Finite Group Databasebeta

← C11×#11071 #14588264

Subgroups — C11×#11071 #14588264

Order 2816.

1018 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
1C11×#2905C211yesmaximal, characteristic, complemented
2C2×C11×#407C212yesmaximal
3C11×#2280C211yesmaximal, characteristic
4C2×C11×#344C212yesmaximal, complemented
5C11×#1742C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C22×C11×M16C2212yes—
8C22×C11×M16C2212yes—
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C11×#424—24no—
12C11×#423—22no—
13C11×#407—24no—
14C11×#407—24no—
15C2×C11×C22⋊C8—24no—
16C11×#381C412yes—
17C11×#380—22no—
18C11×#379C412yes—
19C4×C11×C22⋊C4—22no—
20C11×#344—24no—
21C11×#343—22no—
22C25×C11C2×C411yescharacteristic
23C23×C4×C11—21no—
24C23×C4×C11—21no—
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—21no—
28C23×C4×C11—21no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11D412yes—
33C23×C4×C11Q812yes—
34C23×C4×C11C2311yescharacteristic
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16—22no—
39C2×C11×M16—22no—
40C2×C11×M16—22no—
41C2×C11×M16—22no—
42C2×C11×M16—22no—
43C2×C11×M16—22no—
44C2×C11×M16—22no—
45C2×C11×M16—22no—
46C2×C11×M16D414yes—
47C22×C8×C11—22no—
48C22×C8×C11D414yes—
49C11×#117—22no—
50C11×#117—22no—
51C11×#117—22no—
52C11×#117—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C42×C11—21no—
59C2×C42×C11D412yes—
60C11×C4⋊C8—28no—
61C11×C22⋊C8—216no—
62C11×#95—24no—
63#11071C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11—22no—
66C24×C11—21no—
67C24×C11—22no—
68C24×C11—44no—
69C24×C11C4⋊C412yes—
70C24×C11C22×C411yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—24no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—24no—
83C22×C4×C11—22no—
84C22×C4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—41no—
94C22×C4×C11C22⋊C414yes—
95C22×C4×C11C4⋊C412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4112yes—
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4112yes—
106C11×M16—24no—
107C11×M16—24no—
108C11×M16—42no—
109C11×M16—42no—
110C11×M16—42no—
111C11×M16—42no—
112C11×M16—42no—
113C11×M16—42no—
114C2×C8×C11—24no—
115C2×C8×C11—24no—
116C2×C8×C11—24no—
117C2×C8×C11—24no—
118C2×C8×C11—42no—
119C2×C8×C11—42no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—42no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—48no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—41no—
128C42×C11—41no—
129#2905C2×C1111yescharacteristic, complemented
130C2×#407C2×C1112yes—
131#2280C2×C1111yescharacteristic
132C2×#344C2×C1112yescomplemented
133#1742C2×C1111yescharacteristic, complemented
134C23×C11—24no—
135C23×C11—28no—
136C23×C11—22no—
137C23×C11—24no—
138C23×C11—44no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—48no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11C2×C4⋊C411yescharacteristic
149C23×C11#11711yescharacteristic
150C23×C11C4×D412yes—
151C23×C11C4×D412yes—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—42no—
167C2×C4×C11#12012yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12112yes—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12112yes—
173C2×C4×C11#12112yes—
174C2×C4×C11C22⋊Q812yes—
175C2×C4×C11C22⋊Q811yescharacteristic
176C2×C4×C11C22⋊Q811yescharacteristic
177C2×C4×C11C22⋊Q812yes—
178C2×C4×C11#12312yes—
179C2×C4×C11#12312yes—
180C2×C4×C11#12311yescharacteristic
181C2×C4×C11#12412yes—
182C2×C4×C11#12411yescharacteristic
183C2×C4×C11#12612yes—
184C2×C4×C11#12711yescharacteristic
185C8×C11—44no—
186C8×C11—44no—
187C24×C4C22×C1111yescharacteristic
188C22×M16C22×C1112yes—
189C22×M16C22×C1112yes—
190C2×#117C22×C1111yescharacteristic
191C2×#117C22×C1111yescharacteristic
192#424—24no—
193#423—22no—
194#407—24no—
195#407—24no—
196C2×C22⋊C8—24no—
197#381C4×C1112yes—
198#380—22no—
199#379C4×C1112yes—
200C4×C22⋊C4—22no—
201#344—24no—
202#343—22no—
203C22×C11—22no—
204C22×C11—24no—
205C22×C11—24no—
206C22×C11—28no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—42no—
210C22×C11—44no—
211C22×C11—42no—
212C22×C11—44no—
213C22×C11—48no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11#38011yescharacteristic
217C22×C11#38512yes—
218C22×C11#38611yescharacteristic
219C22×C11#38812yes—
220C22×C11#39011yescharacteristic
221C4×C11—44no—
222C4×C11—42no—
223C4×C11—82no—
224C4×C11#39211yescharacteristic
225C4×C11#39311yescharacteristic
226C4×C11#39412yes—
227C4×C11#39612yes—
228C4×C11#39711yescharacteristic
229C4×C11#39911yescharacteristic
230C25C2×C4×C1111yescharacteristic
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4C2×C4×C1111yescharacteristic
240C23×C4D4×C1112yes—
241C23×C4Q8×C1112yes—
242C23×C4C23×C1111yescharacteristic
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16D4×C1114yes—
255C22×C8—22no—
256C22×C8D4×C1114yes—
257#117—22no—
258#117—22no—
259#117—22no—
260#117—22no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4D4×C1112yes—
263C2×C22⋊C4—24no—
264C2×C22⋊C4C2×C4×C1112yes—
265C2×C22⋊C4C2×C4×C1112yes—
266C2×C42—21no—
267C2×C42D4×C1112yes—
268C4⋊C8—28no—
269C22⋊C8—216no—
270#95—24no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—22no—
274C2×C11—22no—
275C2×C11—44no—
276C2×C11#143911yescharacteristic
277C2×C11#189112yes—
278C24—21no—
279C24—22no—
280C24—21no—
281C24—22no—
282C24—44no—
283C24C11×C4⋊C412yes—
284C24C22×C4×C1111yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4C11×C22⋊C414yes—
309C22×C4C11×C4⋊C412yes—
310C22×C4C2×D4×C1112yes—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1112yes—
313C22×C4C2×D4×C1111yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×Q8×C1111yescharacteristic
316C22×C4C11×#4111yescharacteristic
317C22×C4C11×#4112yes—
318C22×C4C11×#4111yescharacteristic
319C22×C4C11×#4112yes—
320M16—24no—
321M16—24no—
322M16—42no—
323M16—42no—
324M16—42no—
325M16—42no—
326M16—42no—
327M16—42no—
328C2×C8—24no—
329C2×C8—24no—
330C2×C8—24no—
331C2×C8—24no—
332C2×C8—42no—
333C2×C8—42no—
334C4⋊C4—24no—
335C4⋊C4—42no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—48no—
339C42—22no—
340C42—22no—
341C42—41no—
342C42—41no—
343C11#1107111yescharacteristic, direct product factor, Sylow
344C23—24no—
345C23—28no—
346C23—22no—
347C23—24no—
348C23—44no—
349C23—42no—
350C23—42no—
351C23—44no—
352C23—44no—
353C23—48no—
354C23—41no—
355C23—42no—
356C23—41no—
357C23C2×C11×C22⋊C411yescharacteristic
358C23C2×C11×C4⋊C411yescharacteristic
359C23C11×#11711yescharacteristic
360C23C4×D4×C1112yes—
361C23C4×D4×C1112yes—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4C11×#12011yescharacteristic
378C2×C4C11×#12012yes—
379C2×C4C11×#12112yes—
380C2×C4C11×#12111yescharacteristic
381C2×C4C11×#12111yescharacteristic
382C2×C4C11×#12112yes—
383C2×C4C11×#12112yes—
384C2×C4C11×C22⋊Q812yes—
385C2×C4C11×C22⋊Q811yescharacteristic
386C2×C4C11×C22⋊Q811yescharacteristic
387C2×C4C11×C22⋊Q812yes—
388C2×C4C11×#12312yes—
389C2×C4C11×#12312yes—
390C2×C4C11×#12311yescharacteristic
391C2×C4C11×#12412yes—
392C2×C4C11×#12411yescharacteristic
393C2×C4C11×#12612yes—
394C2×C4C11×#12711yescharacteristic
395C8—44no—
396C8—44no—
397C22—22no—
398C22—24no—
399C22—24no—
400C22—28no—
401C22—41no—
402C22—41no—
403C22—42no—
404C22—44no—
405C22—42no—
406C22—44no—
407C22—48no—
408C22—44no—
409C22—42no—
410C22C11×#38011yescharacteristic
411C22C11×#38512yes—
412C22C11×#38611yescharacteristic
413C22C11×#38812yes—
414C22C11×#39011yescharacteristic
415C4—44no—
416C4—42no—
417C4—82no—
418C4C11×#39211yescharacteristic
419C4C11×#39311yescharacteristic
420C4C11×#39412yes—
421C4C11×#39612yes—
422C4C11×#39711yescharacteristic
423C4C11×#39911yescharacteristic
424C2—21no—
425C2—21no—
426C2—22no—
427C2—22no—
428C2—44no—
429C2C11×#143911yescharacteristic
430C2C11×#189112yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#386
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ 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×#2905C2semidirect
4. C2×C11×#344C2semidirect
5. C11×#1742C2semidirect
63. #11071C11direct (N × H)
129. #2905C2×C11semidirect
132. C2×#344C2×C11semidirect
133. #1742C2×C11semidirect
343. C11#11071direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29052
C2×C11×#4072
C11×#22802
C2×C11×#3442
C11×#17422
#1107111