Finite Group Databasebeta

← C11×#10501 #14587694

Subgroups — C11×#10501 #14587694

Order 2816.

440 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3206C211yesmaximal, characteristic
2C11×#1997C211yesmaximal, characteristic, complemented
3C11×#1981C211yesmaximal, characteristic, complemented
4C11×#1980C211yesmaximal, characteristic
5C11×#1565C211yesmaximal, characteristic, complemented
6C11×#1547C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#492—21no—
11C11×#487—21no—
12C11×#461—21no—
13C11×#461—21no—
14C11×#448—22no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#104—21no—
19C2×C11×#104—21no—
20C2×C11×#103—22no—
21C4×C11×M16C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C11×#343—21no—
24C11×#343—21no—
25C11×#335—21no—
26C11×#334—21no—
27C11×#332—21no—
28C11×#331—21no—
29C2×C11×#41—21no—
30C22×Q8×C11D412yes—
31C2×C11×SD16—22no—
32C2×C11×SD16—22no—
33C2×C11×M16—21no—
34C2×C11×M16D411yescharacteristic
35C2×C11×M16D411yescharacteristic
36C22×C8×C11—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×#127D411yescharacteristic
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#104—42no—
60C11×#104—42no—
61C11×#103—22no—
62C11×#103—22no—
63C11×#103—44no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68C11×#95—21no—
69#10501C1111yesmaximal, characteristic, direct product factor, Sylow
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—22no—
75C2×Q8×C11—21no—
76C2×Q8×C11—22no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C11×SD16—82no—
90C11×SD16—82no—
91C11×M16—21no—
92C11×M16—21no—
93C11×M16—21no—
94C11×M16—41no—
95C11×M16—41no—
96C11×M16SD1612yescomplemented
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—21no—
101C2×C8×C11—42no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11#4111yescharacteristic
120#3206C2×C1111yescharacteristic
121#1997C2×C1111yescharacteristic, complemented
122#1981C2×C1111yescharacteristic, complemented
123#1980C2×C1111yescharacteristic
124#1565C2×C1111yescharacteristic, complemented
125#1547C2×C1111yescharacteristic
126#1303C2×C1111yescharacteristic, complemented
127C23×C11—41no—
128C23×C11#12111yescharacteristic
129Q8×C11—44no—
130Q8×C11—42no—
131Q8×C11—42no—
132Q8×C11—41no—
133Q8×C11—41no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C2×C4×C11#12311yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C8×C11—22no—
163C8×C11—41no—
164C8×C11—41no—
165C8×C11—41no—
166C8×C11—81no—
167C8×C11—81no—
168#532C22×C1111yescharacteristic
169C2×C4⋊Q8C22×C1111yescharacteristic
170#492—21no—
171#487—21no—
172#461—21no—
173#461—21no—
174#448—22no—
175#431C22×C1111yescharacteristic
176#423C22×C1111yescharacteristic
177C2×C4⋊C8C22×C1111yescharacteristic
178C2×#104—21no—
179C2×#104—21no—
180C2×#103—22no—
181C4×M16C22×C1111yescharacteristic
182C4×C4⋊C4C22×C1111yescharacteristic
183#343—21no—
184#343—21no—
185#335—21no—
186#334—21no—
187#332—21no—
188#331—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#39411yescharacteristic
195C22×C11#46011yescharacteristic
196C22×C11#46411yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11—81no—
202C4×C11—82no—
203C4×C11#45311yescharacteristic
204C4×C11#45511yescharacteristic
205C4×C11#46111yescharacteristic
206C4×C11#46311yescharacteristic
207C4×C11#46511yescharacteristic
208C4×C11#46811yescharacteristic
209C2×#41—21no—
210C22×Q8D4×C1112yes—
211C2×SD16—22no—
212C2×SD16—22no—
213C2×M16—21no—
214C2×M16D4×C1111yescharacteristic
215C2×M16D4×C1111yescharacteristic
216C22×C8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C1111yescharacteristic
222#127D4×C1111yescharacteristic
223#124—21no—
224#121—21no—
225#121—21no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42—21no—
232C2×C42C23×C1111yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C1111yescharacteristic
238C4⋊C8D4×C1111yescharacteristic
239#104—42no—
240#104—42no—
241#103—22no—
242#103—22no—
243#103—44no—
244C22⋊C8—21no—
245#97—21no—
246C4×C8—21no—
247C4×C8—21no—
248#95—21no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—161no—
252C2×C11#203711yescharacteristic
253C2×C11#204911yescharacteristic
254C2×C11#205511yescharacteristic
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C1111yescharacteristic
272C22×C4C2×D4×C1111yescharacteristic
273C22×C4C11×#4111yescharacteristic
274SD16—82no—
275SD16—82no—
276M16—21no—
277M16—21no—
278M16—21no—
279M16—41no—
280M16—41no—
281M16C11×SD1612yescomplemented
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—42no—
287C2×C8—41no—
288C2×C8—41no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42—41no—
300C42—41no—
301C42C2×D4×C1111yescharacteristic
302C42C2×D4×C1111yescharacteristic
303C42C11×#4111yescharacteristic
304C42C11×#4111yescharacteristic
305C11#1050111yescharacteristic, direct product factor, Sylow
306C23—41no—
307C23C11×#12111yescharacteristic
308Q8—44no—
309Q8—42no—
310Q8—42no—
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4C11×#12011yescharacteristic
332C2×C4C11×#12111yescharacteristic
333C2×C4C11×#12111yescharacteristic
334C2×C4C11×#12311yescharacteristic
335C2×C4C11×#12311yescharacteristic
336C2×C4C11×#12411yescharacteristic
337C2×C4C2×C11×SD1611yescharacteristic
338C2×C4C11×#13511yescharacteristic
339C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
340C2×C4C11×#13711yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C11×#39411yescharacteristic
353C22C11×#46011yescharacteristic
354C22C11×#46411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—81no—
361C4C11×#45311yescharacteristic
362C4C11×#45511yescharacteristic
363C4C11×#46111yescharacteristic
364C4C11×#46311yescharacteristic
365C4C11×#46511yescharacteristic
366C4C11×#46811yescharacteristic
367C2—21no—
368C2—21no—
369C2—161no—
370C2C11×#203711yescharacteristic
371C2C11×#204911yescharacteristic
372C2C11×#205511yescharacteristic
subgroupG/H
center, socleC22×C11#394
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. C11×#1997C2semidirect
3. C11×#1981C2semidirect
5. C11×#1565C2semidirect
7. C11×#1303C2semidirect
69. #10501C11direct (N × H)
96. C11×M16SD16semidirect
121. #1997C2×C11semidirect
122. #1981C2×C11semidirect
124. #1565C2×C11semidirect
126. #1303C2×C11semidirect
281. M16C11×SD16semidirect
305. C11#10501direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C11×#19972
C11×#19812
C11×#19802
C11×#15652
C11×#15472
C11×#13032
#1050111