Finite Group Databasebeta

← C11×#10000 #14587193

Subgroups — C11×#10000 #14587193

Order 2816.

632 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
1C11×#3101C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C11×#2535C211yesmaximal, characteristic
4C11×#1518C211yesmaximal, characteristic, complemented
5C11×#1486C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#483—21no—
13C11×#478—22no—
14C11×#476—21no—
15C11×#476—21no—
16C11×#474—21no—
17C11×#461—21no—
18C11×#450—21no—
19C4×C11×SD16—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#428—21no—
23C11×#423C2211yescharacteristic
24C11×#418—21no—
25C11×#397—21no—
26C11×#392—21no—
27C11×#386—22no—
28C11×#382C2211yescharacteristic
29C11×#380—21no—
30C11×#328—22no—
31C11×D4⋊C8—22no—
32C11×D4⋊C8—22no—
33C22×D4×C11—22no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C2×C11×SD16—22no—
39C2×C11×M16—21no—
40C11×C4⋊Q8D411yescharacteristic, complemented
41C11×C4⋊Q8D411yescharacteristic, complemented
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×#121—42no—
46C11×#121—42no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C11×#117—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C42×C11C2311yescharacteristic
66C11×#107—22no—
67C11×#106—22no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yescomplemented
73C11×#103—22no—
74C11×#102—22no—
75C11×#102—22no—
76C11×#102—22no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C4×C8×C11—21no—
80C4×C8×C11D412yescomplemented
81C11×#95—22no—
82C11×#95—21no—
83C11×#95D412yes—
84#10000C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—42no—
97C2×D4×C11—44no—
98C2×D4×C11—44no—
99C2×D4×C11—82no—
100C2×D4×C11SD1612yescomplemented
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C11×SD16—44no—
117C11×M16—41no—
118C11×M16—41no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—41no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—44no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—82no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146#3101C2×C1111yescharacteristic, complemented
147#3077C2×C1111yescharacteristic, complemented
148#2535C2×C1111yescharacteristic
149#1518C2×C1111yescharacteristic, complemented
150#1486C2×C1111yescharacteristic, complemented
151#1478C2×C1111yescharacteristic, complemented
152#1286C2×C1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12011yescharacteristic
166Q8×C11—42no—
167Q8×C11—81no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—22no—
171D4×C11—22no—
172D4×C11—41no—
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—41no—
176D4×C11—88no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12711yescharacteristic
201C2×C4×C11C2×SD1611yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C11#13711yescharacteristic
205C8×C11—42no—
206C8×C11—42no—
207C8×C11—81no—
208#533C22×C1111yescharacteristic
209C2×#121—21no—
210C2×C4×D4C22×C1111yescharacteristic
211C2×C4×D4C22×C1111yescharacteristic
212#483—21no—
213#478—22no—
214#476—21no—
215#476—21no—
216#474—21no—
217#461—21no—
218#450—21no—
219C4×SD16—22no—
220#431C22×C1111yescharacteristic
221#431C22×C1111yescharacteristic
222#428—21no—
223#423C22×C1111yescharacteristic
224#418—21no—
225#397—21no—
226#392—21no—
227#386—22no—
228#382C22×C1111yescharacteristic
229#380—21no—
230#328—22no—
231D4⋊C8—22no—
232D4⋊C8—22no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—81no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11#39211yescharacteristic
248C22×C11#45011yescharacteristic
249C22×C11#45211yescharacteristic
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11#44811yescharacteristic
260C4×C11#44911yescharacteristic
261C4×C11#46511yescharacteristic
262C4×C11#46811yescharacteristic
263C22×D4—22no—
264C22×D4D4×C1111yescharacteristic
265C22×D4D4×C1111yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C2×SD16—22no—
269C2×M16—21no—
270C4⋊Q8D4×C1111yescharacteristic, complemented
271C4⋊Q8D4×C1111yescharacteristic, complemented
272#125—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—42no—
276#121—42no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4D4×C1111yescharacteristic
290C2×C4⋊C4D4×C1111yescharacteristic
291C2×C22⋊C4—22no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C42C23×C1111yescharacteristic
296#107—22no—
297#106—22no—
298#106—22no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8D4×C1112yescomplemented
303#103—22no—
304#102—22no—
305#102—22no—
306#102—22no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C4×C8—21no—
310C4×C8D4×C1112yescomplemented
311#95—22no—
312#95—21no—
313#95D4×C1112yes—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—82no—
317C2×C11—82no—
318C2×C11#200011yescharacteristic
319C2×C11#200811yescharacteristic
320C2×C11#201011yescharacteristic
321C24—21no—
322C24—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4—82no—
336C2×D4C11×SD1612yescomplemented
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—82no—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352SD16—44no—
353M16—41no—
354M16—41no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C22⋊C4—44no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—82no—
377C42—41no—
378C42C2×D4×C1111yescharacteristic
379C42C2×D4×C1111yescharacteristic
380C42C2×D4×C1111yescharacteristic
381C42C11×#4111yescharacteristic
382C11#1000011yescharacteristic, direct product factor, Sylow
383C23—22no—
384C23—22no—
385C23—41no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23C11×#12011yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—22no—
399D4—22no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—88no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4C11×#12011yescharacteristic
426C2×C4C11×#12011yescharacteristic
427C2×C4C11×#12111yescharacteristic
428C2×C4C11×#12111yescharacteristic
429C2×C4C11×#12111yescharacteristic
430C2×C4C11×#12711yescharacteristic
431C2×C4C2×C11×SD1611yescharacteristic
432C2×C4C11×#13511yescharacteristic
433C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
434C2×C4C11×#13711yescharacteristic
435C8—42no—
436C8—42no—
437C8—81no—
438C22—21no—
439C22—21no—
440C22—42no—
441C22—44no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22C11×#39211yescharacteristic
453C22C11×#45011yescharacteristic
454C22C11×#45211yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4C11×#44811yescharacteristic
465C4C11×#44911yescharacteristic
466C4C11×#46511yescharacteristic
467C4C11×#46811yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—82no—
472C2C11×#200011yescharacteristic
473C2C11×#200811yescharacteristic
474C2C11×#201011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2535C2
LCSG ▷ C2×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×#3101C2semidirect
2. C11×#3077C2semidirect
4. C11×#1518C2semidirect
5. C11×#1486C2semidirect
6. C11×#1478C2semidirect
7. C11×#1286C2semidirect
40. C11×C4⋊Q8D4semidirect
41. C11×C4⋊Q8D4semidirect
72. C11×C4⋊C8D4semidirect
80. C4×C8×C11D4semidirect
84. #10000C11direct (N × H)
100. C2×D4×C11SD16semidirect
146. #3101C2×C11semidirect
147. #3077C2×C11semidirect
149. #1518C2×C11semidirect
150. #1486C2×C11semidirect
151. #1478C2×C11semidirect
152. #1286C2×C11semidirect
270. C4⋊Q8D4×C11semidirect
271. C4⋊Q8D4×C11semidirect
302. C4⋊C8D4×C11semidirect
310. C4×C8D4×C11semidirect
336. C2×D4C11×SD16semidirect
382. C11#10000direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31012
C11×#30772
C11×#25352
C11×#15182
C11×#14862
C11×#14782
C11×#12862
#1000011