Finite Group Databasebeta

← #14690482

Subgroups — #14690482

Order 2816.

1934 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
1C2×#10622842C214yesmaximal
2C2×#10622541C211yesmaximal, characteristic
3C2×#10622589C212yesmaximal
4#13066879C214yesmaximal
5#13066845C212yesmaximal
6C4×C11⋊#95C211yesmaximal, characteristic
7C22×C11×C4⋊Q8C211yesmaximal, characteristic
8C23×Q8×C11C2212yes—
9C2×C11×C4⋊Q8—28no—
10C2×C11×C4⋊Q8—24no—
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2218yes—
18C22×C4×Dic11C2212yes—
19#10622842—216no—
20C2×C11⋊#95C2218yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24#10622589—28no—
25#10622541—24no—
26C22×Q8×C11—28no—
27C22×Q8×C11—24no—
28C22×Q8×C11—28no—
29C22×Q8×C11—44no—
30C23×C4×C11C2314yes—
31C23×C4×C11C2311yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11C2312yes—
35C23×Dic11C2312yes—
36C23×Dic11C2314yes—
37C11×C4⋊Q8—232no—
38C2×C11×C4⋊C4—28no—
39C2×C11×C4⋊C4—24no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4D418yes—
43C2×C42×C11—24no—
44C2×C42×C11D414yes—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—24no—
49C2×C4⋊Dic11Q814yescomplemented
50C2×Dic11⋊C4—24no—
51C2×Dic11⋊C4—28no—
52C2×Dic11⋊C4—216no—
53C2×Dic11⋊C4—216no—
54C2×Dic11⋊C4—48no—
55C2×C4×Dic11—24no—
56C2×C4×Dic11—24no—
57C2×C4×Dic11Q818yescomplemented
58C11⋊#95—24no—
59C11⋊#95—216no—
60C11⋊#95D418yes—
61C11⋊#95Q818yescomplemented
62#15143—111nomaximal, Sylow
63C24×C11C2411yescharacteristic
64C2×Q8×C11—216no—
65C2×Q8×C11—432no—
66C2×Q8×C11—48no—
67C2×Q8×C11—48no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—28no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—28no—
76C22×C4×C11C2×D418yes—
77C22×C4×C11C2×D414yes—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D414yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q814yes—
83C22×C4×C11C2×Q814yes—
84C22×C4×C11C2×Q812yes—
85C22×C4×C11#4112yes—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—22no—
94C22×Dic11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11C2×D418yes—
99C22×Dic11C2×Q814yes—
100C22×Dic11C2×Q818yes—
101C22×Dic11C2×Q818yes—
102C11×C4⋊C4—216no—
103C11×C4⋊C4—216no—
104C42×C11—28no—
105C4⋊Dic11—28no—
106C4⋊Dic11—44no—
107Dic11⋊C4—432no—
108Dic11⋊C4—48no—
109C4×Dic11—216no—
110C22×C4⋊Q8D1111yescharacteristic
111C2×#395—114no—
112C2×#389—111no—
113C2×#384—112no—
114#1444—114no—
115C4⋊#95—112no—
116C4×#95—111no—
117C23×C11C22×D412yes—
118C23×C11C22×D411yescharacteristic
119C23×C11C22×D412yes—
120C23×C11C22×Q812yes—
121C23×C11C22×Q811yescharacteristic
122C23×C11C22×Q812yes—
123C23×C11C2×#4111yescharacteristic
124C23×C11H(5,𝔽2)12yes—
125C23×C112−1+412yes—
126Q8×C11—432no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—28no—
134C2×C4×C11—216no—
135C2×C4×C11—44no—
136C2×C4×C11—44no—
137C2×C4×C11—48no—
138C2×C4×C11#12014yes—
139C2×C4×C11C22⋊Q818yes—
140C2×C4×C11C22⋊Q814yes—
141C2×C4×C11#12714yes—
142C2×C4×C11C4⋊Q814yes—
143C2×C4×C11C4⋊Q814yes—
144C2×C4×C11C4⋊Q818yes—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—28no—
151C2×Dic11—24no—
152C2×Dic11—28no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—44no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—48no—
160C2×Dic11C4⋊Q8116yescomplemented
161C23×Q8C2×D1112yes—
162C2×C4⋊Q8—28no—
163C2×C4⋊Q8—24no—
164C22×C4⋊C4—111no—
165C22×C4⋊C4—112no—
166C22×C4⋊C4—111no—
167C22×C4⋊C4—118no—
168C22×C4⋊C4C2×D1112yes—
169C22×C4⋊C4C2×D1112yes—
170C22×C42—112no—
171C22×C42C2×D1111yescharacteristic
172#395—2216no—
173#389—224no—
174#384—228no—
175C2×#95—112no—
176C2×#95—112no—
177C2×#95—118no—
178C2×#95—112no—
179C22×C11C2×#12011yescharacteristic
180C22×C11C2×C22⋊Q811yescharacteristic
181C22×C11C2×C22⋊Q812yes—
182C22×C11C2×#12711yescharacteristic
183C22×C11C2×C4⋊Q814yes—
184C22×C11C2×C4⋊Q811yescharacteristic
185C22×C11C2×C4⋊Q811yescharacteristic
186C22×C11C2×C4⋊Q812yes—
187C22×C11#53511yescharacteristic
188C22×C11#53611yescharacteristic
189C22×C11#54414yes—
190C22×C11D4214yes—
191C22×C11#54712yes—
192C22×C11D4×Q812yes—
193C22×C11D4×Q814yes—
194C22×C11#55412yes—
195C22×C11Q8212yes—
196C4×C11—24no—
197C4×C11—24no—
198C4×C11—48no—
199C4×C11#39518yescomplemented
200Dic11—216no—
201Dic11—44no—
202Dic11—82no—
203C22×Q8—28no—
204C22×Q8—28no—
205C22×Q8—24no—
206C22×Q8—44no—
207C23×C4—114no—
208C23×C4—112no—
209C23×C4—112no—
210C23×C4C22×D1114yes—
211C23×C4C22×D1111yescharacteristic
212C23×C4C22×D1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C4⋊Q8—232no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—114no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4—2216no—
223C2×C4⋊C4—228no—
224C2×C4⋊C4—2216no—
225C2×C4⋊C4—224no—
226C2×C4⋊C4—224no—
227C2×C4⋊C4—222no—
228C2×C4⋊C4—448no—
229C2×C4⋊C4C22⋊D1118yes—
230C2×C42—24no—
231C2×C42—118no—
232C2×C42—224no—
233C2×C42—224no—
234C2×C42C22⋊D1114yes—
235#95—118no—
236#95—118no—
237#95—2216no—
238#95—224no—
239C2×C11C2×#39511yescharacteristic
240C2×C11#243311yescharacteristic
241C2×C11#243411yescharacteristic
242C2×C11#244014yes—
243C2×C11#254211yescharacteristic
244C2×C11#255114yes—
245C2×C11#256711yescharacteristic
246C2×C11#266011yescharacteristic
247C2×C11#286811yescharacteristic
248C24C23×D1111yescharacteristic
249C2×Q8—216no—
250C2×Q8—432no—
251C2×Q8—48no—
252C2×Q8—48no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—118no—
262C22×C4—118no—
263C22×C4—118no—
264C22×C4—114no—
265C22×C4—224no—
266C22×C4—224no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—224no—
270C22×C4—222no—
271C22×C4—224no—
272C22×C4—222no—
273C22×C4—224no—
274C22×C4—224no—
275C22×C4—222no—
276C22×C4—224no—
277C22×C4D4×D1114yes—
278C22×C4Q8×D1114yes—
279C22×C4Q8×D1114yes—
280C22×C4Q8×D1112yes—
281C22×C4#434312yes—
282C22×C4C2×C22⋊D1118yes—
283C22×C4C2×C22⋊D1112yes—
284C22×C4C2×C22⋊D1112yes—
285C22×C4C2×C22⋊D1114yes—
286C22×C4C2×C22⋊D1112yes—
287C4⋊C4—216no—
288C4⋊C4—216no—
289C4⋊C4—228no—
290C4⋊C4—4432no—
291C4⋊C4—448no—
292C4⋊C4—444no—
293C42—28no—
294C42—2216no—
295C11#1514311yescharacteristic, complemented, Sylow
296C23C2×D4×D1112yes—
297C23#6703712yes—
298C23C2×Q8×D1111yescharacteristic
299C23C2×Q8×D1112yes—
300C23C2×Q8×D1112yes—
301C23C2×#434311yescharacteristic
302C23#6704012yes—
303C23C22×C22⋊D1112yes—
304C23C22×C22⋊D1111yescharacteristic
305Q8—432no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—28no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—216no—
313C2×C4—28no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—1116no—
318C2×C4—228no—
319C2×C4—228no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—228no—
323C2×C4—228no—
324C2×C4—228no—
325C2×C4—224no—
326C2×C4—444no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—448no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4#6699314yes—
334C2×C4#6699714yes—
335C2×C4#6699714yes—
336C2×C4#6699718yes—
337C2×C4#6699918yes—
338C2×C4#6699914yes—
339C2×C4#6700614yes—
340C22#1062325312yes—
341C22D11×C4⋊Q814yes—
342C22#1062325712yes—
343C22#1062325812yes—
344C22#1062326014yes—
345C22#1062326112yes—
346C22D4×C22⋊D1114yes—
347C22C2×#6699311yescharacteristic
348C22#1062333611yescharacteristic
349C22C2×#6699711yescharacteristic
350C22C2×#6699711yescharacteristic
351C22C2×#6699712yes—
352C22C2×#6699911yescharacteristic
353C22C2×#6699912yes—
354C22Q8×C22⋊D1114yes—
355C22#1062334711yescharacteristic
356C22C2×#6700611yescharacteristic
357C4—24no—
358C4—24no—
359C4—48no—
360C4—2216no—
361C4—444no—
362C4—882no—
363C4#1062284218yescomplemented
364C2C2×#1062284211yescharacteristic
365C2#1307224911yescharacteristic
366C2#1307225611yescharacteristic
367C2#1307231414yes—
368C2#1307357011yescharacteristic
369C2#1307364314yes—
370C2#1307382511yescharacteristic
371C2#1307473611yescharacteristic
372C2#1307701211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC22×C11×C4⋊Q8C2
hypercenterC22×C4⋊Q8D11
hypocenterC11#15143
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
49. C2×C4⋊Dic11Q8semidirect
57. C2×C4×Dic11Q8semidirect
61. C11⋊#95Q8semidirect
160. C2×Dic11C4⋊Q8semidirect
199. C4×C11#395semidirect
295. C11#15143semidirect
363. C4#10622842semidirect

Maximal subgroups

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

subgroupindex
C2×#106228422
C2×#106225412
C2×#106225892
#130668792
#130668452
C4×C11⋊#952
C22×C11×C4⋊Q82
#1514311