Finite Group Databasebeta

← C11×#12144 #14589337

Subgroups — C11×#12144 #14589337

Order 2816.

398 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2795C211yesmaximal, characteristic, complemented
2C11×#2039C211yesmaximal, characteristic, complemented
3C11×#1616C211yesmaximal, characteristic, complemented
4C11×#1598C211yesmaximal, characteristic
5C11×#1353C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8C11×#537C2211yescharacteristic
9C11×#481—21no—
10C11×#447—21no—
11C2×C11×#104—21no—
12C11×#417—21no—
13C11×#400C2211yescharacteristic
14C11×#396—21no—
15C11×#394—21no—
16C11×#394C2211yescharacteristic
17C11×#388—21no—
18C11×#388—21no—
19C11×#388—21no—
20C11×#387—21no—
21C11×#384C2211yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×D4×C11D411yescharacteristic
29C2×C11×D8—41no—
30C2×C11×M16—21no—
31C11×C22⋊Q8—41no—
32C11×#121—21no—
33C11×#121—21no—
34C11×#121—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C11×C22⋊C4—21no—
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—21no—
48C2×C42×C11D411yescharacteristic
49C11×#106—41no—
50C11×#104—42no—
51C11×#103—41no—
52C11×#102—41no—
53C11×#102—41no—
54C11×#102—41no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12144C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C11×#41—41no—
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C2×Q8×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—81no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×D8—82no—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—81no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11—81no—
111#2795C2×C1111yescharacteristic, complemented
112#2039C2×C1111yescharacteristic, complemented
113#1616C2×C1111yescharacteristic, complemented
114#1598C2×C1111yescharacteristic
115#1353C2×C1111yescharacteristic, complemented
116#1345C2×C1111yescharacteristic, complemented
117#1325C2×C1111yescharacteristic, complemented
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—41no—
128Q8×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—42no—
132D4×C11—81no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
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—81no—
160C2×C4×C11—81no—
161C2×C4×C11#13511yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
163C8×C11—81no—
164C8×C11—81no—
165C8×C11—81no—
166#537C22×C1111yescharacteristic
167#481—21no—
168#447—21no—
169C2×#104—21no—
170#417—21no—
171#400C22×C1111yescharacteristic
172#396—21no—
173#394—21no—
174#394C22×C1111yescharacteristic
175#388—21no—
176#388—21no—
177#388—21no—
178#387—21no—
179#384C22×C1111yescharacteristic
180#343C22×C1111yescharacteristic
181#327—21no—
182#327—21no—
183#324C22×C1111yescharacteristic
184#324C22×C1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#44911yescharacteristic
198C22×C11#45411yescharacteristic
199C22×C11B(4,𝔽2)11yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C2×#41—21no—
211C22×D4D4×C1111yescharacteristic
212C2×D8—41no—
213C2×M16—21no—
214C22⋊Q8—41no—
215#121—21no—
216#121—21no—
217#121—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4D4×C1111yescharacteristic
222C2×C4⋊C4D4×C1111yescharacteristic
223C2×C4⋊C4C23×C1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C42—21no—
231C2×C42D4×C1111yescharacteristic
232#106—41no—
233#104—42no—
234#103—41no—
235#102—41no—
236#102—41no—
237#102—41no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95D4×C1111yescharacteristic
245#95D4×C1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—161no—
249C2×C11—161no—
250C2×C11#159711yescharacteristic
251C2×C11#220011yescharacteristic
252C2×C11#220411yescharacteristic
253C24—21no—
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—81no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274D8—82no—
275M16—41no—
276M16—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—21no—
298C42—21no—
299C42—81no—
300C11#1214411yescharacteristic, direct product factor, Sylow
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23C11×#12011yescharacteristic
310Q8—41no—
311Q8—41no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—81no—
316D4—81no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4C11×#13511yescharacteristic
345C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
346C8—81no—
347C8—81no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22C11×#44911yescharacteristic
362C22C11×#45411yescharacteristic
363C22C11×B(4,𝔽2)11yescharacteristic
364C4—21no—
365C4—21no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C2—21no—
375C2—21no—
376C2—161no—
377C2—161no—
378C2C11×#159711yescharacteristic
379C2C11×#220011yescharacteristic
380C2C11×#220411yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#1598C2
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
1. C11×#2795C2semidirect
2. C11×#2039C2semidirect
3. C11×#1616C2semidirect
5. C11×#1353C2semidirect
6. C11×#1345C2semidirect
7. C11×#1325C2semidirect
63. #12144C11direct (N × H)
111. #2795C2×C11semidirect
112. #2039C2×C11semidirect
113. #1616C2×C11semidirect
115. #1353C2×C11semidirect
116. #1345C2×C11semidirect
117. #1325C2×C11semidirect
300. C11#12144direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27952
C11×#20392
C11×#16162
C11×#15982
C11×#13532
C11×#13452
C11×#13252
#1214411