Finite Group Databasebeta

← #14660484

Subgroups — #14660484

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66896C214yesmaximal, complemented
2C2×#10622162C211yesmaximal, characteristic, complemented
3#13066846C211yesmaximal, characteristic, complemented
4C22×C11×#127C211yesmaximal, characteristic
5C23×D4×C11—22no—
6C23×D4×C11C2212yes—
7C2×C11×#127—28no—
8C2×C11×#127—22no—
9C2×C11×#127C414yescomplemented
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C23×C11⋊C8C2212yes—
13C2×#66896—28no—
14C2×#66896—28no—
15C2×#66896—28no—
16C2×C11⋊#95—22no—
17#10622162—22no—
18C25×C11—22no—
19C22×D4×C11—216no—
20C22×D4×C11—28no—
21C22×D4×C11—24no—
22C22×D4×C11—24no—
23C22×D4×C11—24no—
24C22×D4×C11—22no—
25C22×D4×C11—24no—
26C22×D4×C11—24no—
27C22×D4×C11—48no—
28C22×D4×C11—44no—
29C22×D4×C11—44no—
30C22×D4×C11C2×C414yes—
31C22×D4×C11D418yes—
32C23×C4×C11D412yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—22no—
35C11×#127—216no—
36C11×#127—216no—
37C2×C42×C11—24no—
38C2×C42×C11C2×C412yes—
39C2×C42×C11D412yes—
40C2×C4⋊Dic11—24no—
41C2×C4⋊Dic11—24no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11D414yescomplemented
44C22×C11⋊C8—24no—
45C22×C11⋊C8—24no—
46C22×C11⋊C8—22no—
47C22×C11⋊C8—22no—
48C22×C11⋊C8D414yescomplemented
49#66896—232no—
50C11⋊#95—44no—
51#11008—111nomaximal, Sylow
52C24×C11—24no—
53C24×C11—28no—
54C24×C11—44no—
55C24×C11—42no—
56C24×C11—42no—
57C24×C11—44no—
58C24×C11—44no—
59C24×C11—48no—
60C24×C11C2×D411yescharacteristic
61C2×D4×C11—232no—
62C2×D4×C11—24no—
63C2×D4×C11—28no—
64C2×D4×C11—28no—
65C2×D4×C11—28no—
66C2×D4×C11—28no—
67C2×D4×C11—28no—
68C2×D4×C11—28no—
69C2×D4×C11—28no—
70C2×D4×C11—416no—
71C2×D4×C11—432no—
72C2×D4×C11—432no—
73C2×D4×C11—416no—
74C2×D4×C11—44no—
75C2×D4×C11—44no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11C22⋊C418yes—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11C22⋊C414yes—
85C22×C4×C11D814yes—
86C22×C4×C11SD1614yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D414yes—
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4112yes—
93C22×C4×C11#4112yes—
94C22×Dic11—24no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—44no—
98C22×Dic11—44no—
99C42×C11—24no—
100C42×C11—24no—
101C4⋊Dic11—28no—
102C4⋊Dic11—44no—
103C2×C11⋊C8—28no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—44no—
107C2×C11⋊C8—42no—
108C22×#127D1111yescharacteristic
109C22×#102—114no—
110C2×#336—111no—
111C4⋊#95—111no—
112C23×C11—28no—
113C23×C11—44no—
114C23×C11—44no—
115C23×C11—48no—
116C23×C11—48no—
117C23×C11—48no—
118C23×C11—48no—
119C23×C11—416no—
120C23×C11—416no—
121C23×C11—88no—
122C23×C11—88no—
123C23×C11—84no—
124C23×C11—84no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11—84no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#12012yes—
130C23×C11#12112yes—
131C23×C11#12411yescharacteristic
132C23×C11#12711yescharacteristic
133C23×C11C2×D812yes—
134C23×C11C2×SD1612yes—
135C23×C11AGL(1,ℤ/8)14yes—
136D4×C11—216no—
137D4×C11—464no—
138D4×C11—48no—
139D4×C11—48no—
140D4×C11—48no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11#10218yescomplemented
146C2×C4×C11C2×C22⋊C412yes—
147C2×C4×C11C4×D412yes—
148C2×C4×C11C4×D412yes—
149C2×C4×C11#12014yes—
150C2×C4×C11#12012yes—
151C2×C4×C11#12112yes—
152C2×C4×C11#12114yes—
153C2×C4×C11#12114yes—
154C2×C4×C11#12314yes—
155C2×C4×C11#12411yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×Dic11—44no—
158C2×Dic11—48no—
159C2×Dic11—84no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C11⋊C8—44no—
163C23×D4—22no—
164C23×D4C2×D1112yes—
165C23×C8—112no—
166C2×#127—28no—
167C2×#127—22no—
168C2×#127Dic1114yescomplemented
169C22×C4⋊C4—112no—
170C22×C42C2×D1111yescharacteristic
171C2×#102—228no—
172C2×#102—228no—
173C2×#102—228no—
174C2×#95—222no—
175#336—222no—
176C22×C11—48no—
177C22×C11—416no—
178C22×C11—84no—
179C22×C11—84no—
180C22×C11—88no—
181C22×C11—88no—
182C22×C11—88no—
183C22×C11—816no—
184C22×C11#37911yescharacteristic
185C22×C11#39011yescharacteristic
186C22×C11#39011yescharacteristic
187C22×C11#39212yes—
188C22×C11#39412yes—
189C22×C11C2×#10212yes—
190C22×C11#41812yes—
191C22×C11#44714yes—
192C22×C11#45014yes—
193C22×C11#45914yes—
194C22×C11#46014yes—
195C22×C11#48612yes—
196C22×C11#49012yes—
197C22×C11#49211yescharacteristic
198C22×C11#49311yescharacteristic
199C22×C11#49612yes—
200C4×C11—28no—
201C4×C11#38614yes—
202C4×C11#39212yes—
203C4×C11#39412yes—
204Dic11—84no—
205C25—22no—
206C22×D4—216no—
207C22×D4—28no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—48no—
215C22×D4—44no—
216C22×D4—44no—
217C22×D4C2×Dic1114yes—
218C22×D4C22⋊D1118yes—
219C23×C4—222no—
220C23×C4C22⋊D1112yes—
221C23×C4C22×D1111yescharacteristic
222C22×C8—114no—
223C22×C8—224no—
224C22×C8—222no—
225C22×C8—222no—
226C22×C8—224no—
227#127—216no—
228#127—216no—
229C2×C4⋊C4—114no—
230C2×C4⋊C4—224no—
231C2×C4⋊C4—224no—
232C2×C4⋊C4—222no—
233C2×C42—24no—
234C2×C42C2×Dic1112yes—
235C2×C42C22⋊D1112yes—
236#102—2232no—
237#95—444no—
238C2×C11—88no—
239C2×C11#143811yescharacteristic
240C2×C11#178612yes—
241C2×C11#195711yescharacteristic
242C2×C11#196111yescharacteristic
243C2×C11#198212yes—
244C2×C11#201112yes—
245C2×C11#201412yes—
246C2×C11#204114yes—
247C24—24no—
248C24—28no—
249C24—44no—
250C24—48no—
251C24—44no—
252C24—42no—
253C24—44no—
254C24—42no—
255C24C2×C22⋊D1111yescharacteristic
256C2×D4—232no—
257C2×D4—28no—
258C2×D4—28no—
259C2×D4—28no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—28no—
263C2×D4—24no—
264C2×D4—28no—
265C2×D4—416no—
266C2×D4—432no—
267C2×D4—432no—
268C2×D4—416no—
269C2×D4—44no—
270C2×D4—42no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—42no—
276C2×D4C22⋊Dic1118yes—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—224no—
280C22×C4—444no—
281C22×C4—444no—
282C22×C4—442no—
283C22×C4—442no—
284C22×C4#432314yes—
285C22×C4#432414yes—
286C22×C4C22⋊Dic1114yes—
287C22×C4D4×D1112yes—
288C22×C4D4×D1112yes—
289C22×C4#434112yes—
290C22×C4#434112yes—
291C22×C4C22×Dic1111yescharacteristic
292C22×C4C2×C22⋊D1114yes—
293C22×C4C2×C22⋊D1111yescharacteristic
294C2×C8—228no—
295C2×C8—224no—
296C2×C8—444no—
297C2×C8—442no—
298C2×C8—442no—
299C4⋊C4—228no—
300C4⋊C4—444no—
301C42—24no—
302C42—24no—
303C11#1100811yescharacteristic, complemented, Sylow
304C23—28no—
305C23—48no—
306C23—48no—
307C23—416no—
308C23—416no—
309C23—44no—
310C23—44no—
311C23—48no—
312C23—48no—
313C23—84no—
314C23—84no—
315C23—88no—
316C23—82no—
317C23—84no—
318C23—88no—
319C23—82no—
320C23C2×#432312yes—
321C23#6698514yes—
322C23C2×#432412yes—
323C23#6698911yescharacteristic
324C23#6699112yes—
325C23#6699311yescharacteristic
326C23C2×C22⋊Dic1111yescharacteristic
327C23#6700612yes—
328D4—216no—
329D4—464no—
330D4—48no—
331D4—48no—
332D4—48no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—444no—
338C2×C4—448no—
339C2×C4—884no—
340C2×C4—882no—
341C2×C4—882no—
342C2×C4#6689618yescomplemented
343C2×C4D4×Dic1112yes—
344C2×C4D4×Dic1112yes—
345C2×C4#6698814yes—
346C2×C4#6698911yescharacteristic
347C2×C4#6699014yes—
348C2×C4#6699112yes—
349C2×C4#6699214yes—
350C2×C4#6699214yes—
351C2×C4#6699311yescharacteristic
352C2×C4C2×C22⋊Dic1112yes—
353C2×C4#6700612yes—
354C8—444no—
355C22—416no—
356C22—48no—
357C22—816no—
358C22—84no—
359C22—88no—
360C22—84no—
361C22—88no—
362C22—88no—
363C22#1062268312yes—
364C22#1062268412yes—
365C22#1062268514yes—
366C22#1062268611yescharacteristic
367C22#1062268712yes—
368C22#1062268814yes—
369C22#1062268911yescharacteristic
370C22C2×#6689612yes—
371C22#1062282812yes—
372C22#1062283014yes—
373C22#1062283114yes—
374C22#1062283411yescharacteristic
375C22#1062283411yescharacteristic
376C22#1062283512yes—
377C22#1062283612yes—
378C22#1062286011yescharacteristic
379C4—28no—
380C4—884no—
381C4#1062283314yes—
382C4#1062283512yes—
383C4#1062283612yes—
384C2—88no—
385C2#1306685711yescharacteristic
386C2#1306854712yes—
387C2#1306942311yescharacteristic
388C2#1306944111yescharacteristic
389C2#1306954412yes—
390C2#1306968712yes—
391C2#1306970412yes—
392C2#1306984714yes—
subgroupG/H
centerC24C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC22×C11×#127C2
socleC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC22×#127D11
hypocenterC11#11008
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×#66896C2semidirect
2. C2×#10622162C2semidirect
3. #13066846C2semidirect
9. C2×C11×#127C4semidirect
43. C2×C4⋊Dic11D4semidirect
48. C22×C11⋊C8D4semidirect
145. C2×C4×C11#102semidirect
168. C2×#127Dic11semidirect
303. C11#11008semidirect
342. C2×C4#66896semidirect

Maximal subgroups

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

subgroupindex
C22×#668962
C2×#106221622
#130668462
C22×C11×#1272
#1100811