Finite Group Databasebeta

← C11×#10294 #14587487

Subgroups — C11×#10294 #14587487

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic
3C11×#2858C211yesmaximal, characteristic
4C11×#1994C211yesmaximal, characteristic, complemented
5C11×#1546C211yesmaximal, characteristic, complemented
6C11×#1545C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C11×#498—21no—
13C11×#492—21no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#483—22no—
17C11×#475—22no—
18C11×#460—22no—
19C11×#450—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#390—22no—
24C11×#390—22no—
25C43×C11C2211yescharacteristic
26C11×#339—22no—
27C11×#332—22no—
28C11×#331—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×SD16—24no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#125—21no—
46C11×#124—44no—
47C11×#124—44no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C11×#117—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—28no—
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11D412yes—
59C2×C42×C11C2311yescharacteristic
60C11×#106—24no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×C4⋊C8D412yes—
65C11×#103—24no—
66C11×#102—24no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#10294C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×SD16—84no—
95C11×M16—42no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—416no—
110C11×C22⋊C4—41no—
111C42×C11—22no—
112C42×C11—42no—
113C42×C11—42no—
114C42×C11—41no—
115C42×C11SD1614yescomplemented
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120#3229C2×C1111yescharacteristic, complemented
121#3208C2×C1111yescharacteristic
122#2858C2×C1111yescharacteristic
123#1994C2×C1111yescharacteristic, complemented
124#1546C2×C1111yescharacteristic, complemented
125#1545C2×C1111yescharacteristic
126#1276C2×C1111yescharacteristic, complemented
127C23×C11—44no—
128C23×C11—44no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11#12011yescharacteristic
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—82no—
135Q8×C11—81no—
136Q8×C11—81no—
137D4×C11—44no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11AGL(1,ℤ/8)12yes—
161C8×C11—42no—
162C8×C11—42no—
163C8×C11—81no—
164#533C22×C1111yescharacteristic
165C2×C4⋊Q8C22×C1111yescharacteristic
166C2×#127C22×C1111yescharacteristic
167C2×#124—22no—
168#498—21no—
169#492—21no—
170#487—21no—
171#486—21no—
172#483—22no—
173#475—22no—
174#460—22no—
175#450—22no—
176#431C22×C1111yescharacteristic
177#431C22×C1111yescharacteristic
178#423C22×C1111yescharacteristic
179#390—22no—
180#390—22no—
181C43C22×C1111yescharacteristic
182#339—22no—
183#332—22no—
184#331—22no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—88no—
188C22×C11—82no—
189C22×C11—82no—
190C22×C11—82no—
191C22×C11#39211yescharacteristic
192C22×C11#45012yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—44no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11#45412yes—
200C4×C11#45512yes—
201C4×C11#46012yes—
202C4×C11#49211yescharacteristic
203C4×C11#49611yescharacteristic
204C22×Q8—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4D4×C1112yes—
208C2×SD16—24no—
209C2×M16—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C1111yescharacteristic
215C4⋊Q8D4×C1111yescharacteristic
216#127—21no—
217#127—21no—
218#127—21no—
219#127—21no—
220#125—21no—
221#124—44no—
222#124—44no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227#117—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C1112yes—
230C2×C22⋊C4—28no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42D4×C1112yes—
234C2×C42C23×C1111yescharacteristic
235#106—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8D4×C1112yes—
239C4⋊C8D4×C1112yes—
240#103—24no—
241#102—24no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C4×C8—21no—
245C4×C8—21no—
246C2×C11—22no—
247C2×C11—162no—
248C2×C11#200311yescharacteristic
249C2×C11#200411yescharacteristic
250C2×C11#201411yescharacteristic
251C24—22no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1111yescharacteristic
273SD16—84no—
274M16—42no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—416no—
289C22⋊C4—41no—
290C42—22no—
291C42—42no—
292C42—42no—
293C42—41no—
294C42C11×SD1614yescomplemented
295C42C2×D4×C1111yescharacteristic
296C42C2×D4×C1111yescharacteristic
297C42C2×D4×C1111yescharacteristic
298C42C11×#4111yescharacteristic
299C11#1029411yescharacteristic, direct product factor, Sylow
300C23—44no—
301C23—44no—
302C23—42no—
303C23—44no—
304C23C11×#12011yescharacteristic
305Q8—42no—
306Q8—42no—
307Q8—81no—
308Q8—81no—
309Q8—82no—
310D4—44no—
311D4—82no—
312D4—82no—
313D4—81no—
314D4—81no—
315D4—82no—
316D4—82no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4C11×#12011yescharacteristic
327C2×C4C11×#12011yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12111yescharacteristic
330C2×C4C11×#12111yescharacteristic
331C2×C4C11×#12711yescharacteristic
332C2×C4C2×C11×SD1612yes—
333C2×C4C11×AGL(1,ℤ/8)12yes—
334C8—42no—
335C8—42no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—88no—
340C22—82no—
341C22—82no—
342C22—82no—
343C22C11×#39211yescharacteristic
344C22C11×#45012yes—
345C4—21no—
346C4—21no—
347C4—44no—
348C4—81no—
349C4—81no—
350C4—82no—
351C4C11×#45412yes—
352C4C11×#45512yes—
353C4C11×#46012yes—
354C4C11×#49211yescharacteristic
355C4C11×#49611yescharacteristic
356C2—22no—
357C2—162no—
358C2C11×#200311yescharacteristic
359C2C11×#200411yescharacteristic
360C2C11×#201411yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3229C2semidirect
4. C11×#1994C2semidirect
5. C11×#1546C2semidirect
7. C11×#1276C2semidirect
71. #10294C11direct (N × H)
115. C42×C11SD16semidirect
120. #3229C2×C11semidirect
123. #1994C2×C11semidirect
124. #1546C2×C11semidirect
126. #1276C2×C11semidirect
294. C42C11×SD16semidirect
299. C11#10294direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#32082
C11×#28582
C11×#19942
C11×#15462
C11×#15452
C11×#12762
#1029411