Finite Group Databasebeta

← C11×#10176 #14587369

Subgroups — C11×#10176 #14587369

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3205C211yesmaximal, characteristic, complemented
2C11×#3036C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C11×#1545C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C22×C11×D8—21no—
10C11×#532C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#493—21no—
14C11×#486—21no—
15C11×#463—22no—
16C11×#461—21no—
17C11×#459—22no—
18C11×#459—22no—
19C11×#459—21no—
20C11×#459—22no—
21C11×#447—22no—
22C11×#431C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#102—21no—
28C11×#331—22no—
29C11×D4⋊C8—22no—
30C11×#323—22no—
31C2×C11×#41—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C11×AGL(1,ℤ/8)—42no—
38C11×AGL(1,ℤ/8)—42no—
39C2×C11×SD16—22no—
40C2×C11×D8—24no—
41C2×C11×D8—22no—
42C2×C11×D8—24no—
43C2×C11×D8—42no—
44C2×C11×D8—42no—
45C2×C11×M16—21no—
46C22×C8×C11—21no—
47C11×C4⋊Q8D411yescharacteristic
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127D411yescharacteristic
52C11×#127D412yes—
53C11×#124—21no—
54C11×#121—21no—
55C11×#121—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8D412yes—
71C11×#103—22no—
72C11×#102—24no—
73C11×#102—22no—
74C11×#102—24no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8D412yes—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79#10176C1111yesmaximal, characteristic, direct product factor, Sylow
80C24×C11—21no—
81C24×C11—41no—
82C11×#41—41no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C2×D4×C11D812yescomplemented
109C22×C4×C11—21no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—82no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C11×SD16—44no—
118C11×D8—48no—
119C11×D8—44no—
120C11×D8—84no—
121C11×M16—41no—
122C11×M16—41no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141#3205C2×C1111yescharacteristic, complemented
142#3036C2×C1111yescharacteristic, complemented
143C2×#459C2×C1111yescharacteristic, complemented
144#1545C2×C1111yescharacteristic, complemented
145#1480C2×C1111yescharacteristic, complemented
146#1460C2×C1111yescharacteristic, complemented
147#1301C2×C1111yescharacteristic, complemented
148C23×C11—22no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—82no—
156C23×C11—82no—
157C23×C11—81no—
158C23×C11—81no—
159C23×C11#12111yescharacteristic
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—42no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—42no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—82no—
174D4×C11—82no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—81no—
179D4×C11—82no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—82no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—82no—
188C2×C4×C11—81no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12711yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11#13511yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C8×C11—42no—
200C8×C11—42no—
201C8×C11—42no—
202C8×C11—81no—
203C2×AGL(1,ℤ/8)—21no—
204C22×D8—21no—
205#532C22×C1111yescharacteristic
206C2×#127C22×C1111yescharacteristic
207C2×C4×D4C22×C1111yescharacteristic
208#493—21no—
209#486—21no—
210#463—22no—
211#461—21no—
212#459—22no—
213#459—22no—
214#459—21no—
215#459—22no—
216#447—22no—
217#431C22×C1111yescharacteristic
218#431C22×C1111yescharacteristic
219#423C22×C1111yescharacteristic
220C2×C4⋊C8C22×C1111yescharacteristic
221#417—21no—
222C2×#102—21no—
223#331—22no—
224D4⋊C8—22no—
225#323—22no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—82no—
239C22×C11—162no—
240C22×C11—162no—
241C22×C11#39211yescharacteristic
242C22×C11#46611yescharacteristic
243C22×C11#46911yescharacteristic
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11#44711yescharacteristic
250C4×C11#44711yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#44911yescharacteristic
253C4×C11#47212yes—
254C2×#41—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4D4×C1111yescharacteristic
259C23×C4—21no—
260AGL(1,ℤ/8)—42no—
261AGL(1,ℤ/8)—42no—
262C2×SD16—22no—
263C2×D8—24no—
264C2×D8—22no—
265C2×D8—24no—
266C2×D8—42no—
267C2×D8—42no—
268C2×M16—21no—
269C22×C8—21no—
270C4⋊Q8D4×C1111yescharacteristic
271#127—21no—
272#127—21no—
273#127—21no—
274#127D4×C1112yes—
275#127D4×C1111yescharacteristic
276#124—21no—
277#121—21no—
278#121—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C2×C4⋊C4D4×C1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C42C23×C1111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8D4×C1112yes—
293C4⋊C8D4×C1112yes—
294#103—22no—
295#102—24no—
296#102—22no—
297#102—24no—
298C22⋊C8—21no—
299C22⋊C8D4×C1112yes—
300C4×C8—21no—
301C4×C8—21no—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—82no—
305C2×C11—161no—
306C2×C11—162no—
307C2×C11#199911yescharacteristic
308C2×C11#200811yescharacteristic
309C2×C11#201811yescharacteristic
310C24—21no—
311C24—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315#41—41no—
316C2×Q8—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—82no—
337C2×D4—82no—
338C2×D4C11×D812yescomplemented
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—82no—
344C22×C4C2×D4×C1111yescharacteristic
345C22×C4C2×D4×C1111yescharacteristic
346C22×C4C11×#4111yescharacteristic
347SD16—44no—
348D8—48no—
349D8—44no—
350D8—84no—
351M16—41no—
352M16—41no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42C2×D4×C1111yescharacteristic
368C42C2×D4×C1111yescharacteristic
369C42C2×D4×C1111yescharacteristic
370C42C2×D4×C1111yescharacteristic
371C11#1017611yescharacteristic, direct product factor, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—81no—
378C23—81no—
379C23—82no—
380C23—82no—
381C23—81no—
382C23—81no—
383C23C11×#12111yescharacteristic
384Q8—41no—
385Q8—41no—
386D4—22no—
387D4—22no—
388D4—42no—
389D4—44no—
390D4—42no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—42no—
395D4—41no—
396D4—42no—
397D4—82no—
398D4—82no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—82no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—82no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—82no—
412C2×C4—81no—
413C2×C4C11×#12011yescharacteristic
414C2×C4C11×#12011yescharacteristic
415C2×C4C11×#12011yescharacteristic
416C2×C4C11×#12111yescharacteristic
417C2×C4C11×#12111yescharacteristic
418C2×C4C11×#12711yescharacteristic
419C2×C4C2×C11×D811yescharacteristic
420C2×C4C11×#13511yescharacteristic
421C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
422C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
423C8—42no—
424C8—42no—
425C8—42no—
426C8—81no—
427C22—21no—
428C22—21no—
429C22—42no—
430C22—82no—
431C22—82no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—82no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—82no—
440C22—162no—
441C22—162no—
442C22C11×#39211yescharacteristic
443C22C11×#46611yescharacteristic
444C22C11×#46911yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4C11×#44711yescharacteristic
451C4C11×#44711yescharacteristic
452C4C11×#44911yescharacteristic
453C4C11×#44911yescharacteristic
454C4C11×#47212yes—
455C2—21no—
456C2—21no—
457C2—82no—
458C2—162no—
459C2—161no—
460C2C11×#199911yescharacteristic
461C2C11×#200811yescharacteristic
462C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
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×#3205C2semidirect
2. C11×#3036C2semidirect
3. C2×C11×#459C2semidirect
4. C11×#1545C2semidirect
5. C11×#1480C2semidirect
6. C11×#1460C2semidirect
7. C11×#1301C2semidirect
79. #10176C11direct (N × H)
108. C2×D4×C11D8semidirect
141. #3205C2×C11semidirect
142. #3036C2×C11semidirect
143. C2×#459C2×C11semidirect
144. #1545C2×C11semidirect
145. #1480C2×C11semidirect
146. #1460C2×C11semidirect
147. #1301C2×C11semidirect
338. C2×D4C11×D8semidirect
371. C11#10176direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#30362
C2×C11×#4592
C11×#15452
C11×#14802
C11×#14602
C11×#13012
#1017611