Finite Group Databasebeta

← C11×#9139 #14586332

Subgroups — C11×#9139 #14586332

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#423C211yesmaximal, characteristic
2C11×#2857C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic
4C2×C11×#332C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C22×C11×M16—21no—
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×C11×C22⋊Q8—21no—
9C22×C42×C11C2211yescharacteristic
10C11×#423—24no—
11C2×C11×C4⋊C8—21no—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8—21no—
15C11×#391—21no—
16C11×#389—21no—
17C11×#389C412yes—
18C11×#384C2211yescharacteristic
19C11×#380—21no—
20C11×#380C412yes—
21C11×#336—21no—
22C11×#332—24no—
23C22×Q8×C11—21no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C2×C11×M16—24no—
28C2×C11×M16—42no—
29C2×C11×M16—42no—
30C22×C8×C11—22no—
31C22×C8×C11—22no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8—22no—
34C11×C22⋊Q8—42no—
35C11×C22⋊Q8—42no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C22⋊C4—22no—
43C2×C42×C11—22no—
44C2×C42×C11—22no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C11×C4⋊C8—24no—
50C11×C4⋊C8—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8—22no—
53C11×C4⋊C8D414yes—
54C11×C22⋊C8—42no—
55C11×#95—22no—
56C11×#95—22no—
57#9139C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11C22⋊C411yescharacteristic
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11D812yes—
82C22×C4×C11SD1612yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C11×M16—48no—
87C2×C8×C11—24no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—44no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—44no—
102C42×C11—22no—
103C42×C11—21no—
104C42×C11—22no—
105C42×C11—21no—
106C42×C11C2×D412yes—
107C42×C11#4112yes—
108C2×#423C2×C1111yescharacteristic
109#2857C2×C1111yescharacteristic
110#1797C2×C1111yescharacteristic
111C2×#332C2×C1112yescomplemented
112#1296C2×C1112yescomplemented
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11#10212yes—
120C23×C11C2×C22⋊C411yescharacteristic
121Q8×C11—81no—
122Q8×C11—81no—
123Q8×C11—81no—
124Q8×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11#10112yes—
148C2×C4×C11#10212yes—
149C2×C4×C11C4×D412yes—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12112yes—
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×C4×C11#13712yes—
159C2×C4×C11#13711yescharacteristic
160C8×C11—44no—
161C8×C11—82no—
162C22×M16—21no—
163C2×C4⋊Q8C22×C1111yescharacteristic
164C2×C22⋊Q8—21no—
165C22×C42C22×C1111yescharacteristic
166#423—24no—
167C2×C4⋊C8—21no—
168C2×C4⋊C8C22×C1112yes—
169C2×C4⋊C8C22×C1112yes—
170C2×C22⋊C8—21no—
171#391—21no—
172#389—21no—
173#389C4×C1112yes—
174#384C22×C1111yescharacteristic
175#380—21no—
176#380C4×C1112yes—
177#336—21no—
178#332—24no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11#38611yescharacteristic
187C22×C11C2×#10111yescharacteristic
188C22×C11#41311yescharacteristic
189C22×C11C2×#10211yescharacteristic
190C22×C11#41711yescharacteristic
191C22×C11#41711yescharacteristic
192C22×C11#41911yescharacteristic
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—41no—
197C4×C11—82no—
198C4×C11—82no—
199C4×C11#44711yescharacteristic
200C4×C11#44811yescharacteristic
201C4×C11#46812yes—
202C4×C11#47012yes—
203C4×C11#48011yescharacteristic
204C4×C11#48111yescharacteristic
205C22×Q8—21no—
206C23×C4C2×C4×C1111yescharacteristic
207C23×C4D4×C1111yescharacteristic
208C23×C4D4×C1111yescharacteristic
209C2×M16—24no—
210C2×M16—42no—
211C2×M16—42no—
212C22×C8—22no—
213C22×C8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—22no—
216C22⋊Q8—42no—
217C22⋊Q8—42no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4C2×C4×C1112yes—
223C2×C4⋊C4C2×C4×C1112yes—
224C2×C22⋊C4—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42C2×C4×C1111yescharacteristic
228C2×C42D4×C1111yescharacteristic
229C2×C42D4×C1111yescharacteristic
230C2×C42C23×C1111yescharacteristic
231C4⋊C8—24no—
232C4⋊C8—22no—
233C4⋊C8—22no—
234C4⋊C8—22no—
235C4⋊C8D4×C1114yes—
236C22⋊C8—42no—
237#95—22no—
238#95—22no—
239C2×C11—42no—
240C2×C11#154611yescharacteristic
241C2×C11#154711yescharacteristic
242C2×C11#155911yescharacteristic
243C2×C11#156111yescharacteristic
244C2×C11#187411yescharacteristic
245C2×C11#189411yescharacteristic
246C2×C11#190111yescharacteristic
247C24C11×C22⋊C411yescharacteristic
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4C11×C22⋊C411yescharacteristic
268C22×C4C11×C22⋊C411yescharacteristic
269C22×C4C11×C22⋊C411yescharacteristic
270C22×C4C11×D812yes—
271C22×C4C11×SD1612yes—
272C22×C4C22×C4×C1111yescharacteristic
273C22×C4C2×D4×C1111yescharacteristic
274C22×C4C2×D4×C1111yescharacteristic
275M16—48no—
276C2×C8—24no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C4⋊C4—24no—
283C4⋊C4—42no—
284C4⋊C4—44no—
285C4⋊C4—42no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C22⋊C4—44no—
291C42—22no—
292C42—21no—
293C42—22no—
294C42—21no—
295C42C2×D4×C1112yes—
296C42C11×#4112yes—
297C11#913911yescharacteristic, direct product factor, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23C11×#10212yes—
305C23C2×C11×C22⋊C411yescharacteristic
306Q8—81no—
307Q8—81no—
308Q8—81no—
309Q8—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4C11×#10112yes—
333C2×C4C11×#10212yes—
334C2×C4C4×D4×C1112yes—
335C2×C4C11×#12011yescharacteristic
336C2×C4C11×#12112yes—
337C2×C4C11×#12311yescharacteristic
338C2×C4C2×C11×D811yescharacteristic
339C2×C4C2×C11×SD1611yescharacteristic
340C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
341C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
342C2×C4C11×#13711yescharacteristic
343C2×C4C11×#13712yes—
344C2×C4C11×#13711yescharacteristic
345C8—44no—
346C8—82no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22C11×#38611yescharacteristic
355C22C2×C11×#10111yescharacteristic
356C22C11×#41311yescharacteristic
357C22C2×C11×#10211yescharacteristic
358C22C11×#41711yescharacteristic
359C22C11×#41711yescharacteristic
360C22C11×#41911yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—82no—
366C4—82no—
367C4C11×#44711yescharacteristic
368C4C11×#44811yescharacteristic
369C4C11×#46812yes—
370C4C11×#47012yes—
371C4C11×#48011yescharacteristic
372C4C11×#48111yescharacteristic
373C2—42no—
374C2C11×#154611yescharacteristic
375C2C11×#154711yescharacteristic
376C2C11×#155911yescharacteristic
377C2C11×#156111yescharacteristic
378C2C11×#187411yescharacteristic
379C2C11×#189411yescharacteristic
380C2C11×#190111yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC24×C11C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×C11×#332C2semidirect
5. C11×#1296C2semidirect
57. #9139C11direct (N × H)
111. C2×#332C2×C11semidirect
112. #1296C2×C11semidirect
297. C11#9139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4232
C11×#28572
C11×#17972
C2×C11×#3322
C11×#12962
#913911