Finite Group Databasebeta

← C11×#10293 #14587486

Subgroups — C11×#10293 #14587486

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic
3C11×#2868C211yesmaximal, characteristic
4C11×#1994C211yesmaximal, characteristic
5C11×#1549C211yesmaximal, characteristic
6C11×#1548C211yesmaximal, characteristic
7C11×#1276C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8—22no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C11×#500—21no—
13C11×#494—21no—
14C11×#487—21no—
15C11×#487—21no—
16C11×#484—22no—
17C11×#477—22no—
18C11×#462—22no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#384—22no—
24C11×#384—22no—
25C43×C11C2211yescharacteristic
26C11×#339—22no—
27C11×#333—22no—
28C11×#332—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11D412yes—
31C2×C11×Q16—24no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—48no—
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8D411yescharacteristic
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C11×#117—21no—
50C2×C11×C4⋊C4—28no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C42×C11—21no—
56C2×C42×C11—21no—
57C2×C42×C11D412yes—
58C2×C42×C11C2311yescharacteristic
59C11×#107—24no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C11×#103—24no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70#10293C1111yesmaximal, characteristic, direct product factor, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×Q16—84no—
86C11×M16—42no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—416no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—24no—
107C42×C11—24no—
108C42×C11—22no—
109C42×C11—41no—
110C42×C11Q1614yescomplemented
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#3230C2×C1111yescharacteristic
116#3209C2×C1111yescharacteristic
117#2868C2×C1111yescharacteristic
118#1994C2×C1111yescharacteristic
119#1549C2×C1111yescharacteristic
120#1548C2×C1111yescharacteristic
121#1276C2×C1111yescharacteristic
122C23×C11#12011yescharacteristic
123Q8×C11—42no—
124Q8×C11—44no—
125Q8×C11—42no—
126Q8×C11—82no—
127Q8×C11—82no—
128Q8×C11—82no—
129C2×C4×C11—24no—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—44no—
135C2×C4×C11—44no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11C2×Q1612yes—
147C2×C4×C11#13712yes—
148C8×C11—42no—
149C8×C11—42no—
150C8×C11—81no—
151#533C22×C1111yescharacteristic
152C2×C4⋊Q8—22no—
153C2×C4⋊Q8C22×C1111yescharacteristic
154C2×C4⋊Q8C22×C1111yescharacteristic
155#500—21no—
156#494—21no—
157#487—21no—
158#487—21no—
159#484—22no—
160#477—22no—
161#462—22no—
162#451—22no—
163#431C22×C1111yescharacteristic
164#431C22×C1111yescharacteristic
165#423C22×C1111yescharacteristic
166#384—22no—
167#384—22no—
168C43C22×C1111yescharacteristic
169#339—22no—
170#333—22no—
171#332—22no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#39211yescharacteristic
175C22×C11#45112yes—
176C4×C11—28no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—82no—
180C4×C11—82no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11#45312yes—
184C4×C11#45612yes—
185C4×C11#46212yes—
186C4×C11#49411yescharacteristic
187C4×C11#49711yescharacteristic
188C22×Q8—21no—
189C22×Q8D4×C1112yes—
190C2×Q16—24no—
191C2×M16—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—48no—
201C4⋊Q8D4×C1111yescharacteristic
202C4⋊Q8D4×C1111yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208#117—21no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4D4×C1112yes—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42D4×C1112yes—
217C2×C42C23×C1111yescharacteristic
218#107—24no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8D4×C1112yes—
222C4⋊C8D4×C1112yes—
223#103—24no—
224#103—24no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C2×C11—22no—
230C2×C11#200211yescharacteristic
231C2×C11#200511yescharacteristic
232C2×C11#201611yescharacteristic
233C2×Q8—21no—
234C2×Q8—22no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—44no—
238C2×Q8—44no—
239C2×Q8—41no—
240C2×Q8—41no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×D4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247Q16—84no—
248M16—42no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—416no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C42—24no—
269C42—24no—
270C42—22no—
271C42—41no—
272C42C11×Q1614yescomplemented
273C42C2×D4×C1111yescharacteristic
274C42C2×D4×C1111yescharacteristic
275C42C2×D4×C1111yescharacteristic
276C42C11×#4111yescharacteristic
277C11#1029311yescharacteristic, direct product factor, Sylow
278C23C11×#12011yescharacteristic
279Q8—42no—
280Q8—44no—
281Q8—42no—
282Q8—82no—
283Q8—82no—
284Q8—82no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C11×#12011yescharacteristic
297C2×C4C11×#12011yescharacteristic
298C2×C4C11×#12111yescharacteristic
299C2×C4C11×#12111yescharacteristic
300C2×C4C11×#12111yescharacteristic
301C2×C4C11×#12711yescharacteristic
302C2×C4C2×C11×Q1612yes—
303C2×C4C11×#13712yes—
304C8—42no—
305C8—42no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C11×#39211yescharacteristic
310C22C11×#45112yes—
311C4—28no—
312C4—21no—
313C4—21no—
314C4—82no—
315C4—82no—
316C4—81no—
317C4—81no—
318C4C11×#45312yes—
319C4C11×#45612yes—
320C4C11×#46212yes—
321C4C11×#49411yescharacteristic
322C4C11×#49711yescharacteristic
323C2—22no—
324C2C11×#200211yescharacteristic
325C2C11×#200511yescharacteristic
326C2C11×#201611yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#120
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
70. #10293C11direct (N × H)
110. C42×C11Q16semidirect
272. C42C11×Q16semidirect
277. C11#10293direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#32092
C11×#28682
C11×#19942
C11×#15492
C11×#15482
C11×#12762
#1029311