Finite Group Databasebeta

← C11×#11208 #14588401

Subgroups — C11×#11208 #14588401

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#389C211yesmaximal, characteristic
2C2×C11×#382C211yesmaximal, characteristic
3C2×C11×#340C212yesmaximal
4C2×C11×#340C212yesmaximal
5C2×C11×#336C211yesmaximal, characteristic
6C23×C8×C11C2212yes—
7C22×C11×C4⋊C4—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C11×#389—22no—
13C11×#389C414yescomplemented
14C11×#382—24no—
15C2×C11×#95—21no—
16C2×C11×#95—21no—
17C2×C11×#95—21no—
18C11×#340—24no—
19C11×#340—24no—
20C11×#336—22no—
21C23×C4×C11—21no—
22C23×C4×C11—22no—
23C23×C4×C11—21no—
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C22×C8×C11—22no—
28C22×C8×C11—22no—
29C22×C8×C11—22no—
30C22×C8×C11—22no—
31C22×C8×C11—22no—
32C22×C8×C11—22no—
33C22×C8×C11Q814yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—44no—
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4D414yes—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4Q812yes—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11C2×C412yes—
55C2×C42×C11D412yes—
56C11×#95—24no—
57C11×#95—24no—
58C11×#95—24no—
59#11208C1111yesmaximal, characteristic, direct product factor, Sylow
60C24×C11C2×D411yescharacteristic
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11C22⋊C412yes—
87C22×C4×C11C22⋊C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×Q811yescharacteristic
93C22×C4×C11C2×Q812yes—
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×C4×C11#4112yes—
97C22×C4×C11#4112yes—
98C2×C8×C11—24no—
99C2×C8×C11—24no—
100C2×C8×C11—24no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—48no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4C4⋊C414yes—
116C42×C11—24no—
117C42×C11—24no—
118C2×#389C2×C1111yescharacteristic
119C2×#382C2×C1111yescharacteristic
120C2×#340C2×C1112yes—
121C2×#340C2×C1112yes—
122C2×#336C2×C1111yescharacteristic
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12011yescharacteristic
125C23×C11#12111yescharacteristic
126C23×C11C22⋊Q811yescharacteristic
127C23×C11#12311yescharacteristic
128C23×C11#12411yescharacteristic
129C23×C11C4⋊Q811yescharacteristic
130C23×C11#13512yes—
131C23×C11#13512yes—
132C23×C11AGL(1,ℤ/8)12yes—
133C23×C11#13712yes—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—82no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11C2×C4⋊C411yescharacteristic
162C2×C4×C11#11711yescharacteristic
163C2×C4×C11C4×D412yes—
164C2×C4×C11C4×Q812yes—
165C2×C4×C11#12112yes—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12112yes—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11C22⋊Q812yes—
171C2×C4×C11C22⋊Q811yescharacteristic
172C2×C4×C11#12312yes—
173C2×C4×C11#12512yes—
174C2×C4×C11#12512yes—
175C2×C4×C11#12612yes—
176C2×C4×C11C4⋊Q812yes—
177C8×C11—44no—
178C23×C8C22×C1112yes—
179C22×C4⋊C4—21no—
180C22×C4⋊C4C22×C1111yescharacteristic
181C22×C4⋊C4C22×C1112yes—
182C22×C4⋊C4C22×C1111yescharacteristic
183C22×C42C22×C1111yescharacteristic
184#389—22no—
185#389C4×C1114yescomplemented
186#382—24no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190#340—24no—
191#340—24no—
192#336—22no—
193C22×C11#38011yescharacteristic
194C22×C11#38611yescharacteristic
195C22×C11#39111yescharacteristic
196C22×C11#39411yescharacteristic
197C22×C11#39511yescharacteristic
198C22×C11#39811yescharacteristic
199C22×C11#40011yescharacteristic
200C22×C11#41611yescharacteristic
201C22×C11#41611yescharacteristic
202C22×C11#41811yescharacteristic
203C22×C11#41911yescharacteristic
204C22×C11#44912yes—
205C22×C11#45212yes—
206C22×C11#46312yes—
207C22×C11#46412yes—
208C22×C11#47812yes—
209C22×C11#47912yes—
210C22×C11#48212yes—
211C22×C11#48512yes—
212C22×C11#48812yes—
213C22×C11#48912yes—
214C22×C11#49912yes—
215C22×C11#50112yes—
216C4×C11—44no—
217C4×C11—42no—
218C4×C11—42no—
219C4×C11—82no—
220C4×C11—84no—
221C4×C11#38712yes—
222C4×C11#38912yes—
223C4×C11#39612yes—
224C4×C11#39812yes—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4D4×C1111yescharacteristic
229C23×C4D4×C1111yescharacteristic
230C23×C4C23×C1111yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233C22×C8—22no—
234C22×C8—22no—
235C22×C8—22no—
236C22×C8—22no—
237C22×C8Q8×C1114yes—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4C2×C4×C1112yes—
252C2×C4⋊C4C2×C4×C1112yes—
253C2×C4⋊C4D4×C1114yes—
254C2×C4⋊C4D4×C1112yes—
255C2×C4⋊C4Q8×C1112yes—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42C2×C4×C1112yes—
259C2×C42D4×C1112yes—
260#95—24no—
261#95—24no—
262#95—24no—
263C2×C11#144111yescharacteristic
264C2×C11#180411yescharacteristic
265C2×C11#180511yescharacteristic
266C2×C11#187311yescharacteristic
267C2×C11#187511yescharacteristic
268C2×C11#199111yescharacteristic
269C2×C11#199311yescharacteristic
270C2×C11#204212yes—
271C2×C11#205912yes—
272C2×C11#208512yes—
273C2×C11#210112yes—
274C24C2×D4×C1111yescharacteristic
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4C11×C22⋊C412yes—
301C22×C4C11×C22⋊C412yes—
302C22×C4C22×C4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1112yes—
305C22×C4C2×D4×C1111yescharacteristic
306C22×C4C2×Q8×C1111yescharacteristic
307C22×C4C2×Q8×C1112yes—
308C22×C4C11×#4111yescharacteristic
309C22×C4C11×#4111yescharacteristic
310C22×C4C11×#4112yes—
311C22×C4C11×#4112yes—
312C2×C8—24no—
313C2×C8—24no—
314C2×C8—24no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—48no—
326C4⋊C4—42no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4C11×C4⋊C414yes—
330C42—24no—
331C42—24no—
332C11#1120811yescharacteristic, direct product factor, Sylow
333C23C2×C11×C22⋊C411yescharacteristic
334C23C11×#12011yescharacteristic
335C23C11×#12111yescharacteristic
336C23C11×C22⋊Q811yescharacteristic
337C23C11×#12311yescharacteristic
338C23C11×#12411yescharacteristic
339C23C11×C4⋊Q811yescharacteristic
340C23C11×#13512yes—
341C23C11×#13512yes—
342C23C11×AGL(1,ℤ/8)12yes—
343C23C11×#13712yes—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4C2×C11×C4⋊C411yescharacteristic
372C2×C4C11×#11711yescharacteristic
373C2×C4C4×D4×C1112yes—
374C2×C4C4×Q8×C1112yes—
375C2×C4C11×#12112yes—
376C2×C4C11×#12111yescharacteristic
377C2×C4C11×#12112yes—
378C2×C4C11×C22⋊Q812yes—
379C2×C4C11×C22⋊Q812yes—
380C2×C4C11×C22⋊Q812yes—
381C2×C4C11×C22⋊Q811yescharacteristic
382C2×C4C11×#12312yes—
383C2×C4C11×#12512yes—
384C2×C4C11×#12512yes—
385C2×C4C11×#12612yes—
386C2×C4C11×C4⋊Q812yes—
387C8—44no—
388C22C11×#38011yescharacteristic
389C22C11×#38611yescharacteristic
390C22C11×#39111yescharacteristic
391C22C11×#39411yescharacteristic
392C22C11×#39511yescharacteristic
393C22C11×#39811yescharacteristic
394C22C11×#40011yescharacteristic
395C22C11×#41611yescharacteristic
396C22C11×#41611yescharacteristic
397C22C11×#41811yescharacteristic
398C22C11×#41911yescharacteristic
399C22C11×#44912yes—
400C22C11×#45212yes—
401C22C11×#46312yes—
402C22C11×#46412yes—
403C22C11×#47812yes—
404C22C11×#47912yes—
405C22C11×#48212yes—
406C22C11×#48512yes—
407C22C11×#48812yes—
408C22C11×#48912yes—
409C22C11×#49912yes—
410C22C11×#50112yes—
411C4—42no—
412C4—42no—
413C4—44no—
414C4—82no—
415C4—84no—
416C4C11×#38712yes—
417C4C11×#38912yes—
418C4C11×#39612yes—
419C4C11×#39812yes—
420C2C11×#144111yescharacteristic
421C2C11×#180411yescharacteristic
422C2C11×#180511yescharacteristic
423C2C11×#187311yescharacteristic
424C2C11×#187511yescharacteristic
425C2C11×#199111yescharacteristic
426C2C11×#199311yescharacteristic
427C2C11×#204212yes—
428C2C11×#205912yes—
429C2C11×#208512yes—
430C2C11×#210112yes—
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
13. C11×#389C4semidirect
59. #11208C11direct (N × H)
185. #389C4×C11semidirect
332. C11#11208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3892
C2×C11×#3822
C2×C11×#3402
C2×C11×#3362
#1120811