111yescharacteristic
155C4×M16C2×D1111yescharacteristic
156C4×M16C2×D1111yescharacteristic
157C2×C4×C8—111no—
158#343Dic1111yescharacteristic
159#343Dic1111yescharacteristic
160#335—221no—
161#334—221no—
162D4⋊C8—221no—
163D4⋊C8—221no—
164D4⋊C8—221no—
165D4⋊C8—221no—
166#322—221no—
167C82—221no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—42no—
171C22×C11—82no—
172C22×C11—82no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38811yescharacteristic
176C22×C11#43111yescharacteristic
177C22×C11#43311yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11C8×D411yescharacteristic
183C4×C11C8×D411yescharacteristic
184C4×C11#43511yescharacteristic
185C4×C11#43611yescharacteristic
186C4×C11#47111yescharacteristic
187C4×C11#47211yescharacteristic
188C22×D4C2×Dic1111yescharacteristic
189C23×C4—21no—
190C2×M16C2×Dic1111yescharacteristic
191C2×M16C2×Dic1111yescharacteristic
192C2×M16C2×Dic1111yescharacteristic
193C2×M16C2×Dic1111yescharacteristic
194C22×C8—221no—
195C22×C8—221no—
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200C2×C4⋊C4C2×Dic1111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C42C22×D1111yescharacteristic
203C4⋊C8—111no—
204C4⋊C8—111no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#100—22no—
209#100C11⋊C814yescomplemented
210C22⋊C8—221no—
211C22⋊C8—221no—
212#97—21no—
213#97—21no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—111no—
217C4×C8—111no—
218C4×C8—221no—
219C4×C8—221no—
220C4×C8—221no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—82no—
224C2×C11#192311yescharacteristic
225C2×C11#193111yescharacteristic
226C2×C11#193211yescharacteristic
227C24—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4C2×C11⋊C812yes—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4#433911yescharacteristic
240C22×C4#433911yescharacteristic
241C22×C4C22×Dic1111yescharacteristic
242M16—21no—
243M16—21no—
244M16—21no—
245M16—21no—
246M16—21no—
247M16C2×C11⋊C812yes—
248M16C2×C11⋊C812yes—
249M16#431812yes—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—442no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—881no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42D4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C42#434111yescharacteristic
269C42#434111yescharacteristic
270C11#955011yescharacteristic, complemented, Sylow
271C23—22no—
272C23—41no—
273C23—41no—
274C23—81no—
275C23—81no—
276C23#6697911yescharacteristic
277D4—22no—
278D4—22no—
279D4—41no—
280D4—41no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#6693211yescharacteristic
290C2×C4#6693611yescharacteristic
291C2×C4#6693711yescharacteristic
292C2×C4#6693811yescharacteristic
293C2×C4C22×C11⋊C811yescharacteristic
294C2×C4C2×#431811yescharacteristic
295C2×C4D4×Dic1111yescharacteristic
296C2×C4D4×Dic1111yescharacteristic
297C2×C4#6700111yescharacteristic
298C2×C4#6700111yescharacteristic
299C8—22no—
300C8—22no—
301C8—22no—
302C8—41no—
303C8—222no—
304C8—441no—
305C8—441no—
306C8—441no—
307C8—881no—
308C8—881no—
309C22—21no—
310C22—21no—
311C22—42no—
312C22—82no—
313C22—82no—
314C22—81no—
315C22—81no—
316C22#1062253811yescharacteristic
317C22#1062256411yescharacteristic
318C22#1062261311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—81no—
323C4#1062236111yescharacteristic
324C4#1062236211yescharacteristic
325C4D4×C11⋊C811yescharacteristic
326C4D4×C11⋊C811yescharacteristic
327C4#1062262411yescharacteristic
328C4#1062262511yescharacteristic
329C2—21no—
330C2—21no—
331C2—82no—
332C2#1306922411yescharacteristic
333C2#1306928011yescharacteristic
334C2#1306928711yescharacteristic
subgroupG/H
centerC2×C4#66937
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC4×C11×#100C2
socleC22×C11#388
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC4×#100D11
hypocenterC11#9550
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
1. #13067368C2semidirect
4. M16×C11⋊C8C2semidirect
5. #13066467C2semidirect
6. #13066454C2semidirect
43. C11×#100C8semidirect
209. #100C11⋊C8semidirect
270. C11#9550semidirect

Maximal subgroups

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

subgroupindex
#130673682
#130670072
C2×D4⋊(C11⋊C8)2
M16×C11⋊C82
#130664672
#130664542
C4×C11×#1002
#955011