Finite Group Databasebeta

← C11×#11287 #14588480

Subgroups — C11×#11287 #14588480

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2315C211yesmaximal, characteristic
2C2×C11×#342C212yesmaximal
3C2×C11×#342C211yesmaximal, characteristic
4C11×C22⋊#95C212yesmaximal
5C11×C22⋊#95C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C22×C11×C22⋊C4C2212yes—
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C11×#385—24no—
12C11×#380—22no—
13C2×C11×#95—24no—
14C2×C11×#95—22no—
15C11×#342—24no—
16C11×#342C414yescomplemented
17C25×C11C2311yescharacteristic
18C23×C4×C11—21no—
19C23×C4×C11—22no—
20C23×C4×C11—22no—
21C23×C4×C11—21no—
22C23×C4×C11—22no—
23C23×C4×C11—21no—
24C23×C4×C11—44no—
25C23×C4×C11D414yes—
26C23×C4×C11D412yes—
27C23×C4×C11Q812yes—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4C2×C414yes—
47C2×C11×C22⋊C4C2×C412yes—
48C2×C11×C22⋊C4D412yes—
49C2×C11×C22⋊C4Q812yes—
50C11×#95—24no—
51C11×#95—44no—
52C11×#95—48no—
53#11287C1111yesmaximal, characteristic, direct product factor, Sylow
54C24×C11—42no—
55C24×C11—42no—
56C24×C11C22×C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C24×C11C2×D412yes—
59C24×C11C2×D411yescharacteristic
60C24×C11C2×Q811yescharacteristic
61C24×C11C2×Q811yescharacteristic
62C24×C11#4112yes—
63C24×C11#4112yes—
64C24×C11#4112yes—
65C24×C11#4111yescharacteristic
66C24×C11#4111yescharacteristic
67C22×C4×C11—24no—
68C22×C4×C11—28no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—22no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—44no—
79C22×C4×C11—48no—
80C22×C4×C11—44no—
81C22×C4×C11—42no—
82C22×C4×C11—44no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—44no—
88C22×C4×C11—42no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11—42no—
92C22×C4×C11—44no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C4⋊C414yes—
99C11×C4⋊C4—82no—
100C11×C4⋊C4—82no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113#2315C2×C1111yescharacteristic
114C2×#342C2×C1112yes—
115C2×#342C2×C1111yescharacteristic
116C22⋊#95C2×C1112yes—
117C22⋊#95C2×C1111yescharacteristic
118C23×C11—22no—
119C23×C11—24no—
120C23×C11—22no—
121C23×C11—24no—
122C23×C11—41no—
123C23×C11—42no—
124C23×C11—41no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—44no—
130C23×C11—42no—
131C23×C11—41no—
132C23×C11—42no—
133C23×C11—44no—
134C23×C11C2×C4⋊C411yescharacteristic
135C23×C11#11712yes—
136C23×C11C4×D412yes—
137C23×C11C4×D411yescharacteristic
138C23×C11C4×Q811yescharacteristic
139C23×C11#12011yescharacteristic
140C23×C11#12112yes—
141C23×C11#12111yescharacteristic
142C23×C11C22⋊Q812yes—
143C23×C11C22⋊Q812yes—
144C23×C11C22⋊Q811yescharacteristic
145C23×C11#12311yescharacteristic
146C23×C11#12312yes—
147C23×C11#12312yes—
148C23×C11#12411yescharacteristic
149C23×C11#12411yescharacteristic
150C23×C11#12412yes—
151C23×C11#12512yes—
152C23×C11#12512yes—
153C23×C11#12511yescharacteristic
154C23×C11#12612yes—
155C23×C11#12612yes—
156C23×C11C4⋊Q811yescharacteristic
157C2×C4×C11—28no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—48no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—44no—
167C2×C4×C11—42no—
168C2×C4×C11—44no—
169C2×C4×C11—48no—
170C2×C4×C11—44no—
171C2×C4×C11—48no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11—82no—
182C2×C4×C11—81no—
183C2×C4×C11—84no—
184C2×C4×C11—84no—
185C24×C4C22×C1111yescharacteristic
186C22×C22⋊C4C22×C1112yes—
187C22×C22⋊C4C22×C1112yes—
188C22×C22⋊C4C22×C1111yescharacteristic
189C22×C22⋊C4C22×C1111yescharacteristic
190#385—24no—
191#380—22no—
192C2×#95—24no—
193C2×#95—22no—
194#342—24no—
195#342C4×C1114yescomplemented
196C22×C11—22no—
197C22×C11—24no—
198C22×C11—22no—
199C22×C11—24no—
200C22×C11—22no—
201C22×C11—21no—
202C22×C11—22no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—21no—
206C22×C11—22no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—24no—
210C22×C11—24no—
211C22×C11—22no—
212C22×C11—42no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—41no—
222C22×C11#38211yescharacteristic
223C22×C11#38511yescharacteristic
224C22×C11#38712yes—
225C22×C11#38812yes—
226C22×C11#38911yescharacteristic
227C22×C11#39311yescharacteristic
228C22×C11#39411yescharacteristic
229C22×C11#39711yescharacteristic
230C22×C11#39812yes—
231C22×C11#40012yes—
232C22×C11#40011yescharacteristic
233C22×C11B(4,𝔽2)12yes—
234C22×C11#45812yes—
235C4×C11—44no—
236C4×C11—44no—
237C4×C11—84no—
238C4×C11—82no—
239C4×C11—84no—
240C25C23×C1111yescharacteristic
241C23×C4—21no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—21no—
245C23×C4—22no—
246C23×C4—21no—
247C23×C4—44no—
248C23×C4D4×C1114yes—
249C23×C4D4×C1112yes—
250C23×C4Q8×C1112yes—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4C2×C4×C1114yes—
270C2×C22⋊C4C2×C4×C1112yes—
271C2×C22⋊C4D4×C1112yes—
272C2×C22⋊C4Q8×C1112yes—
273#95—24no—
274#95—44no—
275#95—48no—
276C2×C11—22no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—22no—
280C2×C11—21no—
281C2×C11—22no—
282C2×C11—21no—
283C2×C11—22no—
284C2×C11#144211yescharacteristic
285C2×C11#186712yes—
286C2×C11#202911yescharacteristic
287C2×C11#203011yescharacteristic
288C2×C11#204412yes—
289C24—42no—
290C24—42no—
291C24C22×C4×C1111yescharacteristic
292C24C2×D4×C1111yescharacteristic
293C24C2×D4×C1112yes—
294C24C2×D4×C1111yescharacteristic
295C24C2×Q8×C1111yescharacteristic
296C24C2×Q8×C1111yescharacteristic
297C24C11×#4112yes—
298C24C11×#4112yes—
299C24C11×#4112yes—
300C24C11×#4111yescharacteristic
301C24C11×#4111yescharacteristic
302C22×C4—24no—
303C22×C4—28no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—44no—
314C22×C4—48no—
315C22×C4—44no—
316C22×C4—42no—
317C22×C4—44no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—44no—
323C22×C4—42no—
324C22×C4—44no—
325C22×C4—44no—
326C22×C4—42no—
327C22×C4—44no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4C11×C4⋊C414yes—
334C4⋊C4—82no—
335C4⋊C4—82no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C11#1128711yescharacteristic, direct product factor, Sylow
349C23—22no—
350C23—24no—
351C23—22no—
352C23—24no—
353C23—41no—
354C23—42no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—41no—
360C23—44no—
361C23—42no—
362C23—41no—
363C23—42no—
364C23—44no—
365C23C2×C11×C4⋊C411yescharacteristic
366C23C11×#11712yes—
367C23C4×D4×C1112yes—
368C23C4×D4×C1111yescharacteristic
369C23C4×Q8×C1111yescharacteristic
370C23C11×#12011yescharacteristic
371C23C11×#12112yes—
372C23C11×#12111yescharacteristic
373C23C11×C22⋊Q812yes—
374C23C11×C22⋊Q812yes—
375C23C11×C22⋊Q811yescharacteristic
376C23C11×#12311yescharacteristic
377C23C11×#12312yes—
378C23C11×#12312yes—
379C23C11×#12411yescharacteristic
380C23C11×#12411yescharacteristic
381C23C11×#12412yes—
382C23C11×#12512yes—
383C23C11×#12512yes—
384C23C11×#12511yescharacteristic
385C23C11×#12612yes—
386C23C11×#12612yes—
387C23C11×C4⋊Q811yescharacteristic
388C2×C4—28no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—48no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—48no—
401C2×C4—44no—
402C2×C4—48no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4—82no—
413C2×C4—81no—
414C2×C4—84no—
415C2×C4—84no—
416C22—22no—
417C22—24no—
418C22—22no—
419C22—24no—
420C22—22no—
421C22—21no—
422C22—22no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—21no—
428C22—22no—
429C22—24no—
430C22—24no—
431C22—22no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—41no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22C11×#38211yescharacteristic
443C22C11×#38511yescharacteristic
444C22C11×#38712yes—
445C22C11×#38812yes—
446C22C11×#38911yescharacteristic
447C22C11×#39311yescharacteristic
448C22C11×#39411yescharacteristic
449C22C11×#39711yescharacteristic
450C22C11×#39812yes—
451C22C11×#40012yes—
452C22C11×#40011yescharacteristic
453C22C11×B(4,𝔽2)12yes—
454C22C11×#45812yes—
455C4—44no—
456C4—44no—
457C4—84no—
458C4—82no—
459C4—84no—
460C2—22no—
461C2—21no—
462C2—21no—
463C2—22no—
464C2—21no—
465C2—22no—
466C2—21no—
467C2—22no—
468C2C11×#144211yescharacteristic
469C2C11×#186712yes—
470C2C11×#202911yescharacteristic
471C2C11×#203011yescharacteristic
472C2C11×#204412yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
16. C11×#342C4semidirect
53. #11287C11direct (N × H)
195. #342C4×C11semidirect
348. C11#11287direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C2×C11×#3422
C11×C22⋊#952
#1128711