Finite Group Databasebeta

← C11×#10979 #14588172

Subgroups — C11×#10979 #14588172

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#421C212yesmaximal, complemented
3C2×C11×#410C211yesmaximal, characteristic, complemented
4C11×#2879C211yesmaximal, characteristic, complemented
5C2×C11×#339C212yesmaximal, complemented
6C22×C11×#41C2211yescharacteristic
7C22×C11×#41C2211yescharacteristic
8C22×C11×M16C2212yes—
9C11×#532—24no—
10C11×#532—24no—
11C2×C11×C4⋊Q8C411yescharacteristic, complemented
12C2×C11×#127C411yescharacteristic, complemented
13C2×C11×#124C411yescharacteristic, complemented
14C2×C11×#124C411yescharacteristic, complemented
15C2×C11×#121—22no—
16C2×C4×D4×C11—22no—
17C2×C11×#117C2212yes—
18C22×C42×C11C2211yescharacteristic
19C11×#421—24no—
20C11×#421—24no—
21C2×C11×#104—24no—
22C11×#410—24no—
23C2×C11×#99—22no—
24C11×#408—24no—
25C11×#407—22no—
26C11×#339—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—22no—
37C2×C11×#41—22no—
38C2×C11×#41D414yes—
39C22×Q8×C11C2×C411yescharacteristic
40C22×Q8×C11C2×C411yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11D412yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—22no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16D414yescomplemented
56C22×C8×C11—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×#127—22no—
60C11×#127—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#121—216no—
66C4×D4×C11—216no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117D414yescomplemented
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11C2×C411yescharacteristic
81C2×C42×C11D414yes—
82C11×#104—216no—
83C11×#99—28no—
84C11×C22⋊C8—28no—
85#10979C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11—21no—
87C24×C11C22⋊C412yes—
88C24×C11C2×D411yescharacteristic
89C11×#41—24no—
90C11×#41—24no—
91C11×#41—24no—
92C11×#41—24no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C11×#41—42no—
100C11×#41—42no—
101C11×#41—42no—
102C11×#41—42no—
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C22⋊C412yes—
113C2×D4×C11—28no—
114C2×D4×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—48no—
127C2×D4×C11—41no—
128C2×D4×C11—42no—
129C2×D4×C11—41no—
130C2×D4×C11C22⋊C412yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—44no—
141C22×C4×C11—41no—
142C22×C4×C11—42no—
143C22×C4×C11—41no—
144C22×C4×C11—42no—
145C22×C4×C11C22⋊C412yes—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C11×M16—24no—
155C11×M16—24no—
156C11×M16—42no—
157C11×M16—42no—
158C2×C8×C11—24no—
159C2×C8×C11—42no—
160C2×C8×C11—42no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—42no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—42no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—24no—
171C42×C11—24no—
172C42×C11—42no—
173C42×C11C22⋊C412yes—
174C42×C11C22⋊C412yes—
175C2×#532C2×C1111yescharacteristic
176C2×#421C2×C1112yescomplemented
177C2×#410C2×C1111yescharacteristic, complemented
178#2879C2×C1111yescharacteristic, complemented
179C2×#339C2×C1112yescomplemented
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—44no—
186C23×C11—44no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11C2×C22⋊C411yescharacteristic
190C23×C11#12012yes—
191C23×C11#12011yescharacteristic
192C23×C11#12112yes—
193C23×C11#12311yescharacteristic
194Q8×C11—24no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198D4×C11—24no—
199D4×C11—416no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—44no—
203D4×C11—44no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—84no—
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C22⋊C411yescharacteristic
226C2×C4×C11C4×D412yes—
227C2×C4×C11C4×D412yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#12012yes—
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12112yes—
232C2×C4×C11#12112yes—
233C2×C4×C11#12112yes—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12312yes—
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12412yes—
239C2×C4×C11#12712yes—
240C8×C11—44no—
241C22×#41C22×C1111yescharacteristic
242C22×#41C22×C1111yescharacteristic
243C22×M16C22×C1112yes—
244#532—24no—
245#532—24no—
246C2×C4⋊Q8C4×C1111yescharacteristic, complemented
247C2×#127C4×C1111yescharacteristic, complemented
248C2×#124C4×C1111yescharacteristic, complemented
249C2×#124C4×C1111yescharacteristic, complemented
250C2×#121—22no—
251C2×C4×D4—22no—
252C2×#117C22×C1112yes—
253C22×C42C22×C1111yescharacteristic
254#421—24no—
255#421—24no—
256C2×#104—24no—
257#410—24no—
258C2×#99—22no—
259#408—24no—
260#407—22no—
261#339—24no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—42no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11#37911yescharacteristic
276C22×C11#38611yescharacteristic
277C22×C11#38611yescharacteristic
278C22×C11#39212yes—
279C22×C11#39412yes—
280C4×C11—24no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—84no—
285C4×C11#38612yes—
286C4×C11#39012yes—
287C4×C11#39212yes—
288C4×C11#39412yes—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41D4×C1114yes—
301C22×Q8C2×C4×C1111yescharacteristic
302C22×Q8C2×C4×C1111yescharacteristic
303C22×D4—22no—
304C22×D4—21no—
305C22×D4C2×C4×C1111yescharacteristic
306C22×D4C2×C4×C1111yescharacteristic
307C22×D4D4×C1112yes—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4D4×C1112yes—
311C23×C4C23×C1111yescharacteristic
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16D4×C1114yescomplemented
318C22×C8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321#127—22no—
322#127—22no—
323#124—22no—
324#124—22no—
325#124—22no—
326#124—22no—
327#121—216no—
328C4×D4—216no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117D4×C1114yescomplemented
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C42—21no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42C2×C4×C1111yescharacteristic
342C2×C42C2×C4×C1111yescharacteristic
343C2×C42D4×C1114yes—
344#104—216no—
345#99—28no—
346C22⋊C8—28no—
347C2×C11—21no—
348C2×C11—22no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—82no—
352C2×C11—82no—
353C2×C11#143811yescharacteristic
354C2×C11#188412yes—
355C24—21no—
356C24C11×C22⋊C412yes—
357C24C2×D4×C1111yescharacteristic
358#41—24no—
359#41—24no—
360#41—24no—
361#41—24no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—42no—
373#41—42no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8C11×C22⋊C412yes—
382C2×D4—28no—
383C2×D4—22no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—48no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4C11×C22⋊C412yes—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—42no—
412C22×C4—41no—
413C22×C4—42no—
414C22×C4C11×C22⋊C412yes—
415C22×C4C22×C4×C1111yescharacteristic
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1112yes—
418C22×C4C2×D4×C1112yes—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C11×#4112yes—
422C22×C4C11×#4112yes—
423M16—24no—
424M16—24no—
425M16—42no—
426M16—42no—
427C2×C8—24no—
428C2×C8—42no—
429C2×C8—42no—
430C4⋊C4—28no—
431C4⋊C4—24no—
432C4⋊C4—42no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—24no—
436C22⋊C4—42no—
437C42—21no—
438C42—21no—
439C42—24no—
440C42—24no—
441C42—42no—
442C42C11×C22⋊C412yes—
443C42C11×C22⋊C412yes—
444C11#1097911yescharacteristic, direct product factor, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—42no—
450C23—44no—
451C23—44no—
452C23—41no—
453C23—41no—
454C23C2×C11×C22⋊C411yescharacteristic
455C23C11×#12012yes—
456C23C11×#12011yescharacteristic
457C23C11×#12112yes—
458C23C11×#12311yescharacteristic
459Q8—24no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463D4—24no—
464D4—416no—
465D4—44no—
466D4—44no—
467D4—44no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—48no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—84no—
489C2×C4C2×C11×C22⋊C411yescharacteristic
490C2×C4C2×C11×C22⋊C411yescharacteristic
491C2×C4C4×D4×C1112yes—
492C2×C4C4×D4×C1112yes—
493C2×C4C11×#12012yes—
494C2×C4C11×#12011yescharacteristic
495C2×C4C11×#12012yes—
496C2×C4C11×#12112yes—
497C2×C4C11×#12112yes—
498C2×C4C11×#12112yes—
499C2×C4C11×#12112yes—
500C2×C4C11×#12112yes—
501C2×C4C11×#12312yes—
502C2×C4C11×#12311yescharacteristic
503C2×C4C11×#12412yes—
504C2×C4C11×#12712yes—
505C8—44no—
506C22—22no—
507C22—24no—
508C22—42no—
509C22—41no—
510C22—41no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—42no—
515C22—42no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22C11×#37911yescharacteristic
520C22C11×#38611yescharacteristic
521C22C11×#38611yescharacteristic
522C22C11×#39212yes—
523C22C11×#39412yes—
524C4—24no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—84no—
529C4C11×#38612yes—
530C4C11×#39012yes—
531C4C11×#39212yes—
532C4C11×#39412yes—
533C2—21no—
534C2—22no—
535C2—21no—
536C2—22no—
537C2—82no—
538C2—82no—
539C2C11×#143811yescharacteristic
540C2C11×#188412yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#386
prime radicalC2×C11×#532C2
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
2. C2×C11×#421C2semidirect
3. C2×C11×#410C2semidirect
4. C11×#2879C2semidirect
5. C2×C11×#339C2semidirect
11. C2×C11×C4⋊Q8C4semidirect
12. C2×C11×#127C4semidirect
13. C2×C11×#124C4semidirect
14. C2×C11×#124C4semidirect
55. C2×C11×M16D4semidirect
70. C11×#117D4semidirect
85. #10979C11direct (N × H)
176. C2×#421C2×C11semidirect
177. C2×#410C2×C11semidirect
178. #2879C2×C11semidirect
179. C2×#339C2×C11semidirect
246. C2×C4⋊Q8C4×C11semidirect
247. C2×#127C4×C11semidirect
248. C2×#124C4×C11semidirect
249. C2×#124C4×C11semidirect
317. C2×M16D4×C11semidirect
332. #117D4×C11semidirect
444. C11#10979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4212
C2×C11×#4102
C11×#28792
C2×C11×#3392
#1097911