Finite Group Databasebeta

← C11×#9134 #14586327

Subgroups — C11×#9134 #14586327

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#431C211yesmaximal, characteristic, complemented
2C11×#2856C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic, complemented
4C2×C11×#331C212yesmaximal, complemented
5C11×#1296C212yesmaximal, complemented
6C2×C11×#127C2211yescharacteristic
7C2×C11×#121—21no—
8C2×C11×#121—21no—
9C2×C11×#121C412yes—
10C22×C42×C11C2211yescharacteristic
11C11×#431—24no—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8—21no—
15C2×C11×C22⋊C8—21no—
16C2×C4×C8×C11—21no—
17C11×#390—21no—
18C11×#390—21no—
19C11×#390C412yes—
20C11×#384C2211yescharacteristic
21C11×#336—21no—
22C11×#331—24no—
23C22×D4×C11—22no—
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11C2×C412yes—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C22×C8×C11—22no—
31C22×C8×C11—22no—
32C11×#127—22no—
33C11×#127—22no—
34C11×#121—44no—
35C11×#121—42no—
36C11×#121—42no—
37C11×#121—44no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C42×C11—22no—
45C2×C42×C11—22no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C11×C4⋊C8—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8—22no—
53C11×C4⋊C8D414yescomplemented
54C11×C22⋊C8—24no—
55C11×C22⋊C8—42no—
56C4×C8×C11—24no—
57#9134C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—22no—
59C24×C11C22⋊C411yescharacteristic
60C2×D4×C11—24no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—44no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—41no—
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11D812yes—
88C22×C4×C11SD1612yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C2×C8×C11—24no—
93C2×C8×C11—42no—
94C2×C8×C11—42no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C2×C8×C11—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—42no—
102C11×C22⋊C4—44no—
103C11×C22⋊C4—44no—
104C11×C22⋊C4—44no—
105C42×C11—22no—
106C42×C11—21no—
107C42×C11—22no—
108C42×C11—21no—
109C42×C11C2×D412yes—
110C42×C11#4112yes—
111C2×#431C2×C1111yescharacteristic, complemented
112#2856C2×C1111yescharacteristic
113#1797C2×C1111yescharacteristic, complemented
114C2×#331C2×C1112yescomplemented
115#1296C2×C1112yescomplemented
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11#10212yes—
130C23×C11C2×C22⋊C411yescharacteristic
131D4×C11—84no—
132D4×C11—88no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11#10012yes—
155C2×C4×C11#10212yes—
156C2×C4×C11C4×D412yes—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12112yes—
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×SD1611yescharacteristic
162C2×C4×C11#13512yes—
163C2×C4×C11#13512yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C8×C11—44no—
166C8×C11—82no—
167C2×#127C22×C1111yescharacteristic
168C2×#121—21no—
169C2×#121—21no—
170C2×#121C4×C1112yes—
171C22×C42C22×C1111yescharacteristic
172#431—24no—
173C2×C4⋊C8C22×C1112yes—
174C2×C4⋊C8C22×C1112yes—
175C2×C22⋊C8—21no—
176C2×C22⋊C8—21no—
177C2×C4×C8—21no—
178#390—21no—
179#390—21no—
180#390C4×C1112yes—
181#384C22×C1111yescharacteristic
182#336—21no—
183#331—24no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11#38611yescharacteristic
199C22×C11C2×#10011yescharacteristic
200C22×C11#41311yescharacteristic
201C22×C11C2×#10211yescharacteristic
202C22×C11#41611yescharacteristic
203C22×C11#41611yescharacteristic
204C22×C11#41811yescharacteristic
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—22no—
208C4×C11—41no—
209C4×C11—82no—
210C4×C11#44912yes—
211C4×C11#46512yes—
212C4×C11#46612yes—
213C4×C11#48212yes—
214C22×D4—22no—
215C22×D4—21no—
216C22×D4—21no—
217C22×D4C2×C4×C1112yes—
218C23×C4C2×C4×C1111yescharacteristic
219C23×C4D4×C1111yescharacteristic
220C23×C4D4×C1111yescharacteristic
221C22×C8—22no—
222C22×C8—22no—
223#127—22no—
224#127—22no—
225#121—44no—
226#121—42no—
227#121—42no—
228#121—44no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×C4×C1112yes—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C42—22no—
236C2×C42—22no—
237C2×C42C2×C4×C1111yescharacteristic
238C2×C42D4×C1111yescharacteristic
239C2×C42D4×C1111yescharacteristic
240C2×C42C23×C1111yescharacteristic
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8D4×C1114yescomplemented
245C22⋊C8—24no—
246C22⋊C8—42no—
247C4×C8—24no—
248C2×C11—42no—
249C2×C11—162no—
250C2×C11#154011yescharacteristic
251C2×C11#154311yescharacteristic
252C2×C11#154511yescharacteristic
253C2×C11#155311yescharacteristic
254C2×C11#187511yescharacteristic
255C2×C11#189311yescharacteristic
256C2×C11#190011yescharacteristic
257C24—22no—
258C24C11×C22⋊C411yescharacteristic
259C2×D4—24no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4C11×C22⋊C411yescharacteristic
284C22×C4C11×C22⋊C411yescharacteristic
285C22×C4C11×C22⋊C411yescharacteristic
286C22×C4C11×D812yes—
287C22×C4C11×SD1612yes—
288C22×C4C22×C4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C22⋊C4—44no—
302C22⋊C4—44no—
303C22⋊C4—44no—
304C42—22no—
305C42—21no—
306C42—22no—
307C42—21no—
308C42C2×D4×C1112yes—
309C42C11×#4112yes—
310C11#913411yescharacteristic, direct product factor, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23C11×#10212yes—
325C23C2×C11×C22⋊C411yescharacteristic
326D4—84no—
327D4—88no—
328D4—82no—
329D4—82no—
330D4—82no—
331D4—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4C11×#10012yes—
350C2×C4C11×#10212yes—
351C2×C4C4×D4×C1112yes—
352C2×C4C11×#12011yescharacteristic
353C2×C4C11×#12112yes—
354C2×C4C11×#12311yescharacteristic
355C2×C4C2×C11×D811yescharacteristic
356C2×C4C2×C11×SD1611yescharacteristic
357C2×C4C11×#13512yes—
358C2×C4C11×#13512yes—
359C2×C4C11×AGL(1,ℤ/8)12yes—
360C8—44no—
361C8—82no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22C11×#38611yescharacteristic
377C22C2×C11×#10011yescharacteristic
378C22C11×#41311yescharacteristic
379C22C2×C11×#10211yescharacteristic
380C22C11×#41611yescharacteristic
381C22C11×#41611yescharacteristic
382C22C11×#41811yescharacteristic
383C4—22no—
384C4—22no—
385C4—22no—
386C4—41no—
387C4—82no—
388C4C11×#44912yes—
389C4C11×#46512yes—
390C4C11×#46612yes—
391C4C11×#48212yes—
392C2—42no—
393C2—162no—
394C2C11×#154011yescharacteristic
395C2C11×#154311yescharacteristic
396C2C11×#154511yescharacteristic
397C2C11×#155311yescharacteristic
398C2C11×#187511yescharacteristic
399C2C11×#189311yescharacteristic
400C2C11×#190011yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2856C2
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
1. C2×C11×#431C2semidirect
3. C11×#1797C2semidirect
4. C2×C11×#331C2semidirect
5. C11×#1296C2semidirect
53. C11×C4⋊C8D4semidirect
57. #9134C11direct (N × H)
111. C2×#431C2×C11semidirect
113. #1797C2×C11semidirect
114. C2×#331C2×C11semidirect
115. #1296C2×C11semidirect
244. C4⋊C8D4×C11semidirect
310. C11#9134direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4312
C11×#28562
C11×#17972
C2×C11×#3312
C11×#12962
#913411