Finite Group Databasebeta

← C11×#8943 #14586136

Subgroups — C11×#8943 #14586136

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#432C211yesmaximal, characteristic, complemented
2C4×C11×#121C211yesmaximal, characteristic
3C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C11×D4⋊C8C212yesmaximal, complemented
5C11×#1279C212yesmaximal, complemented
6C2×C11×#121C411yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#432—24no—
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C22⋊C8—21no—
13C2×C11×C22⋊C8—21no—
14C2×C11×#97—21no—
15C2×C4×C8×C11C2212yes—
16C11×#390C411yescharacteristic
17C11×#389C411yescharacteristic
18C11×#388—21no—
19C11×#386—21no—
20C11×#380C411yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C22⋊C4—21no—
23C11×#336—21no—
24C11×D4⋊C8—24no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C11×#121—22no—
34C11×#121—22no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C4×D4×C11—44no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C42×C11—22no—
48C2×C42×C11—22no—
49C2×C42×C11—21no—
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—22no—
55C11×C4⋊C8D414yescomplemented
56C11×C22⋊C8—24no—
57C11×C22⋊C8—24no—
58C11×#97—24no—
59C4×C8×C11—22no—
60C4×C8×C11—22no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#8943C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11C22⋊C411yescharacteristic
67C2×D4×C11—24no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—22no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11M1612yes—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—42no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4M1612yes—
109C11×C22⋊C4—24no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C42×C11—22no—
115C42×C11—21no—
116C42×C11—22no—
117C42×C11—21no—
118C42×C11—42no—
119C42×C11C2×D412yes—
120C42×C11#4112yes—
121C2×#432C2×C1111yescharacteristic, complemented
122C4×#121C2×C1111yescharacteristic
123C4×C22⋊C8C2×C1111yescharacteristic, complemented
124C2×D4⋊C8C2×C1112yescomplemented
125#1279C2×C1112yescomplemented
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#10412yes—
140C23×C11C2×C22⋊C411yescharacteristic
141D4×C11—24no—
142D4×C11—48no—
143D4×C11—42no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—44no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11C4×D412yes—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12112yes—
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11C2×M1611yescharacteristic
176C2×C4×C11C2×M1611yescharacteristic
177C2×C4×C11#13112yes—
178C2×C4×C11#13512yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C8×C11—44no—
181C8×C11—44no—
182C2×#121C4×C1111yescharacteristic
183C2×C4×D4—21no—
184C2×C4×D4C22×C1111yescharacteristic
185C22×C42C22×C1111yescharacteristic
186#432—24no—
187C2×C4⋊C8C22×C1112yes—
188C2×C22⋊C8—21no—
189C2×C22⋊C8—21no—
190C2×#97—21no—
191C2×C4×C8C22×C1112yes—
192#390C4×C1111yescharacteristic
193#389C4×C1111yescharacteristic
194#388—21no—
195#386—21no—
196#380C4×C1111yescharacteristic
197C4×C4⋊C4C22×C1111yescharacteristic
198C4×C22⋊C4—21no—
199#336—21no—
200D4⋊C8—24no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—42no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11#38611yescharacteristic
216C22×C11#40711yescharacteristic
217C22×C11#40811yescharacteristic
218C22×C11#41611yescharacteristic
219C22×C11#41811yescharacteristic
220C22×C11C2×#10411yescharacteristic
221C22×C11#42111yescharacteristic
222C4×C11—22no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—41no—
226C4×C11—42no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#43512yes—
230C4×C11#43612yes—
231C4×C11#44912yes—
232C4×C11#48212yes—
233C22×D4—21no—
234C22×D4C2×C4×C1111yescharacteristic
235C23×C4—21no—
236C23×C4C2×C4×C1111yescharacteristic
237C23×C4D4×C1111yescharacteristic
238C23×C4D4×C1111yescharacteristic
239C22×C8—22no—
240C22×C8—22no—
241#121—22no—
242#121—22no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—44no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4C2×C4×C1111yescharacteristic
248C2×C4⋊C4C2×C4×C1111yescharacteristic
249C2×C4⋊C4C2×C4×C1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C42—22no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42C2×C4×C1111yescharacteristic
259C2×C42D4×C1111yescharacteristic
260C2×C42D4×C1111yescharacteristic
261C2×C42C23×C1111yescharacteristic
262C4⋊C8—22no—
263C4⋊C8D4×C1114yescomplemented
264C22⋊C8—24no—
265C22⋊C8—24no—
266#97—24no—
267C4×C8—22no—
268C4×C8—22no—
269#95—21no—
270#95—21no—
271#95—21no—
272C2×C11—42no—
273C2×C11—82no—
274C2×C11#148811yescharacteristic
275C2×C11#149011yescharacteristic
276C2×C11#149411yescharacteristic
277C2×C11#149611yescharacteristic
278C2×C11#187011yescharacteristic
279C2×C11#187111yescharacteristic
280C2×C11#187511yescharacteristic
281C24—21no—
282C24C11×C22⋊C411yescharacteristic
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—22no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4C11×M1612yes—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4C11×C22⋊C411yescharacteristic
309C22×C4C11×C22⋊C411yescharacteristic
310C22×C4C11×C22⋊C411yescharacteristic
311C22×C4C22×C4×C1111yescharacteristic
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C2×D4×C1111yescharacteristic
314C2×C8—24no—
315C2×C8—24no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—42no—
324C4⋊C4C11×M1612yes—
325C22⋊C4—24no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C42—22no—
331C42—21no—
332C42—22no—
333C42—21no—
334C42—42no—
335C42C2×D4×C1112yes—
336C42C11×#4112yes—
337C11#894311yescharacteristic, direct product factor, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—22no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23C11×#10412yes—
352C23C2×C11×C22⋊C411yescharacteristic
353D4—24no—
354D4—48no—
355D4—42no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—44no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4C4×D4×C1112yes—
384C2×C4C11×#12011yescharacteristic
385C2×C4C11×#12112yes—
386C2×C4C11×#12311yescharacteristic
387C2×C4C2×C11×M1611yescharacteristic
388C2×C4C2×C11×M1611yescharacteristic
389C2×C4C11×#13112yes—
390C2×C4C11×#13512yes—
391C2×C4C11×AGL(1,ℤ/8)12yes—
392C8—44no—
393C8—44no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22C11×#38611yescharacteristic
409C22C11×#40711yescharacteristic
410C22C11×#40811yescharacteristic
411C22C11×#41611yescharacteristic
412C22C11×#41811yescharacteristic
413C22C2×C11×#10411yescharacteristic
414C22C11×#42111yescharacteristic
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—81no—
421C4—81no—
422C4C11×#43512yes—
423C4C11×#43612yes—
424C4C11×#44912yes—
425C4C11×#48212yes—
426C2—42no—
427C2—82no—
428C2C11×#148811yescharacteristic
429C2C11×#149011yescharacteristic
430C2C11×#149411yescharacteristic
431C2C11×#149611yescharacteristic
432C2C11×#187011yescharacteristic
433C2C11×#187111yescharacteristic
434C2C11×#187511yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#432C2semidirect
3. C4×C11×C22⋊C8C2semidirect
4. C2×C11×D4⋊C8C2semidirect
5. C11×#1279C2semidirect
55. C11×C4⋊C8D4semidirect
64. #8943C11direct (N × H)
121. C2×#432C2×C11semidirect
123. C4×C22⋊C8C2×C11semidirect
124. C2×D4⋊C8C2×C11semidirect
125. #1279C2×C11semidirect
263. C4⋊C8D4×C11semidirect
337. C11#8943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C4×C11×#1212
C4×C11×C22⋊C82
C2×C11×D4⋊C82
C11×#12792
#894311