Finite Group Databasebeta

← C11×#10291 #14587484

Subgroups — C11×#10291 #14587484

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic
3C11×#2858C211yesmaximal, characteristic
4C11×#1994C211yesmaximal, characteristic, complemented
5C11×#1548C211yesmaximal, characteristic, complemented
6C11×#1545C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#124—22no—
12C11×#494—21no—
13C11×#492—21no—
14C11×#487—21no—
15C11×#486—21no—
16C11×#462—22no—
17C11×#460—22no—
18C11×#451—22no—
19C11×#450—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#390—22no—
24C11×#390—22no—
25C43×C11C2211yescharacteristic
26C11×#339—22no—
27C11×#333—22no—
28C11×#331—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×Q16—24no—
34C2×C11×SD16—24no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#127—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#125—21no—
47C11×#124—48no—
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⋊C4—21no—
55C2×C11×C22⋊C4—28no—
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11D412yes—
59C2×C42×C11C2311yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C11×#102—24no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#10291C1111yesmaximal, characteristic, direct product factor, Sylow
71C24×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—44no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C11×Q16—84no—
93C11×SD16—84no—
94C11×M16—42no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—416no—
109C11×C22⋊C4—41no—
110C42×C11—24no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—42no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119#3209C2×C1111yescharacteristic, complemented
120#3208C2×C1111yescharacteristic
121#2858C2×C1111yescharacteristic
122#1994C2×C1111yescharacteristic, complemented
123#1548C2×C1111yescharacteristic, complemented
124#1545C2×C1111yescharacteristic
125#1276C2×C1111yescharacteristic, complemented
126C23×C11—44no—
127C23×C11—44no—
128C23×C11—42no—
129C23×C11—44no—
130C23×C11#12011yescharacteristic
131Q8×C11—42no—
132Q8×C11—44no—
133Q8×C11—42no—
134Q8×C11—82no—
135D4×C11—44no—
136D4×C11—82no—
137D4×C11—82no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—24no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11#13512yes—
158C2×C4×C11#13712yes—
159C8×C11—42no—
160C8×C11—42no—
161C8×C11—81no—
162#533C22×C1111yescharacteristic
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×#127C22×C1111yescharacteristic
165C2×#124—22no—
166#494—21no—
167#492—21no—
168#487—21no—
169#486—21no—
170#462—22no—
171#460—22no—
172#451—22no—
173#450—22no—
174#431C22×C1111yescharacteristic
175#431C22×C1111yescharacteristic
176#423C22×C1111yescharacteristic
177#390—22no—
178#390—22no—
179C43C22×C1111yescharacteristic
180#339—22no—
181#333—22no—
182#331—22no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—88no—
186C22×C11—82no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11#39211yescharacteristic
190C22×C11#45212yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—44no—
194C4×C11—82no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#45312yes—
198C4×C11#45512yes—
199C4×C11#46412yes—
200C4×C11#49511yescharacteristic
201C4×C11#49711yescharacteristic
202C22×Q8D4×C1112yes—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4D4×C1112yes—
206C2×Q16—24no—
207C2×SD16—24no—
208C2×M16—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8D4×C1111yescharacteristic
214C4⋊Q8D4×C1111yescharacteristic
215#127—21no—
216#127—21no—
217#127—21no—
218#127—21no—
219#125—21no—
220#124—48no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225#117—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C22⋊C4—28no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C1112yes—
232C2×C42C23×C1111yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8D4×C1112yes—
236C4⋊C8D4×C1112yes—
237#103—24no—
238#102—24no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C2×C11—22no—
244C2×C11—162no—
245C2×C11#200211yescharacteristic
246C2×C11#200411yescharacteristic
247C2×C11#201511yescharacteristic
248C24—22no—
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—44no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4C2×D4×C1111yescharacteristic
267C22×C4C2×D4×C1111yescharacteristic
268C22×C4C2×D4×C1111yescharacteristic
269Q16—84no—
270SD16—84no—
271M16—42no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—416no—
286C22⋊C4—41no—
287C42—24no—
288C42—22no—
289C42—22no—
290C42—42no—
291C42—41no—
292C42C2×D4×C1111yescharacteristic
293C42C2×D4×C1111yescharacteristic
294C42C2×D4×C1111yescharacteristic
295C42C11×#4111yescharacteristic
296C11#1029111yescharacteristic, direct product factor, Sylow
297C23—44no—
298C23—44no—
299C23—42no—
300C23—44no—
301C23C11×#12011yescharacteristic
302Q8—42no—
303Q8—44no—
304Q8—42no—
305Q8—82no—
306D4—44no—
307D4—82no—
308D4—82no—
309D4—81no—
310D4—81no—
311D4—82no—
312D4—82no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—24no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4C11×#12011yescharacteristic
323C2×C4C11×#12011yescharacteristic
324C2×C4C11×#12111yescharacteristic
325C2×C4C11×#12111yescharacteristic
326C2×C4C11×#12111yescharacteristic
327C2×C4C11×#12711yescharacteristic
328C2×C4C11×#13512yes—
329C2×C4C11×#13712yes—
330C8—42no—
331C8—42no—
332C8—81no—
333C22—21no—
334C22—21no—
335C22—88no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22C11×#39211yescharacteristic
340C22C11×#45212yes—
341C4—21no—
342C4—21no—
343C4—44no—
344C4—82no—
345C4—81no—
346C4—81no—
347C4C11×#45312yes—
348C4C11×#45512yes—
349C4C11×#46412yes—
350C4C11×#49511yescharacteristic
351C4C11×#49711yescharacteristic
352C2—22no—
353C2—162no—
354C2C11×#200211yescharacteristic
355C2C11×#200411yescharacteristic
356C2C11×#201511yescharacteristic
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×#3209C2semidirect
4. C11×#1994C2semidirect
5. C11×#1548C2semidirect
7. C11×#1276C2semidirect
70. #10291C11direct (N × H)
119. #3209C2×C11semidirect
122. #1994C2×C11semidirect
123. #1548C2×C11semidirect
125. #1276C2×C11semidirect
296. C11#10291direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#32082
C11×#28582
C11×#19942
C11×#15482
C11×#15452
C11×#12762
#1029111