Finite Group Databasebeta

← C11×#10189 #14587382

Subgroups — C11×#10189 #14587382

Order 2816.

518 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic
4C11×#1548C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#498—21no—
13C11×#486—21no—
14C11×#481—22no—
15C11×#476—22no—
16C11×#475—22no—
17C11×#475—22no—
18C11×#464—22no—
19C11×#462—21no—
20C11×#460—21no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C2×C11×#106—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#103—21no—
28C11×#333—22no—
29C11×D4⋊C8—22no—
30C11×#324—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×M16—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D411yescharacteristic
44C11×C4⋊Q8D412yes—
45C11×#127D411yescharacteristic
46C11×#124—21no—
47C11×#121—21no—
48C11×#121—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#106—24no—
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C11×#103—22no—
71C11×#102—22no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10189C1111yesmaximal, characteristic, direct product factor, Sylow
78C11×#41—41no—
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—41no—
90C2×Q8×C11—82no—
91C2×Q8×C11SD1612yes—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C11×Q16—44no—
104C11×SD16—44no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131#3227C2×C1111yescharacteristic
132C2×#475C2×C1111yescharacteristic, complemented
133#3037C2×C1111yescharacteristic
134#1548C2×C1111yescharacteristic, complemented
135#1480C2×C1111yescharacteristic
136#1461C2×C1111yescharacteristic, complemented
137#1301C2×C1111yescharacteristic, complemented
138C23×C11—41no—
139C23×C11#12111yescharacteristic
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—82no—
147Q8×C11—82no—
148D4×C11—42no—
149D4×C11—41no—
150D4×C11—41no—
151D4×C11—42no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12711yescharacteristic
172C2×C4×C11C2×SD1611yescharacteristic
173C2×C4×C11#13511yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C8×C11—42no—
177C8×C11—42no—
178C8×C11—42no—
179C8×C11—81no—
180C2×#137—21no—
181#532C22×C1111yescharacteristic
182C2×C4⋊Q8C22×C1111yescharacteristic
183C2×C4×Q8C22×C1111yescharacteristic
184#498—21no—
185#486—21no—
186#481—22no—
187#476—22no—
188#475—22no—
189#475—22no—
190#464—22no—
191#462—21no—
192#460—21no—
193#431C22×C1111yescharacteristic
194#431C22×C1111yescharacteristic
195C2×#106—21no—
196#423C22×C1111yescharacteristic
197C2×C4⋊C8C22×C1111yescharacteristic
198#417—21no—
199C2×#103—21no—
200#333—22no—
201D4⋊C8—22no—
202#324—22no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#46511yescharacteristic
210C22×C11#46811yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—82no—
218C4×C11#44811yescharacteristic
219C4×C11#44911yescharacteristic
220C4×C11#45011yescharacteristic
221C4×C11#45211yescharacteristic
222C4×C11#47112yes—
223C2×#41—21no—
224C22×Q8—21no—
225C22×Q8D4×C1111yescharacteristic
226#137—42no—
227#137—42no—
228C2×Q16—22no—
229C2×SD16—22no—
230C2×M16—21no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D4×C1112yes—
236C4⋊Q8D4×C1111yescharacteristic
237#127D4×C1111yescharacteristic
238#124—21no—
239#121—21no—
240#121—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C42—21no—
252C2×C42C23×C1111yescharacteristic
253#106—24no—
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C1112yes—
260C4⋊C8D4×C1112yes—
261#103—24no—
262#103—22no—
263#102—22no—
264#102—24no—
265C22⋊C8—21no—
266C22⋊C8D4×C1112yes—
267C4×C8—21no—
268C4×C8—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—161no—
272C2×C11#200011yescharacteristic
273C2×C11#200911yescharacteristic
274C2×C11#201911yescharacteristic
275#41—41no—
276#41—41no—
277#41—41no—
278#41—41no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—22no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—82no—
288C2×Q8C11×SD1612yes—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C2×D4×C1111yescharacteristic
299C22×C4C11×#4111yescharacteristic
300Q16—44no—
301SD16—44no—
302M16—41no—
303M16—41no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C42—41no—
323C42—41no—
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C42C2×D4×C1111yescharacteristic
327C42C2×D4×C1111yescharacteristic
328C11#1018911yescharacteristic, direct product factor, Sylow
329C23—41no—
330C23C11×#12111yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—41no—
334Q8—41no—
335Q8—41no—
336Q8—41no—
337Q8—82no—
338Q8—82no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—42no—
343D4—81no—
344D4—81no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12011yescharacteristic
359C2×C4C11×#12011yescharacteristic
360C2×C4C11×#12111yescharacteristic
361C2×C4C11×#12111yescharacteristic
362C2×C4C11×#12711yescharacteristic
363C2×C4C2×C11×SD1611yescharacteristic
364C2×C4C11×#13511yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C2×C4C11×#13711yescharacteristic
367C8—42no—
368C8—42no—
369C8—42no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22C11×#39211yescharacteristic
377C22C11×#46511yescharacteristic
378C22C11×#46811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—81no—
385C4—82no—
386C4C11×#44811yescharacteristic
387C4C11×#44911yescharacteristic
388C4C11×#45011yescharacteristic
389C4C11×#45211yescharacteristic
390C4C11×#47112yes—
391C2—21no—
392C2—21no—
393C2—161no—
394C2C11×#200011yescharacteristic
395C2C11×#200911yescharacteristic
396C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C2×C11×#475C2semidirect
4. C11×#1548C2semidirect
6. C11×#1461C2semidirect
7. C11×#1301C2semidirect
77. #10189C11direct (N × H)
132. C2×#475C2×C11semidirect
134. #1548C2×C11semidirect
136. #1461C2×C11semidirect
137. #1301C2×C11semidirect
328. C11#10189direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C2×C11×#4752
C11×#30372
C11×#15482
C11×#14802
C11×#14612
C11×#13012
#1018911