Finite Group Databasebeta

← C11×#23484 #14600677

Subgroups — C11×#23484 #14600677

Order 2816.

1418 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#428C211yesmaximal, characteristic, complemented
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C22×C11×#103C211yesmaximal, characteristic, complemented
5C2×C11×#408C211yesmaximal, characteristic
6C11×#2311C211yesmaximal, characteristic
7C11×#2036C214yesmaximal, complemented
8C11×#2035C214yesmaximal, complemented
9C11×#1735C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536—24no—
16C2×C11×C4⋊Q8—21no—
17C2×C11×#124—21no—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#428—24no—
25C2×C11×#107C2212yes—
26C2×C11×#106C2212yes—
27C11×#419—24no—
28C2×C11×#103—24no—
29C2×C11×#103C2214yes—
30C2×C11×#103C2214yes—
31C11×#408—24no—
32C2×C11×C22⋊C8C2214yes—
33C11×#391—21no—
34C11×#390—21no—
35C11×#386—22no—
36C11×#380C2214yes—
37C11×#340C2212yes—
38C11×#340C2212yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C22×Q8×C11—21no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11D414yes—
52C22×Q8×C11D411yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11D412yes—
55C22×D4×C11D411yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C2×C11×M16—22no—
61C2×C11×M16—22no—
62C2×C11×M16D414yes—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—28no—
69C11×#124—28no—
70C11×#123—216no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117—22no—
78C11×#117D414yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—24no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#107—24no—
96C11×#106—24no—
97C11×#103—28no—
98C11×#103—28no—
99C11×C22⋊C8—28no—
100C11×#95—24no—
101#23484C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C2×D412yes—
103C24×C11C2×D411yescharacteristic
104C11×#41—44no—
105C11×#41—44no—
106C11×#41—44no—
107C11×#41—44no—
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—28no—
114C2×Q8×C11—28no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—42no—
120C2×Q8×C11—44no—
121C2×Q8×C11—42no—
122C2×Q8×C11—44no—
123C2×Q8×C11C2×D414yes—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—24no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—82no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C11×M16—28no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—44no—
162C2×C8×C11C2×D414yes—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—84no—
179C42×C11—24no—
180C42×C11—42no—
181C2×#536C2×C1111yescharacteristic
182C2×#428C2×C1111yescharacteristic, complemented
183C2×#419C2×C1111yescharacteristic, complemented
184C22×#103C2×C1111yescharacteristic, complemented
185C2×#408C2×C1111yescharacteristic
186#2311C2×C1111yescharacteristic
187#2036C2×C1114yescomplemented
188#2035C2×C1114yescomplemented
189#1735C2×C1111yescharacteristic, complemented
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11#12012yes—
198C23×C11#12112yes—
199C23×C11#12312yes—
200C23×C11C22×D411yescharacteristic
201Q8×C11—24no—
202Q8×C11—24no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—48no—
206Q8×C11—44no—
207D4×C11—48no—
208D4×C11—44no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—48no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—84no—
230C2×C4×C11#12012yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12114yes—
233C2×C4×C11#12112yes—
234C2×C4×C11#12314yes—
235C2×C4×C11#12312yes—
236C2×C4×C11#12414yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C8×C11—24no—
244C8×C11—42no—
245C22×#41C22×C1111yescharacteristic
246C23×Q8C22×C1111yescharacteristic
247C22×M16C22×C1111yescharacteristic
248C23×C8C22×C1111yescharacteristic
249#536—24no—
250#536—24no—
251C2×C4⋊Q8—21no—
252C2×#124—21no—
253C2×#123—22no—
254C2×C22⋊Q8C22×C1112yes—
255C2×C22⋊Q8C22×C1112yes—
256C2×#117C22×C1111yescharacteristic
257C2×#117C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1111yescharacteristic
259#428—24no—
260C2×#107C22×C1112yes—
261C2×#106C22×C1112yes—
262#419—24no—
263C2×#103—24no—
264C2×#103C22×C1114yes—
265C2×#103C22×C1114yes—
266#408—24no—
267C2×C22⋊C8C22×C1114yes—
268#391—21no—
269#390—21no—
270#386—22no—
271#380C22×C1114yes—
272#340C22×C1112yes—
273#340C22×C1112yes—
274C22×C11—24no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—24no—
278C22×C11—44no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11#39414yes—
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11C2×#12311yescharacteristic
287C22×C11#57712yes—
288C22×C11#57812yes—
289C4×C11—42no—
290C4×C11—44no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11—82no—
295C4×C11#39414yes—
296C4×C11C2×#12111yescharacteristic
297C4×C11C2×#12111yescharacteristic
298C4×C11C2×#12311yescharacteristic
299C4×C11C2×#12411yescharacteristic
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C22×Q8—21no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8D4×C1114yes—
313C22×Q8D4×C1111yescharacteristic
314C22×Q8C23×C1112yes—
315C22×D4D4×C1112yes—
316C22×D4D4×C1111yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C23×C4C23×C1112yes—
320C23×C4C23×C1111yescharacteristic
321C2×M16—22no—
322C2×M16—22no—
323C2×M16D4×C1114yes—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8C23×C1112yes—
328C22×C8C23×C1112yes—
329C4⋊Q8—28no—
330#124—28no—
331#123—216no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117D4×C1114yes—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1112yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—24no—
354C2×C42—21no—
355C2×C42—21no—
356#107—24no—
357#106—24no—
358#103—28no—
359#103—28no—
360C22⋊C8—28no—
361#95—24no—
362C2×C11—24no—
363C2×C11—82no—
364C2×C11C2×#39411yescharacteristic
365C2×C11#301011yescharacteristic
366C2×C11#301111yescharacteristic
367C2×C11#306312yes—
368C2×C11#309712yes—
369C24C2×D4×C1112yes—
370C24C2×D4×C1111yescharacteristic
371#41—44no—
372#41—44no—
373#41—44no—
374#41—44no—
375C2×Q8—24no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—28no—
381C2×Q8—28no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—42no—
387C2×Q8—44no—
388C2×Q8—42no—
389C2×Q8—44no—
390C2×Q8C2×D4×C1114yes—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C22×C4—24no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—82no—
413C22×C4C2×D4×C1112yes—
414C22×C4C2×D4×C1111yescharacteristic
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1112yes—
418C22×C4C11×#4112yes—
419C22×C4C11×#4112yes—
420C22×C4C11×#4112yes—
421C22×C4C24×C1111yescharacteristic
422M16—28no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—44no—
429C2×C8C2×D4×C1114yes—
430C4⋊C4—28no—
431C4⋊C4—28no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C4⋊C4C2×D4×C1112yes—
440C4⋊C4C2×D4×C1112yes—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—24no—
444C22⋊C4—42no—
445C22⋊C4—84no—
446C42—24no—
447C42—42no—
448C11#2348411yescharacteristic, direct product factor, Sylow
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—24no—
455C23—24no—
456C23C11×#12012yes—
457C23C11×#12112yes—
458C23C11×#12312yes—
459C23C22×D4×C1111yescharacteristic
460Q8—24no—
461Q8—24no—
462Q8—42no—
463Q8—42no—
464Q8—48no—
465Q8—44no—
466D4—48no—
467D4—44no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—48no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4C11×#12012yes—
490C2×C4C11×#12114yes—
491C2×C4C11×#12114yes—
492C2×C4C11×#12112yes—
493C2×C4C11×#12314yes—
494C2×C4C11×#12312yes—
495C2×C4C11×#12414yes—
496C2×C4C22×D4×C1111yescharacteristic
497C2×C4C22×D4×C1111yescharacteristic
498C2×C4C22×D4×C1111yescharacteristic
499C2×C4C2×C11×#4111yescharacteristic
500C2×C4C2×C11×#4111yescharacteristic
501C2×C4C2×C11×#4111yescharacteristic
502C8—24no—
503C8—42no—
504C22—22no—
505C22—22no—
506C22—24no—
507C22—24no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—44no—
512C22—44no—
513C22C11×#39414yes—
514C22C2×C11×#12011yescharacteristic
515C22C2×C11×#12111yescharacteristic
516C22C2×C11×#12311yescharacteristic
517C22C11×#57712yes—
518C22C11×#57812yes—
519C4—42no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—82no—
524C4—82no—
525C4C11×#39414yes—
526C4C2×C11×#12111yescharacteristic
527C4C2×C11×#12111yescharacteristic
528C4C2×C11×#12311yescharacteristic
529C4C2×C11×#12411yescharacteristic
530C2—24no—
531C2—82no—
532C2C2×C11×#39411yescharacteristic
533C2C11×#301011yescharacteristic
534C2C11×#301111yescharacteristic
535C2C11×#306312yes—
536C2C11×#309712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#428C2semidirect
3. C2×C11×#419C2semidirect
4. C22×C11×#103C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1735C2semidirect
101. #23484C11direct (N × H)
182. C2×#428C2×C11semidirect
183. C2×#419C2×C11semidirect
184. C22×#103C2×C11semidirect
187. #2036C2×C11semidirect
188. #2035C2×C11semidirect
189. #1735C2×C11semidirect
448. C11#23484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4282
C2×C11×#4192
C22×C11×#1032
C2×C11×#4082
C11×#23112
C11×#20362
C11×#20352
C11×#17352
#2348411