Finite Group Databasebeta

← C2×C11×#3480 #14639904

Subgroups — C2×C11×#3480 #14639904

Order 2816.

7802 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3480C2132yesmaximal, direct product factor
2C2×C11×#559C213yesmaximal, complemented
3C2×C11×#557C211yesmaximal, characteristic, complemented
4C2×C11×#556C213yesmaximal, complemented
5C2×C11×#553C216yesmaximal, complemented
6C2×C11×#550C211yesmaximal, characteristic, complemented
7C2×C11×#548C212yesmaximal, complemented
8C2×C11×#532C213yesmaximal, complemented
9C2×C11×#529C216yesmaximal, complemented
10C2×C4×C11×#41C213yesmaximal, complemented
11C2×C4×C11×#41C212yesmaximal, complemented
12C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
13C22×C11×#41C2213yes—
14C22×C11×#41C2212yes—
15C23×Q8×C11C2211yescharacteristic
16C11×#559C22148yescomplemented
17C11×#557C22116yescomplemented
18C11×#556C22148yescomplemented
19C11×#553C22196yescomplemented
20C11×#550C22116yescomplemented
21C11×#548C22132yescomplemented
22C11×#532C22148yescomplemented
23C2×C11×C4⋊Q8C2213yes—
24C2×C11×#127C2213yes—
25C11×#529C22196yescomplemented
26C2×C11×#126C22112yes—
27C2×C11×#125C2216yes—
28C2×C11×#124C2216yes—
29C2×C11×#124C2216yes—
30C2×C11×#123C22112yes—
31C2×C11×C22⋊Q8C2216yes—
32C2×C11×#121C2216yes—
33C2×C11×#121C2216yes—
34C2×C11×#121C2216yes—
35C4×C11×#41C22148yescomplemented
36C4×C11×#41C22132yescomplemented
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×Q8×C11C2213yes—
39C2×C4×Q8×C11C2211yescharacteristic
40C2×C4×Q8×C11C2213yes—
41C2×C4×Q8×C11C2212yes—
42C2×C4×Q8×C11C2213yes—
43C2×C4×Q8×C11C2213yes—
44C2×C4×Q8×C11C22116yescomplemented
45C2×C4×D4×C11C2216yes—
46C2×C4×D4×C11C2216yes—
47C2×C4×D4×C11C2213yes—
48C2×C4×D4×C11C2216yes—
49C2×C4×D4×C11C2216yes—
50C2×C4×D4×C11C2213yes—
51C2×C4×D4×C11C2216yes—
52C2×C11×#117C2211yescharacteristic
53C2×C11×#117C2216yes—
54C2×C11×#117C2216yes—
55C22×C11×C4⋊C4C2213yes—
56C22×C42×C11C2213yes—
57C22×C42×C11C2216yes—
58C2×C11×#41—216no—
59C2×C11×#41—224no—
60C2×C11×#41C23124yes—
61C2×C11×#41C23116yes—
62C22×Q8×C11—28no—
63C22×Q8×C11C2313yes—
64C22×Q8×C11C2313yes—
65C22×Q8×C11C2318yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11C2316yes—
68C22×D4×C11C2316yes—
69C22×D4×C11C2313yes—
70C22×D4×C11C2316yes—
71C23×C4×C11C2313yes—
72C23×C4×C11C2316yes—
73C23×C4×C11C2316yes—
74C23×C4×C11C2313yes—
75C23×C4×C11C2316yes—
76C23×C4×C11C2311yescharacteristic
77C11×C4⋊Q8C23124yes—
78C11×#127C23124yes—
79C11×#126C23196yes—
80C11×#125C23148yes—
81C11×#124C23148yes—
82C11×#124C23148yes—
83C11×#123C23196yes—
84C11×C22⋊Q8C23148yes—
85C11×#121C23148yes—
86C11×#121C23148yes—
87C11×#121C23148yes—
88C4×Q8×C11C2318yes—
89C4×Q8×C11C23124yes—
90C4×Q8×C11C2318yes—
91C4×Q8×C11C23124yes—
92C4×Q8×C11C23116yes—
93C4×Q8×C11C23124yes—
94C4×Q8×C11C23124yes—
95C4×D4×C11C23148yes—
96C4×D4×C11C23148yes—
97C4×D4×C11C23124yes—
98C4×D4×C11C23148yes—
99C4×D4×C11C23148yes—
100C4×D4×C11C23124yes—
101C4×D4×C11C23148yes—
102C11×#117C2318yes—
103C11×#117C23148yes—
104C11×#117C23148yes—
105C2×C11×C4⋊C4C2313yes—
106C2×C11×C4⋊C4C2313yes—
107C2×C11×C4⋊C4C2316yes—
108C2×C11×C4⋊C4C23124yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2316yes—
112C2×C11×C4⋊C4C2316yes—
113C2×C11×C4⋊C4C2316yes—
114C2×C11×C4⋊C4C2316yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2316yes—
117C2×C11×C22⋊C4C23112yes—
118C2×C11×C22⋊C4C2316yes—
119C2×C11×C22⋊C4C23112yes—
120C2×C42×C11C2316yes—
121C2×C42×C11C2316yes—
122C2×C42×C11C2313yes—
123C2×C42×C11C2313yes—
124C2×C42×C11C23124yes—
125C2×C42×C11C23148yes—
126C2×C42×C11C2312yes—
127C2×C42×C11C2313yes—
128C2×C42×C11C2313yes—
129C2×#3480C1111yesmaximal, characteristic, direct product factor, Sylow
130C24×C11C2416yes—
131C24×C11C2411yescharacteristic
132C11×#41—264no—
133C11×#41—296no—
134C2×Q8×C11—232no—
135C2×Q8×C11—212no—
136C2×Q8×C11—212no—
137C2×Q8×C11#4118yescomplemented
138C2×Q8×C11C24112yes—
139C2×Q8×C11C24112yes—
140C2×Q8×C11C2414yes—
141C2×D4×C11—224no—
142C2×D4×C11—224no—
143C2×D4×C11—212no—
144C2×D4×C11—412no—
145C2×D4×C11C24124yes—
146C2×D4×C11C24124yes—
147C2×D4×C11C24112yes—
148C2×D4×C11C24124yes—
149C22×C4×C11—212no—
150C22×C4×C11—224no—
151C22×C4×C11—224no—
152C22×C4×C11—412no—
153C22×C4×C11—46no—
154C22×C4×C11#4118yescomplemented
155C22×C4×C11C2412yes—
156C22×C4×C11C2413yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2413yes—
159C22×C4×C11C2416yes—
160C22×C4×C11C2413yes—
161C22×C4×C11C24112yes—
162C22×C4×C11C24124yes—
163C22×C4×C11C24124yes—
164C22×C4×C11C24112yes—
165C22×C4×C11C24124yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2413yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2411yescharacteristic
170C11×C4⋊C4C24112yes—
171C11×C4⋊C4C24112yes—
172C11×C4⋊C4C24124yes—
173C11×C4⋊C4C2414yes—
174C11×C4⋊C4C2414yes—
175C11×C4⋊C4C24124yes—
176C11×C4⋊C4C24124yes—
177C11×C4⋊C4C24124yes—
178C11×C4⋊C4C24124yes—
179C11×C22⋊C4C2418yes—
180C11×C22⋊C4C24124yes—
181C11×C22⋊C4C24148yes—
182C11×C22⋊C4C24124yes—
183C11×C22⋊C4C24148yes—
184C42×C11C2418yes—
185C42×C11C24112yes—
186C42×C11C24112yes—
187C42×C11C24124yes—
188C42×C11C24124yes—
189C42×C11C24112yes—
190C42×C11C24112yes—
191#3480C2×C11132yesdirect product factor
192C2×#559C2×C1113yescomplemented
193C2×#557C2×C1111yescharacteristic, complemented
194C2×#556C2×C1113yescomplemented
195C2×#553C2×C1116yescomplemented
196C2×#550C2×C1111yescharacteristic, complemented
197C2×#548C2×C1112yescomplemented
198C2×#532C2×C1113yescomplemented
199C2×#529C2×C1116yescomplemented
200C2×C4×#41C2×C1113yescomplemented
201C2×C4×#41C2×C1112yescomplemented
202C22×C4×Q8C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—212no—
206C23×C11—212no—
207C23×C11—212no—
208C23×C11C2×#4114yes—
209C23×C11C25112yes—
210C23×C11C2512yes—
211C23×C11C2511yescharacteristic
212Q8×C11—224no—
213Q8×C11—224no—
214Q8×C11C2×#41116yescomplemented
215D4×C11—248no—
216D4×C11—248no—
217D4×C11—224no—
218D4×C11—424no—
219C2×C4×C11—24no—
220C2×C4×C11—212no—
221C2×C4×C11—26no—
222C2×C4×C11—24no—
223C2×C4×C11—26no—
224C2×C4×C11—26no—
225C2×C4×C11—224no—
226C2×C4×C11—248no—
227C2×C4×C11—248no—
228C2×C4×C11—424no—
229C2×C4×C11—412no—
230C2×C4×C11C2×#4114yes—
231C2×C4×C11C2×#41112yes—
232C2×C4×C11C2×#4114yes—
233C2×C4×C11C2×#41116yescomplemented
234C2×C4×C11C2514yes—
235C2×C4×C11C2514yes—
236C2×C4×C11C2516yes—
237C2×C4×C11C2516yes—
238C2×C4×C11C25112yes—
239C2×C4×C11C2516yes—
240C2×C4×C11C2512yes—
241C2×C4×C11C2512yes—
242C2×C4×C11C2516yes—
243C22×#41C22×C1113yes—
244C22×#41C22×C1112yes—
245C23×Q8C22×C1111yescharacteristic
246#559C22×C11148yescomplemented
247#557C22×C11116yescomplemented
248#556C22×C11148yescomplemented
249#553C22×C11196yescomplemented
250#550C22×C11116yescomplemented
251#548C22×C11132yescomplemented
252#532C22×C11148yescomplemented
253C2×C4⋊Q8C22×C1113yes—
254C2×#127C22×C1113yes—
255#529C22×C11196yescomplemented
256C2×#126C22×C11112yes—
257C2×#125C22×C1116yes—
258C2×#124C22×C1116yes—
259C2×#124C22×C1116yes—
260C2×#123C22×C11112yes—
261C2×C22⋊Q8C22×C1116yes—
262C2×#121C22×C1116yes—
263C2×#121C22×C1116yes—
264C2×#121C22×C1116yes—
265C4×#41C22×C11148yescomplemented
266C4×#41C22×C11132yescomplemented
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×Q8C22×C1113yes—
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×Q8C22×C1113yes—
271C2×C4×Q8C22×C1112yes—
272C2×C4×Q8C22×C1113yes—
273C2×C4×Q8C22×C1113yes—
274C2×C4×Q8C22×C11116yescomplemented
275C2×C4×D4C22×C1116yes—
276C2×C4×D4C22×C1116yes—
277C2×C4×D4C22×C1113yes—
278C2×C4×D4C22×C1116yes—
279C2×C4×D4C22×C1116yes—
280C2×C4×D4C22×C1113yes—
281C2×C4×D4C22×C1116yes—
282C2×#117C22×C1111yescharacteristic
283C2×#117C22×C1116yes—
284C2×#117C22×C1116yes—
285C22×C4⋊C4C22×C1113yes—
286C22×C42C22×C1113yes—
287C22×C42C22×C1116yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—28no—
291C22×C11—212no—
292C22×C11—212no—
293C22×C11—212no—
294C22×C11—424no—
295C22×C11C22×#4114yes—
296C22×C11C22×#4112yes—
297C22×C11C22×#4112yes—
298C22×C11#58512yes—
299C22×C11C2611yescharacteristic
300C4×C11—24no—
301C4×C11—212no—
302C4×C11—26no—
303C4×C11—24no—
304C4×C11—26no—
305C4×C11—26no—
306C4×C11C22×#4114yes—
307C4×C11C22×#41112yes—
308C4×C11C22×#4114yes—
309C2×#41—216no—
310C2×#41—224no—
311C2×#41C23×C11124yes—
312C2×#41C23×C11116yes—
313C22×Q8—28no—
314C22×Q8C23×C1113yes—
315C22×Q8C23×C1113yes—
316C22×Q8C23×C1118yes—
317C22×Q8C23×C1111yescharacteristic
318C22×D4C23×C1116yes—
319C22×D4C23×C1116yes—
320C22×D4C23×C1113yes—
321C22×D4C23×C1116yes—
322C23×C4C23×C1113yes—
323C23×C4C23×C1116yes—
324C23×C4C23×C1116yes—
325C23×C4C23×C1113yes—
326C23×C4C23×C1116yes—
327C23×C4C23×C1111yescharacteristic
328C4⋊Q8C23×C11124yes—
329#127C23×C11124yes—
330#126C23×C11196yes—
331#125C23×C11148yes—
332#124C23×C11148yes—
333#124C23×C11148yes—
334#123C23×C11196yes—
335C22⋊Q8C23×C11148yes—
336#121C23×C11148yes—
337#121C23×C11148yes—
338#121C23×C11148yes—
339C4×Q8C23×C1118yes—
340C4×Q8C23×C11124yes—
341C4×Q8C23×C1118yes—
342C4×Q8C23×C11124yes—
343C4×Q8C23×C11116yes—
344C4×Q8C23×C11124yes—
345C4×Q8C23×C11124yes—
346C4×D4C23×C11148yes—
347C4×D4C23×C11148yes—
348C4×D4C23×C11124yes—
349C4×D4C23×C11148yes—
350C4×D4C23×C11148yes—
351C4×D4C23×C11124yes—
352C4×D4C23×C11148yes—
353#117C23×C1118yes—
354#117C23×C11148yes—
355#117C23×C11148yes—
356C2×C4⋊C4C23×C1113yes—
357C2×C4⋊C4C23×C1113yes—
358C2×C4⋊C4C23×C1116yes—
359C2×C4⋊C4C23×C11124yes—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1116yes—
363C2×C4⋊C4C23×C1116yes—
364C2×C4⋊C4C23×C1116yes—
365C2×C4⋊C4C23×C1116yes—
366C2×C22⋊C4C23×C1112yes—
367C2×C22⋊C4C23×C1116yes—
368C2×C22⋊C4C23×C11112yes—
369C2×C22⋊C4C23×C1116yes—
370C2×C22⋊C4C23×C11112yes—
371C2×C42C23×C1112yes—
372C2×C42C23×C1113yes—
373C2×C42C23×C1116yes—
374C2×C42C23×C1116yes—
375C2×C42C23×C1113yes—
376C2×C42C23×C1113yes—
377C2×C42C23×C1113yes—
378C2×C42C23×C11124yes—
379C2×C42C23×C11148yes—
380C2×C11—24no—
381C2×C11—412no—
382C2×C11#348014yesdirect product factor
383C2×C11C23×#4111yescharacteristic
384C2×C11C23×#4111yescharacteristic
385C2×C11C2×#58511yescharacteristic
386C24C24×C1116yes—
387C24C24×C1111yescharacteristic
388#41—264no—
389#41—296no—
390C2×Q8—232no—
391C2×Q8—212no—
392C2×Q8—212no—
393C2×Q8C11×#4118yescomplemented
394C2×Q8C24×C11112yes—
395C2×Q8C24×C11112yes—
396C2×Q8C24×C1114yes—
397C2×D4—224no—
398C2×D4—224no—
399C2×D4—212no—
400C2×D4—412no—
401C2×D4C24×C11124yes—
402C2×D4C24×C11124yes—
403C2×D4C24×C11112yes—
404C2×D4C24×C11124yes—
405C22×C4—212no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—412no—
409C22×C4—46no—
410C22×C4C11×#4118yescomplemented
411C22×C4C24×C1112yes—
412C22×C4C24×C1112yes—
413C22×C4C24×C1113yes—
414C22×C4C24×C1113yes—
415C22×C4C24×C1116yes—
416C22×C4C24×C1113yes—
417C22×C4C24×C11112yes—
418C22×C4C24×C11124yes—
419C22×C4C24×C11124yes—
420C22×C4C24×C11112yes—
421C22×C4C24×C11124yes—
422C22×C4C24×C1111yescharacteristic
423C22×C4C24×C1111yescharacteristic
424C22×C4C24×C1113yes—
425C22×C4C24×C1114yes—
426C4⋊C4C24×C11112yes—
427C4⋊C4C24×C11112yes—
428C4⋊C4C24×C11124yes—
429C4⋊C4C24×C1114yes—
430C4⋊C4C24×C1114yes—
431C4⋊C4C24×C11124yes—
432C4⋊C4C24×C11124yes—
433C4⋊C4C24×C11124yes—
434C4⋊C4C24×C11124yes—
435C22⋊C4C24×C1118yes—
436C22⋊C4C24×C11124yes—
437C22⋊C4C24×C11148yes—
438C22⋊C4C24×C11124yes—
439C22⋊C4C24×C11148yes—
440C42C24×C1118yes—
441C42C24×C11112yes—
442C42C24×C11112yes—
443C42C24×C11124yes—
444C42C24×C11124yes—
445C42C24×C11112yes—
446C42C24×C11112yes—
447C11C2×#348011yescharacteristic, direct product factor, Sylow
448C23—22no—
449C23—22no—
450C23—212no—
451C23—212no—
452C23—212no—
453C23C2×C11×#4114yes—
454C23C25×C11112yes—
455C23C25×C1112yes—
456C23C25×C1111yescharacteristic
457Q8—224no—
458Q8—224no—
459Q8C2×C11×#41116yescomplemented
460D4—248no—
461D4—248no—
462D4—224no—
463D4—424no—
464C2×C4—24no—
465C2×C4—212no—
466C2×C4—26no—
467C2×C4—24no—
468C2×C4—26no—
469C2×C4—26no—
470C2×C4—224no—
471C2×C4—248no—
472C2×C4—248no—
473C2×C4—424no—
474C2×C4—412no—
475C2×C4C2×C11×#4114yes—
476C2×C4C2×C11×#41112yes—
477C2×C4C2×C11×#4114yes—
478C2×C4C2×C11×#41116yescomplemented
479C2×C4C25×C1114yes—
480C2×C4C25×C1114yes—
481C2×C4C25×C1116yes—
482C2×C4C25×C1116yes—
483C2×C4C25×C11112yes—
484C2×C4C25×C1116yes—
485C2×C4C25×C1112yes—
486C2×C4C25×C1112yes—
487C2×C4C25×C1116yes—
488C22—28no—
489C22—22no—
490C22—22no—
491C22—212no—
492C22—212no—
493C22—212no—
494C22—424no—
495C22C22×C11×#4114yes—
496C22C22×C11×#4112yes—
497C22C22×C11×#4112yes—
498C22C11×#58512yes—
499C22C26×C1111yescharacteristic
500C4—24no—
501C4—212no—
502C4—26no—
503C4—24no—
504C4—26no—
505C4—26no—
506C4C22×C11×#4114yes—
507C4C22×C11×#41112yes—
508C4C22×C11×#4114yes—
509C2—24no—
510C2—412no—
511C2C11×#348014yesdirect product factor
512C2C23×C11×#4111yescharacteristic
513C2C23×C11×#4111yescharacteristic
514C2C2×C11×#58511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC22C26×C11
socleC23×C11C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3480C2direct (N × H)
2. C2×C11×#559C2semidirect
3. C2×C11×#557C2semidirect
4. C2×C11×#556C2semidirect
5. C2×C11×#553C2semidirect
6. C2×C11×#550C2semidirect
7. C2×C11×#548C2semidirect
8. C2×C11×#532C2semidirect
9. C2×C11×#529C2semidirect
10. C2×C4×C11×#41C2semidirect
11. C2×C4×C11×#41C2semidirect
12. C22×C4×Q8×C11C2semidirect
16. C11×#559C22semidirect
17. C11×#557C22semidirect
18. C11×#556C22semidirect
19. C11×#553C22semidirect
20. C11×#550C22semidirect
21. C11×#548C22semidirect
22. C11×#532C22semidirect
25. C11×#529C22semidirect
35. C4×C11×#41C22semidirect
36. C4×C11×#41C22semidirect
44. C2×C4×Q8×C11C22semidirect
129. C2×#3480C11direct (N × H)
137. C2×Q8×C11#41semidirect
154. C22×C4×C11#41semidirect
191. #3480C2×C11direct (N × H)
192. C2×#559C2×C11semidirect
193. C2×#557C2×C11semidirect
194. C2×#556C2×C11semidirect
195. C2×#553C2×C11semidirect
196. C2×#550C2×C11semidirect
197. C2×#548C2×C11semidirect
198. C2×#532C2×C11semidirect
199. C2×#529C2×C11semidirect
200. C2×C4×#41C2×C11semidirect
201. C2×C4×#41C2×C11semidirect
202. C22×C4×Q8C2×C11semidirect
214. Q8×C11C2×#41semidirect
233. C2×C4×C11C2×#41semidirect
246. #559C22×C11semidirect
247. #557C22×C11semidirect
248. #556C22×C11semidirect
249. #553C22×C11semidirect
250. #550C22×C11semidirect
251. #548C22×C11semidirect
252. #532C22×C11semidirect
255. #529C22×C11semidirect
265. C4×#41C22×C11semidirect
266. C4×#41C22×C11semidirect
274. C2×C4×Q8C22×C11semidirect
382. C2×C11#3480direct (N × H)
393. C2×Q8C11×#41semidirect
410. C22×C4C11×#41semidirect
447. C11C2×#3480direct (N × H)
459. Q8C2×C11×#41semidirect
478. C2×C4C2×C11×#41semidirect
511. C2C11×#3480direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34802
C2×C11×#5592
C2×C11×#5572
C2×C11×#5562
C2×C11×#5532
C2×C11×#5502
C2×C11×#5482
C2×C11×#5322
C2×C11×#5292
C2×C4×C11×#412
C22×C4×Q8×C112
C2×#348011