Finite Group Databasebeta

← C2×C11×#2128 #14610549

Subgroups — C2×C11×#2128 #14610549

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#410C212yesmaximal, complemented
3C11×#2128C218yesmaximal, direct product factor
4C2×C11×#353C214yesmaximal, complemented
5C22×C11×#41C2211yescharacteristic
6C23×D4×C11C411yescharacteristic, complemented
7C11×#535—24no—
8C11×#535C414yescomplemented
9C11×#535C2214yes—
10C2×C11×#127C2212yes—
11C2×C11×#124C412yescomplemented
12C2×C11×#121—22no—
13C2×C11×#120—22no—
14C2×C11×#117—22no—
15C2×C11×#117C411yescharacteristic, complemented
16C11×#410—24no—
17C11×#410C2218yescomplemented
18C2×C11×#99—22no—
19C2×C11×#99C2214yescomplemented
20C11×#353C22116yescomplemented
21C25×C11—21no—
22C2×C11×#41—42no—
23C2×C11×#41—42no—
24C2×C11×#41C2×C412yes—
25C2×C11×#41D414yes—
26C2×C11×#41C2312yes—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D4×C11—24no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11—42no—
32C22×D4×C11—42no—
33C22×D4×C11C2×C412yes—
34C22×D4×C11C2×C414yescomplemented
35C22×D4×C11D412yes—
36C22×D4×C11C2311yescharacteristic
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11D412yes—
39C11×#127—24no—
40C11×#127C2×C414yes—
41C11×#127C2314yes—
42C11×#124—24no—
43C11×#124C2×C418yescomplemented
44C11×#121—28no—
45C11×#121—28no—
46C11×#120—28no—
47C11×#120—28no—
48C11×#117—22no—
49C11×#117—28no—
50C11×#117—44no—
51C11×#117C2×C414yescomplemented
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—24no—
57C2×C42×C11—42no—
58C2×C42×C11C2×C412yes—
59C11×#99—28no—
60C11×#99—24no—
61C11×#99C2318yescomplemented
62C2×#2128C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—22no—
64C24×C11—24no—
65C24×C11—42no—
66C24×C11—42no—
67C24×C11—84no—
68C24×C11C22⋊C411yescharacteristic
69C24×C11C2×D412yes—
70C11×#41—44no—
71C11×#41—44no—
72C11×#41—44no—
73C11×#41—44no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11C22⋊C412yes—
77C2×Q8×C11C22×C412yes—
78C2×D4×C11—28no—
79C2×D4×C11—28no—
80C2×D4×C11—24no—
81C2×D4×C11—22no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—48no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—48no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—88no—
93C2×D4×C11C22⋊C414yes—
94C2×D4×C11C22×C414yes—
95C2×D4×C11C22×C411yescharacteristic
96C2×D4×C11C2×D414yes—
97C2×D4×C11C2×D412yes—
98C2×D4×C11C2411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11C22⋊C412yes—
107C22×C4×C11C22⋊C412yes—
108C22×C4×C11C22⋊C414yes—
109C22×C4×C11C22⋊C411yescharacteristic
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D414yes—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—48no—
115C11×C22⋊C4—24no—
116C11×C22⋊C4—216no—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—44no—
119C42×C11—22no—
120C42×C11—48no—
121C42×C11C22×C414yes—
122C2×#535C2×C1111yescharacteristic
123C2×#410C2×C1112yescomplemented
124#2128C2×C1118yesdirect product factor
125C2×#353C2×C1114yescomplemented
126C23×C11—21no—
127C23×C11—22no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—24no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—48no—
134C23×C11—48no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—88no—
138C23×C11—88no—
139C23×C11—88no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11C2×C22⋊C412yes—
142C23×C11C2×C22⋊C412yes—
143C23×C11C22×D412yes—
144Q8×C11—42no—
145Q8×C11—42no—
146D4×C11—44no—
147D4×C11—41no—
148D4×C11—42no—
149D4×C11—44no—
150D4×C11—41no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—48no—
154D4×C11—88no—
155D4×C11—88no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—44no—
168C2×C4×C11—48no—
169C2×C4×C11—88no—
170C2×C4×C11#9912yes—
171C2×C4×C11#9912yes—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C2×C22⋊C414yes—
174C2×C4×C11C2×C22⋊C412yes—
175C2×C4×C11C23×C411yescharacteristic
176C22×#41C22×C1111yescharacteristic
177C23×D4C4×C1111yescharacteristic, complemented
178#535—24no—
179#535C4×C1114yescomplemented
180#535C22×C1114yes—
181C2×#127C22×C1112yes—
182C2×#124C4×C1112yescomplemented
183C2×#121—22no—
184C2×#120—22no—
185C2×#117—22no—
186C2×#117C4×C1111yescharacteristic, complemented
187#410—24no—
188#410C22×C1118yescomplemented
189C2×#99—22no—
190C2×#99C22×C1114yescomplemented
191#353C22×C11116yescomplemented
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—48no—
201C22×C11—44no—
202C22×C11—42no—
203C22×C11—44no—
204C22×C11—82no—
205C22×C11—84no—
206C22×C11—816no—
207C22×C11—84no—
208C22×C11C2×#9911yescharacteristic
209C22×C11C2×#9911yescharacteristic
210C22×C11C22×C22⋊C411yescharacteristic
211C4×C11—21no—
212C4×C11—24no—
213C4×C11—21no—
214C4×C11—44no—
215C4×C11—88no—
216C4×C11C2×#9914yes—
217C25—21no—
218C2×#41—42no—
219C2×#41—42no—
220C2×#41C2×C4×C1112yes—
221C2×#41D4×C1114yes—
222C2×#41C23×C1112yes—
223C22×Q8C2×C4×C1111yescharacteristic
224C22×D4—24no—
225C22×D4—21no—
226C22×D4—22no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C2×C4×C1112yes—
230C22×D4C2×C4×C1114yescomplemented
231C22×D4D4×C1112yes—
232C22×D4C23×C1111yescharacteristic
233C23×C4C2×C4×C1111yescharacteristic
234C23×C4D4×C1112yes—
235#127—24no—
236#127C2×C4×C1114yes—
237#127C23×C1114yes—
238#124—24no—
239#124C2×C4×C1118yescomplemented
240#121—28no—
241#121—28no—
242#120—28no—
243#120—28no—
244#117—22no—
245#117—28no—
246#117—44no—
247#117C2×C4×C1114yescomplemented
248C2×C4⋊C4—21no—
249C2×C4⋊C4—42no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—24no—
252C2×C22⋊C4—24no—
253C2×C42—42no—
254C2×C42C2×C4×C1112yes—
255#99—28no—
256#99—24no—
257#99C23×C1118yescomplemented
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—42no—
261C2×C11—42no—
262C2×C11—42no—
263C2×C11—84no—
264C2×C11#212812yesdirect product factor
265C2×C11C22×#9911yescharacteristic
266C24—22no—
267C24—24no—
268C24—42no—
269C24—42no—
270C24—84no—
271C24C11×C22⋊C411yescharacteristic
272C24C2×D4×C1112yes—
273#41—44no—
274#41—44no—
275#41—44no—
276#41—44no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C11×C22⋊C412yes—
280C2×Q8C22×C4×C1112yes—
281C2×D4—28no—
282C2×D4—28no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—48no—
292C2×D4—48no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—88no—
296C2×D4C11×C22⋊C414yes—
297C2×D4C22×C4×C1114yes—
298C2×D4C22×C4×C1111yescharacteristic
299C2×D4C2×D4×C1114yes—
300C2×D4C2×D4×C1112yes—
301C2×D4C24×C1111yescharacteristic
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—44no—
309C22×C4C11×C22⋊C412yes—
310C22×C4C11×C22⋊C412yes—
311C22×C4C11×C22⋊C414yes—
312C22×C4C11×C22⋊C411yescharacteristic
313C22×C4C22×C4×C1111yescharacteristic
314C22×C4C22×C4×C1112yes—
315C22×C4C2×D4×C1114yes—
316C4⋊C4—24no—
317C4⋊C4—48no—
318C22⋊C4—24no—
319C22⋊C4—216no—
320C22⋊C4—28no—
321C22⋊C4—44no—
322C42—22no—
323C42—48no—
324C42C22×C4×C1114yes—
325C11C2×#212811yescharacteristic, direct product factor, Sylow
326C23—22no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—24no—
331C23—42no—
332C23—44no—
333C23—48no—
334C23—48no—
335C23—42no—
336C23—42no—
337C23—88no—
338C23—88no—
339C23—88no—
340C23C2×C11×C22⋊C411yescharacteristic
341C23C2×C11×C22⋊C412yes—
342C23C2×C11×C22⋊C412yes—
343C23C22×D4×C1112yes—
344Q8—42no—
345Q8—42no—
346D4—44no—
347D4—41no—
348D4—42no—
349D4—44no—
350D4—41no—
351D4—44no—
352D4—44no—
353D4—48no—
354D4—88no—
355D4—88no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—44no—
368C2×C4—48no—
369C2×C4—88no—
370C2×C4C11×#9912yes—
371C2×C4C11×#9912yes—
372C2×C4C2×C11×C22⋊C411yescharacteristic
373C2×C4C2×C11×C22⋊C414yes—
374C2×C4C2×C11×C22⋊C412yes—
375C2×C4C23×C4×C1111yescharacteristic
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—48no—
385C22—44no—
386C22—42no—
387C22—44no—
388C22—82no—
389C22—84no—
390C22—816no—
391C22—84no—
392C22C2×C11×#9911yescharacteristic
393C22C2×C11×#9911yescharacteristic
394C22C22×C11×C22⋊C411yescharacteristic
395C4—21no—
396C4—24no—
397C4—21no—
398C4—44no—
399C4—88no—
400C4C2×C11×#9914yes—
401C2—21no—
402C2—21no—
403C2—42no—
404C2—42no—
405C2—42no—
406C2—84no—
407C2C11×#212812yesdirect product factor
408C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×D4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#410C2semidirect
3. C11×#2128C2direct (N × H)
4. C2×C11×#353C2semidirect
6. C23×D4×C11C4semidirect
8. C11×#535C4semidirect
11. C2×C11×#124C4semidirect
15. C2×C11×#117C4semidirect
17. C11×#410C22semidirect
19. C2×C11×#99C22semidirect
20. C11×#353C22semidirect
34. C22×D4×C11C2×C4semidirect
43. C11×#124C2×C4semidirect
51. C11×#117C2×C4semidirect
61. C11×#99C23semidirect
62. C2×#2128C11direct (N × H)
123. C2×#410C2×C11semidirect
124. #2128C2×C11direct (N × H)
125. C2×#353C2×C11semidirect
177. C23×D4C4×C11semidirect
179. #535C4×C11semidirect
182. C2×#124C4×C11semidirect
186. C2×#117C4×C11semidirect
188. #410C22×C11semidirect
190. C2×#99C22×C11semidirect
191. #353C22×C11semidirect
230. C22×D4C2×C4×C11semidirect
239. #124C2×C4×C11semidirect
247. #117C2×C4×C11semidirect
257. #99C23×C11semidirect
264. C2×C11#2128direct (N × H)
325. C11C2×#2128direct (N × H)
407. C2C11×#2128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4102
C11×#21282
C2×C11×#3532
C2×#212811