Finite Group Databasebeta

← C11×#10236 #14587429

Subgroups — C11×#10236 #14587429

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#477C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C11×#2538C211yesmaximal, characteristic
4C11×#1956C211yesmaximal, characteristic, complemented
5C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#477—22no—
13C11×#477—22no—
14C11×#476—22no—
15C11×#476—22no—
16C2×C11×#107—21no—
17C2×C11×#106—21no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—21no—
21C2×C11×#103—22no—
22C2×C11×#102—21no—
23C2×C4×C8×C11C2211yescharacteristic
24C11×#396—22no—
25C11×#390—21no—
26C11×#389—21no—
27C11×#384C2211yescharacteristic
28C11×#380—21no—
29C11×Q8⋊C8—22no—
30C11×D4⋊C8—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yes—
42C11×C22⋊Q8—42no—
43C11×C22⋊Q8—42no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D412yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×#107—24no—
67C11×#106—24no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8D412yes—
72C11×#103—24no—
73C11×#103—44no—
74C11×#102—24no—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77C11×#95—22no—
78#10236C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—41no—
89C2×Q8×C11SD1612yes—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11Q1612yes—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—44no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—82no—
139C42×C11—41no—
140C42×C11—41no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C2×#477C2×C1111yescharacteristic, complemented
146C2×#476C2×C1111yescharacteristic
147#2538C2×C1111yescharacteristic
148#1956C2×C1111yescharacteristic, complemented
149C2×Q8⋊C8C2×C1111yescharacteristic, complemented
150C2×D4⋊C8C2×C1111yescharacteristic
151#1296C2×C1111yescharacteristic, complemented
152C23×C11—22no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11#12011yescharacteristic
160Q8×C11—22no—
161Q8×C11—22no—
162Q8×C11—44no—
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—82no—
166D4×C11—22no—
167D4×C11—22no—
168D4×C11—41no—
169D4×C11—41no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12711yescharacteristic
197C2×C4×C11C2×SD1611yescharacteristic
198C2×C4×C11C2×Q1611yescharacteristic
199C2×C4×C11#13511yescharacteristic
200C2×C4×C11#13511yescharacteristic
201C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C11#13711yescharacteristic
203C2×C4×C11#13711yescharacteristic
204C2×C4×C11#13711yescharacteristic
205C8×C11—42no—
206C8×C11—42no—
207C8×C11—42no—
208C2×C4⋊Q8C22×C1111yescharacteristic
209C2×C22⋊Q8—21no—
210C2×C4×Q8C22×C1111yescharacteristic
211C2×C4×D4C22×C1111yescharacteristic
212#477—22no—
213#477—22no—
214#476—22no—
215#476—22no—
216C2×#107—21no—
217C2×#106—21no—
218C2×C4⋊C8C22×C1111yescharacteristic
219C2×C4⋊C8C22×C1111yescharacteristic
220C2×#103—21no—
221C2×#103—22no—
222C2×#102—21no—
223C2×C4×C8C22×C1111yescharacteristic
224#396—22no—
225#390—21no—
226#389—21no—
227#384C22×C1111yescharacteristic
228#380—21no—
229Q8⋊C8—22no—
230D4⋊C8—22no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11#39211yescharacteristic
239C22×C11#45011yescharacteristic
240C22×C11#45111yescharacteristic
241C22×C11#45211yescharacteristic
242C22×C11#45211yescharacteristic
243C22×C11#45311yescharacteristic
244C22×C11#45411yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—42no—
248C4×C11—82no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—82no—
252C4×C11#44811yescharacteristic
253C4×C11#44911yescharacteristic
254C4×C11#45111yescharacteristic
255C4×C11#45211yescharacteristic
256C4×C11#46511yescharacteristic
257C4×C11#46711yescharacteristic
258C4×C11#46811yescharacteristic
259C4×C11#47011yescharacteristic
260C22×Q8—21no—
261C22×Q8D4×C1111yescharacteristic
262C22×D4D4×C1111yescharacteristic
263C23×C4—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C1112yes—
271C22⋊Q8—42no—
272C22⋊Q8—42no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4D4×C1111yescharacteristic
288C2×C4⋊C4D4×C1111yescharacteristic
289C2×C4⋊C4D4×C1112yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C42—21no—
294C2×C42C23×C1111yescharacteristic
295#107—24no—
296#106—24no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8D4×C1112yes—
300C4⋊C8D4×C1112yes—
301#103—24no—
302#103—44no—
303#102—24no—
304C4×C8—21no—
305C4×C8—21no—
306#95—22no—
307C2×C11—82no—
308C2×C11#163111yescharacteristic
309C2×C11#163211yescharacteristic
310C2×C11#163711yescharacteristic
311C2×C11#163811yescharacteristic
312C2×C11#200011yescharacteristic
313C2×C11#200111yescharacteristic
314C2×C11#200611yescharacteristic
315C24—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—22no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—41no—
325C2×Q8C11×SD1612yes—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4C11×Q1612yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4C2×D4×C1111yescharacteristic
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1111yescharacteristic
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—42no—
362C4⋊C4—44no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C22⋊C4—44no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—82no—
375C42—41no—
376C42—41no—
377C42C2×D4×C1111yescharacteristic
378C42C2×D4×C1111yescharacteristic
379C42C2×D4×C1111yescharacteristic
380C42C11×#4111yescharacteristic
381C11#1023611yescharacteristic, direct product factor, Sylow
382C23—22no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23C11×#12011yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—44no—
393Q8—41no—
394Q8—41no—
395Q8—82no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4C11×#12011yescharacteristic
422C2×C4C11×#12011yescharacteristic
423C2×C4C11×#12111yescharacteristic
424C2×C4C11×#12111yescharacteristic
425C2×C4C11×#12111yescharacteristic
426C2×C4C11×#12711yescharacteristic
427C2×C4C2×C11×SD1611yescharacteristic
428C2×C4C2×C11×Q1611yescharacteristic
429C2×C4C11×#13511yescharacteristic
430C2×C4C11×#13511yescharacteristic
431C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
432C2×C4C11×#13711yescharacteristic
433C2×C4C11×#13711yescharacteristic
434C2×C4C11×#13711yescharacteristic
435C8—42no—
436C8—42no—
437C8—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22C11×#39211yescharacteristic
446C22C11×#45011yescharacteristic
447C22C11×#45111yescharacteristic
448C22C11×#45211yescharacteristic
449C22C11×#45211yescharacteristic
450C22C11×#45311yescharacteristic
451C22C11×#45411yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—82no—
456C4—81no—
457C4—81no—
458C4—82no—
459C4C11×#44811yescharacteristic
460C4C11×#44911yescharacteristic
461C4C11×#45111yescharacteristic
462C4C11×#45211yescharacteristic
463C4C11×#46511yescharacteristic
464C4C11×#46711yescharacteristic
465C4C11×#46811yescharacteristic
466C4C11×#47011yescharacteristic
467C2—82no—
468C2C11×#163111yescharacteristic
469C2C11×#163211yescharacteristic
470C2C11×#163711yescharacteristic
471C2C11×#163811yescharacteristic
472C2C11×#200011yescharacteristic
473C2C11×#200111yescharacteristic
474C2C11×#200611yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#477C2semidirect
4. C11×#1956C2semidirect
5. C2×C11×Q8⋊C8C2semidirect
7. C11×#1296C2semidirect
78. #10236C11direct (N × H)
145. C2×#477C2×C11semidirect
148. #1956C2×C11semidirect
149. C2×Q8⋊C8C2×C11semidirect
151. #1296C2×C11semidirect
381. C11#10236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4772
C2×C11×#4762
C11×#25382
C11×#19562
C2×C11×Q8⋊C82
C2×C11×D4⋊C82
C11×#12962
#1023611