Finite Group Databasebeta

← C11×#19082 #14596275

Subgroups — C11×#19082 #14596275

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3553C211yesmaximal, characteristic, complemented
2C11×#3180C212yesmaximal, complemented
3C11×#3142C211yesmaximal, characteristic, complemented
4C11×#1664C212yesmaximal, complemented
5C11×#1663C211yesmaximal, characteristic, complemented
6C11×#1662C211yesmaximal, characteristic, complemented
7C11×#1658C211yesmaximal, characteristic, complemented
8C11×#1657C212yesmaximal, complemented
9C11×#1656C211yesmaximal, characteristic, complemented
10C11×#1524C212yesmaximal, complemented
11C2×C11×#330C211yesmaximal, characteristic, complemented
12C11×#564C2211yescharacteristic
13C11×#563C2212yes—
14C11×#562C2211yescharacteristic
15C11×#554—22no—
16C11×#553—22no—
17C11×#552—22no—
18C11×#541—22no—
19C11×#539—22no—
20C11×#539—22no—
21C11×#532C2211yescharacteristic
22C11×#529C2212yes—
23C2×C11×#125C2211yescharacteristic
24C11×#501C2212yes—
25C11×#496C2212yes—
26C11×#491C2211yescharacteristic
27C11×#491C2211yescharacteristic
28C11×#490C2212yes—
29C11×#490C2211yescharacteristic
30C11×#490C2211yescharacteristic
31C11×#489C2212yes—
32C11×#488—22no—
33C11×#466—22no—
34C11×#465—22no—
35C11×#442—22no—
36C11×#440—22no—
37C11×#417—22no—
38C4×C11×M16C2211yescharacteristic
39C2×C11×#97C2212yes—
40C11×#330C2211yescharacteristic
41C11×#330C2212yes—
42C11×#330C2212yes—
43C11×#330C2211yescharacteristic
44C11×#330C2212yes—
45C11×#329C2212yes—
46C11×#329C2212yes—
47C2×C11×#41—21no—
48C2×C11×SD16—22no—
49C2×C11×D8—22no—
50C2×C11×M16—21no—
51C22×C8×C11—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×#127C2311yescharacteristic
55C11×#126—22no—
56C11×#126—22no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#125—22no—
61C11×#125—22no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#125D412yes—
67C11×#125C2311yescharacteristic
68C11×#125C2311yescharacteristic
69C11×#125C2312yes—
70C11×#124—21no—
71C11×#124C2312yes—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8D412yes—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121D412yes—
88C4×Q8×C11—22no—
89C4×Q8×C11D412yes—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11D412yes—
96C11×#117—22no—
97C11×#117—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4D412yes—
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×#106—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#103—22no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#97—22no—
113C11×#97C2312yes—
114C11×#97C2311yescharacteristic
115C11×#97C2311yescharacteristic
116C11×#97C2312yes—
117C4×C8×C11—21no—
118#19082C1111yesmaximal, characteristic, direct product factor, Sylow
119C11×#41—44no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—41no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C11×SD16—44no—
137C11×D8—44no—
138C11×M16—42no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—44no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—42no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D412yes—
179C42×C11C2411yescharacteristic
180#3553C2×C1111yescharacteristic, complemented
181#3180C2×C1112yescomplemented
182#3142C2×C1111yescharacteristic, complemented
183#1664C2×C1112yescomplemented
184#1663C2×C1111yescharacteristic, complemented
185#1662C2×C1111yescharacteristic, complemented
186#1658C2×C1111yescharacteristic, complemented
187#1657C2×C1112yescomplemented
188#1656C2×C1111yescharacteristic, complemented
189#1524C2×C1112yescomplemented
190C2×#330C2×C1111yescharacteristic, complemented
191C23×C11—22no—
192C23×C11—41no—
193C23×C11#12011yescharacteristic
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—82no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—82no—
203D4×C11—82no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—82no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D412yes—
221C8×C11—24no—
222C8×C11—42no—
223C8×C11—41no—
224C8×C11—41no—
225#564C22×C1111yescharacteristic
226#563C22×C1112yes—
227#562C22×C1111yescharacteristic
228#554—22no—
229#553—22no—
230#552—22no—
231#541—22no—
232#539—22no—
233#539—22no—
234#532C22×C1111yescharacteristic
235#529C22×C1112yes—
236C2×#125C22×C1111yescharacteristic
237#501C22×C1112yes—
238#496C22×C1112yes—
239#491C22×C1111yescharacteristic
240#491C22×C1111yescharacteristic
241#490C22×C1111yescharacteristic
242#490C22×C1111yescharacteristic
243#490C22×C1112yes—
244#489C22×C1112yes—
245#488—22no—
246#466—22no—
247#465—22no—
248#442—22no—
249#440—22no—
250#417—22no—
251C4×M16C22×C1111yescharacteristic
252C2×#97C22×C1112yes—
253#330C22×C1111yescharacteristic
254#330C22×C1112yes—
255#330C22×C1112yes—
256#330C22×C1111yescharacteristic
257#330C22×C1112yes—
258#329C22×C1112yes—
259#329C22×C1112yes—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—81no—
265C22×C11—82no—
266C22×C11#45412yes—
267C22×C11C2×#12011yescharacteristic
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—81no—
278C2×#41—21no—
279C2×SD16—22no—
280C2×D8—22no—
281C2×M16—21no—
282C22×C8—22no—
283C4⋊Q8—22no—
284C4⋊Q8C23×C1111yescharacteristic
285#127C23×C1111yescharacteristic
286#126—22no—
287#126—22no—
288#126—22no—
289#126—22no—
290#126—22no—
291#125—22no—
292#125—22no—
293#125—22no—
294#125—22no—
295#125—22no—
296#125—22no—
297#125D4×C1112yes—
298#125C23×C1111yescharacteristic
299#125C23×C1111yescharacteristic
300#125C23×C1112yes—
301#124—21no—
302#124C23×C1112yes—
303#123—22no—
304#123—22no—
305#123—22no—
306#123—22no—
307#123—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8D4×C1112yes—
315#121—22no—
316#121—22no—
317#121—22no—
318#121D4×C1112yes—
319C4×Q8—22no—
320C4×Q8D4×C1112yes—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4D4×C1112yes—
327#117—22no—
328#117—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4D4×C1112yes—
332C2×C42C23×C1111yescharacteristic
333#107—22no—
334#106—22no—
335#103—22no—
336#103—22no—
337#103—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#97—22no—
344#97C23×C1111yescharacteristic
345#97C23×C1111yescharacteristic
346#97C23×C1112yes—
347#97C23×C1112yes—
348C4×C8—21no—
349C2×C11—22no—
350C2×C11—82no—
351C2×C11—161no—
352C2×C11C2×#45411yescharacteristic
353C2×C11#301812yes—
354#41—44no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8C2×D4×C1112yes—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—41no—
363C2×D4C2×D4×C1112yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C2×D4×C1112yes—
371SD16—44no—
372D8—44no—
373M16—42no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—22no—
378C2×C8—44no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4C2×D4×C1112yes—
396C4⋊C4C2×D4×C1112yes—
397C4⋊C4C2×D4×C1112yes—
398C4⋊C4C2×D4×C1112yes—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—42no—
409C42—22no—
410C42—22no—
411C42—22no—
412C42C2×D4×C1111yescharacteristic
413C42C2×D4×C1112yes—
414C42C24×C1111yescharacteristic
415C11#1908211yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23—41no—
418C23C11×#12011yescharacteristic
419Q8—42no—
420Q8—42no—
421Q8—82no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—44no—
427D4—82no—
428D4—82no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4C11×#12012yes—
443C2×C4C11×#12011yescharacteristic
444C2×C4C22×D4×C1111yescharacteristic
445C2×C4C22×D4×C1112yes—
446C8—24no—
447C8—42no—
448C8—41no—
449C8—41no—
450C22—22no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—81no—
455C22—82no—
456C22C11×#45412yes—
457C22C2×C11×#12011yescharacteristic
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—81no—
468C2—22no—
469C2—82no—
470C2—161no—
471C2C2×C11×#45411yescharacteristic
472C2C11×#301812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3553C2semidirect
2. C11×#3180C2semidirect
3. C11×#3142C2semidirect
4. C11×#1664C2semidirect
5. C11×#1663C2semidirect
6. C11×#1662C2semidirect
7. C11×#1658C2semidirect
8. C11×#1657C2semidirect
9. C11×#1656C2semidirect
10. C11×#1524C2semidirect
11. C2×C11×#330C2semidirect
118. #19082C11direct (N × H)
180. #3553C2×C11semidirect
181. #3180C2×C11semidirect
182. #3142C2×C11semidirect
183. #1664C2×C11semidirect
184. #1663C2×C11semidirect
185. #1662C2×C11semidirect
186. #1658C2×C11semidirect
187. #1657C2×C11semidirect
188. #1656C2×C11semidirect
189. #1524C2×C11semidirect
190. C2×#330C2×C11semidirect
415. C11#19082direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35532
C11×#31802
C11×#31422
C11×#16642
C11×#16632
C11×#16622
C11×#16582
C11×#16572
C11×#16562
C11×#15242
C2×C11×#3302
#1908211