Finite Group Databasebeta

← #14682286

Subgroups — #14682286

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C212yesmaximal
2#13066887C212yesmaximal
3#13066869C214yesmaximal
4#13066848C214yesmaximal
5#13066843C212yesmaximal
6C22×C11×C4⋊Q8C211yesmaximal, characteristic
7C23×Q8×C11C2211yescharacteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊Q8—28no—
10C2×C11×C4⋊Q8C418yescomplemented
11C22×C11×C4⋊C4C2214yes—
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C22×C4×Dic11C2212yes—
15#10622843—28no—
16C2×C11⋊#95C2214yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2214yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C22×Q8×C11—24no—
25C22×Q8×C11—41no—
26C22×Q8×C11—42no—
27C22×Q8×C11—41no—
28C22×Q8×C11—42no—
29C22×Q8×C11—41no—
30C22×Q8×C11—41no—
31C22×Q8×C11C2×C414yes—
32C22×Q8×C11C2×C414yes—
33C22×Q8×C11D418yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×Dic11C2314yes—
39C23×Dic11C2314yes—
40C11×C4⋊Q8—232no—
41C2×C11×C4⋊C4—28no—
42C2×C11×C4⋊C4—28no—
43C2×C11×C4⋊C4C2×C4116yes—
44C2×C42×C11—24no—
45C2×C42×C11C2×C414yes—
46C2×C4⋊Dic11—24no—
47C2×C4⋊Dic11—42no—
48C2×C4⋊Dic11—42no—
49C2×C4×Dic11—24no—
50C2×C4×Dic11—42no—
51C2×C4×Dic11—42no—
52C11⋊#95—28no—
53C11⋊#95—28no—
54C11⋊#95—28no—
55C11⋊#95—24no—
56C11⋊#95—42no—
57C11⋊#95—44no—
58C11⋊#95—42no—
59C11⋊#95Q818yescomplemented
60#14450—111nomaximal, Sylow
61C24×C11C2411yescharacteristic
62C2×Q8×C11—28no—
63C2×Q8×C11—44no—
64C2×Q8×C11—44no—
65C2×Q8×C11—44no—
66C2×Q8×C11—44no—
67C2×Q8×C11—48no—
68C2×Q8×C11—48no—
69C2×Q8×C11—48no—
70C2×Q8×C11—48no—
71C2×Q8×C11C22⋊C4116yes—
72C22×C4×C11—24no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C414yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C414yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2×D414yes—
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2×Q814yes—
93C22×C4×C11#4114yes—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—24no—
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—24no—
107C22×Dic11C2×Q818yes—
108C11×C4⋊C4—232no—
109C42×C11—28no—
110C4⋊Dic11—48no—
111C4×Dic11—48no—
112C22×C4⋊Q8D1111yescharacteristic
113C2×#391—112no—
114#1446—112no—
115#1441—114no—
116#1436—114no—
117#1434—112no—
118C23×C11C23×C411yescharacteristic
119C23×C11C22×D412yes—
120C23×C11C22×Q812yes—
121C23×C11C2×#4112yes—
122C23×C11H(5,𝔽2)12yes—
123C23×C11H(5,𝔽2)11yescharacteristic
124C23×C11H(5,𝔽2)11yescharacteristic
125C23×C112−1+414yes—
126Q8×C11—416no—
127Q8×C11—416no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—24no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11C2×C22⋊C414yes—
148C2×C4×C11C2×C22⋊C418yes—
149C2×C4×C11C4×Q818yes—
150C2×Dic11—28no—
151C2×Dic11—28no—
152C2×Dic11—28no—
153C2×Dic11—44no—
154C2×Dic11—44no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C23×Q8C2×D1111yescharacteristic
165C23×Q8C2×D1111yescharacteristic
166C2×C4⋊Q8—28no—
167C2×C4⋊Q8Dic1118yescomplemented
168C22×C4⋊C4—112no—
169C22×C4⋊C4C2×D1114yes—
170C22×C42—112no—
171C22×C42C2×D1111yescharacteristic
172#391—228no—
173C2×#95—112no—
174C2×#95—114no—
175C2×#95—112no—
176C2×#95—114no—
177C2×#95—114no—
178C2×#95—112no—
179C2×#95—114no—
180C2×#95—112no—
181C22×C11C22×C22⋊C411yescharacteristic
182C22×C11C2×C4×Q812yes—
183C22×C11#51811yescharacteristic
184C22×C11#51811yescharacteristic
185C22×C11#51912yes—
186C22×C11#53412yes—
187C22×C11#53412yes—
188C22×C11#54214yes—
189C22×C11#54414yes—
190C22×C11#54814yes—
191C22×C11D4×Q814yes—
192C22×C11#55412yes—
193C22×C11#55511yescharacteristic
194C22×C11Q8211yescharacteristic
195C22×C11#56312yes—
196C22×C11#56312yes—
197C4×C11—28no—
198C4×C11—24no—
199C4×C11—28no—
200C4×C11—44no—
201Dic11—48no—
202Dic11—84no—
203C22×Q8—24no—
204C22×Q8—41no—
205C22×Q8—42no—
206C22×Q8—41no—
207C22×Q8—41no—
208C22×Q8—42no—
209C22×Q8—41no—
210C22×Q8C2×Dic1114yes—
211C22×Q8C2×Dic1114yes—
212C22×Q8C22⋊D1118yes—
213C23×C4—114no—
214C23×C4—114no—
215C23×C4C22×D1112yes—
216C23×C4C22×D1112yes—
217C23×C4C22×D1112yes—
218C23×C4C22×D1111yescharacteristic
219C4⋊Q8—232no—
220C2×C4⋊C4—28no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—224no—
223C2×C4⋊C4—442no—
224C2×C4⋊C4—442no—
225C2×C4⋊C4C2×Dic11116yes—
226C2×C42—24no—
227C2×C42—224no—
228C2×C42—442no—
229C2×C42—442no—
230C2×C42C2×Dic1114yes—
231#95—118no—
232#95—228no—
233#95—224no—
234#95—228no—
235#95—228no—
236#95—442no—
237#95—444no—
238#95—442no—
239C2×C11#230811yescharacteristic
240C2×C11#233112yes—
241C2×C11Q8×C22⋊C412yes—
242C2×C11#236911yescharacteristic
243C2×C11#238111yescharacteristic
244C2×C11#272914yes—
245C2×C11#273112yes—
246C2×C11#273412yes—
247C24C23×D1111yescharacteristic
248C2×Q8—28no—
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—48no—
254C2×Q8—48no—
255C2×Q8—48no—
256C2×Q8—48no—
257C2×Q8C22⋊Dic11116yes—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—118no—
272C22×C4—224no—
273C22×C4—224no—
274C22×C4—224no—
275C22×C4—224no—
276C22×C4—224no—
277C22×C4—224no—
278C22×C4—224no—
279C22×C4—224no—
280C22×C4—224no—
281C22×C4—224no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—224no—
285C22×C4Q8×D1114yes—
286C22×C4#434314yes—
287C22×C4C22×Dic1114yes—
288C22×C4C22×Dic1114yes—
289C22×C4C22×Dic1112yes—
290C22×C4C22×Dic1114yes—
291C22×C4C2×C22⋊D1114yes—
292C22×C4C2×C22⋊D1114yes—
293C22×C4C2×C22⋊D1114yes—
294C4⋊C4—232no—
295C4⋊C4—448no—
296C42—28no—
297C42—448no—
298C11#1445011yescharacteristic, complemented, Sylow
299C23#6703711yescharacteristic
300C23#6703712yes—
301C23#6703711yescharacteristic
302C23C2×Q8×D1112yes—
303C23C2×#434312yes—
304C23#6704014yes—
305C23C23×Dic1111yescharacteristic
306C23C22×C22⋊D1112yes—
307Q8—416no—
308Q8—416no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—28no—
321C2×C4—28no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—228no—
329C2×C4—228no—
330C2×C4—228no—
331C2×C4—444no—
332C2×C4—444no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4—444no—
339C2×C4—444no—
340C2×C4—444no—
341C2×C4—444no—
342C2×C4Q8×Dic1118yes—
343C2×C4C2×C22⋊Dic1114yes—
344C2×C4C2×C22⋊Dic1118yes—
345C22#1062325311yescharacteristic
346C22#1062326014yes—
347C22#1062326112yes—
348C22#1062326414yes—
349C22#1062326511yescharacteristic
350C22#1062326612yes—
351C22#1062326612yes—
352C22#1062332911yescharacteristic
353C22#1062332911yescharacteristic
354C22#1062333512yes—
355C22#1062333512yes—
356C22C2×Q8×Dic1112yes—
357C22#1062334312yes—
358C22Q8×C22⋊D1114yes—
359C22#1062334814yes—
360C22C22×C22⋊Dic1111yescharacteristic
361C4—24no—
362C4—28no—
363C4—28no—
364C4—44no—
365C4—448no—
366C4—884no—
367C2#1307119411yescharacteristic
368C2#1307136512yes—
369C2Q8×C22⋊Dic1112yes—
370C2#1307170611yescharacteristic
371C2#1307179711yescharacteristic
372C2#1307559214yes—
373C2#1307562212yes—
374C2#1307564612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×C4⋊Q8C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#14450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
10. C2×C11×C4⋊Q8C4semidirect
59. C11⋊#95Q8semidirect
167. C2×C4⋊Q8Dic11semidirect
298. C11#14450semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
#130668872
#130668692
#130668482
#130668432
C22×C11×C4⋊Q82
#1445011