Finite Group Databasebeta

← C11×#10267 #14587460

Subgroups — C11×#10267 #14587460

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#486C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic
4C11×#1954C211yesmaximal, characteristic, complemented
5C2×C11×#333C211yesmaximal, characteristic, complemented
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#486—22no—
13C11×#486—22no—
14C11×#476—22no—
15C11×#476—22no—
16C11×#459—22no—
17C11×#459—22no—
18C2×C11×#106—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102—21no—
23C2×C11×#102—22no—
24C2×C11×#102—21no—
25C2×C11×C22⋊C8—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#333—22no—
28C11×#331—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×C11×D8—24no—
36C2×C11×D8—42no—
37C2×C11×D8—42no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C22×C8×C11D412yes—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8D412yes—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127D412yes—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C11×#106—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C4⋊C8D412yes—
66C11×#102—24no—
67C11×#102—24no—
68C11×#102—28no—
69C11×C22⋊C8—44no—
70C4×C8×C11—21no—
71C4×C8×C11—21no—
72#10267C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—21no—
74C24×C11—41no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C2×D4×C11—82no—
96C2×D4×C11SD1612yes—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×D8—48no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—42no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C2×#486C2×C1111yescharacteristic, complemented
131C2×#476C2×C1111yescharacteristic, complemented
132C2×#459C2×C1111yescharacteristic
133#1954C2×C1111yescharacteristic, complemented
134C2×#333C2×C1111yescharacteristic, complemented
135C2×#331C2×C1111yescharacteristic, complemented
136#1277C2×C1111yescharacteristic, complemented
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—82no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—82no—
147C23×C11#12111yescharacteristic
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—41no—
153D4×C11—44no—
154D4×C11—42no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—81no—
160D4×C11—81no—
161D4×C11—81no—
162D4×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—82no—
168C2×C4×C11—82no—
169C2×C4×C11—81no—
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×C11#13512yes—
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11#13711yescharacteristic
183C8×C11—42no—
184C8×C11—42no—
185C8×C11—42no—
186C8×C11—81no—
187C22×D8—21no—
188C2×C4⋊Q8C22×C1111yescharacteristic
189C2×#127C22×C1111yescharacteristic
190C2×C4×D4C22×C1111yescharacteristic
191#486—22no—
192#486—22no—
193#476—22no—
194#476—22no—
195#459—22no—
196#459—22no—
197C2×#106—21no—
198C2×C4⋊C8C22×C1111yescharacteristic
199C2×C4⋊C8C22×C1111yescharacteristic
200C2×C4⋊C8C22×C1111yescharacteristic
201C2×#102—21no—
202C2×#102—22no—
203C2×#102—21no—
204C2×C22⋊C8—22no—
205C2×C4×C8C22×C1111yescharacteristic
206#333—22no—
207#331—22no—
208C22×C11—44no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—162no—
217C22×C11—162no—
218C22×C11#39211yescharacteristic
219C22×C11#46312yes—
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C22×C11#47212yes—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11—82no—
227C4×C11#44811yescharacteristic
228C4×C11#44911yescharacteristic
229C4×C11#44912yes—
230C4×C11#45011yescharacteristic
231C4×C11#45211yescharacteristic
232C4×C11#49511yescharacteristic
233C4×C11#49611yescharacteristic
234C22×Q8—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4D4×C1111yescharacteristic
239C23×C4—21no—
240C2×D8—24no—
241C2×D8—42no—
242C2×D8—42no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8D4×C1112yes—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8D4×C1112yes—
251#127—21no—
252#127—21no—
253#127—21no—
254#127D4×C1112yes—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4D4×C1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C23×C1111yescharacteristic
264#106—24no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8D4×C1112yes—
270C4⋊C8D4×C1112yes—
271#102—24no—
272#102—24no—
273#102—28no—
274C22⋊C8—44no—
275C4×C8—21no—
276C4×C8—21no—
277C2×C11—82no—
278C2×C11—162no—
279C2×C11#167712yes—
280C2×C11#169712yes—
281C2×C11#200011yescharacteristic
282C2×C11#201211yescharacteristic
283C2×C11#201811yescharacteristic
284C24—21no—
285C24—41no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—82no—
307C2×D4C11×SD1612yes—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C11×#4111yescharacteristic
317D8—48no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—42no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42C2×D4×C1111yescharacteristic
338C42C2×D4×C1111yescharacteristic
339C42C2×D4×C1111yescharacteristic
340C42C2×D4×C1111yescharacteristic
341C11#1026711yescharacteristic, direct product factor, Sylow
342C23—22no—
343C23—41no—
344C23—42no—
345C23—41no—
346C23—42no—
347C23—42no—
348C23—82no—
349C23—81no—
350C23—81no—
351C23—82no—
352C23C11×#12111yescharacteristic
353Q8—82no—
354Q8—82no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—44no—
359D4—42no—
360D4—41no—
361D4—42no—
362D4—82no—
363D4—82no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4C11×#12011yescharacteristic
377C2×C4C11×#12011yescharacteristic
378C2×C4C11×#12011yescharacteristic
379C2×C4C11×#12111yescharacteristic
380C2×C4C11×#12111yescharacteristic
381C2×C4C11×#12711yescharacteristic
382C2×C4C2×C11×SD1611yescharacteristic
383C2×C4C11×#13512yes—
384C2×C4C11×#13511yescharacteristic
385C2×C4C11×AGL(1,ℤ/8)12yes—
386C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
387C2×C4C11×#13711yescharacteristic
388C8—42no—
389C8—42no—
390C8—42no—
391C8—81no—
392C22—44no—
393C22—42no—
394C22—82no—
395C22—81no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—162no—
401C22—162no—
402C22C11×#39211yescharacteristic
403C22C11×#46312yes—
404C22C11×#46511yescharacteristic
405C22C11×#46811yescharacteristic
406C22C11×#47212yes—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—82no—
411C4C11×#44811yescharacteristic
412C4C11×#44911yescharacteristic
413C4C11×#44912yes—
414C4C11×#45011yescharacteristic
415C4C11×#45211yescharacteristic
416C4C11×#49511yescharacteristic
417C4C11×#49611yescharacteristic
418C2—82no—
419C2—162no—
420C2C11×#167712yes—
421C2C11×#169712yes—
422C2C11×#200011yescharacteristic
423C2C11×#201211yescharacteristic
424C2C11×#201811yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#459C2
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×#486C2semidirect
2. C2×C11×#476C2semidirect
4. C11×#1954C2semidirect
5. C2×C11×#333C2semidirect
6. C2×C11×#331C2semidirect
7. C11×#1277C2semidirect
72. #10267C11direct (N × H)
130. C2×#486C2×C11semidirect
131. C2×#476C2×C11semidirect
133. #1954C2×C11semidirect
134. C2×#333C2×C11semidirect
135. C2×#331C2×C11semidirect
136. #1277C2×C11semidirect
341. C11#10267direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4862
C2×C11×#4762
C2×C11×#4592
C11×#19542
C2×C11×#3332
C2×C11×#3312
C11×#12772
#1026711