Finite Group Databasebeta

← C11×#19423 #14596616

Subgroups — C11×#19423 #14596616

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3209C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C2×C11×#474C211yesmaximal, characteristic
4C11×#2975C211yesmaximal, characteristic
5C11×#1703C214yesmaximal, complemented
6C11×#1689C214yesmaximal, complemented
7C11×#1570C211yesmaximal, characteristic, complemented
8C11×#1549C211yesmaximal, characteristic, complemented
9C11×#1542C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C11×#494C2212yescomplemented
14C11×#487C2212yescomplemented
15C11×#478—22no—
16C11×#476C2212yes—
17C11×#474—22no—
18C11×#474C2212yes—
19C11×#474C2214yes—
20C11×#462—22no—
21C11×#451—22no—
22C11×#436—22no—
23C11×#436C2214yes—
24C11×#431C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#428—21no—
27C2×C11×#107—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C11×#418—21no—
31C2×C11×#102—21no—
32C11×#407—22no—
33C11×#334C2214yescomplemented
34C11×#333C2212yescomplemented
35C11×#332C2212yescomplemented
36C11×#332C2214yescomplemented
37C22×Q8×C11—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C2×C11×Q16—24no—
41C2×C11×M16—21no—
42C2×C11×M16—24no—
43C22×C8×C11—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2311yescharacteristic
48C11×C4⋊Q8C2312yes—
49C11×C4⋊Q8C2311yescharacteristic
50C11×#125—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11D412yes—
58C4×D4×C11C2312yes—
59C11×#117—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C11×#107—24no—
66C11×#107—22no—
67C11×#106—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×#103—24no—
75C11×#102—24no—
76C11×#102—22no—
77C11×#102—22no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—24no—
80C11×C22⋊C8D412yes—
81C4×C8×C11—21no—
82C4×C8×C11C2312yes—
83#19423C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—82no—
90C2×D4×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11C2×D412yes—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—41no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C11×Q16—84no—
103C11×M16—42no—
104C11×M16—84no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—42no—
109C2×C8×C11C2×D414yes—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130#3209C2×C1111yescharacteristic, complemented
131#3077C2×C1111yescharacteristic
132C2×#474C2×C1111yescharacteristic
133#2975C2×C1111yescharacteristic
134#1703C2×C1114yescomplemented
135#1689C2×C1114yescomplemented
136#1570C2×C1111yescharacteristic, complemented
137#1549C2×C1111yescharacteristic, complemented
138#1542C2×C1111yescharacteristic, complemented
139C23×C11—22no—
140C23×C11—42no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11#12111yescharacteristic
144Q8×C11—42no—
145Q8×C11—44no—
146Q8×C11—81no—
147Q8×C11—82no—
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—42no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—81no—
160C2×C4×C11—82no—
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#13712yes—
165C2×C4×C11#13712yes—
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C8×C11—24no—
170C8×C11—42no—
171C8×C11—42no—
172C8×C11—42no—
173#533C22×C1111yescharacteristic
174C2×C4⋊Q8C22×C1111yescharacteristic
175C2×C4×D4C22×C1111yescharacteristic
176#494C22×C1112yescomplemented
177#487C22×C1112yescomplemented
178#478—22no—
179#476C22×C1112yes—
180#474—22no—
181#474C22×C1112yes—
182#474C22×C1114yes—
183#462—22no—
184#451—22no—
185#436—22no—
186#436C22×C1114yes—
187#431C22×C1111yescharacteristic
188#431C22×C1111yescharacteristic
189#428—21no—
190C2×#107—21no—
191#423C22×C1111yescharacteristic
192C2×C4⋊C8C22×C1111yescharacteristic
193#418—21no—
194C2×#102—21no—
195#407—22no—
196#334C22×C1114yescomplemented
197#333C22×C1112yescomplemented
198#332C22×C1112yescomplemented
199#332C22×C1114yescomplemented
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—84no—
206C22×C11#47012yes—
207C22×C11C2×#12111yescharacteristic
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11#47012yes—
216C4×C11C2×#13711yescharacteristic
217C4×C11C2×#13711yescharacteristic
218C4×C11#57612yes—
219C22×Q8—21no—
220C22×D4D4×C1111yescharacteristic
221C23×C4—21no—
222C2×Q16—24no—
223C2×M16—21no—
224C2×M16—24no—
225C22×C8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C23×C1112yes—
230C4⋊Q8C23×C1111yescharacteristic
231C4⋊Q8C23×C1111yescharacteristic
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4D4×C1112yes—
240C4×D4C23×C1112yes—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4D4×C1111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C23×C1111yescharacteristic
247#107—24no—
248#107—22no—
249#106—22no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C1112yes—
253C4⋊C8C23×C1112yes—
254C4⋊C8C23×C1112yes—
255C4⋊C8C23×C1112yes—
256#103—24no—
257#102—24no—
258#102—22no—
259#102—22no—
260C22⋊C8—21no—
261C22⋊C8—24no—
262C22⋊C8D4×C1112yes—
263C4×C8—21no—
264C4×C8C23×C1112yes—
265C2×C11—22no—
266C2×C11—82no—
267C2×C11#304111yescharacteristic
268C2×C11C2×#47011yescharacteristic
269C2×C11#306911yescharacteristic
270C24—21no—
271C2×Q8—22no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×D4—21no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4C2×D4×C1112yes—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—82no—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C11×#4111yescharacteristic
288Q16—84no—
289M16—42no—
290M16—84no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8—42no—
295C2×C8C2×D4×C1114yes—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4C2×D4×C1112yes—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C42—41no—
312C42C2×D4×C1111yescharacteristic
313C42C2×D4×C1111yescharacteristic
314C42C11×#4111yescharacteristic
315C42C24×C1111yescharacteristic
316C11#1942311yescharacteristic, direct product factor, Sylow
317C23—22no—
318C23—42no—
319C23—81no—
320C23—81no—
321C23C11×#12111yescharacteristic
322Q8—42no—
323Q8—44no—
324Q8—81no—
325Q8—82no—
326D4—22no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—82no—
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#13712yes—
343C2×C4C11×#13712yes—
344C2×C4C22×D4×C1111yescharacteristic
345C2×C4C22×D4×C1111yescharacteristic
346C2×C4C2×C11×#4111yescharacteristic
347C8—24no—
348C8—42no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—84no—
357C22C11×#47012yes—
358C22C2×C11×#12111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4C11×#47012yes—
367C4C2×C11×#13711yescharacteristic
368C4C2×C11×#13711yescharacteristic
369C4C11×#57612yes—
370C2—22no—
371C2—82no—
372C2C11×#304111yescharacteristic
373C2C2×C11×#47011yescharacteristic
374C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ 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×#3209C2semidirect
5. C11×#1703C2semidirect
6. C11×#1689C2semidirect
7. C11×#1570C2semidirect
8. C11×#1549C2semidirect
9. C11×#1542C2semidirect
13. C11×#494C22semidirect
14. C11×#487C22semidirect
33. C11×#334C22semidirect
34. C11×#333C22semidirect
35. C11×#332C22semidirect
36. C11×#332C22semidirect
83. #19423C11direct (N × H)
130. #3209C2×C11semidirect
134. #1703C2×C11semidirect
135. #1689C2×C11semidirect
136. #1570C2×C11semidirect
137. #1549C2×C11semidirect
138. #1542C2×C11semidirect
176. #494C22×C11semidirect
177. #487C22×C11semidirect
196. #334C22×C11semidirect
197. #333C22×C11semidirect
198. #332C22×C11semidirect
199. #332C22×C11semidirect
316. C11#19423direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32092
C11×#30772
C2×C11×#4742
C11×#29752
C11×#17032
C11×#16892
C11×#15702
C11×#15492
C11×#15422
#1942311