Finite Group Databasebeta

← C2×C11×#3461 #14639875

Subgroups — C2×C11×#3461 #14639875

Order 2816.

7130 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
1C11×#3461C2132yesmaximal, direct product factor
2C2×C11×#544C211yesmaximal, characteristic, complemented
3C2×C11×#542C214yesmaximal, complemented
4C2×C11×#541C214yesmaximal, complemented
5C2×C11×#539C214yesmaximal, complemented
6C2×C11×#537C211yesmaximal, characteristic
7C2×C11×#536C212yesmaximal, complemented
8C2×C11×#533C214yesmaximal, complemented
9C2×C11×#529C214yesmaximal, complemented
10C2×C11×#529C214yesmaximal, complemented
11C2×C4×C11×#41C212yesmaximal, complemented
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C23×Q8×C11C2211yescharacteristic
15C11×#544C22116yescomplemented
16C11×#542C22164yescomplemented
17C11×#541C22164yescomplemented
18C11×#539C22164yescomplemented
19C11×#537C22116yes—
20C11×#536C22132yescomplemented
21C11×#533C22164yescomplemented
22C2×C11×C4⋊Q8C2214yes—
23C2×C11×C4⋊Q8C2214yes—
24C11×#529C22164yescomplemented
25C11×#529C22164yescomplemented
26C2×C11×#126C2218yes—
27C2×C11×#126C2218yes—
28C2×C11×#125C2214yes—
29C2×C11×#125C2214yes—
30C2×C11×#125C2218yes—
31C2×C11×#124C2214yes—
32C2×C11×#124C2214yes—
33C2×C11×#123C2218yes—
34C2×C11×#123C2218yes—
35C2×C11×C22⋊Q8C2214yes—
36C2×C11×C22⋊Q8C2214yes—
37C2×C11×C22⋊Q8C2214yes—
38C2×C11×C22⋊Q8C2214yes—
39C2×C11×C22⋊Q8C2218yes—
40C2×C11×#121C2214yes—
41C2×C11×#121C2214yes—
42C4×C11×#41C22132yescomplemented
43C2×C4×Q8×C11C2214yes—
44C2×C4×Q8×C11C2214yes—
45C2×C4×Q8×C11C2212yes—
46C2×C4×Q8×C11C2212yes—
47C2×C4×Q8×C11C2214yes—
48C2×C4×Q8×C11C22116yescomplemented
49C2×C4×D4×C11C2212yes—
50C2×C4×D4×C11C2214yes—
51C2×C4×D4×C11C2214yes—
52C2×C4×D4×C11C2212yes—
53C2×C4×D4×C11C2214yes—
54C2×C11×#117C2212yes—
55C2×C11×#117C2214yes—
56C2×C11×#117C2218yes—
57C22×C11×C4⋊C4C2211yescharacteristic
58C22×C11×C4⋊C4C2212yes—
59C22×C42×C11C2211yescharacteristic
60C22×C42×C11C2212yes—
61C22×C42×C11C2214yes—
62C2×C11×#41—216no—
63C2×C11×#41C23116yes—
64C22×Q8×C11—28no—
65C22×Q8×C11C2314yes—
66C22×Q8×C11C2312yes—
67C22×Q8×C11C2318yes—
68C22×Q8×C11C2314yes—
69C22×D4×C11C2314yes—
70C22×D4×C11C2312yes—
71C22×D4×C11C2314yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2314yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2312yes—
78C23×C4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C11×C4⋊Q8C23132yes—
81C11×C4⋊Q8C23132yes—
82C11×#126C23164yes—
83C11×#126C23164yes—
84C11×#125C23132yes—
85C11×#125C23132yes—
86C11×#125C23164yes—
87C11×#124C23132yes—
88C11×#124C23132yes—
89C11×#123C23164yes—
90C11×#123C23164yes—
91C11×C22⋊Q8C23132yes—
92C11×C22⋊Q8C23132yes—
93C11×C22⋊Q8C23132yes—
94C11×C22⋊Q8C23132yes—
95C11×C22⋊Q8C23164yes—
96C11×#121C23132yes—
97C11×#121C23132yes—
98C4×Q8×C11C23132yes—
99C4×Q8×C11C23132yes—
100C4×Q8×C11C23116yes—
101C4×Q8×C11C23116yes—
102C4×Q8×C11C23132yes—
103C4×D4×C11C23116yes—
104C4×D4×C11C23132yes—
105C4×D4×C11C23132yes—
106C4×D4×C11C23116yes—
107C4×D4×C11C23132yes—
108C11×#117C23116yes—
109C11×#117C23132yes—
110C11×#117C23164yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C4⋊C4C2318yes—
113C2×C11×C4⋊C4C2318yes—
114C2×C11×C4⋊C4C23116yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2318yes—
120C2×C11×C4⋊C4C2318yes—
121C2×C11×C4⋊C4C2314yes—
122C2×C11×C4⋊C4C2314yes—
123C2×C11×C4⋊C4C2318yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127C2×C11×C22⋊C4C2318yes—
128C2×C11×C22⋊C4C2318yes—
129C2×C11×C22⋊C4C2318yes—
130C2×C42×C11C2312yes—
131C2×C42×C11C2314yes—
132C2×C42×C11C2314yes—
133C2×C42×C11C2314yes—
134C2×C42×C11C2318yes—
135C2×C42×C11C23116yes—
136C2×C42×C11C23132yes—
137C2×C42×C11C2312yes—
138C2×C42×C11C2314yes—
139C2×C42×C11C2314yes—
140C2×#3461C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11C2414yes—
142C24×C11C2411yescharacteristic
143C11×#41—264no—
144C2×Q8×C11—216no—
145C2×Q8×C11—232no—
146C2×Q8×C11—28no—
147C2×Q8×C11—48no—
148C2×Q8×C11C24116yes—
149C2×Q8×C11C2418yes—
150C2×Q8×C11C24116yes—
151C2×D4×C11—216no—
152C2×D4×C11—28no—
153C2×D4×C11—48no—
154C2×D4×C11C24116yes—
155C2×D4×C11C2418yes—
156C2×D4×C11C24116yes—
157C22×C4×C11—28no—
158C22×C4×C11—216no—
159C22×C4×C11—24no—
160C22×C4×C11—216no—
161C22×C4×C11—42no—
162C22×C4×C11—48no—
163C22×C4×C11—44no—
164C22×C4×C11#4118yes—
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2414yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C2418yes—
174C22×C4×C11C24116yes—
175C22×C4×C11C24116yes—
176C22×C4×C11C2414yes—
177C22×C4×C11C2418yes—
178C22×C4×C11C24116yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2414yes—
181C22×C4×C11C2411yescharacteristic
182C11×C4⋊C4C24116yes—
183C11×C4⋊C4C24132yes—
184C11×C4⋊C4C24116yes—
185C11×C4⋊C4C2418yes—
186C11×C4⋊C4C2418yes—
187C11×C4⋊C4C24116yes—
188C11×C4⋊C4C24132yes—
189C11×C4⋊C4C24132yes—
190C11×C4⋊C4C24116yes—
191C11×C4⋊C4C24116yes—
192C11×C4⋊C4C24132yes—
193C11×C22⋊C4C24116yes—
194C11×C22⋊C4C24116yes—
195C11×C22⋊C4C24116yes—
196C11×C22⋊C4C24132yes—
197C11×C22⋊C4C24132yes—
198C11×C22⋊C4C24132yes—
199C42×C11C2418yes—
200C42×C11C2418yes—
201C42×C11C24116yes—
202C42×C11C24116yes—
203C42×C11C24116yes—
204C42×C11C24116yes—
205C42×C11C24116yes—
206#3461C2×C11132yesdirect product factor
207C2×#544C2×C1111yescharacteristic, complemented
208C2×#542C2×C1114yescomplemented
209C2×#541C2×C1114yescomplemented
210C2×#539C2×C1114yescomplemented
211C2×#537C2×C1111yescharacteristic
212C2×#536C2×C1112yescomplemented
213C2×#533C2×C1114yescomplemented
214C2×#529C2×C1114yescomplemented
215C2×#529C2×C1114yescomplemented
216C2×C4×#41C2×C1112yescomplemented
217C22×C4×Q8C2×C1111yescharacteristic, complemented
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—28no—
221C23×C11—28no—
222C23×C11—28no—
223C23×C11C2×#4114yes—
224C23×C11C2518yes—
225C23×C11C2512yes—
226C23×C11C2511yescharacteristic
227Q8×C11—232no—
228Q8×C11—216no—
229Q8×C11—416no—
230D4×C11—232no—
231D4×C11—216no—
232D4×C11—416no—
233C2×C4×C11—28no—
234C2×C4×C11—216no—
235C2×C4×C11—28no—
236C2×C4×C11—22no—
237C2×C4×C11—28no—
238C2×C4×C11—24no—
239C2×C4×C11—28no—
240C2×C4×C11—28no—
241C2×C4×C11—232no—
242C2×C4×C11—28no—
243C2×C4×C11—232no—
244C2×C4×C11—44no—
245C2×C4×C11—416no—
246C2×C4×C11—48no—
247C2×C4×C11C2×#4118yes—
248C2×C4×C11C2×#41116yes—
249C2×C4×C112−1+414yes—
250C2×C4×C11C2512yes—
251C2×C4×C11C2514yes—
252C2×C4×C11C2518yes—
253C2×C4×C11C2518yes—
254C2×C4×C11C2518yes—
255C2×C4×C11C2518yes—
256C2×C4×C11C2518yes—
257C2×C4×C11C2514yes—
258C2×C4×C11C2512yes—
259C22×#41C22×C1112yes—
260C23×Q8C22×C1111yescharacteristic
261#544C22×C11116yescomplemented
262#542C22×C11164yescomplemented
263#541C22×C11164yescomplemented
264#539C22×C11164yescomplemented
265#537C22×C11116yes—
266#536C22×C11132yescomplemented
267#533C22×C11164yescomplemented
268C2×C4⋊Q8C22×C1114yes—
269C2×C4⋊Q8C22×C1114yes—
270#529C22×C11164yescomplemented
271#529C22×C11164yescomplemented
272C2×#126C22×C1118yes—
273C2×#126C22×C1118yes—
274C2×#125C22×C1114yes—
275C2×#125C22×C1114yes—
276C2×#125C22×C1118yes—
277C2×#124C22×C1114yes—
278C2×#124C22×C1114yes—
279C2×#123C22×C1118yes—
280C2×#123C22×C1118yes—
281C2×C22⋊Q8C22×C1114yes—
282C2×C22⋊Q8C22×C1114yes—
283C2×C22⋊Q8C22×C1114yes—
284C2×C22⋊Q8C22×C1114yes—
285C2×C22⋊Q8C22×C1118yes—
286C2×#121C22×C1114yes—
287C2×#121C22×C1114yes—
288C4×#41C22×C11132yescomplemented
289C2×C4×Q8C22×C1114yes—
290C2×C4×Q8C22×C1114yes—
291C2×C4×Q8C22×C1112yes—
292C2×C4×Q8C22×C1112yes—
293C2×C4×Q8C22×C1114yes—
294C2×C4×Q8C22×C11116yescomplemented
295C2×C4×D4C22×C1114yes—
296C2×C4×D4C22×C1112yes—
297C2×C4×D4C22×C1114yes—
298C2×C4×D4C22×C1112yes—
299C2×C4×D4C22×C1114yes—
300C2×#117C22×C1112yes—
301C2×#117C22×C1114yes—
302C2×#117C22×C1118yes—
303C22×C4⋊C4C22×C1111yescharacteristic
304C22×C4⋊C4C22×C1112yes—
305C22×C42C22×C1111yescharacteristic
306C22×C42C22×C1112yes—
307C22×C42C22×C1114yes—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—28no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—28no—
314C22×C11—416no—
315C22×C11C22×#4114yes—
316C22×C11C22×#4112yes—
317C22×C11C2×2−1+412yes—
318C22×C11#58512yes—
319C22×C11C2611yescharacteristic
320C4×C11—28no—
321C4×C11—28no—
322C4×C11—22no—
323C4×C11—28no—
324C4×C11—24no—
325C4×C11—28no—
326C4×C11—28no—
327C4×C11C22×#4118yes—
328C4×C11C2×2−1+414yes—
329C2×#41—216no—
330C2×#41C23×C11116yes—
331C22×Q8—28no—
332C22×Q8C23×C1114yes—
333C22×Q8C23×C1112yes—
334C22×Q8C23×C1118yes—
335C22×Q8C23×C1114yes—
336C22×D4C23×C1114yes—
337C22×D4C23×C1112yes—
338C22×D4C23×C1114yes—
339C23×C4C23×C1112yes—
340C23×C4C23×C1114yes—
341C23×C4C23×C1114yes—
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1111yescharacteristic
344C23×C4C23×C1112yes—
345C23×C4C23×C1114yes—
346C23×C4C23×C1111yescharacteristic
347C4⋊Q8C23×C11132yes—
348C4⋊Q8C23×C11132yes—
349#126C23×C11164yes—
350#126C23×C11164yes—
351#125C23×C11132yes—
352#125C23×C11132yes—
353#125C23×C11164yes—
354#124C23×C11132yes—
355#124C23×C11132yes—
356#123C23×C11164yes—
357#123C23×C11164yes—
358C22⋊Q8C23×C11132yes—
359C22⋊Q8C23×C11132yes—
360C22⋊Q8C23×C11132yes—
361C22⋊Q8C23×C11132yes—
362C22⋊Q8C23×C11164yes—
363#121C23×C11132yes—
364#121C23×C11132yes—
365C4×Q8C23×C11132yes—
366C4×Q8C23×C11132yes—
367C4×Q8C23×C11116yes—
368C4×Q8C23×C11116yes—
369C4×Q8C23×C11132yes—
370C4×D4C23×C11116yes—
371C4×D4C23×C11132yes—
372C4×D4C23×C11132yes—
373C4×D4C23×C11116yes—
374C4×D4C23×C11132yes—
375#117C23×C11116yes—
376#117C23×C11132yes—
377#117C23×C11164yes—
378C2×C4⋊C4C23×C1114yes—
379C2×C4⋊C4C23×C1118yes—
380C2×C4⋊C4C23×C1118yes—
381C2×C4⋊C4C23×C11116yes—
382C2×C4⋊C4C23×C1114yes—
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1112yes—
385C2×C4⋊C4C23×C1114yes—
386C2×C4⋊C4C23×C1118yes—
387C2×C4⋊C4C23×C1118yes—
388C2×C4⋊C4C23×C1114yes—
389C2×C4⋊C4C23×C1114yes—
390C2×C4⋊C4C23×C1118yes—
391C2×C22⋊C4C23×C1114yes—
392C2×C22⋊C4C23×C1114yes—
393C2×C22⋊C4C23×C1114yes—
394C2×C22⋊C4C23×C1118yes—
395C2×C22⋊C4C23×C1118yes—
396C2×C22⋊C4C23×C1118yes—
397C2×C42C23×C1112yes—
398C2×C42C23×C1114yes—
399C2×C42C23×C1114yes—
400C2×C42C23×C1114yes—
401C2×C42C23×C1112yes—
402C2×C42C23×C1114yes—
403C2×C42C23×C1114yes—
404C2×C42C23×C1118yes—
405C2×C42C23×C11116yes—
406C2×C42C23×C11132yes—
407C2×C11—24no—
408C2×C11—48no—
409C2×C11#346114yesdirect product factor
410C2×C11C23×#4111yescharacteristic
411C2×C11C22×2−1+411yescharacteristic
412C2×C11C2×#58511yescharacteristic
413C24C24×C1114yes—
414C24C24×C1111yescharacteristic
415#41—264no—
416C2×Q8—216no—
417C2×Q8—232no—
418C2×Q8—28no—
419C2×Q8—48no—
420C2×Q8C24×C11116yes—
421C2×Q8C24×C1118yes—
422C2×Q8C24×C11116yes—
423C2×D4—216no—
424C2×D4—28no—
425C2×D4—48no—
426C2×D4C24×C11116yes—
427C2×D4C24×C1118yes—
428C2×D4C24×C11116yes—
429C22×C4—28no—
430C22×C4—216no—
431C22×C4—24no—
432C22×C4—216no—
433C22×C4—42no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4C11×#4118yes—
437C22×C4C24×C1111yescharacteristic
438C22×C4C24×C1114yes—
439C22×C4C24×C1112yes—
440C22×C4C24×C1114yes—
441C22×C4C24×C1114yes—
442C22×C4C24×C1114yes—
443C22×C4C24×C1114yes—
444C22×C4C24×C1114yes—
445C22×C4C24×C1118yes—
446C22×C4C24×C11116yes—
447C22×C4C24×C11116yes—
448C22×C4C24×C1114yes—
449C22×C4C24×C1118yes—
450C22×C4C24×C11116yes—
451C22×C4C24×C1112yes—
452C22×C4C24×C1114yes—
453C22×C4C24×C1111yescharacteristic
454C4⋊C4C24×C11116yes—
455C4⋊C4C24×C11132yes—
456C4⋊C4C24×C11116yes—
457C4⋊C4C24×C1118yes—
458C4⋊C4C24×C1118yes—
459C4⋊C4C24×C11116yes—
460C4⋊C4C24×C11132yes—
461C4⋊C4C24×C11132yes—
462C4⋊C4C24×C11116yes—
463C4⋊C4C24×C11116yes—
464C4⋊C4C24×C11132yes—
465C22⋊C4C24×C11116yes—
466C22⋊C4C24×C11116yes—
467C22⋊C4C24×C11116yes—
468C22⋊C4C24×C11132yes—
469C22⋊C4C24×C11132yes—
470C22⋊C4C24×C11132yes—
471C42C24×C1118yes—
472C42C24×C1118yes—
473C42C24×C11116yes—
474C42C24×C11116yes—
475C42C24×C11116yes—
476C42C24×C11116yes—
477C42C24×C11116yes—
478C11C2×#346111yescharacteristic, direct product factor, Sylow
479C23—22no—
480C23—22no—
481C23—28no—
482C23—28no—
483C23—28no—
484C23C2×C11×#4114yes—
485C23C25×C1118yes—
486C23C25×C1112yes—
487C23C25×C1111yescharacteristic
488Q8—232no—
489Q8—216no—
490Q8—416no—
491D4—232no—
492D4—216no—
493D4—416no—
494C2×C4—28no—
495C2×C4—216no—
496C2×C4—28no—
497C2×C4—22no—
498C2×C4—28no—
499C2×C4—24no—
500C2×C4—28no—
501C2×C4—28no—
502C2×C4—232no—
503C2×C4—28no—
504C2×C4—232no—
505C2×C4—44no—
506C2×C4—416no—
507C2×C4—48no—
508C2×C4C2×C11×#4118yes—
509C2×C4C2×C11×#41116yes—
510C2×C4C11×2−1+414yes—
511C2×C4C25×C1112yes—
512C2×C4C25×C1114yes—
513C2×C4C25×C1118yes—
514C2×C4C25×C1118yes—
515C2×C4C25×C1118yes—
516C2×C4C25×C1118yes—
517C2×C4C25×C1118yes—
518C2×C4C25×C1114yes—
519C2×C4C25×C1112yes—
520C22—28no—
521C22—22no—
522C22—22no—
523C22—28no—
524C22—28no—
525C22—28no—
526C22—416no—
527C22C22×C11×#4114yes—
528C22C22×C11×#4112yes—
529C22C2×C11×2−1+412yes—
530C22C11×#58512yes—
531C22C26×C1111yescharacteristic
532C4—28no—
533C4—28no—
534C4—22no—
535C4—28no—
536C4—24no—
537C4—28no—
538C4—28no—
539C4C22×C11×#4118yes—
540C4C2×C11×2−1+414yes—
541C2—24no—
542C2—48no—
543C2C11×#346114yesdirect product factor
544C2C23×C11×#4111yescharacteristic
545C2C22×C11×2−1+411yescharacteristic
546C2C2×C11×#58511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC22C26×C11
socleC23×C11C25
prime radicalC2×C11×#537C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3461C2direct (N × H)
2. C2×C11×#544C2semidirect
3. C2×C11×#542C2semidirect
4. C2×C11×#541C2semidirect
5. C2×C11×#539C2semidirect
7. C2×C11×#536C2semidirect
8. C2×C11×#533C2semidirect
9. C2×C11×#529C2semidirect
10. C2×C11×#529C2semidirect
11. C2×C4×C11×#41C2semidirect
12. C22×C4×Q8×C11C2semidirect
15. C11×#544C22semidirect
16. C11×#542C22semidirect
17. C11×#541C22semidirect
18. C11×#539C22semidirect
20. C11×#536C22semidirect
21. C11×#533C22semidirect
24. C11×#529C22semidirect
25. C11×#529C22semidirect
42. C4×C11×#41C22semidirect
48. C2×C4×Q8×C11C22semidirect
140. C2×#3461C11direct (N × H)
206. #3461C2×C11direct (N × H)
207. C2×#544C2×C11semidirect
208. C2×#542C2×C11semidirect
209. C2×#541C2×C11semidirect
210. C2×#539C2×C11semidirect
212. C2×#536C2×C11semidirect
213. C2×#533C2×C11semidirect
214. C2×#529C2×C11semidirect
215. C2×#529C2×C11semidirect
216. C2×C4×#41C2×C11semidirect
217. C22×C4×Q8C2×C11semidirect
261. #544C22×C11semidirect
262. #542C22×C11semidirect
263. #541C22×C11semidirect
264. #539C22×C11semidirect
266. #536C22×C11semidirect
267. #533C22×C11semidirect
270. #529C22×C11semidirect
271. #529C22×C11semidirect
288. C4×#41C22×C11semidirect
294. C2×C4×Q8C22×C11semidirect
409. C2×C11#3461direct (N × H)
478. C11C2×#3461direct (N × H)
543. C2C11×#3461direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34612
C2×C11×#5442
C2×C11×#5422
C2×C11×#5412
C2×C11×#5392
C2×C11×#5372
C2×C11×#5362
C2×C11×#5332
C2×C11×#5292
C2×C4×C11×#412
C22×C4×Q8×C112
C2×#346111