Finite Group Databasebeta

← C11×#8512 #14585705

Subgroups — C11×#8512 #14585705

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic
2C11×#1989C211yesmaximal, characteristic, complemented
3C11×#1986C211yesmaximal, characteristic, complemented
4C11×#1552C211yesmaximal, characteristic, complemented
5C11×#1528C211yesmaximal, characteristic, complemented
6C11×#1509C211yesmaximal, characteristic
7C11×#1483C211yesmaximal, characteristic
8C11×#564C412yescomplemented
9C11×#563C412yescomplemented
10C11×#557—21no—
11C11×#554—21no—
12C11×#552—21no—
13C11×#552—22no—
14C11×#552—21no—
15C11×#544—21no—
16C11×#544—21no—
17C11×#541—21no—
18C11×#541—22no—
19C11×#539—21no—
20C11×#533C2211yescharacteristic
21C11×#529C2211yescharacteristic
22C2×C11×#125C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C4×C11×M16C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#340—21no—
28C11×#340—21no—
29C11×#339—22no—
30C11×#332—21no—
31C11×#332—21no—
32C11×#330—22no—
33C11×#328—21no—
34C11×#327—21no—
35C11×Q8⋊C8—21no—
36C11×D4⋊C8—21no—
37C2×C11×M16—21no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—22no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×#126—22no—
45C11×#126—22no—
46C11×#126—22no—
47C11×#126—22no—
48C11×#126—21no—
49C11×#125—22no—
50C11×#125—22no—
51C11×#125—21no—
52C11×#125—22no—
53C11×#125—22no—
54C11×#125—22no—
55C11×#125—22no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#125—21no—
59C11×#125—21no—
60C11×#125C2×C412yes—
61C11×#125C2×C411yescharacteristic
62C11×#125C2×C412yes—
63C11×#125D412yes—
64C11×#124C2×C411yescharacteristic
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—21no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—22no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11D411yescharacteristic
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11D411yescharacteristic
87C11×#117—22no—
88C11×#117—21no—
89C11×#117—22no—
90C11×#117—21no—
91C11×#117D412yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11—21no—
107C11×#95—21no—
108#8512C1111yesmaximal, characteristic, direct product factor, Sylow
109C2×Q8×C11—22no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C22⋊C411yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11C22⋊C411yescharacteristic
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C11×M16—22no—
124C11×M16—41no—
125C2×C8×C11—42no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4C22⋊C412yes—
154C11×C4⋊C4C22⋊C412yes—
155C11×C4⋊C4C22⋊C412yes—
156C11×C4⋊C4C22⋊C412yes—
157C11×C4⋊C4C22⋊C411yescharacteristic
158C11×C4⋊C4C22⋊C411yescharacteristic
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—21no—
173C42×C11—42no—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178#3563C2×C1111yescharacteristic
179#1989C2×C1111yescharacteristic, complemented
180#1986C2×C1111yescharacteristic, complemented
181#1552C2×C1111yescharacteristic, complemented
182#1528C2×C1111yescharacteristic, complemented
183#1509C2×C1111yescharacteristic
184#1483C2×C1111yescharacteristic
185C23×C11—21no—
186C23×C11#12011yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11—81no—
191Q8×C11—82no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—81no—
213C2×C4×C11—82no—
214C2×C4×C11—81no—
215C2×C4×C11—81no—
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C8×C11—42no—
223C8×C11—81no—
224C8×C11—81no—
225#564C4×C1112yescomplemented
226#563C4×C1112yescomplemented
227#557—21no—
228#554—21no—
229#552—21no—
230#552—22no—
231#552—21no—
232#544—21no—
233#544—21no—
234#541—21no—
235#541—22no—
236#539—21no—
237#533C22×C1111yescharacteristic
238#529C22×C1111yescharacteristic
239C2×#125C22×C1111yescharacteristic
240#432C22×C1111yescharacteristic
241C2×C4⋊C8C22×C1111yescharacteristic
242C4×M16C22×C1111yescharacteristic
243C4×C4⋊C4C22×C1111yescharacteristic
244#340—21no—
245#340—21no—
246#339—22no—
247#332—21no—
248#332—21no—
249#330—22no—
250#328—21no—
251#327—21no—
252Q8⋊C8—21no—
253D4⋊C8—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11#37911yescharacteristic
260C22×C11#45411yescharacteristic
261C22×C11#45611yescharacteristic
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—41no—
274C4×C11—82no—
275C4×C11#45411yescharacteristic
276C4×C11#45611yescharacteristic
277C2×M16—21no—
278C22×C8—21no—
279C4⋊Q8—22no—
280C4⋊Q8—21no—
281C4⋊Q8—22no—
282C4⋊Q8D4×C1111yescharacteristic
283C4⋊Q8D4×C1111yescharacteristic
284#126—22no—
285#126—22no—
286#126—22no—
287#126—22no—
288#126—21no—
289#125—22no—
290#125—22no—
291#125—21no—
292#125—22no—
293#125—22no—
294#125—22no—
295#125—22no—
296#125—22no—
297#125—22no—
298#125—21no—
299#125—21no—
300#125C2×C4×C1112yes—
301#125C2×C4×C1111yescharacteristic
302#125C2×C4×C1112yes—
303#125D4×C1112yes—
304#124C2×C4×C1111yescharacteristic
305#123—22no—
306#123—22no—
307#123—21no—
308C22⋊Q8—22no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—22no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8D4×C1111yescharacteristic
317#121D4×C1111yescharacteristic
318C4×Q8—21no—
319C4×Q8—22no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8D4×C1111yescharacteristic
324C4×D4—22no—
325C4×D4—21no—
326C4×D4D4×C1111yescharacteristic
327#117—22no—
328#117—21no—
329#117—22no—
330#117—21no—
331#117D4×C1112yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C1111yescharacteristic
337C2×C4⋊C4D4×C1111yescharacteristic
338C2×C42—21no—
339C2×C42C23×C1111yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C22⋊C8—21no—
344#97—21no—
345#97—21no—
346C4×C8—21no—
347#95—21no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—81no—
351C2×C11#179311yescharacteristic
352C2×C11#179311yescharacteristic
353C2×C11#179411yescharacteristic
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8C11×C22⋊C411yescharacteristic
358C2×D4—21no—
359C2×D4C11×C22⋊C411yescharacteristic
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4C2×D4×C1111yescharacteristic
366C22×C4C2×D4×C1111yescharacteristic
367C22×C4C2×D4×C1111yescharacteristic
368M16—22no—
369M16—41no—
370C2×C8—41no—
371C2×C8—42no—
372C2×C8—41no—
373C2×C8—41no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—41no—
398C4⋊C4C11×C22⋊C412yes—
399C4⋊C4C11×C22⋊C412yes—
400C4⋊C4C11×C22⋊C412yes—
401C4⋊C4C11×C22⋊C412yes—
402C4⋊C4C11×C22⋊C411yescharacteristic
403C4⋊C4C11×C22⋊C411yescharacteristic
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—21no—
408C22⋊C4—22no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C42—22no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—21no—
418C42—42no—
419C42C22×C4×C1111yescharacteristic
420C42C2×D4×C1111yescharacteristic
421C42C2×D4×C1111yescharacteristic
422C42C2×D4×C1111yescharacteristic
423C11#851211yescharacteristic, direct product factor, Sylow
424C23—21no—
425C23C11×#12011yescharacteristic
426Q8—41no—
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—82no—
431D4—41no—
432D4—41no—
433D4—41no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4C2×C11×C22⋊C411yescharacteristic
456C2×C4C2×C11×C22⋊C411yescharacteristic
457C2×C4C2×C11×C22⋊C411yescharacteristic
458C2×C4C11×#12011yescharacteristic
459C2×C4C11×#12011yescharacteristic
460C2×C4C11×#12011yescharacteristic
461C8—42no—
462C8—81no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22C11×#37911yescharacteristic
470C22C11×#45411yescharacteristic
471C22C11×#45611yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—41no—
479C4—41no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—41no—
484C4—82no—
485C4C11×#45411yescharacteristic
486C4C11×#45611yescharacteristic
487C2—21no—
488C2—21no—
489C2—81no—
490C2C11×#179311yescharacteristic
491C2C11×#179311yescharacteristic
492C2C11×#179411yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#121D4
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
2. C11×#1989C2semidirect
3. C11×#1986C2semidirect
4. C11×#1552C2semidirect
5. C11×#1528C2semidirect
8. C11×#564C4semidirect
9. C11×#563C4semidirect
108. #8512C11direct (N × H)
179. #1989C2×C11semidirect
180. #1986C2×C11semidirect
181. #1552C2×C11semidirect
182. #1528C2×C11semidirect
225. #564C4×C11semidirect
226. #563C4×C11semidirect
423. C11#8512direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#19892
C11×#19862
C11×#15522
C11×#15282
C11×#15092
C11×#14832
#851211