Finite Group Databasebeta

← C2×C11×#2638 #14611754

Subgroups — C2×C11×#2638 #14611754

Order 2816.

2958 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic
3C11×#2638C2116yesmaximal, direct product factor
4C2×C11×#398C211yesmaximal, characteristic, complemented
5C2×C11×#397C211yesmaximal, characteristic, complemented
6C2×C11×#397C212yesmaximal, complemented
7C2×C11×#395C211yesmaximal, characteristic, complemented
8C2×C11×#394C212yesmaximal
9C2×C11×#393C211yesmaximal, characteristic, complemented
10C2×C11×#387C212yesmaximal, complemented
11C2×C11×#385C212yesmaximal, complemented
12C2×C11×#381C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×C22⋊Q8—28no—
18C2×C11×C22⋊Q8C2218yescomplemented
19C2×C4×D4×C11—28no—
20C2×C4×D4×C11C2218yes—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2212yes—
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2212yes—
31C22×C11×C22⋊C4C2212yes—
32C22×C42×C11C2211yescharacteristic
33C11×#398C2218yescomplemented
34C11×#397C2218yescomplemented
35C11×#397C22116yescomplemented
36C11×#395C2218yescomplemented
37C11×#394C22116yes—
38C11×#393C2218yescomplemented
39C11×#387C22116yescomplemented
40C11×#385C22116yescomplemented
41C11×#381C2218yescomplemented
42C2×C11×#95C2212yes—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2212yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2212yes—
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11C2314yes—
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11—44no—
61C23×C4×C11D418yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2312yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2314yes—
72C23×C4×C11C2314yes—
73C11×C22⋊Q8—232no—
74C4×D4×C11—232no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4—44no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4—28no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—44no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C11×C22⋊C4C2318yes—
95C2×C11×C22⋊C4C2318yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C42×C11—24no—
98C2×C42×C11C2314yes—
99C11×#95C2318yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2318yes—
105C11×#95C2318yes—
106C2×#2638C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C2×D414yes—
116C24×C11#4114yes—
117C24×C11C2412yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C2×Q8×C11—28no—
121C2×Q8×C11—48no—
122C2×Q8×C11—416no—
123C2×D4×C11—232no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—28no—
148C22×C4×C11—416no—
149C22×C4×C11—48no—
150C22×C4×C11—48no—
151C22×C4×C11—416no—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D4116yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2414yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—216no—
168C11×C4⋊C4—216no—
169C11×C4⋊C4—48no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—216no—
172C11×C22⋊C4—216no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—48no—
175C11×C22⋊C4—48no—
176C42×C11—28no—
177C22×C22⋊Q8C2×C1111yescharacteristic, complemented
178C22×C4×D4C2×C1111yescharacteristic
179#2638C2×C11116yesdirect product factor
180C2×#398C2×C1111yescharacteristic, complemented
181C2×#397C2×C1111yescharacteristic, complemented
182C2×#397C2×C1112yescomplemented
183C2×#395C2×C1111yescharacteristic, complemented
184C2×#394C2×C1112yes—
185C2×#393C2×C1111yescharacteristic, complemented
186C2×#387C2×C1112yescomplemented
187C2×#385C2×C1112yescomplemented
188C2×#381C2×C1111yescharacteristic, complemented
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—216no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11C22×D414yes—
208C23×C11C22×D412yes—
209C23×C11C2×#4114yes—
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C11H(5,𝔽2)14yes—
213C23×C112−1+414yes—
214C23×C11C2511yescharacteristic
215Q8×C11—416no—
216D4×C11—232no—
217C2×C4×C11—28no—
218C2×C4×C11—28no—
219C2×C4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—416no—
241C2×C4×C11—416no—
242C2×C4×C11—48no—
243C2×C4×C11—44no—
244C2×C4×C11—48no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11—48no—
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C2×#4114yes—
251C23×Q8C22×C1111yescharacteristic
252C23×D4C22×C1111yescharacteristic
253C24×C4C22×C1111yescharacteristic
254C24×C4C22×C1111yescharacteristic
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8C22×C1118yescomplemented
257C2×C4×D4—28no—
258C2×C4×D4C22×C1118yes—
259C22×C4⋊C4C22×C1112yes—
260C22×C4⋊C4C22×C1111yescharacteristic
261C22×C4⋊C4C22×C1111yescharacteristic
262C22×C4⋊C4C22×C1112yes—
263C22×C4⋊C4C22×C1112yes—
264C22×C22⋊C4C22×C1111yescharacteristic
265C22×C22⋊C4C22×C1112yes—
266C22×C22⋊C4C22×C1112yes—
267C22×C22⋊C4C22×C1111yescharacteristic
268C22×C22⋊C4C22×C1112yes—
269C22×C22⋊C4C22×C1112yes—
270C22×C42C22×C1111yescharacteristic
271#398C22×C1118yescomplemented
272#397C22×C1118yescomplemented
273#397C22×C11116yescomplemented
274#395C22×C1118yescomplemented
275#394C22×C11116yes—
276#393C22×C1118yescomplemented
277#387C22×C11116yescomplemented
278#385C22×C11116yescomplemented
279#381C22×C1118yescomplemented
280C2×#95C22×C1112yes—
281C2×#95C22×C1111yescharacteristic
282C2×#95C22×C1112yes—
283C2×#95C22×C1111yescharacteristic
284C2×#95C22×C1112yes—
285C2×#95C22×C1112yes—
286C2×#95C22×C1112yes—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—28no—
292C22×C11—416no—
293C22×C11—416no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11#52514yes—
300C22×C11#53414yes—
301C22×C11#53614yes—
302C22×C11#53918yes—
303C22×C11#54218yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C22×#4111yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C2×H(5,𝔽2)12yes—
308C22×C11C2×2−1+412yes—
309C4×C11—24no—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—44no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11—44no—
318C25C23×C1111yescharacteristic
319C25C23×C1111yescharacteristic
320C22×Q8—24no—
321C22×Q8—44no—
322C22×Q8C23×C1114yes—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4C23×C1114yes—
327C23×C4—24no—
328C23×C4—44no—
329C23×C4—44no—
330C23×C4D4×C1118yes—
331C23×C4C23×C1112yes—
332C23×C4C23×C1112yes—
333C23×C4C23×C1112yes—
334C23×C4C23×C1112yes—
335C23×C4C23×C1111yescharacteristic
336C23×C4C23×C1111yescharacteristic
337C23×C4C23×C1111yescharacteristic
338C23×C4C23×C1111yescharacteristic
339C23×C4C23×C1111yescharacteristic
340C23×C4C23×C1114yes—
341C23×C4C23×C1114yes—
342C22⋊Q8—232no—
343C4×D4—232no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C23×C1114yes—
350C2×C4⋊C4C23×C1118yes—
351C2×C4⋊C4C23×C1114yes—
352C2×C4⋊C4C23×C1118yes—
353C2×C4⋊C4C23×C1118yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C23×C1114yes—
361C2×C22⋊C4C23×C1114yes—
362C2×C22⋊C4C23×C1118yes—
363C2×C22⋊C4C23×C1118yes—
364C2×C22⋊C4C23×C1118yes—
365C2×C22⋊C4C23×C1118yes—
366C2×C42—24no—
367C2×C42C23×C1114yes—
368#95C23×C1118yes—
369#95C23×C1114yes—
370#95C23×C1114yes—
371#95C23×C1118yes—
372#95C23×C1118yes—
373#95C23×C1118yes—
374#95C23×C1118yes—
375C2×C11—44no—
376C2×C11—44no—
377C2×C11#263818yesdirect product factor
378C2×C11C2×#52511yescharacteristic
379C2×C11C2×#53411yescharacteristic
380C2×C11C2×#53611yescharacteristic
381C2×C11C2×#53912yes—
382C2×C11C2×#54212yes—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24C2×D4×C1114yes—
392C24C11×#4114yes—
393C24C24×C1112yes—
394C24C24×C1112yes—
395C24C24×C1111yescharacteristic
396C2×Q8—28no—
397C2×Q8—48no—
398C2×Q8—416no—
399C2×D4—232no—
400C2×D4—28no—
401C2×D4—28no—
402C2×D4—28no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—28no—
424C22×C4—416no—
425C22×C4—48no—
426C22×C4—48no—
427C22×C4—416no—
428C22×C4C2×D4×C1114yes—
429C22×C4C2×D4×C1114yes—
430C22×C4C2×D4×C11116yes—
431C22×C4C11×#4114yes—
432C22×C4C24×C1112yes—
433C22×C4C24×C1114yes—
434C22×C4C24×C1114yes—
435C22×C4C24×C1114yes—
436C22×C4C24×C1114yes—
437C22×C4C24×C1112yes—
438C22×C4C24×C1112yes—
439C22×C4C24×C1112yes—
440C22×C4C24×C1112yes—
441C4⋊C4—28no—
442C4⋊C4—28no—
443C4⋊C4—216no—
444C4⋊C4—216no—
445C4⋊C4—48no—
446C22⋊C4—28no—
447C22⋊C4—216no—
448C22⋊C4—216no—
449C22⋊C4—28no—
450C22⋊C4—48no—
451C22⋊C4—48no—
452C42—28no—
453C11C2×#263811yescharacteristic, direct product factor, Sylow
454C23—28no—
455C23—28no—
456C23—28no—
457C23—28no—
458C23—216no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—24no—
467C23—44no—
468C23—44no—
469C23—48no—
470C23—48no—
471C23—48no—
472C23C22×D4×C1114yes—
473C23C22×D4×C1112yes—
474C23C2×C11×#4114yes—
475C23C2×C11×#4112yes—
476C23C2×C11×#4112yes—
477C23C11×H(5,𝔽2)14yes—
478C23C11×2−1+414yes—
479C23C25×C1111yescharacteristic
480Q8—416no—
481D4—232no—
482C2×C4—28no—
483C2×C4—28no—
484C2×C4—28no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—416no—
506C2×C4—416no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—44no—
511C2×C4—48no—
512C2×C4—48no—
513C2×C4C22×D4×C1114yes—
514C2×C4C22×D4×C1114yes—
515C2×C4C2×C11×#4114yes—
516C22—24no—
517C22—24no—
518C22—24no—
519C22—24no—
520C22—28no—
521C22—416no—
522C22—416no—
523C22—42no—
524C22—42no—
525C22—44no—
526C22—44no—
527C22—44no—
528C22C11×#52514yes—
529C22C11×#53414yes—
530C22C11×#53614yes—
531C22C11×#53918yes—
532C22C11×#54218yes—
533C22C23×D4×C1111yescharacteristic
534C22C22×C11×#4111yescharacteristic
535C22C22×C11×#4111yescharacteristic
536C22C2×C11×H(5,𝔽2)12yes—
537C22C2×C11×2−1+412yes—
538C4—24no—
539C4—24no—
540C4—24no—
541C4—44no—
542C4—42no—
543C4—44no—
544C4—42no—
545C4—44no—
546C4—44no—
547C2—44no—
548C2—44no—
549C2C11×#263818yesdirect product factor
550C2C2×C11×#52511yescharacteristic
551C2C2×C11×#53411yescharacteristic
552C2C2×C11×#53611yescharacteristic
553C2C2×C11×#53912yes—
554C2C2×C11×#54212yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊Q8C2semidirect
3. C11×#2638C2direct (N × H)
4. C2×C11×#398C2semidirect
5. C2×C11×#397C2semidirect
6. C2×C11×#397C2semidirect
7. C2×C11×#395C2semidirect
9. C2×C11×#393C2semidirect
10. C2×C11×#387C2semidirect
11. C2×C11×#385C2semidirect
12. C2×C11×#381C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
33. C11×#398C22semidirect
34. C11×#397C22semidirect
35. C11×#397C22semidirect
36. C11×#395C22semidirect
38. C11×#393C22semidirect
39. C11×#387C22semidirect
40. C11×#385C22semidirect
41. C11×#381C22semidirect
106. C2×#2638C11direct (N × H)
177. C22×C22⋊Q8C2×C11semidirect
179. #2638C2×C11direct (N × H)
180. C2×#398C2×C11semidirect
181. C2×#397C2×C11semidirect
182. C2×#397C2×C11semidirect
183. C2×#395C2×C11semidirect
185. C2×#393C2×C11semidirect
186. C2×#387C2×C11semidirect
187. C2×#385C2×C11semidirect
188. C2×#381C2×C11semidirect
256. C2×C22⋊Q8C22×C11semidirect
271. #398C22×C11semidirect
272. #397C22×C11semidirect
273. #397C22×C11semidirect
274. #395C22×C11semidirect
276. #393C22×C11semidirect
277. #387C22×C11semidirect
278. #385C22×C11semidirect
279. #381C22×C11semidirect
377. C2×C11#2638direct (N × H)
453. C11C2×#2638direct (N × H)
549. C2C11×#2638direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C4×D4×C112
C11×#26382
C2×C11×#3982
C2×C11×#3972
C2×C11×#3952
C2×C11×#3942
C2×C11×#3932
C2×C11×#3872
C2×C11×#3852
C2×C11×#3812
C2×#263811