Finite Group Databasebeta

← C11×#10183 #14587376

Subgroups — C11×#10183 #14587376

Order 2816.

476 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×#3209C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic
3C2×C11×#477C211yesmaximal, characteristic
4C11×#1549C211yesmaximal, characteristic
5C11×#1481C211yesmaximal, characteristic
6C11×#1461C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#494—21no—
12C11×#487—21no—
13C11×#479—22no—
14C11×#477—22no—
15C11×#477—21no—
16C11×#477—22no—
17C11×#475—21no—
18C11×#462—22no—
19C11×#451—22no—
20C11×#431C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#428—21no—
23C2×C11×#107—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#419—21no—
27C2×C11×#103—21no—
28C11×#332—22no—
29C11×Q8⋊C8—22no—
30C11×#324—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C2×C11×Q16—24no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×C4⋊Q8D412yes—
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—24no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8D412yes—
67C11×#103—24no—
68C11×#103—22no—
69C11×#103—22no—
70C11×#103—24no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8D412yes—
73C4×C8×C11—21no—
74C4×C8×C11—21no—
75#10183C1111yesmaximal, characteristic, direct product factor, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—82no—
86C2×Q8×C11Q1612yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C11×Q16—84no—
94C11×M16—41no—
95C11×M16—41no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—41no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#3209C2×C1111yescharacteristic
125#3078C2×C1111yescharacteristic
126C2×#477C2×C1111yescharacteristic
127#1549C2×C1111yescharacteristic
128#1481C2×C1111yescharacteristic
129#1461C2×C1111yescharacteristic
130#1301C2×C1111yescharacteristic
131C23×C11#12111yescharacteristic
132Q8×C11—22no—
133Q8×C11—22no—
134Q8×C11—42no—
135Q8×C11—44no—
136Q8×C11—41no—
137Q8×C11—41no—
138Q8×C11—42no—
139Q8×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—81no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×Q1611yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C8×C11—42no—
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—81no—
165#533C22×C1111yescharacteristic
166C2×C4⋊Q8C22×C1111yescharacteristic
167C2×C4×Q8C22×C1111yescharacteristic
168#494—21no—
169#487—21no—
170#479—22no—
171#477—22no—
172#477—21no—
173#477—22no—
174#475—21no—
175#462—22no—
176#451—22no—
177#431C22×C1111yescharacteristic
178#431C22×C1111yescharacteristic
179#428—21no—
180C2×#107—21no—
181#423C22×C1111yescharacteristic
182C2×C4⋊C8C22×C1111yescharacteristic
183#419—21no—
184C2×#103—21no—
185#332—22no—
186Q8⋊C8—22no—
187#324—22no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#39211yescharacteristic
191C22×C11#46711yescharacteristic
192C22×C11#47011yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—42no—
197C4×C11—81no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11#45111yescharacteristic
202C4×C11#45111yescharacteristic
203C4×C11#45211yescharacteristic
204C4×C11#45211yescharacteristic
205C4×C11#47312yes—
206C22×Q8—21no—
207C22×Q8D4×C1111yescharacteristic
208C2×Q16—24no—
209C2×M16—21no—
210C22×C8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C1112yes—
215C4⋊Q8D4×C1111yescharacteristic
216C4⋊Q8D4×C1111yescharacteristic
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226#117—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C1111yescharacteristic
231C2×C42—21no—
232C2×C42C23×C1111yescharacteristic
233#107—24no—
234#107—22no—
235#106—22no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C1112yes—
241C4⋊C8D4×C1112yes—
242#103—24no—
243#103—22no—
244#103—22no—
245#103—24no—
246C22⋊C8—21no—
247C22⋊C8D4×C1112yes—
248C4×C8—21no—
249C4×C8—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#200111yescharacteristic
253C2×C11#200811yescharacteristic
254C2×C11#202011yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—41no—
264C2×Q8—82no—
265C2×Q8C11×Q1612yescomplemented
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271C22×C4C11×#4111yescharacteristic
272Q16—84no—
273M16—41no—
274M16—41no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C22⋊C4—41no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42C2×D4×C1111yescharacteristic
300C42C2×D4×C1111yescharacteristic
301C42C2×D4×C1111yescharacteristic
302C42C2×D4×C1111yescharacteristic
303C11#1018311yescharacteristic, direct product factor, Sylow
304C23C11×#12111yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—42no—
308Q8—44no—
309Q8—41no—
310Q8—41no—
311Q8—42no—
312Q8—82no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—81no—
324C2×C4C11×#12011yescharacteristic
325C2×C4C11×#12011yescharacteristic
326C2×C4C11×#12011yescharacteristic
327C2×C4C11×#12111yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12711yescharacteristic
330C2×C4C2×C11×Q1611yescharacteristic
331C2×C4C11×#13511yescharacteristic
332C2×C4C11×#13711yescharacteristic
333C2×C4C11×#13711yescharacteristic
334C8—42no—
335C8—42no—
336C8—42no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22C11×#39211yescharacteristic
341C22C11×#46711yescharacteristic
342C22C11×#47011yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—82no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4C11×#45111yescharacteristic
352C4C11×#45111yescharacteristic
353C4C11×#45211yescharacteristic
354C4C11×#45211yescharacteristic
355C4C11×#47312yes—
356C2—21no—
357C2—21no—
358C2C11×#200111yescharacteristic
359C2C11×#200811yescharacteristic
360C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11#121
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
75. #10183C11direct (N × H)
86. C2×Q8×C11Q16semidirect
265. C2×Q8C11×Q16semidirect
303. C11#10183direct (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×#30782
C2×C11×#4772
C11×#15492
C11×#14812
C11×#14612
C11×#13012
#1018311