Finite Group Databasebeta

← C2×C11×#2814 #14613844

Subgroups — C2×C11×#2814 #14613844

Order 2816.

2674 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C11×#2814C2116yesmaximal, direct product factor
4C2×C11×#398C212yesmaximal, complemented
5C2×C11×#398C211yesmaximal, characteristic, complemented
6C2×C11×#397C211yesmaximal, characteristic, complemented
7C2×C11×#397C212yesmaximal, complemented
8C2×C11×#396C212yesmaximal, complemented
9C2×C11×#395C211yesmaximal, characteristic, complemented
10C2×C11×#394C212yesmaximal
11C2×C11×#393C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C2×C11×#123—28no—
17C2×C11×#123C2218yes—
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2218yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2212yes—
32C22×C11×C22⋊C4C2212yes—
33C22×C11×C22⋊C4C2212yes—
34C11×#398C2218yescomplemented
35C11×#398C22116yescomplemented
36C11×#397C2218yescomplemented
37C11×#397C22116yescomplemented
38C11×#396C22116yescomplemented
39C11×#395C2218yescomplemented
40C11×#394C22116yes—
41C11×#393C2218yescomplemented
42C11×#380C2218yescomplemented
43C2×C11×#95C2212yes—
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2212yes—
46C2×C11×#95C2212yes—
47C2×C11×#95C2211yescharacteristic
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—44no—
56C22×D4×C11C2314yes—
57C23×C4×C11—44no—
58C23×C4×C11D418yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2314yes—
69C11×#123—232no—
70C11×C22⋊Q8—232no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—44no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—44no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4—44no—
92C2×C11×C22⋊C4C2318yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C11×C22⋊C4C2318yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2318yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2318yes—
105C2×#2814C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—22no—
115C24×C11C2×D414yes—
116C24×C11C2412yes—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C2×Q8×C11—28no—
120C2×Q8×C11—48no—
121C2×Q8×C11—416no—
122C2×D4×C11—28no—
123C2×D4×C11—48no—
124C2×D4×C11—416no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
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—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—416no—
147C22×C4×C11—48no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D4116yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—216no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—48no—
165C11×C4⋊C4—48no—
166C11×C4⋊C4—48no—
167C11×C22⋊C4—216no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—48no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4—48no—
174C22×#123C2×C1111yescharacteristic
175C22×C22⋊Q8C2×C1111yescharacteristic, complemented
176#2814C2×C11116yesdirect product factor
177C2×#398C2×C1111yescharacteristic, complemented
178C2×#398C2×C1112yescomplemented
179C2×#397C2×C1111yescharacteristic, complemented
180C2×#397C2×C1112yescomplemented
181C2×#396C2×C1112yescomplemented
182C2×#395C2×C1111yescharacteristic, complemented
183C2×#394C2×C1112yes—
184C2×#393C2×C1111yescharacteristic, complemented
185C2×#380C2×C1111yescharacteristic, complemented
186C23×C11—28no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11C22×D414yes—
206C23×C11C22×D412yes—
207C23×C11H(5,𝔽2)14yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+414yes—
210C23×C112−1+412yes—
211C23×C11C2511yescharacteristic
212Q8×C11—416no—
213D4×C11—416no—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—416no—
238C2×C4×C11—44no—
239C2×C4×C11—48no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
244C2×C4×C11—48no—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D414yes—
247C23×Q8C22×C1111yescharacteristic
248C23×D4C22×C1111yescharacteristic
249C24×C4C22×C1111yescharacteristic
250C2×#123—28no—
251C2×#123C22×C1118yes—
252C2×C22⋊Q8—28no—
253C2×C22⋊Q8C22×C1118yescomplemented
254C22×C4⋊C4C22×C1111yescharacteristic
255C22×C4⋊C4C22×C1112yes—
256C22×C4⋊C4C22×C1111yescharacteristic
257C22×C4⋊C4C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1112yes—
259C22×C4⋊C4C22×C1112yes—
260C22×C4⋊C4C22×C1112yes—
261C22×C22⋊C4C22×C1111yescharacteristic
262C22×C22⋊C4C22×C1112yes—
263C22×C22⋊C4C22×C1111yescharacteristic
264C22×C22⋊C4C22×C1111yescharacteristic
265C22×C22⋊C4C22×C1112yes—
266C22×C22⋊C4C22×C1112yes—
267C22×C22⋊C4C22×C1112yes—
268#398C22×C1118yescomplemented
269#398C22×C11116yescomplemented
270#397C22×C1118yescomplemented
271#397C22×C11116yescomplemented
272#396C22×C11116yescomplemented
273#395C22×C1118yescomplemented
274#394C22×C11116yes—
275#393C22×C1118yescomplemented
276#380C22×C1118yescomplemented
277C2×#95C22×C1112yes—
278C2×#95C22×C1111yescharacteristic
279C2×#95C22×C1112yes—
280C2×#95C22×C1112yes—
281C2×#95C22×C1111yescharacteristic
282C2×#95C22×C1112yes—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—416no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—88no—
295C22×C11#53414yes—
296C22×C11#53614yes—
297C22×C11#53714yes—
298C22×C11#56218yes—
299C22×C11#56318yes—
300C22×C11C23×D411yescharacteristic
301C22×C11C2×H(5,𝔽2)12yes—
302C22×C11C2×H(5,𝔽2)11yescharacteristic
303C22×C11C2×2−1+412yes—
304C22×C11C2×2−1+411yescharacteristic
305C4×C11—24no—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11—44no—
313C4×C11—44no—
314C25C23×C1111yescharacteristic
315C25C23×C1111yescharacteristic
316C22×Q8—24no—
317C22×Q8—44no—
318C22×Q8C23×C1114yes—
319C22×D4—24no—
320C22×D4—44no—
321C22×D4C23×C1114yes—
322C23×C4—44no—
323C23×C4D4×C1118yes—
324C23×C4C23×C1111yescharacteristic
325C23×C4C23×C1112yes—
326C23×C4C23×C1112yes—
327C23×C4C23×C1112yes—
328C23×C4C23×C1112yes—
329C23×C4C23×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C23×C4C23×C1111yescharacteristic
332C23×C4C23×C1111yescharacteristic
333C23×C4C23×C1114yes—
334#123—232no—
335C22⋊Q8—232no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C23×C1118yes—
344C2×C4⋊C4C23×C1114yes—
345C2×C4⋊C4C23×C1114yes—
346C2×C4⋊C4C23×C1114yes—
347C2×C4⋊C4C23×C1118yes—
348C2×C4⋊C4C23×C1118yes—
349C2×C4⋊C4C23×C1118yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C23×C1118yes—
358C2×C22⋊C4C23×C1114yes—
359C2×C22⋊C4C23×C1114yes—
360C2×C22⋊C4C23×C1114yes—
361C2×C22⋊C4C23×C1118yes—
362C2×C22⋊C4C23×C1118yes—
363C2×C22⋊C4C23×C1118yes—
364#95C23×C1114yes—
365#95C23×C1114yes—
366#95C23×C1118yes—
367#95C23×C1118yes—
368#95C23×C1118yes—
369#95C23×C1118yes—
370C2×C11—44no—
371C2×C11—82no—
372C2×C11#281418yesdirect product factor
373C2×C11C2×#53411yescharacteristic
374C2×C11C2×#53611yescharacteristic
375C2×C11C2×#53711yescharacteristic
376C2×C11C2×#56212yes—
377C2×C11C2×#56312yes—
378C24—22no—
379C24—24no—
380C24—24no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—24no—
385C24—24no—
386C24—22no—
387C24C2×D4×C1114yes—
388C24C24×C1112yes—
389C24C24×C1112yes—
390C24C24×C1111yescharacteristic
391C2×Q8—28no—
392C2×Q8—48no—
393C2×Q8—416no—
394C2×D4—28no—
395C2×D4—48no—
396C2×D4—416no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—416no—
419C22×C4—48no—
420C22×C4C2×D4×C1114yes—
421C22×C4C2×D4×C1114yes—
422C22×C4C2×D4×C11116yes—
423C22×C4C24×C1112yes—
424C22×C4C24×C1114yes—
425C22×C4C24×C1114yes—
426C22×C4C24×C1112yes—
427C22×C4C24×C1114yes—
428C22×C4C24×C1114yes—
429C22×C4C24×C1112yes—
430C22×C4C24×C1112yes—
431C22×C4C24×C1112yes—
432C4⋊C4—28no—
433C4⋊C4—216no—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—48no—
437C4⋊C4—48no—
438C4⋊C4—48no—
439C22⋊C4—216no—
440C22⋊C4—28no—
441C22⋊C4—28no—
442C22⋊C4—28no—
443C22⋊C4—48no—
444C22⋊C4—48no—
445C22⋊C4—48no—
446C11C2×#281411yescharacteristic, direct product factor, Sylow
447C23—28no—
448C23—28no—
449C23—28no—
450C23—22no—
451C23—24no—
452C23—24no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—24no—
458C23—22no—
459C23—48no—
460C23—48no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—48no—
465C23—48no—
466C23C22×D4×C1114yes—
467C23C22×D4×C1112yes—
468C23C11×H(5,𝔽2)14yes—
469C23C11×H(5,𝔽2)12yes—
470C23C11×2−1+414yes—
471C23C11×2−1+412yes—
472C23C25×C1111yescharacteristic
473Q8—416no—
474D4—416no—
475C2×C4—28no—
476C2×C4—28no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—416no—
499C2×C4—44no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—48no—
504C2×C4—48no—
505C2×C4—48no—
506C2×C4C22×D4×C1114yes—
507C2×C4C22×D4×C1114yes—
508C22—24no—
509C22—24no—
510C22—24no—
511C22—44no—
512C22—44no—
513C22—416no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—44no—
519C22—88no—
520C22C11×#53414yes—
521C22C11×#53614yes—
522C22C11×#53714yes—
523C22C11×#56218yes—
524C22C11×#56318yes—
525C22C23×D4×C1111yescharacteristic
526C22C2×C11×H(5,𝔽2)12yes—
527C22C2×C11×H(5,𝔽2)11yescharacteristic
528C22C2×C11×2−1+412yes—
529C22C2×C11×2−1+411yescharacteristic
530C4—24no—
531C4—24no—
532C4—42no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—44no—
537C4—44no—
538C4—44no—
539C2—44no—
540C2—82no—
541C2C11×#281418yesdirect product factor
542C2C2×C11×#53411yescharacteristic
543C2C2×C11×#53611yescharacteristic
544C2C2×C11×#53711yescharacteristic
545C2C2×C11×#56212yes—
546C2C2×C11×#56312yes—
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
2. C22×C11×C22⋊Q8C2semidirect
3. C11×#2814C2direct (N × H)
4. C2×C11×#398C2semidirect
5. C2×C11×#398C2semidirect
6. C2×C11×#397C2semidirect
7. C2×C11×#397C2semidirect
8. C2×C11×#396C2semidirect
9. C2×C11×#395C2semidirect
11. C2×C11×#393C2semidirect
12. C2×C11×#380C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
34. C11×#398C22semidirect
35. C11×#398C22semidirect
36. C11×#397C22semidirect
37. C11×#397C22semidirect
38. C11×#396C22semidirect
39. C11×#395C22semidirect
41. C11×#393C22semidirect
42. C11×#380C22semidirect
105. C2×#2814C11direct (N × H)
175. C22×C22⋊Q8C2×C11semidirect
176. #2814C2×C11direct (N × H)
177. C2×#398C2×C11semidirect
178. C2×#398C2×C11semidirect
179. C2×#397C2×C11semidirect
180. C2×#397C2×C11semidirect
181. C2×#396C2×C11semidirect
182. C2×#395C2×C11semidirect
184. C2×#393C2×C11semidirect
185. C2×#380C2×C11semidirect
253. C2×C22⋊Q8C22×C11semidirect
268. #398C22×C11semidirect
269. #398C22×C11semidirect
270. #397C22×C11semidirect
271. #397C22×C11semidirect
272. #396C22×C11semidirect
273. #395C22×C11semidirect
275. #393C22×C11semidirect
276. #380C22×C11semidirect
372. C2×C11#2814direct (N × H)
446. C11C2×#2814direct (N × H)
541. C2C11×#2814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C22×C11×C22⋊Q82
C11×#28142
C2×C11×#3982
C2×C11×#3972
C2×C11×#3962
C2×C11×#3952
C2×C11×#3942
C2×C11×#3932
C2×C11×#3802
C2×#281411