Finite Group Databasebeta

← C11×#11100 #14588293

Subgroups — C11×#11100 #14588293

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2911C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic
3C11×#2280C212yesmaximal
4C11×#1733C212yesmaximal, complemented
5C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16C2211yescharacteristic
8C22×C11×M16C2211yescharacteristic
9C2×C11×#117C2212yes—
10C2×C11×#117C2212yes—
11C11×#428—24no—
12C11×#427—22no—
13C11×#407—22no—
14C11×#407C414yescomplemented
15C2×C11×C22⋊C8—22no—
16C11×#381—22no—
17C11×#380—24no—
18C11×#379—22no—
19C4×C11×C22⋊C4—24no—
20C11×#339—24no—
21C11×H(3,ℤ/4)—22no—
22C25×C11D411yescharacteristic
23C23×C4×C11—22no—
24C23×C4×C11—22no—
25C23×C4×C11—21no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11C2×C412yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11Q812yes—
34C23×C4×C11C2311yescharacteristic
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16—21no—
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16C2×C412yes—
41C2×C11×M16C2×C412yes—
42C2×C11×M16D412yes—
43C22×C8×C11—21no—
44C22×C8×C11D412yes—
45C11×#117—22no—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117—22no—
50C11×#117—22no—
51C11×#117—22no—
52C11×#117—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4D414yes—
55C2×C11×C22⋊C4—28no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C42×C11—22no—
59C2×C42×C11D414yes—
60C11×#107—24no—
61C11×#106—24no—
62C11×C22⋊C8—28no—
63C11×#95—28no—
64#11100C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—22no—
66C24×C11—21no—
67C24×C11—21no—
68C24×C11—22no—
69C24×C11—44no—
70C24×C11C4⋊C412yes—
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—41no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11C4⋊C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×Q811yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C11×M16—24no—
108C11×M16—24no—
109C11×M16—24no—
110C11×M16—42no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11C22⋊C414yescomplemented
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—42no—
121C11×C22⋊C4—416no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—42no—
126C42×C11—24no—
127C42×C11—24no—
128C42×C11—42no—
129C42×C11—42no—
130#2911C2×C1111yescharacteristic, complemented
131C2×#407C2×C1111yescharacteristic
132#2280C2×C1112yes—
133#1733C2×C1112yescomplemented
134C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
135C23×C11—28no—
136C23×C11—24no—
137C23×C11—22no—
138C23×C11—24no—
139C23×C11—44no—
140C23×C11—42no—
141C23×C11—44no—
142C23×C11—42no—
143C23×C11—44no—
144C23×C11—48no—
145C23×C11—41no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11C2×C4⋊C411yescharacteristic
149C23×C11#12012yes—
150C23×C11#12111yescharacteristic
151C23×C11#12111yescharacteristic
152C23×C11#12312yes—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—48no—
165C2×C4×C11—48no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11C2×C22⋊C411yescharacteristic
169C2×C4×C11#11711yescharacteristic
170C2×C4×C11C4×D412yes—
171C2×C4×C11C4×D412yes—
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12112yes—
174C2×C4×C11#12112yes—
175C2×C4×C11#12112yes—
176C2×C4×C11C22⋊Q812yes—
177C2×C4×C11C22⋊Q811yescharacteristic
178C2×C4×C11C22⋊Q811yescharacteristic
179C2×C4×C11C22⋊Q812yes—
180C2×C4×C11#12311yescharacteristic
181C2×C4×C11#12312yes—
182C2×C4×C11#12412yes—
183C2×C4×C11#12411yescharacteristic
184C2×C4×C11#12612yes—
185C2×C4×C11#12711yescharacteristic
186C8×C11—24no—
187C8×C11—42no—
188C24×C4C22×C1111yescharacteristic
189C22×M16C22×C1111yescharacteristic
190C22×M16C22×C1111yescharacteristic
191C2×#117C22×C1112yes—
192C2×#117C22×C1112yes—
193#428—24no—
194#427—22no—
195#407—22no—
196#407C4×C1114yescomplemented
197C2×C22⋊C8—22no—
198#381—22no—
199#380—24no—
200#379—22no—
201C4×C22⋊C4—24no—
202#339—24no—
203H(3,ℤ/4)—22no—
204C22×C11—24no—
205C22×C11—22no—
206C22×C11—24no—
207C22×C11—28no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—42no—
211C22×C11—48no—
212C22×C11—42no—
213C22×C11—44no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—44no—
217C22×C11#38011yescharacteristic
218C22×C11#38512yes—
219C22×C11#39211yescharacteristic
220C22×C11#39412yes—
221C22×C11#39711yescharacteristic
222C4×C11—42no—
223C4×C11—84no—
224C4×C11—84no—
225C4×C11#38611yescharacteristic
226C4×C11#38812yes—
227C4×C11#39011yescharacteristic
228C4×C11#39311yescharacteristic
229C4×C11#39612yes—
230C4×C11#39911yescharacteristic
231C25D4×C1111yescharacteristic
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4C2×C4×C1112yes—
241C23×C4D4×C1111yescharacteristic
242C23×C4Q8×C1112yes—
243C23×C4C23×C1111yescharacteristic
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—21no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16C2×C4×C1112yes—
250C2×M16C2×C4×C1112yes—
251C2×M16D4×C1112yes—
252C22×C8—21no—
253C22×C8D4×C1112yes—
254#117—22no—
255#117—22no—
256#117—22no—
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261#117—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4D4×C1114yes—
264C2×C22⋊C4—28no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C42—22no—
268C2×C42D4×C1114yes—
269#107—24no—
270#106—24no—
271C22⋊C8—28no—
272#95—28no—
273C2×C11—22no—
274C2×C11—21no—
275C2×C11—22no—
276C2×C11—21no—
277C2×C11—44no—
278C2×C11#143911yescharacteristic
279C2×C11#201012yes—
280C24—22no—
281C24—21no—
282C24—21no—
283C24—22no—
284C24—44no—
285C24C11×C4⋊C412yes—
286C24C2×D4×C1111yescharacteristic
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4C11×C4⋊C412yes—
312C22×C4C22×C4×C1111yescharacteristic
313C22×C4C2×D4×C1111yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1112yes—
316C22×C4C2×D4×C1112yes—
317C22×C4C2×Q8×C1111yescharacteristic
318C22×C4C11×#4111yescharacteristic
319C22×C4C11×#4111yescharacteristic
320C22×C4C11×#4112yes—
321C22×C4C11×#4112yes—
322M16—24no—
323M16—24no—
324M16—24no—
325M16—42no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8C11×C22⋊C414yescomplemented
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C22⋊C4—416no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C42—24no—
342C42—24no—
343C42—42no—
344C42—42no—
345C11#1110011yescharacteristic, direct product factor, Sylow
346C23—28no—
347C23—24no—
348C23—22no—
349C23—24no—
350C23—44no—
351C23—42no—
352C23—44no—
353C23—42no—
354C23—44no—
355C23—48no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23C2×C11×C4⋊C411yescharacteristic
360C23C11×#12012yes—
361C23C11×#12111yescharacteristic
362C23C11×#12111yescharacteristic
363C23C11×#12312yes—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—48no—
376C2×C4—48no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4C2×C11×C22⋊C411yescharacteristic
380C2×C4C11×#11711yescharacteristic
381C2×C4C4×D4×C1112yes—
382C2×C4C4×D4×C1112yes—
383C2×C4C11×#12011yescharacteristic
384C2×C4C11×#12112yes—
385C2×C4C11×#12112yes—
386C2×C4C11×#12112yes—
387C2×C4C11×C22⋊Q812yes—
388C2×C4C11×C22⋊Q811yescharacteristic
389C2×C4C11×C22⋊Q811yescharacteristic
390C2×C4C11×C22⋊Q812yes—
391C2×C4C11×#12311yescharacteristic
392C2×C4C11×#12312yes—
393C2×C4C11×#12412yes—
394C2×C4C11×#12411yescharacteristic
395C2×C4C11×#12612yes—
396C2×C4C11×#12711yescharacteristic
397C8—24no—
398C8—42no—
399C22—24no—
400C22—22no—
401C22—24no—
402C22—28no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22—48no—
407C22—42no—
408C22—44no—
409C22—44no—
410C22—42no—
411C22—44no—
412C22C11×#38011yescharacteristic
413C22C11×#38512yes—
414C22C11×#39211yescharacteristic
415C22C11×#39412yes—
416C22C11×#39711yescharacteristic
417C4—42no—
418C4—84no—
419C4—84no—
420C4C11×#38611yescharacteristic
421C4C11×#38812yes—
422C4C11×#39011yescharacteristic
423C4C11×#39311yescharacteristic
424C4C11×#39612yes—
425C4C11×#39911yescharacteristic
426C2—22no—
427C2—21no—
428C2—22no—
429C2—21no—
430C2—44no—
431C2C11×#143911yescharacteristic
432C2C11×#201012yes—
subgroupG/H
centerC2×C4×C11#127
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#392
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2911C2semidirect
4. C11×#1733C2semidirect
5. C2×C11×H(3,ℤ/4)C2semidirect
14. C11×#407C4semidirect
64. #11100C11direct (N × H)
116. C2×C8×C11C22⋊C4semidirect
130. #2911C2×C11semidirect
133. #1733C2×C11semidirect
134. C2×H(3,ℤ/4)C2×C11semidirect
196. #407C4×C11semidirect
331. C2×C8C11×C22⋊C4semidirect
345. C11#11100direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29112
C2×C11×#4072
C11×#22802
C11×#17332
C2×C11×H(3,ℤ/4)2
#1110011