Finite Group Databasebeta

← C11×#23487 #14600680

Subgroups — C11×#23487 #14600680

Order 2816.

1418 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#427C211yesmaximal, 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×#1736C211yesmaximal, 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⋊Q8C2214yes—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#427—24no—
24C2×C11×#107C2212yes—
25C2×C11×#106C2212yes—
26C11×#419—24no—
27C2×C11×#103—24no—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2214yes—
31C11×#408—24no—
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C11×#391—21no—
35C11×#390—21no—
36C11×#386—22no—
37C11×#380C2214yes—
38C11×#340C2214yes—
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×M16—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11D414yes—
66C22×C8×C11C2312yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—28no—
70C11×#124—28no—
71C11×#123—216no—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—28no—
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—22no—
77C11×#117D414yes—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C11×#107—24no—
92C11×#106—24no—
93C11×#103—28no—
94C11×#103—24no—
95C11×#103—24no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—24no—
98C11×#95—24no—
99#23487C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D412yes—
101C24×C11C2×D411yescharacteristic
102C11×#41—44no—
103C11×#41—44no—
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—44no—
119C2×Q8×C11—42no—
120C2×Q8×C11—44no—
121C2×Q8×C11C2×D414yes—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
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—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C11×M16—44no—
153C2×C8×C11—28no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—22no—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D412yes—
163C11×C4⋊C4—216no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D414yes—
171C11×C22⋊C4—216no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—84no—
175C42×C11—24no—
176C42×C11—42no—
177C2×#536C2×C1111yescharacteristic
178C2×#427C2×C1111yescharacteristic, complemented
179C2×#419C2×C1111yescharacteristic, complemented
180C22×#103C2×C1111yescharacteristic, complemented
181C2×#408C2×C1111yescharacteristic
182#2311C2×C1111yescharacteristic
183#2036C2×C1114yescomplemented
184#2035C2×C1114yescomplemented
185#1736C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11#12012yes—
194C23×C11#12112yes—
195C23×C11#12312yes—
196C23×C11C22×D411yescharacteristic
197Q8×C11—24no—
198Q8×C11—24no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—48no—
202Q8×C11—44no—
203D4×C11—48no—
204D4×C11—44no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12114yes—
227C2×C4×C11#12114yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12312yes—
231C2×C4×C11#12414yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C8×C11—22no—
239C8×C11—22no—
240C8×C11—42no—
241C22×#41C22×C1111yescharacteristic
242C23×Q8C22×C1111yescharacteristic
243C22×M16C22×C1111yescharacteristic
244C23×C8C22×C1111yescharacteristic
245#536—24no—
246#536—24no—
247C2×C4⋊Q8—21no—
248C2×#124—21no—
249C2×#123—22no—
250C2×C22⋊Q8C22×C1114yes—
251C2×#117C22×C1111yescharacteristic
252C2×#117C22×C1111yescharacteristic
253C22×C4⋊C4C22×C1111yescharacteristic
254#427—24no—
255C2×#107C22×C1112yes—
256C2×#106C22×C1112yes—
257#419—24no—
258C2×#103—24no—
259C2×#103C22×C1112yes—
260C2×#103C22×C1112yes—
261C2×#103C22×C1114yes—
262#408—24no—
263C2×C22⋊C8C22×C1112yes—
264C2×C22⋊C8C22×C1112yes—
265#391—21no—
266#390—21no—
267#386—22no—
268#380C22×C1114yes—
269#340C22×C1114yes—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—44no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11#39414yes—
280C22×C11C2×#12011yescharacteristic
281C22×C11C2×#12111yescharacteristic
282C22×C11C2×#12311yescharacteristic
283C22×C11#57712yes—
284C22×C11#57812yes—
285C4×C11—42no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11—82no—
289C4×C11—82no—
290C4×C11#39414yes—
291C4×C11C2×#12111yescharacteristic
292C4×C11C2×#12111yescharacteristic
293C4×C11C2×#12311yescharacteristic
294C4×C11C2×#12411yescharacteristic
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C22×Q8—21no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8—22no—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8D4×C1114yes—
308C22×Q8D4×C1111yescharacteristic
309C22×Q8C23×C1112yes—
310C22×D4D4×C1112yes—
311C22×D4D4×C1111yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C23×C1112yes—
315C23×C4C23×C1111yescharacteristic
316C2×M16—22no—
317C2×M16—22no—
318C2×M16—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8D4×C1114yes—
322C22×C8C23×C1112yes—
323C22×C8C23×C1111yescharacteristic
324C22×C8C23×C1111yescharacteristic
325C4⋊Q8—28no—
326#124—28no—
327#123—216no—
328C22⋊Q8—28no—
329C22⋊Q8—28no—
330#117—22no—
331#117—22no—
332#117—22no—
333#117D4×C1114yes—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C23×C1112yes—
339C2×C4⋊C4C23×C1112yes—
340C2×C4⋊C4C23×C1112yes—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—24no—
345C2×C42—21no—
346C2×C42—21no—
347#107—24no—
348#106—24no—
349#103—28no—
350#103—24no—
351#103—24no—
352C22⋊C8—24no—
353C22⋊C8—24no—
354#95—24no—
355C2×C11—24no—
356C2×C11—82no—
357C2×C11C2×#39411yescharacteristic
358C2×C11#301312yes—
359C2×C11#305711yescharacteristic
360C2×C11#305911yescharacteristic
361C2×C11#309712yes—
362C24C2×D4×C1112yes—
363C24C2×D4×C1111yescharacteristic
364#41—44no—
365#41—44no—
366#41—44no—
367#41—44no—
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—28no—
374C2×Q8—28no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—42no—
380C2×Q8—44no—
381C2×Q8—42no—
382C2×Q8—44no—
383C2×Q8C2×D4×C1114yes—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—82no—
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1112yes—
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1112yes—
410C22×C4C11×#4112yes—
411C22×C4C11×#4112yes—
412C22×C4C11×#4112yes—
413C22×C4C24×C1111yescharacteristic
414M16—44no—
415C2×C8—28no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8C2×D4×C1112yes—
424C2×C8C2×D4×C1112yes—
425C4⋊C4—216no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—42no—
432C4⋊C4C2×D4×C1114yes—
433C22⋊C4—216no—
434C22⋊C4—24no—
435C22⋊C4—42no—
436C22⋊C4—84no—
437C42—24no—
438C42—42no—
439C11#2348711yescharacteristic, direct product factor, Sylow
440C23—22no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—24no—
446C23—24no—
447C23C11×#12012yes—
448C23C11×#12112yes—
449C23C11×#12312yes—
450C23C22×D4×C1111yescharacteristic
451Q8—24no—
452Q8—24no—
453Q8—42no—
454Q8—42no—
455Q8—48no—
456Q8—44no—
457D4—48no—
458D4—44no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—48no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—84no—
479C2×C4C11×#12012yes—
480C2×C4C11×#12114yes—
481C2×C4C11×#12114yes—
482C2×C4C11×#12112yes—
483C2×C4C11×#12314yes—
484C2×C4C11×#12312yes—
485C2×C4C11×#12414yes—
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C22×D4×C1111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C2×C11×#4111yescharacteristic
491C2×C4C2×C11×#4111yescharacteristic
492C8—22no—
493C8—22no—
494C8—42no—
495C22—24no—
496C22—22no—
497C22—22no—
498C22—24no—
499C22—42no—
500C22—44no—
501C22—42no—
502C22—42no—
503C22—44no—
504C22C11×#39414yes—
505C22C2×C11×#12011yescharacteristic
506C22C2×C11×#12111yescharacteristic
507C22C2×C11×#12311yescharacteristic
508C22C11×#57712yes—
509C22C11×#57812yes—
510C4—42no—
511C4—44no—
512C4—44no—
513C4—82no—
514C4—82no—
515C4C11×#39414yes—
516C4C2×C11×#12111yescharacteristic
517C4C2×C11×#12111yescharacteristic
518C4C2×C11×#12311yescharacteristic
519C4C2×C11×#12411yescharacteristic
520C2—24no—
521C2—82no—
522C2C2×C11×#39411yescharacteristic
523C2C11×#301312yes—
524C2C11×#305711yescharacteristic
525C2C11×#305911yescharacteristic
526C2C11×#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×#427C2semidirect
3. C2×C11×#419C2semidirect
4. C22×C11×#103C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1736C2semidirect
99. #23487C11direct (N × H)
178. C2×#427C2×C11semidirect
179. C2×#419C2×C11semidirect
180. C22×#103C2×C11semidirect
183. #2036C2×C11semidirect
184. #2035C2×C11semidirect
185. #1736C2×C11semidirect
439. C11#23487direct (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×#4272
C2×C11×#4192
C22×C11×#1032
C2×C11×#4082
C11×#23112
C11×#20362
C11×#20352
C11×#17362
#2348711