Finite Group Databasebeta

← C11×#12211 #14589404

Subgroups — C11×#12211 #14589404

Order 2816.

464 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2699C211yesmaximal, characteristic
2C11×#2027C211yesmaximal, characteristic, complemented
3C11×#1611C211yesmaximal, characteristic, complemented
4C11×#1599C211yesmaximal, characteristic, complemented
5C11×#1346C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C2×C11×#121—21no—
10C11×#483—21no—
11C11×#450—21no—
12C11×#418—21no—
13C11×#398C2211yescharacteristic
14C11×#394—21no—
15C11×#394C2211yescharacteristic
16C11×#392—21no—
17C11×#390C2211yescharacteristic
18C11×#388—21no—
19C11×#386—21no—
20C11×#381—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23C11×#328—21no—
24C11×#328—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C2×C11×SD16—41no—
33C2×C11×M16—21no—
34C11×C4⋊Q8—41no—
35C11×#125—41no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×#121—42no—
39C11×#121—42no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11D411yescharacteristic
52C11×#106—41no—
53C11×#103—41no—
54C11×#102—41no—
55C11×#102—41no—
56C11×#102—41no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#12211C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—81no—
77C2×D4×C11—81no—
78C2×D4×C11—81no—
79C2×D4×C11—81no—
80C2×D4×C11SD1612yescomplemented
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—81no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C11×SD16—82no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4—81no—
115C11×C22⋊C4—81no—
116C42×C11—41no—
117C42×C11—41no—
118#2699C2×C1111yescharacteristic
119#2027C2×C1111yescharacteristic, complemented
120#1611C2×C1111yescharacteristic, complemented
121#1599C2×C1111yescharacteristic, complemented
122#1346C2×C1111yescharacteristic, complemented
123#1345C2×C1111yescharacteristic, complemented
124#1318C2×C1111yescharacteristic, complemented
125C23×C11—22no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#12011yescharacteristic
140Q8×C11—81no—
141Q8×C11—81no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—81no—
145D4×C11—84no—
146D4×C11—81no—
147D4×C11—84no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—84no—
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C8×C11—81no—
172C8×C11—81no—
173C8×C11—81no—
174#544C22×C1111yescharacteristic
175C2×#121—21no—
176#483—21no—
177#450—21no—
178#418—21no—
179#398C22×C1111yescharacteristic
180#394—21no—
181#394C22×C1111yescharacteristic
182#392—21no—
183#390C22×C1111yescharacteristic
184#388—21no—
185#386—21no—
186#381—21no—
187#343C22×C1111yescharacteristic
188#339—21no—
189#328—21no—
190#328—21no—
191#324C22×C1111yescharacteristic
192#324C22×C1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#45011yescharacteristic
210C22×C11#45511yescharacteristic
211C22×C11B(4,𝔽2)11yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4D4×C1111yescharacteristic
225C22×D4D4×C1111yescharacteristic
226C23×C4—21no—
227C2×SD16—41no—
228C2×M16—21no—
229C4⋊Q8—41no—
230#125—41no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233#121—42no—
234#121—42no—
235#117—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C1111yescharacteristic
238C2×C4⋊C4C23×C1111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42D4×C1111yescharacteristic
247#106—41no—
248#103—41no—
249#102—41no—
250#102—41no—
251#102—41no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95D4×C1111yescharacteristic
258#95D4×C1111yescharacteristic
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—82no—
262C2×C11—161no—
263C2×C11#160111yescharacteristic
264C2×C11#220011yescharacteristic
265C2×C11#220411yescharacteristic
266C24—21no—
267C24—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—81no—
278C2×D4—81no—
279C2×D4—81no—
280C2×D4—81no—
281C2×D4C11×SD1612yescomplemented
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—81no—
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292SD16—82no—
293M16—41no—
294M16—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C22⋊C4—81no—
316C22⋊C4—81no—
317C42—41no—
318C42—41no—
319C11#1221111yescharacteristic, direct product factor, Sylow
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23C11×#12011yescharacteristic
335Q8—81no—
336Q8—81no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—84no—
341D4—81no—
342D4—84no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—84no—
364C2×C4C2×C11×SD1611yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C8—81no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C11×#45011yescharacteristic
386C22C11×#45511yescharacteristic
387C22C11×B(4,𝔽2)11yescharacteristic
388C4—21no—
389C4—21no—
390C4—42no—
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C2—21no—
399C2—21no—
400C2—82no—
401C2—161no—
402C2C11×#160111yescharacteristic
403C2C11×#220011yescharacteristic
404C2C11×#220411yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#2699C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2027C2semidirect
3. C11×#1611C2semidirect
4. C11×#1599C2semidirect
5. C11×#1346C2semidirect
6. C11×#1345C2semidirect
7. C11×#1318C2semidirect
64. #12211C11direct (N × H)
80. C2×D4×C11SD16semidirect
119. #2027C2×C11semidirect
120. #1611C2×C11semidirect
121. #1599C2×C11semidirect
122. #1346C2×C11semidirect
123. #1345C2×C11semidirect
124. #1318C2×C11semidirect
281. C2×D4C11×SD16semidirect
319. C11#12211direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26992
C11×#20272
C11×#16112
C11×#15992
C11×#13462
C11×#13452
C11×#13182
#1221111