Finite Group Databasebeta

← C11×#10145 #14587338

Subgroups — C11×#10145 #14587338

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic, complemented
2C2×C11×#493C211yesmaximal, characteristic
3C11×#3138C211yesmaximal, characteristic, complemented
4C11×#1965C211yesmaximal, characteristic, complemented
5C11×#1545C211yesmaximal, characteristic, complemented
6C11×#1493C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C22×C11×D8—22no—
9C11×#533C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C11×#127C2211yescharacteristic
12C11×#493—22no—
13C11×#493—22no—
14C11×#492—21no—
15C11×#490—22no—
16C11×#486—21no—
17C11×#486—21no—
18C11×#486—21no—
19C11×#460—22no—
20C11×#450—22no—
21C11×#431C2211yescharacteristic
22C11×#423C2211yescharacteristic
23C11×#418—22no—
24C2×C11×#100—22no—
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C11×#331—22no—
28C11×Q8⋊C8—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D412yes—
35C2×C11×SD16—24no—
36C2×C11×D8—28no—
37C2×C11×D8—48no—
38C2×C11×M16—21no—
39C2×C11×M16D412yes—
40C22×C8×C11—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127D412yes—
51C11×#125—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C11×#117—21no—
57C2×C42×C11C2311yescharacteristic
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#102—24no—
62C11×#102—24no—
63C11×#102—24no—
64C11×#100—44no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67C4×C8×C11—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C4×C8×C11D412yes—
71#10145C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C24×C11—41no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—42no—
94C2×D4×C11—82no—
95C2×D4×C11—82no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C11×SD16—84no—
100C11×D8—416no—
101C11×M16—22no—
102C11×M16—22no—
103C11×M16—42no—
104C2×C8×C11—24no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121#3208C2×C1111yescharacteristic, complemented
122C2×#493C2×C1111yescharacteristic
123#3138C2×C1111yescharacteristic, complemented
124#1965C2×C1111yescharacteristic, complemented
125#1545C2×C1111yescharacteristic, complemented
126#1493C2×C1111yescharacteristic, complemented
127#1278C2×C1111yescharacteristic, complemented
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11—82no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139D4×C11—44no—
140D4×C11—44no—
141D4×C11—44no—
142D4×C11—44no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—82no—
149D4×C11—81no—
150D4×C11—81no—
151D4×C11—81no—
152D4×C11—81no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12711yescharacteristic
163C2×C4×C11#13512yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C8×C11—24no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—81no—
169C22×D8—22no—
170#533C22×C1111yescharacteristic
171C2×#127C22×C1111yescharacteristic
172C2×#127C22×C1111yescharacteristic
173#493—22no—
174#493—22no—
175#492—21no—
176#490—22no—
177#486—21no—
178#486—21no—
179#486—21no—
180#460—22no—
181#450—22no—
182#431C22×C1111yescharacteristic
183#423C22×C1111yescharacteristic
184#418—22no—
185C2×#100—22no—
186C4×M16C22×C1111yescharacteristic
187C2×C4×C8C22×C1111yescharacteristic
188#331—22no—
189Q8⋊C8—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—164no—
199C22×C11—164no—
200C22×C11#39211yescharacteristic
201C22×C11#46312yes—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11#44912yes—
207C4×C11#45312yes—
208C4×C11#47212yes—
209C4×C11#49511yescharacteristic
210C4×C11#49611yescharacteristic
211C22×D4—21no—
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4D4×C1112yes—
217C2×SD16—24no—
218C2×D8—28no—
219C2×D8—48no—
220C2×M16—21no—
221C2×M16D4×C1112yes—
222C22×C8—21no—
223C4⋊Q8D4×C1111yescharacteristic
224C4⋊Q8D4×C1111yescharacteristic
225#127—21no—
226#127—21no—
227#127—21no—
228#127—21no—
229#127—21no—
230#127—21no—
231#127—21no—
232#127D4×C1112yes—
233#125—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238#117—21no—
239C2×C42C23×C1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8D4×C1112yes—
243#102—24no—
244#102—24no—
245#102—24no—
246#100—44no—
247C22⋊C8—21no—
248#97—21no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8D4×C1112yes—
253C2×C11—22no—
254C2×C11—162no—
255C2×C11—162no—
256C2×C11#200211yescharacteristic
257C2×C11#201211yescharacteristic
258C2×C11#201811yescharacteristic
259C24—22no—
260C24—41no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—82no—
282C2×D4—82no—
283C22×C4C2×D4×C1111yescharacteristic
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C11×#4111yescharacteristic
286SD16—84no—
287D8—416no—
288M16—22no—
289M16—22no—
290M16—42no—
291C2×C8—24no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42C2×D4×C1111yescharacteristic
305C42C2×D4×C1111yescharacteristic
306C42C2×D4×C1111yescharacteristic
307C42C2×D4×C1111yescharacteristic
308C11#1014511yescharacteristic, direct product factor, Sylow
309C23—42no—
310C23—42no—
311C23—44no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—82no—
316C23—82no—
317C23C11×#12111yescharacteristic
318Q8—42no—
319Q8—42no—
320D4—44no—
321D4—44no—
322D4—44no—
323D4—44no—
324D4—82no—
325D4—82no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—82no—
331D4—82no—
332D4—82no—
333D4—82no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C11×#12011yescharacteristic
339C2×C4C11×#12011yescharacteristic
340C2×C4C11×#12011yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#12111yescharacteristic
343C2×C4C11×#12711yescharacteristic
344C2×C4C11×#13512yes—
345C2×C4C11×AGL(1,ℤ/8)12yes—
346C8—24no—
347C8—42no—
348C8—42no—
349C8—81no—
350C22—21no—
351C22—21no—
352C22—82no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—164no—
359C22—164no—
360C22C11×#39211yescharacteristic
361C22C11×#46312yes—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4C11×#44912yes—
367C4C11×#45312yes—
368C4C11×#47212yes—
369C4C11×#49511yescharacteristic
370C4C11×#49611yescharacteristic
371C2—22no—
372C2—162no—
373C2—162no—
374C2C11×#200211yescharacteristic
375C2C11×#201211yescharacteristic
376C2C11×#201811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#493C2
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
1. C11×#3208C2semidirect
3. C11×#3138C2semidirect
4. C11×#1965C2semidirect
5. C11×#1545C2semidirect
6. C11×#1493C2semidirect
7. C11×#1278C2semidirect
71. #10145C11direct (N × H)
121. #3208C2×C11semidirect
123. #3138C2×C11semidirect
124. #1965C2×C11semidirect
125. #1545C2×C11semidirect
126. #1493C2×C11semidirect
127. #1278C2×C11semidirect
308. C11#10145direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C2×C11×#4932
C11×#31382
C11×#19652
C11×#15452
C11×#14932
C11×#12782
#1014511