Finite Group Databasebeta

← C2×C11×#1488 #14594635

Subgroups — C2×C11×#1488 #14594635

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C11×#41C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic, complemented
3C2×C11×#431C211yesmaximal, characteristic, complemented
4C11×#1488C218yesmaximal, direct product factor
5C2×C11×Q8⋊C8C212yesmaximal, complemented
6C2×C11×D4⋊C8C212yesmaximal, complemented
7C22×C11×#41C411yescharacteristic
8C4×C11×#41—22no—
9C4×C11×#41—22no—
10C4×C11×#41C414yes—
11C4×C11×#41C2214yes—
12C2×C4×Q8×C11C411yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11—21no—
16C2×C4×D4×C11C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117—21no—
19C2×C11×#117C411yescharacteristic
20C22×C42×C11—21no—
21C22×C42×C11C2211yescharacteristic
22C11×#432—22no—
23C11×#432C2214yescomplemented
24C11×#431—22no—
25C11×#431C2214yescomplemented
26C2×C11×C4⋊C8—21no—
27C2×C11×C4⋊C8C2212yes—
28C2×C11×C22⋊C8—21no—
29C2×C11×C22⋊C8—21no—
30C2×C11×#97—21no—
31C2×C4×C8×C11C2212yes—
32C11×Q8⋊C8C2218yescomplemented
33C11×D4⋊C8C2218yescomplemented
34C2×C11×#41—24no—
35C2×C11×#41—24no—
36C2×C11×#41—22no—
37C2×C11×#41C2×C414yes—
38C22×Q8×C11C2×C411yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11C2×C414yes—
53C4×Q8×C11C2×C412yes—
54C4×Q8×C11C2312yes—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11C2×C414yes—
63C4×D4×C11C2×C412yes—
64C4×D4×C11C2312yes—
65C11×#117—22no—
66C11×#117—24no—
67C11×#117—24no—
68C11×#117C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—24no—
80C2×C42×C11—24no—
81C2×C42×C11C2×C411yescharacteristic
82C2×C42×C11C2×C412yes—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D412yes—
85C2×C42×C11D412yes—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11C2312yes—
88C2×C42×C11C2311yescharacteristic
89C11×C4⋊C8—24no—
90C11×C4⋊C8—22no—
91C11×C4⋊C8C2314yes—
92C11×C22⋊C8—24no—
93C11×C22⋊C8—24no—
94C11×#97—24no—
95C4×C8×C11—22no—
96C4×C8×C11C2314yes—
97C2×#1488C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C22⋊C411yescharacteristic
100C11×#41—216no—
101C11×#41—28no—
102C11×#41—28no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11M1614yes—
106C2×Q8×C11C22×C412yes—
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11M1614yes—
112C2×D4×C11C22×C412yes—
113C22×C4×C11—28no—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11C22⋊C411yescharacteristic
128C22×C4×C11C22⋊C411yescharacteristic
129C22×C4×C11C22⋊C411yescharacteristic
130C22×C4×C11C22⋊C412yes—
131C22×C4×C11C22⋊C412yes—
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C2×C8×C11—24no—
140C2×C8×C11—24no—
141C2×C8×C11—44no—
142C2×C8×C11—44no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C22×C412yes—
149C11×C4⋊C4C22×C412yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C42×C11—24no—
155C42×C11—24no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11C22⋊C412yes—
159C42×C11C22⋊C412yes—
160C42×C11C22⋊C412yes—
161C42×C11C22×C412yes—
162C42×C11C22×C411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C42×C11C2×D411yescharacteristic
167C42×C11C2411yescharacteristic
168C2×C4×#41C2×C1111yescharacteristic
169C2×#432C2×C1111yescharacteristic, complemented
170C2×#431C2×C1111yescharacteristic, complemented
171#1488C2×C1118yesdirect product factor
172C2×Q8⋊C8C2×C1112yescomplemented
173C2×D4⋊C8C2×C1112yescomplemented
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11C2×C22⋊C412yes—
182C23×C11C2×C22⋊C411yescharacteristic
183Q8×C11—22no—
184Q8×C11—24no—
185Q8×C11C2×M1614yes—
186D4×C11—216no—
187D4×C11—22no—
188D4×C11—24no—
189D4×C11C2×M1614yes—
190C2×C4×C11—216no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—48no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11C2×C22⋊C412yes—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×M1612yes—
218C2×C4×C11C2×M1612yes—
219C2×C4×C11#13514yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C8×C11—44no—
224C8×C11—44no—
225C22×#41C4×C1111yescharacteristic
226C4×#41—22no—
227C4×#41—22no—
228C4×#41C4×C1114yes—
229C4×#41C22×C1114yes—
230C2×C4×Q8C4×C1111yescharacteristic
231C2×C4×Q8C22×C1111yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C4×C1111yescharacteristic
235C2×C4×D4C22×C1111yescharacteristic
236C2×#117—21no—
237C2×#117C4×C1111yescharacteristic
238C22×C42—21no—
239C22×C42C22×C1111yescharacteristic
240#432—22no—
241#432C22×C1114yescomplemented
242#431—22no—
243#431C22×C1114yescomplemented
244C2×C4⋊C8—21no—
245C2×C4⋊C8C22×C1112yes—
246C2×C22⋊C8—21no—
247C2×C22⋊C8—21no—
248C2×#97—21no—
249C2×C4×C8C22×C1112yes—
250Q8⋊C8C22×C1118yescomplemented
251D4⋊C8C22×C1118yescomplemented
252C22×C11—22no—
253C22×C11—24no—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—44no—
259C22×C11—48no—
260C22×C11#40712yes—
261C22×C11#41612yes—
262C22×C11#42112yes—
263C22×C11C22×C22⋊C411yescharacteristic
264C4×C11—22no—
265C4×C11—24no—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11#40712yes—
273C4×C11#41612yes—
274C4×C11C22×M1611yescharacteristic
275C4×C11C22×M1611yescharacteristic
276C4×C11C2×#13512yes—
277C2×#41—24no—
278C2×#41—24no—
279C2×#41—22no—
280C2×#41C2×C4×C1114yes—
281C22×Q8C2×C4×C1111yescharacteristic
282C22×D4—21no—
283C22×D4C2×C4×C1111yescharacteristic
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4C2×C4×C1111yescharacteristic
288C23×C4D4×C1111yescharacteristic
289C23×C4D4×C1111yescharacteristic
290C22×C8—22no—
291C22×C8—22no—
292C4×Q8—22no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8C2×C4×C1114yes—
296C4×Q8C2×C4×C1112yes—
297C4×Q8C23×C1112yes—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—24no—
301C4×D4—24no—
302C4×D4—22no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4C2×C4×C1114yes—
306C4×D4C2×C4×C1112yes—
307C4×D4C23×C1112yes—
308#117—22no—
309#117—24no—
310#117—24no—
311#117C2×C4×C1114yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4C2×C4×C1111yescharacteristic
315C2×C4⋊C4C2×C4×C1111yescharacteristic
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42C2×C4×C1111yescharacteristic
325C2×C42C2×C4×C1112yes—
326C2×C42D4×C1111yescharacteristic
327C2×C42D4×C1112yes—
328C2×C42D4×C1112yes—
329C2×C42D4×C1111yescharacteristic
330C2×C42C23×C1111yescharacteristic
331C2×C42C23×C1112yes—
332C4⋊C8—24no—
333C4⋊C8—22no—
334C4⋊C8C23×C1114yes—
335C22⋊C8—24no—
336C22⋊C8—24no—
337#97—24no—
338C4×C8—22no—
339C4×C8C23×C1114yes—
340C2×C11—42no—
341C2×C11—44no—
342C2×C11#148814yesdirect product factor
343C2×C11C2×#40711yescharacteristic
344C2×C11C2×#41611yescharacteristic
345C2×C11C2×#42111yescharacteristic
346C24—21no—
347C24C11×C22⋊C411yescharacteristic
348#41—216no—
349#41—28no—
350#41—28no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8C11×M1614yes—
354C2×Q8C22×C4×C1112yes—
355C2×D4—28no—
356C2×D4—24no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4C11×M1614yes—
360C2×D4C22×C4×C1112yes—
361C22×C4—28no—
362C22×C4—21no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4C11×C22⋊C411yescharacteristic
376C22×C4C11×C22⋊C411yescharacteristic
377C22×C4C11×C22⋊C411yescharacteristic
378C22×C4C11×C22⋊C412yes—
379C22×C4C11×C22⋊C412yes—
380C22×C4C11×C22⋊C412yes—
381C22×C4C22×C4×C1112yes—
382C22×C4C22×C4×C1111yescharacteristic
383C22×C4C2×D4×C1112yes—
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1111yescharacteristic
387C2×C8—24no—
388C2×C8—24no—
389C2×C8—44no—
390C2×C8—44no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4C22×C4×C1112yes—
397C4⋊C4C22×C4×C1112yes—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C42—24no—
403C42—24no—
404C42—22no—
405C42—22no—
406C42C11×C22⋊C412yes—
407C42C11×C22⋊C412yes—
408C42C11×C22⋊C412yes—
409C42C22×C4×C1112yes—
410C42C22×C4×C1111yescharacteristic
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1112yes—
413C42C2×D4×C1112yes—
414C42C2×D4×C1111yescharacteristic
415C42C24×C1111yescharacteristic
416C11C2×#148811yescharacteristic, direct product factor, Sylow
417C23—22no—
418C23—22no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—42no—
423C23—42no—
424C23C2×C11×C22⋊C412yes—
425C23C2×C11×C22⋊C411yescharacteristic
426Q8—24no—
427Q8—22no—
428Q8C2×C11×M1614yes—
429D4—216no—
430D4—24no—
431D4—22no—
432D4C2×C11×M1614yes—
433C2×C4—216no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—48no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4C2×C11×C22⋊C412yes—
455C2×C4C2×C11×C22⋊C412yes—
456C2×C4C2×C11×C22⋊C412yes—
457C2×C4C2×C11×C22⋊C411yescharacteristic
458C2×C4C2×C11×C22⋊C411yescharacteristic
459C2×C4C2×C11×C22⋊C411yescharacteristic
460C2×C4C2×C11×M1612yes—
461C2×C4C2×C11×M1612yes—
462C2×C4C11×#13514yes—
463C2×C4C23×C4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1111yescharacteristic
466C8—44no—
467C8—44no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—24no—
472C22—42no—
473C22—42no—
474C22—44no—
475C22—48no—
476C22C11×#40712yes—
477C22C11×#41612yes—
478C22C11×#42112yes—
479C22C22×C11×C22⋊C411yescharacteristic
480C4—22no—
481C4—21no—
482C4—22no—
483C4—21no—
484C4—22no—
485C4—24no—
486C4—42no—
487C4—42no—
488C4C11×#40712yes—
489C4C11×#41612yes—
490C4C22×C11×M1611yescharacteristic
491C4C22×C11×M1611yescharacteristic
492C4C2×C11×#13512yes—
493C2—42no—
494C2—44no—
495C2C11×#148814yesdirect product factor
496C2C2×C11×#40711yescharacteristic
497C2C2×C11×#41611yescharacteristic
498C2C2×C11×#42111yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC42C24×C11
socleC23×C11C2×C22⋊C4
prime radicalC22×C11×#41C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#432C2semidirect
3. C2×C11×#431C2semidirect
4. C11×#1488C2direct (N × H)
5. C2×C11×Q8⋊C8C2semidirect
6. C2×C11×D4⋊C8C2semidirect
23. C11×#432C22semidirect
25. C11×#431C22semidirect
32. C11×Q8⋊C8C22semidirect
33. C11×D4⋊C8C22semidirect
97. C2×#1488C11direct (N × H)
169. C2×#432C2×C11semidirect
170. C2×#431C2×C11semidirect
171. #1488C2×C11direct (N × H)
172. C2×Q8⋊C8C2×C11semidirect
173. C2×D4⋊C8C2×C11semidirect
241. #432C22×C11semidirect
243. #431C22×C11semidirect
250. Q8⋊C8C22×C11semidirect
251. D4⋊C8C22×C11semidirect
342. C2×C11#1488direct (N × H)
416. C11C2×#1488direct (N × H)
495. C2C11×#1488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C11×#412
C2×C11×#4322
C2×C11×#4312
C11×#14882
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C2×#148811