Finite Group Databasebeta

← C11×#10188 #14587381

Subgroups — C11×#10188 #14587381

Order 2816.

550 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#474—22no—
17C11×#474—22no—
18C11×#463—22no—
19C11×#461—21no—
20C11×#459—21no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C2×C11×#107—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#102—21no—
28C11×#333—22no—
29C11×D4⋊C8—22no—
30C11×#323—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8D411yescharacteristic
45C11×C4⋊Q8D412yes—
46C11×#127D411yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—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—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—24no—
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#102—24no—
71C11×#102—22no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10188C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—21no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—41no—
86C2×Q8×C11—82no—
87C2×D4×C11—21no—
88C2×D4×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—41no—
96C2×D4×C11SD1612yes—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×SD16—44no—
107C11×D8—44no—
108C11×M16—41no—
109C11×M16—41no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#3227C2×C1111yescharacteristic, complemented
133C2×#474C2×C1111yescharacteristic, complemented
134#3036C2×C1111yescharacteristic
135#1548C2×C1111yescharacteristic, complemented
136#1480C2×C1111yescharacteristic, complemented
137#1460C2×C1111yescharacteristic, complemented
138#1301C2×C1111yescharacteristic, complemented
139C23×C11—22no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12111yescharacteristic
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—42no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—42no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—82no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12711yescharacteristic
177C2×C4×C11C2×SD1611yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11#13711yescharacteristic
181C8×C11—42no—
182C8×C11—42no—
183C8×C11—42no—
184C8×C11—81no—
185C2×AGL(1,ℤ/8)—21no—
186#532C22×C1111yescharacteristic
187C2×C4⋊Q8C22×C1111yescharacteristic
188C2×C4×D4C22×C1111yescharacteristic
189#498—21no—
190#486—21no—
191#481—22no—
192#476—22no—
193#474—22no—
194#474—22no—
195#463—22no—
196#461—21no—
197#459—21no—
198#431C22×C1111yescharacteristic
199#431C22×C1111yescharacteristic
200C2×#107—21no—
201#423C22×C1111yescharacteristic
202C2×C4⋊C8C22×C1111yescharacteristic
203#417—21no—
204C2×#102—21no—
205#333—22no—
206D4⋊C8—22no—
207#323—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—42no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#39211yescharacteristic
219C22×C11#46511yescharacteristic
220C22×C11#46811yescharacteristic
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—81no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#47212yes—
232C2×#41—21no—
233C22×Q8—21no—
234C22×D4D4×C1111yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—42no—
237AGL(1,ℤ/8)—42no—
238C2×SD16—22no—
239C2×D8—22no—
240C2×M16—21no—
241C22×C8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8D4×C1112yes—
246C4⋊Q8D4×C1111yescharacteristic
247#127D4×C1111yescharacteristic
248#124—21no—
249#121—21no—
250#121—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4D4×C1111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C42C23×C1111yescharacteristic
262#107—24no—
263#106—24no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C1112yes—
269C4⋊C8D4×C1112yes—
270#103—22no—
271#102—24no—
272#102—22no—
273#102—24no—
274C22⋊C8—21no—
275C22⋊C8D4×C1112yes—
276C4×C8—21no—
277C4×C8—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—82no—
281C2×C11—161no—
282C2×C11#200011yescharacteristic
283C2×C11#200911yescharacteristic
284C2×C11#201811yescharacteristic
285C24—21no—
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—41no—
303C2×D4C11×SD1612yes—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—82no—
310C22×C4C2×D4×C1111yescharacteristic
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C11×#4111yescharacteristic
313SD16—44no—
314D8—44no—
315M16—41no—
316M16—41no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42C2×D4×C1111yescharacteristic
336C42C2×D4×C1111yescharacteristic
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C11#1018811yescharacteristic, direct product factor, Sylow
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—81no—
345C23—81no—
346C23C11×#12111yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—82no—
350Q8—82no—
351D4—22no—
352D4—22no—
353D4—42no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—42no—
359D4—81no—
360D4—81no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—81no—
372C2×C4C11×#12011yescharacteristic
373C2×C4C11×#12011yescharacteristic
374C2×C4C11×#12011yescharacteristic
375C2×C4C11×#12111yescharacteristic
376C2×C4C11×#12111yescharacteristic
377C2×C4C11×#12711yescharacteristic
378C2×C4C2×C11×SD1611yescharacteristic
379C2×C4C11×#13511yescharacteristic
380C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
381C2×C4C11×#13711yescharacteristic
382C8—42no—
383C8—42no—
384C8—42no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—82no—
390C22—82no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C11×#39211yescharacteristic
397C22C11×#46511yescharacteristic
398C22C11×#46811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—82no—
405C4C11×#44811yescharacteristic
406C4C11×#44911yescharacteristic
407C4C11×#45011yescharacteristic
408C4C11×#45211yescharacteristic
409C4C11×#47212yes—
410C2—21no—
411C2—21no—
412C2—82no—
413C2—161no—
414C2C11×#200011yescharacteristic
415C2C11×#200911yescharacteristic
416C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3036C2
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×#3227C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#1548C2semidirect
5. C11×#1480C2semidirect
6. C11×#1460C2semidirect
7. C11×#1301C2semidirect
77. #10188C11direct (N × H)
132. #3227C2×C11semidirect
133. C2×#474C2×C11semidirect
135. #1548C2×C11semidirect
136. #1480C2×C11semidirect
137. #1460C2×C11semidirect
138. #1301C2×C11semidirect
339. C11#10188direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C2×C11×#4742
C11×#30362
C11×#15482
C11×#14802
C11×#14602
C11×#13012
#1018811