Finite Group Databasebeta

← C2×C11×#1642 #14595705

Subgroups — C2×C11×#1642 #14595705

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#486C211yesmaximal, characteristic, complemented
3C2×C11×#475C211yesmaximal, characteristic, complemented
4C2×C11×#461C211yesmaximal, characteristic, complemented
5C11×#1642C218yesmaximal, direct product factor
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×C11×#41—21no—
10C22×C11×SD16—21no—
11C11×#550—22no—
12C11×#550—22no—
13C11×#550—22no—
14C11×#550C2214yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127—21no—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—22no—
19C2×C11×#121—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#486—22no—
24C11×#486C2214yescomplemented
25C11×#475—22no—
26C11×#475C2214yescomplemented
27C11×#461—22no—
28C11×#461C2214yescomplemented
29C2×C11×#106—21no—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103—21no—
33C2×C11×#103—21no—
34C2×C11×#102—22no—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#331C2214yescomplemented
37C11×Q8⋊C8C2214yescomplemented
38C11×D4⋊C8C2214yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—44no—
42C2×C11×#41—44no—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D412yes—
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C2×C11×SD16—24no—
54C2×C11×SD16—44no—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×#127—24no—
63C11×#127—24no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127D412yes—
67C11×#127C2312yes—
68C11×#121—24no—
69C11×#121—28no—
70C11×#121—28no—
71C11×#121—24no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11D412yes—
75C4×Q8×C11C2312yes—
76C4×D4×C11—24no—
77C4×D4×C11—24no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11D412yes—
81C4×D4×C11C2312yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C11×#106—24no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2312yes—
96C11×#103—24no—
97C11×#103—24no—
98C11×#102—28no—
99C4×C8×C11—21no—
100C4×C8×C11C2312yes—
101C2×#1642C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—22no—
104C11×#41—48no—
105C11×#41—416no—
106C11×#41—48no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—41no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×Q8×C11SD1614yescomplemented
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—48no—
126C2×D4×C11—44no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—84no—
132C2×D4×C11C2×D412yes—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—21no—
135C22×C4×C11—28no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—48no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C11×SD16—48no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C2×C8×C11—42no—
153C2×C8×C11—42no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173C2×#550C2×C1111yescharacteristic
174C2×#486C2×C1111yescharacteristic, complemented
175C2×#475C2×C1111yescharacteristic, complemented
176C2×#461C2×C1111yescharacteristic, complemented
177#1642C2×C1118yesdirect product factor
178C2×#331C2×C1111yescharacteristic, complemented
179C2×Q8⋊C8C2×C1111yescharacteristic, complemented
180C2×D4⋊C8C2×C1111yescharacteristic, complemented
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—44no—
186C23×C11—42no—
187C23×C11—44no—
188C23×C11—42no—
189C23×C11#12011yescharacteristic
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—82no—
195Q8×C11C2×SD1614yescomplemented
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—44no—
199D4×C11—416no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—44no—
206D4×C11—44no—
207D4×C11—82no—
208D4×C11—88no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—416no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11C2×SD1612yes—
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C8×C11—42no—
233C8×C11—42no—
234C8×C11—42no—
235C22×#41—21no—
236C22×SD16—21no—
237#550—22no—
238#550—22no—
239#550—22no—
240#550C22×C1114yes—
241C2×C4⋊Q8C22×C1111yescharacteristic
242C2×#127—21no—
243C2×#127C22×C1111yescharacteristic
244C2×#121—22no—
245C2×#121—21no—
246C2×C4×Q8C22×C1111yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C22×C1111yescharacteristic
249#486—22no—
250#486C22×C1114yescomplemented
251#475—22no—
252#475C22×C1114yescomplemented
253#461—22no—
254#461C22×C1114yescomplemented
255C2×#106—21no—
256C2×C4⋊C8C22×C1111yescharacteristic
257C2×C4⋊C8C22×C1111yescharacteristic
258C2×#103—21no—
259C2×#103—21no—
260C2×#102—22no—
261C2×C4×C8C22×C1111yescharacteristic
262#331C22×C1114yescomplemented
263Q8⋊C8C22×C1114yescomplemented
264D4⋊C8C22×C1114yescomplemented
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—84no—
272C22×C11—88no—
273C22×C11#44912yes—
274C22×C11#45012yes—
275C22×C11#45512yes—
276C22×C11C2×#12011yescharacteristic
277C4×C11—24no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—82no—
283C4×C11#44912yes—
284C4×C11#45012yes—
285C4×C11C22×SD1611yescharacteristic
286C4×C11C2×#13511yescharacteristic
287C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C2×#41—24no—
290C2×#41—24no—
291C2×#41—44no—
292C2×#41—44no—
293C22×Q8—21no—
294C22×Q8D4×C1111yescharacteristic
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4D4×C1111yescharacteristic
300C22×D4D4×C1112yes—
301C23×C4—22no—
302C23×C4—21no—
303C2×SD16—24no—
304C2×SD16—44no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C23×C1112yes—
312#127—24no—
313#127—24no—
314#127—21no—
315#127—21no—
316#127D4×C1112yes—
317#127C23×C1112yes—
318#121—24no—
319#121—28no—
320#121—28no—
321#121—24no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8D4×C1112yes—
325C4×Q8C23×C1112yes—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4D4×C1112yes—
331C4×D4C23×C1112yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C1111yescharacteristic
336C2×C4⋊C4D4×C1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42C23×C1111yescharacteristic
341#106—24no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8C23×C1112yes—
345C4⋊C8C23×C1112yes—
346#103—24no—
347#103—24no—
348#102—28no—
349C4×C8—21no—
350C4×C8C23×C1112yes—
351C2×C11—82no—
352C2×C11—84no—
353C2×C11#164214yesdirect product factor
354C2×C11C2×#45011yescharacteristic
355C2×C11C2×#44911yescharacteristic
356C2×C11C2×#45511yescharacteristic
357C24—21no—
358C24—22no—
359#41—48no—
360#41—416no—
361#41—48no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—41no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C11×SD1614yescomplemented
369C2×Q8C2×D4×C1112yes—
370C2×D4—28no—
371C2×D4—28no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—48no—
381C2×D4—44no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—84no—
387C2×D4C2×D4×C1112yes—
388C2×D4C2×D4×C1114yes—
389C22×C4—21no—
390C22×C4—28no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—48no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402SD16—48no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—42no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C2×D4×C1112yes—
418C4⋊C4C2×D4×C1112yes—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C42—22no—
423C42—22no—
424C42C2×D4×C1111yescharacteristic
425C42C2×D4×C1111yescharacteristic
426C42C2×D4×C1111yescharacteristic
427C42C24×C1111yescharacteristic
428C11C2×#164211yescharacteristic, direct product factor, Sylow
429C23—22no—
430C23—24no—
431C23—42no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—44no—
436C23—42no—
437C23C11×#12011yescharacteristic
438Q8—22no—
439Q8—24no—
440Q8—42no—
441Q8—42no—
442Q8—82no—
443Q8C2×C11×SD1614yescomplemented
444D4—22no—
445D4—22no—
446D4—44no—
447D4—416no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—44no—
455D4—82no—
456D4—88no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—416no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4C11×#12011yescharacteristic
471C2×C4C11×#12011yescharacteristic
472C2×C4C11×#12011yescharacteristic
473C2×C4C2×C11×SD1612yes—
474C2×C4C11×#13512yes—
475C2×C4C11×AGL(1,ℤ/8)12yes—
476C2×C4C11×AGL(1,ℤ/8)12yes—
477C2×C4C22×D4×C1111yescharacteristic
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C22×D4×C1111yescharacteristic
480C8—42no—
481C8—42no—
482C8—42no—
483C22—44no—
484C22—42no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—84no—
490C22—88no—
491C22C11×#44912yes—
492C22C11×#45012yes—
493C22C11×#45512yes—
494C22C2×C11×#12011yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—42no—
500C4—82no—
501C4C11×#44912yes—
502C4C11×#45012yes—
503C4C22×C11×SD1611yescharacteristic
504C4C2×C11×#13511yescharacteristic
505C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
506C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
507C2—82no—
508C2—84no—
509C2C11×#164214yesdirect product factor
510C2C2×C11×#45011yescharacteristic
511C2C2×C11×#44911yescharacteristic
512C2C2×C11×#45511yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#550C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#486C2semidirect
3. C2×C11×#475C2semidirect
4. C2×C11×#461C2semidirect
5. C11×#1642C2direct (N × H)
6. C2×C11×#331C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
8. C2×C11×D4⋊C8C2semidirect
24. C11×#486C22semidirect
26. C11×#475C22semidirect
28. C11×#461C22semidirect
36. C11×#331C22semidirect
37. C11×Q8⋊C8C22semidirect
38. C11×D4⋊C8C22semidirect
101. C2×#1642C11direct (N × H)
113. C2×Q8×C11SD16semidirect
174. C2×#486C2×C11semidirect
175. C2×#475C2×C11semidirect
176. C2×#461C2×C11semidirect
177. #1642C2×C11direct (N × H)
178. C2×#331C2×C11semidirect
179. C2×Q8⋊C8C2×C11semidirect
180. C2×D4⋊C8C2×C11semidirect
195. Q8×C11C2×SD16semidirect
250. #486C22×C11semidirect
252. #475C22×C11semidirect
254. #461C22×C11semidirect
262. #331C22×C11semidirect
263. Q8⋊C8C22×C11semidirect
264. D4⋊C8C22×C11semidirect
353. C2×C11#1642direct (N × H)
368. C2×Q8C11×SD16semidirect
428. C11C2×#1642direct (N × H)
443. Q8C2×C11×SD16semidirect
509. C2C11×#1642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4862
C2×C11×#4752
C2×C11×#4612
C11×#16422
C2×C11×#3312
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C2×#164211