Finite Group Databasebeta

← C11×#10254 #14587447

Subgroups — C11×#10254 #14587447

Order 2816.

634 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3245C211yesmaximal, characteristic, complemented
2C11×#3036C212yesmaximal, complemented
3C11×#1954C211yesmaximal, characteristic, complemented
4C11×#1492C212yesmaximal, complemented
5C11×#1292C211yesmaximal, characteristic, complemented
6C2×C11×AGL(1,ℤ/8)—22no—
7C11×#532C2212yes—
8C2×C4×D4×C11C2211yescharacteristic
9C11×#474—22no—
10C11×#466—22no—
11C11×#463—24no—
12C11×#461—22no—
13C11×#459—22no—
14C11×#459—22no—
15C11×#423C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C11×#417—22no—
18C2×C11×C22⋊C8—22no—
19C2×C4×C8×C11C2211yescharacteristic
20C11×D4⋊C8—24no—
21C2×C11×#41—22no—
22C22×D4×C11D411yescharacteristic
23C23×C4×C11—21no—
24C11×AGL(1,ℤ/8)—44no—
25C11×AGL(1,ℤ/8)—44no—
26C2×C11×SD16—24no—
27C2×C11×D8—24no—
28C2×C11×D8—22no—
29C2×C11×M16—22no—
30C22×C8×C11—21no—
31C22×C8×C11D412yes—
32C11×C4⋊Q8D412yes—
33C11×#127D412yes—
34C11×#124—22no—
35C11×#121—22no—
36C11×#121—22no—
37C4×D4×C11—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C4×D4×C11—22no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C11×#107—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8—22no—
47C11×C4⋊C8D414yes—
48C11×#103—24no—
49C11×#102—24no—
50C11×#102—24no—
51C11×C22⋊C8—44no—
52C4×C8×C11—22no—
53#10254C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—21no—
55C11×#41—42no—
56C11×#41—42no—
57C11×#41—42no—
58C11×#41—42no—
59C2×Q8×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—21no—
65C2×D4×C11—22no—
66C2×D4×C11—42no—
67C2×D4×C11D812yescomplemented
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—41no—
72C22×C4×C11—42no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C11×SD16—48no—
78C11×D8—48no—
79C11×D8—82no—
80C11×M16—42no—
81C11×M16—42no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—24no—
85C2×C8×C11—42no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C22⋊C4—42no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C42×C11C2×D412yes—
95C42×C11C2×D412yes—
96#3245C2×C1111yescharacteristic, complemented
97#3036C2×C1112yescomplemented
98#1954C2×C1111yescharacteristic, complemented
99#1492C2×C1112yescomplemented
100#1292C2×C1111yescharacteristic, complemented
101C23×C11—22no—
102C23×C11—42no—
103C23×C11—42no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—42no—
107C23×C11#12111yescharacteristic
108Q8×C11—42no—
109Q8×C11—42no—
110D4×C11—24no—
111D4×C11—44no—
112D4×C11—42no—
113D4×C11—42no—
114D4×C11—42no—
115D4×C11—42no—
116D4×C11—42no—
117D4×C11—82no—
118D4×C11—82no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11—82no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#12012yes—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12112yes—
133C2×C4×C11#12711yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C8×C11—42no—
138C8×C11—44no—
139C8×C11—42no—
140C2×AGL(1,ℤ/8)—22no—
141#532C22×C1112yes—
142C2×C4×D4C22×C1111yescharacteristic
143#474—22no—
144#466—22no—
145#463—24no—
146#461—22no—
147#459—22no—
148#459—22no—
149#423C22×C1112yes—
150C2×C4⋊C8C22×C1111yescharacteristic
151#417—22no—
152C2×C22⋊C8—22no—
153C2×C4×C8C22×C1111yescharacteristic
154D4⋊C8—24no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—82no—
160C22×C11—81no—
161C22×C11—81no—
162C22×C11—82no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11#39211yescharacteristic
166C22×C11#46611yescharacteristic
167C22×C11#46911yescharacteristic
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—82no—
171C4×C11—81no—
172C4×C11#44712yes—
173C4×C11#44912yes—
174C4×C11#45311yescharacteristic
175C4×C11#45411yescharacteristic
176C2×#41—22no—
177C22×D4D4×C1111yescharacteristic
178C23×C4—21no—
179AGL(1,ℤ/8)—44no—
180AGL(1,ℤ/8)—44no—
181C2×SD16—24no—
182C2×D8—24no—
183C2×D8—22no—
184C2×M16—22no—
185C22×C8—21no—
186C22×C8D4×C1112yes—
187C4⋊Q8D4×C1112yes—
188#127D4×C1112yes—
189#124—22no—
190#121—22no—
191#121—22no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—22no—
195C4×D4—22no—
196C2×C4⋊C4D4×C1111yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C23×C1111yescharacteristic
199#107—22no—
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8D4×C1114yes—
203#103—24no—
204#102—24no—
205#102—24no—
206C22⋊C8—44no—
207C4×C8—22no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—82no—
211C2×C11—162no—
212C2×C11#199911yescharacteristic
213C2×C11#200611yescharacteristic
214C2×C11#201711yescharacteristic
215C24—21no—
216#41—42no—
217#41—42no—
218#41—42no—
219#41—42no—
220C2×Q8—22no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—21no—
226C2×D4—22no—
227C2×D4—42no—
228C2×D4C11×D812yescomplemented
229C22×C4—21no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4C2×D4×C1111yescharacteristic
236C22×C4C2×D4×C1111yescharacteristic
237C22×C4C11×#4111yescharacteristic
238SD16—48no—
239D8—48no—
240D8—82no—
241M16—42no—
242M16—42no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—24no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—42no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42C2×D4×C1112yes—
256C42C2×D4×C1112yes—
257C11#1025411yescharacteristic, direct product factor, Sylow
258C23—22no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23—42no—
264C23C11×#12111yescharacteristic
265Q8—42no—
266Q8—42no—
267D4—24no—
268D4—44no—
269D4—42no—
270D4—42no—
271D4—42no—
272D4—42no—
273D4—42no—
274D4—82no—
275D4—82no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C11×#12012yes—
288C2×C4C11×#12011yescharacteristic
289C2×C4C11×#12112yes—
290C2×C4C11×#12711yescharacteristic
291C2×C4C2×C11×D811yescharacteristic
292C2×C4C11×#13511yescharacteristic
293C2×C4C11×AGL(1,ℤ/8)12yes—
294C8—42no—
295C8—44no—
296C8—42no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22—42no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22—82no—
305C22—82no—
306C22—82no—
307C22C11×#39211yescharacteristic
308C22C11×#46611yescharacteristic
309C22C11×#46911yescharacteristic
310C4—21no—
311C4—22no—
312C4—82no—
313C4—81no—
314C4C11×#44712yes—
315C4C11×#44912yes—
316C4C11×#45311yescharacteristic
317C4C11×#45411yescharacteristic
318C2—21no—
319C2—21no—
320C2—82no—
321C2—162no—
322C2C11×#199911yescharacteristic
323C2C11×#200611yescharacteristic
324C2C11×#201711yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
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×#3245C2semidirect
2. C11×#3036C2semidirect
3. C11×#1954C2semidirect
4. C11×#1492C2semidirect
5. C11×#1292C2semidirect
53. #10254C11direct (N × H)
67. C2×D4×C11D8semidirect
96. #3245C2×C11semidirect
97. #3036C2×C11semidirect
98. #1954C2×C11semidirect
99. #1492C2×C11semidirect
100. #1292C2×C11semidirect
228. C2×D4C11×D8semidirect
257. C11#10254direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32452
C11×#30362
C11×#19542
C11×#14922
C11×#12922
#1025411