Finite Group Databasebeta

← #14644397

Subgroups — #14644397

Order 2816.

698 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic11C211yesmaximal, characteristic
2#13068471C211yesmaximal, characteristic, complemented
3#13068361C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×D4×Dic11C412yes—
10C22×C4×Dic11—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C4×C22⋊Dic11—21no—
14C2×#66879—21no—
15C4⋊C4×Dic11C412yes—
16C22⋊C4×Dic11—22no—
17C4×C4⋊Dic11C2211yescharacteristic
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×D4⋊C8C414yescomplemented
22#10622188—22no—
23#10622188—21no—
24D4⋊(C11⋊C8)C414yescomplemented
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×Dic11—22no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11C2×C412yes—
33C4×D4×C11C2×C412yes—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38D4×Dic11—24no—
39D4×Dic11—24no—
40C2×C4⋊Dic11C2×C412yes—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11—42no—
44C2×C4×Dic11—42no—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D412yes—
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8C2×C412yescomplemented
53C4×C8×C11—21no—
54C4×C8×C11C2×C412yescomplemented
55C11⋊#95—21no—
56C11⋊#95—22no—
57#66879—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)C2×C412yescomplemented
60C4×C11⋊C8—21no—
61C4×C11⋊C8C2×C412yescomplemented
62#8174—111nomaximal, Sylow
63C24×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—22no—
66C2×D4×C11C4212yes—
67C2×D4×C11M1614yes—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—28no—
79C22×Dic11—22no—
80C22×Dic11—44no—
81C22×Dic11—44no—
82C22×Dic11C22⋊C412yes—
83C22×Dic11C22⋊C412yes—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—42no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4C4212yes—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C42×C11C22×C411yescharacteristic
94C42×C11C22×C411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C22⋊Dic11—28no—
98C4⋊Dic11—22no—
99C4⋊Dic11M1614yes—
100C4×Dic11—22no—
101C4×Dic11—22no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—42no—
105C4×Dic11—44no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108C4×Dic11D812yes—
109C4×Dic11SD1612yes—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C42×D4—111no—
116#1767—111no—
117#1744—111no—
118C2×D4⋊C8—111no—
119C2×D4⋊C8D1111yescharacteristic
120#1279—111no—
121#1279—111no—
122C23×C11—22no—
123C23×C11—24no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—42no—
127C23×C11C2×C22⋊C411yescharacteristic
128D4×C11—22no—
129D4×C11—24no—
130D4×C11#9714yescomplemented
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C2×C4211yescharacteristic
140C2×C4×C11#11711yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C2×M1612yes—
146C2×C4×C11C2×M1612yes—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—24no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—416no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11#10214yes—
161C8×C11—42no—
162C8×C11—42no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C2×C4×D4—112no—
166C2×C4×D4C2×D1111yescharacteristic
167C22×C42—221no—
168C2×C4⋊C8—111no—
169C2×C4⋊C8C2×D1111yescharacteristic
170C2×#97—221no—
171C2×C4×C8—111no—
172C2×C4×C8C2×D1111yescharacteristic
173C4×C4⋊C4—112no—
174C4×C4⋊C4—111no—
175C4×C22⋊C4—222no—
176C4×C22⋊C4—221no—
177C43—111no—
178#336—222no—
179#336—221no—
180D4⋊C8—114no—
181D4⋊C8Dic1114yescomplemented
182C22×C11—24no—
183C22×C11—44no—
184C22×C11—44no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11C4×C22⋊C411yescharacteristic
188C22×C11#40712yes—
189C22×C11C2×#10211yescharacteristic
190C22×C11#41611yescharacteristic
191C22×C11#42112yes—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11C2×#9711yescharacteristic
196C4×C11C4×M1611yescharacteristic
197C4×C11#43212yes—
198C4×C11C4×D811yescharacteristic
199C4×C11C4×D811yescharacteristic
200C4×C11C4×SD1611yescharacteristic
201C4×C11C4×SD1611yescharacteristic
202Dic11—24no—
203Dic11—44no—
204Dic11—42no—
205C22×D4C4×D1111yescharacteristic
206C23×C4—21no—
207C23×C4—222no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—221no—
211C22×C8—221no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—224no—
215C4×D4—224no—
216C4×D4C4×D1112yes—
217C4×D4C2×Dic1112yes—
218C2×C4⋊C4—112no—
219C2×C4⋊C4C4×D1111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—222no—
222C2×C42—111no—
223C2×C42—112no—
224C2×C42—111no—
225C2×C42—112no—
226C2×C42—222no—
227C2×C42—221no—
228C2×C42—442no—
229C2×C42—442no—
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—112no—
233C4⋊C8—221no—
234C4⋊C8C2×Dic1112yescomplemented
235#97—442no—
236C4×C8—21no—
237C4×C8—112no—
238C4×C8—221no—
239C4×C8C2×Dic1112yescomplemented
240#95—222no—
241#95—221no—
242C2×C11—44no—
243C2×C11#148612yes—
244C2×C11#148812yes—
245C2×C11#174911yescharacteristic
246C2×C11#175911yescharacteristic
247C2×C11C4×#10211yescharacteristic
248C24—21no—
249C2×D4—21no—
250C2×D4—22no—
251C2×D4#431314yes—
252C2×D4C4×Dic1112yes—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—112no—
261C22×C4—112no—
262C22×C4—228no—
263C22×C4—222no—
264C22×C4—444no—
265C22×C4—444no—
266C22×C4C2×C4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—442no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—114no—
281C4⋊C4—222no—
282C4⋊C4C4×Dic1112yes—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—228no—
286C42—112no—
287C42—112no—
288C42—222no—
289C42—222no—
290C42—221no—
291C42—221no—
292C42—442no—
293C42—444no—
294C42—441no—
295C42—441no—
296C42C2×C4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42#434111yescharacteristic
299C42C22×Dic1111yescharacteristic
300C11#817411yescharacteristic, complemented, Sylow
301C23—22no—
302C23—24no—
303C23—41no—
304C23—41no—
305C23—42no—
306C23C22⋊C4×D1111yescharacteristic
307D4—22no—
308D4—24no—
309D4#6687914yescomplemented
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—114no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—224no—
323C2×C4—222no—
324C2×C4—222no—
325C2×C4—4416no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4#6693011yescharacteristic
329C2×C4(C22⋊D11)⋊C411yescharacteristic
330C2×C4(C22⋊D11)⋊C411yescharacteristic
331C2×C4C2×#431312yes—
332C2×C4M16×D1112yes—
333C2×C4D8×D1111yescharacteristic
334C2×C4#6696511yescharacteristic
335C2×C4SD16×D1111yescharacteristic
336C2×C4#6696911yescharacteristic
337C2×C4C2×C4×Dic1111yescharacteristic
338C2×C4D4×Dic1111yescharacteristic
339C2×C4D4×Dic1111yescharacteristic
340C8—42no—
341C8—42no—
342C8—442no—
343C8—442no—
344C22—24no—
345C22—44no—
346C22—44no—
347C22—42no—
348C22—42no—
349C22#1062233912yes—
350C22D11×#10211yescharacteristic
351C22#1062238511yescharacteristic
352C22#1062243412yes—
353C22C22⋊C4×Dic1111yescharacteristic
354C4—21no—
355C4—21no—
356C4—42no—
357C4—224no—
358C4—444no—
359C4—442no—
360C4#1062233212yes—
361C4#1062236911yescharacteristic
362C4#1062237111yescharacteristic
363C4C2×#6687911yescharacteristic
364C4M16×Dic1111yescharacteristic
365C4D8×Dic1111yescharacteristic
366C4SD16×Dic1111yescharacteristic
367C2—44no—
368C2#1306703912yes—
369C2#1306704712yes—
370C2#1306838011yescharacteristic
371C2#1306842811yescharacteristic
372C2#102×Dic1111yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×D4⋊C8D11
hypocenterC11#8174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068471C2semidirect
3. #13068361C2semidirect
5. #13066456C2semidirect
6. #13066455C2semidirect
21. C11×D4⋊C8C4semidirect
24. D4⋊(C11⋊C8)C4semidirect
52. C11×C4⋊C8C2×C4semidirect
54. C4×C8×C11C2×C4semidirect
59. C4⋊(C11⋊C8)C2×C4semidirect
61. C4×C11⋊C8C2×C4semidirect
130. D4×C11#97semidirect
181. D4⋊C8Dic11semidirect
234. C4⋊C8C2×Dic11semidirect
239. C4×C8C2×Dic11semidirect
300. C11#8174semidirect
309. D4#66879semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic112
#130684712
#130683612
C2×D4⋊(C11⋊C8)2
#130664562
#130664552
C2×C11×D4⋊C82
#817411