Finite Group Databasebeta

← C11×#12200 #14589393

Subgroups — C11×#12200 #14589393

Order 2816.

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

normal subgroups only

This group has 424 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×#2830C211yesmaximal, characteristic, complemented
2C11×#2006C211yesmaximal, characteristic
3C11×#1610C211yesmaximal, characteristic, complemented
4C11×#1604C211yesmaximal, characteristic, complemented
5C11×#1354C211yesmaximal, characteristic, complemented
6C11×#1346C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#537C2211yescharacteristic
10C11×#480—21no—
11C11×#448—21no—
12C2×C11×#104—21no—
13C11×#398C2211yescharacteristic
14C11×#397—21no—
15C11×#397—21no—
16C11×#396—21no—
17C11×#395C2211yescharacteristic
18C11×#394—21no—
19C11×#393—21no—
20C11×#390C2211yescharacteristic
21C11×#387—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C11×AGL(1,ℤ/8)—42no—
31C11×AGL(1,ℤ/8)—42no—
32C2×C11×SD16—41no—
33C2×C11×SD16—41no—
34C2×C11×D8—41no—
35C2×C11×M16—21no—
36C11×C22⋊Q8—41no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—41no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
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×#107—41no—
53C11×#104—42no—
54C11×#103—41no—
55C11×#102—41no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12200C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—41no—
73C2×Q8×C11—81no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C11×SD16—44no—
92C11×SD16—82no—
93C11×D8—44no—
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
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—81no—
106C11×C4⋊C4—81no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4—81no—
115C42×C11—41no—
116#2830C2×C1111yescharacteristic, complemented
117#2006C2×C1111yescharacteristic
118#1610C2×C1111yescharacteristic, complemented
119#1604C2×C1111yescharacteristic, complemented
120#1354C2×C1111yescharacteristic, complemented
121#1346C2×C1111yescharacteristic, complemented
122#1318C2×C1111yescharacteristic, complemented
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—42no—
135Q8×C11—81no—
136D4×C11—41no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
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—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—81no—
167C2×C4×C11—81no—
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C8×C11—42no—
171C8×C11—81no—
172C8×C11—81no—
173C2×AGL(1,ℤ/8)—21no—
174#537C22×C1111yescharacteristic
175#480—21no—
176#448—21no—
177C2×#104—21no—
178#398C22×C1111yescharacteristic
179#397—21no—
180#397—21no—
181#396—21no—
182#395C22×C1111yescharacteristic
183#394—21no—
184#393—21no—
185#390C22×C1111yescharacteristic
186#387—21no—
187#343C22×C1111yescharacteristic
188#327—21no—
189#327—21no—
190#324C22×C1111yescharacteristic
191#324C22×C1111yescharacteristic
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11#44911yescharacteristic
205C22×C11#45311yescharacteristic
206C22×C11B(4,𝔽2)11yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C2×#41—21no—
218C22×Q8D4×C1111yescharacteristic
219C22×D4D4×C1111yescharacteristic
220AGL(1,ℤ/8)—42no—
221AGL(1,ℤ/8)—42no—
222C2×SD16—41no—
223C2×SD16—41no—
224C2×D8—41no—
225C2×M16—21no—
226C22⋊Q8—41no—
227#121—21no—
228#121—21no—
229#121—41no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4D4×C1111yescharacteristic
234C2×C4⋊C4C23×C1111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42D4×C1111yescharacteristic
242#107—41no—
243#104—42no—
244#103—41no—
245#102—41no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95D4×C1111yescharacteristic
254#95D4×C1111yescharacteristic
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—161no—
258C2×C11—161no—
259C2×C11#160011yescharacteristic
260C2×C11#220011yescharacteristic
261C2×C11#220311yescharacteristic
262C24—21no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—81no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287SD16—44no—
288SD16—82no—
289D8—44no—
290M16—22no—
291M16—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—81no—
302C4⋊C4—81no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—81no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C42—41no—
312C11#1220011yescharacteristic, direct product factor, Sylow
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C11×#12011yescharacteristic
322Q8—41no—
323Q8—41no—
324Q8—42no—
325Q8—81no—
326D4—41no—
327D4—42no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
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—81no—
357C2×C4—81no—
358C2×C4C11×#13511yescharacteristic
359C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
360C8—42no—
361C8—81no—
362C8—81no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22C11×#44911yescharacteristic
376C22C11×#45311yescharacteristic
377C22C11×B(4,𝔽2)11yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C2—21no—
389C2—21no—
390C2—161no—
391C2—161no—
392C2C11×#160011yescharacteristic
393C2C11×#220011yescharacteristic
394C2C11×#220311yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#2006C2
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×#2830C2semidirect
3. C11×#1610C2semidirect
4. C11×#1604C2semidirect
5. C11×#1354C2semidirect
6. C11×#1346C2semidirect
7. C11×#1318C2semidirect
65. #12200C11direct (N × H)
116. #2830C2×C11semidirect
118. #1610C2×C11semidirect
119. #1604C2×C11semidirect
120. #1354C2×C11semidirect
121. #1346C2×C11semidirect
122. #1318C2×C11semidirect
312. C11#12200direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28302
C11×#20062
C11×#16102
C11×#16042
C11×#13542
C11×#13462
C11×#13182
#1220011