Finite Group Databasebeta

← C11×#10973 #14588166

Subgroups — C11×#10973 #14588166

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#413C211yesmaximal, characteristic, complemented
3C22×C11×#100C212yesmaximal, complemented
4C11×#2879C211yesmaximal, characteristic, complemented
5C2×C11×#344C212yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C23×D4×C11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C22×C11×M16C2212yes—
10C11×#535—24no—
11C11×#535—24no—
12C2×C11×#127—21no—
13C2×C11×#124—21no—
14C2×C11×#121—22no—
15C2×C11×#120C414yes—
16C2×C11×#117C2211yescharacteristic
17C11×#413—24no—
18C2×C11×#101—21no—
19C2×C11×#100—24no—
20C2×C11×#100—21no—
21C2×C11×#100—24no—
22C2×C11×#100—24no—
23C11×#408—24no—
24C11×#407—22no—
25C11×#344—24no—
26C25×C11C2×C412yes—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11—24no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11D414yes—
45C23×C4×C11D412yes—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16D414yescomplemented
58C2×C11×M16D414yescomplemented
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C11×#127—28no—
62C11×#124—28no—
63C11×#121—216no—
64C11×#120—28no—
65C11×#120—28no—
66C11×#117—22no—
67C11×#117D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4C2×C412yes—
71C2×C42×C11—21no—
72C11×#101—24no—
73C11×#100—216no—
74C11×#100—24no—
75C11×C22⋊C8—28no—
76#10973C1111yesmaximal, characteristic, direct product factor, Sylow
77C24×C11—22no—
78C24×C11—22no—
79C24×C11—24no—
80C24×C11—24no—
81C24×C11—84no—
82C24×C11C22⋊C412yes—
83C24×C11C22⋊C414yes—
84C24×C11C22×C411yescharacteristic
85C11×#41—42no—
86C11×#41—42no—
87C11×#41—42no—
88C11×#41—42no—
89C11×#41—42no—
90C11×#41—42no—
91C11×#41—42no—
92C11×#41—42no—
93C2×Q8×C11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—216no—
102C2×D4×C11—24no—
103C2×D4×C11—21no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—24no—
111C2×D4×C11—21no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—88no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C22⋊C412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C11×M16—24no—
138C11×M16—24no—
139C11×M16—24no—
140C11×M16—24no—
141C11×M16—42no—
142C11×M16—42no—
143C11×M16—42no—
144C11×M16—42no—
145C2×C8×C11—24no—
146C2×C8×C11—24no—
147C2×C8×C11—42no—
148C2×C8×C11—42no—
149C2×C8×C11—42no—
150C2×C8×C11—42no—
151C11×C4⋊C4—24no—
152C11×C22⋊C4—216no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4C22⋊C414yes—
155C42×C11—24no—
156C2×#535C2×C1111yescharacteristic
157C2×#413C2×C1111yescharacteristic, complemented
158C22×#100C2×C1112yescomplemented
159#2879C2×C1111yescharacteristic, complemented
160C2×#344C2×C1112yescomplemented
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—28no—
166C23×C11—42no—
167C23×C11—44no—
168C23×C11—48no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—44no—
172C23×C11—88no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11—88no—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11C2×C22⋊C411yescharacteristic
178C23×C11C2×C22⋊C411yescharacteristic
179C23×C11C4×D412yes—
180C23×C11C4×D412yes—
181Q8×C11—42no—
182Q8×C11—42no—
183D4×C11—44no—
184D4×C11—44no—
185D4×C11—44no—
186D4×C11—44no—
187D4×C11—42no—
188D4×C11—44no—
189D4×C11—44no—
190D4×C11—42no—
191D4×C11—816no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11#12012yes—
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12012yes—
203C2×C4×C11#12012yes—
204C2×C4×C11#12112yes—
205C2×C4×C11#12112yes—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11#12312yes—
211C2×C4×C11#12311yescharacteristic
212C2×C4×C11#12311yescharacteristic
213C2×C4×C11#12412yes—
214C2×C4×C11#12712yes—
215C8×C11—44no—
216C8×C11—44no—
217C22×#41C22×C1111yescharacteristic
218C23×D4C22×C1111yescharacteristic
219C22×M16C22×C1112yes—
220C22×M16C22×C1112yes—
221#535—24no—
222#535—24no—
223C2×#127—21no—
224C2×#124—21no—
225C2×#121—22no—
226C2×#120C4×C1114yes—
227C2×#117C22×C1111yescharacteristic
228#413—24no—
229C2×#101—21no—
230C2×#100—24no—
231C2×#100—21no—
232C2×#100—24no—
233C2×#100—24no—
234#408—24no—
235#407—22no—
236#344—24no—
237C22×C11—22no—
238C22×C11—24no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—42no—
242C22×C11—44no—
243C22×C11—48no—
244C22×C11—44no—
245C22×C11—42no—
246C22×C11—44no—
247C22×C11—82no—
248C22×C11—88no—
249C22×C11—84no—
250C22×C11—88no—
251C22×C11—84no—
252C22×C11#37911yescharacteristic
253C22×C11#38611yescharacteristic
254C22×C11#38612yes—
255C22×C11#38611yescharacteristic
256C22×C11#39012yes—
257C4×C11—44no—
258C4×C11—42no—
259C4×C11#39212yes—
260C4×C11#39212yes—
261C4×C11#39412yes—
262C4×C11#39412yes—
263C25C2×C4×C1112yes—
264C2×#41—22no—
265C2×#41—22no—
266C2×#41—22no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C22×Q8D4×C1111yescharacteristic
271C22×D4—24no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4C2×C4×C1112yes—
280C22×D4D4×C1111yescharacteristic
281C22×D4D4×C1114yes—
282C23×C4D4×C1112yes—
283C23×C4C23×C1111yescharacteristic
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—22no—
287C2×M16—22no—
288C2×M16—22no—
289C2×M16—22no—
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—22no—
294C2×M16D4×C1114yescomplemented
295C2×M16D4×C1114yescomplemented
296C22×C8—22no—
297C22×C8—22no—
298#127—28no—
299#124—28no—
300#121—216no—
301#120—28no—
302#120—28no—
303#117—22no—
304#117D4×C1114yes—
305C2×C4⋊C4—21no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4C2×C4×C1112yes—
308C2×C42—21no—
309#101—24no—
310#100—216no—
311#100—24no—
312C22⋊C8—28no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—82no—
318C2×C11—84no—
319C2×C11#143811yescharacteristic
320C2×C11#191412yes—
321C24—22no—
322C24—22no—
323C24—24no—
324C24—24no—
325C24—84no—
326C24C11×C22⋊C412yes—
327C24C11×C22⋊C414yes—
328C24C22×C4×C1111yescharacteristic
329#41—42no—
330#41—42no—
331#41—42no—
332#41—42no—
333#41—42no—
334#41—42no—
335#41—42no—
336#41—42no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—24no—
344C2×D4—24no—
345C2×D4—216no—
346C2×D4—24no—
347C2×D4—21no—
348C2×D4—24no—
349C2×D4—24no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—24no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—88no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4C11×C22⋊C412yes—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1112yes—
377C22×C4C2×D4×C1112yes—
378C22×C4C2×D4×C1112yes—
379C22×C4C11×#4112yes—
380C22×C4C11×#4112yes—
381M16—24no—
382M16—24no—
383M16—24no—
384M16—24no—
385M16—42no—
386M16—42no—
387M16—42no—
388M16—42no—
389C2×C8—24no—
390C2×C8—24no—
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C4⋊C4—24no—
396C22⋊C4—216no—
397C22⋊C4—22no—
398C22⋊C4C11×C22⋊C414yes—
399C42—24no—
400C11#1097311yescharacteristic, direct product factor, Sylow
401C23—24no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—28no—
406C23—42no—
407C23—44no—
408C23—48no—
409C23—42no—
410C23—42no—
411C23—44no—
412C23—88no—
413C23—84no—
414C23—84no—
415C23—88no—
416C23C2×C11×C22⋊C411yescharacteristic
417C23C2×C11×C22⋊C411yescharacteristic
418C23C2×C11×C22⋊C411yescharacteristic
419C23C4×D4×C1112yes—
420C23C4×D4×C1112yes—
421Q8—42no—
422Q8—42no—
423D4—44no—
424D4—44no—
425D4—44no—
426D4—44no—
427D4—42no—
428D4—44no—
429D4—44no—
430D4—42no—
431D4—816no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4C11×#12011yescharacteristic
440C2×C4C11×#12012yes—
441C2×C4C11×#12011yescharacteristic
442C2×C4C11×#12012yes—
443C2×C4C11×#12012yes—
444C2×C4C11×#12112yes—
445C2×C4C11×#12112yes—
446C2×C4C11×#12112yes—
447C2×C4C11×#12112yes—
448C2×C4C11×#12112yes—
449C2×C4C11×#12112yes—
450C2×C4C11×#12311yescharacteristic
451C2×C4C11×#12312yes—
452C2×C4C11×#12311yescharacteristic
453C2×C4C11×#12412yes—
454C2×C4C11×#12712yes—
455C8—44no—
456C8—44no—
457C22—22no—
458C22—24no—
459C22—41no—
460C22—41no—
461C22—42no—
462C22—44no—
463C22—48no—
464C22—44no—
465C22—42no—
466C22—44no—
467C22—82no—
468C22—88no—
469C22—84no—
470C22—88no—
471C22—84no—
472C22C11×#37911yescharacteristic
473C22C11×#38611yescharacteristic
474C22C11×#38612yes—
475C22C11×#38611yescharacteristic
476C22C11×#39012yes—
477C4—44no—
478C4—42no—
479C4C11×#39212yes—
480C4C11×#39212yes—
481C4C11×#39412yes—
482C4C11×#39412yes—
483C2—21no—
484C2—21no—
485C2—22no—
486C2—22no—
487C2—82no—
488C2—84no—
489C2C11×#143811yescharacteristic
490C2C11×#191412yes—
subgroupG/H
center, socleC22×C11#386
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC2×C11×#535C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#413C2semidirect
3. C22×C11×#100C2semidirect
4. C11×#2879C2semidirect
5. C2×C11×#344C2semidirect
57. C2×C11×M16D4semidirect
58. C2×C11×M16D4semidirect
76. #10973C11direct (N × H)
157. C2×#413C2×C11semidirect
158. C22×#100C2×C11semidirect
159. #2879C2×C11semidirect
160. C2×#344C2×C11semidirect
294. C2×M16D4×C11semidirect
295. C2×M16D4×C11semidirect
400. C11#10973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4132
C22×C11×#1002
C11×#28792
C2×C11×#3442
#1097311