Finite Group Databasebeta

← C2×C11×#3482 #14639908

Subgroups — C2×C11×#3482 #14639908

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C2132yesmaximal, direct product factor
2C2×C11×#557C211yesmaximal, characteristic, complemented
3C2×C11×#556C213yesmaximal, complemented
4C2×C11×#552C216yesmaximal, complemented
5C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
6C2×C11×#548C212yesmaximal, complemented
7C2×C11×#547C213yesmaximal, complemented
8C2×C11×#533C213yesmaximal, complemented
9C2×C11×#529C216yesmaximal, complemented
10C2×C4×C11×#41C213yesmaximal, complemented
11C2×C4×C11×#41C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C11C212yesmaximal, complemented
13C22×C11×#41C2213yes—
14C22×C11×#41C2211yescharacteristic
15C23×Q8×C11C2212yes—
16C11×#557C22116yescomplemented
17C11×#556C22148yescomplemented
18C11×#552C22196yescomplemented
19D4×Q8×C11C22116yescomplemented
20C11×#548C22132yescomplemented
21C11×#547C22148yescomplemented
22C11×#533C22148yescomplemented
23C2×C11×C4⋊Q8C2213yes—
24C2×C11×C4⋊Q8C2213yes—
25C11×#529C22196yescomplemented
26C2×C11×#126C22112yes—
27C2×C11×#125C2216yes—
28C2×C11×#125C2216yes—
29C2×C11×#124C2216yes—
30C2×C11×#123C22112yes—
31C2×C11×C22⋊Q8C2216yes—
32C2×C11×C22⋊Q8C2216yes—
33C2×C11×C22⋊Q8C2216yes—
34C2×C11×#121C2216yes—
35C4×C11×#41C22148yescomplemented
36C4×C11×#41C22116yescomplemented
37C2×C4×Q8×C11C2211yescharacteristic
38C2×C4×Q8×C11C2216yes—
39C2×C4×Q8×C11C2212yes—
40C2×C4×Q8×C11C2216yes—
41C2×C4×Q8×C11C2213yes—
42C2×C4×Q8×C11C2211yescharacteristic
43C2×C4×Q8×C11C2213yes—
44C2×C4×Q8×C11C22132yescomplemented
45C2×C4×D4×C11C2211yescharacteristic
46C2×C4×D4×C11C2213yes—
47C2×C4×D4×C11C2216yes—
48C2×C4×D4×C11C2213yes—
49C2×C4×D4×C11C2213yes—
50C2×C4×D4×C11C2216yes—
51C2×C11×#117C2213yes—
52C2×C11×#117C2216yes—
53C2×C11×#117C2213yes—
54C2×C11×#117C2216yes—
55C22×C11×C4⋊C4C2216yes—
56C22×C42×C11C2216yes—
57C22×C42×C11C2213yes—
58C2×C11×#41—28no—
59C2×C11×#41—224no—
60C2×C11×#41C23124yes—
61C2×C11×#41C2318yes—
62C22×Q8×C11—216no—
63C22×Q8×C11C2316yes—
64C22×Q8×C11C2313yes—
65C22×Q8×C11C23116yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11C2316yes—
68C22×D4×C11C2313yes—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2316yes—
71C23×C4×C11C2316yes—
72C23×C4×C11C2313yes—
73C23×C4×C11C2313yes—
74C23×C4×C11C2312yes—
75C23×C4×C11C2313yes—
76C11×C4⋊Q8C23124yes—
77C11×C4⋊Q8C23124yes—
78C11×#126C23196yes—
79C11×#125C23148yes—
80C11×#125C23148yes—
81C11×#124C23148yes—
82C11×#123C23196yes—
83C11×C22⋊Q8C23148yes—
84C11×C22⋊Q8C23148yes—
85C11×C22⋊Q8C23148yes—
86C11×#121C23148yes—
87C4×Q8×C11C2318yes—
88C4×Q8×C11C23148yes—
89C4×Q8×C11C23116yes—
90C4×Q8×C11C23148yes—
91C4×Q8×C11C23124yes—
92C4×Q8×C11C2318yes—
93C4×Q8×C11C23124yes—
94C4×D4×C11C2318yes—
95C4×D4×C11C23124yes—
96C4×D4×C11C23148yes—
97C4×D4×C11C23124yes—
98C4×D4×C11C23124yes—
99C4×D4×C11C23148yes—
100C11×#117C23124yes—
101C11×#117C23148yes—
102C11×#117C23124yes—
103C11×#117C23148yes—
104C2×C11×C4⋊C4C2313yes—
105C2×C11×C4⋊C4C2316yes—
106C2×C11×C4⋊C4C23112yes—
107C2×C11×C4⋊C4C23148yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2316yes—
110C2×C11×C4⋊C4C2313yes—
111C2×C11×C4⋊C4C2313yes—
112C2×C11×C4⋊C4C2316yes—
113C2×C11×C4⋊C4C2316yes—
114C2×C11×C4⋊C4C2316yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2316yes—
117C2×C11×C22⋊C4C2316yes—
118C2×C11×C22⋊C4C2316yes—
119C2×C11×C22⋊C4C23112yes—
120C2×C42×C11C2313yes—
121C2×C42×C11C2316yes—
122C2×C42×C11C2313yes—
123C2×C42×C11C2316yes—
124C2×C42×C11C23148yes—
125C2×C42×C11C23124yes—
126C2×C42×C11C2313yes—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2316yes—
129C2×#3482C1111yesmaximal, characteristic, direct product factor, Sylow
130C24×C11C2413yes—
131C24×C11C2412yes—
132C11×#41—232no—
133C11×#41—296no—
134C2×Q8×C11—264no—
135C2×Q8×C11—224no—
136C2×Q8×C11—212no—
137C2×Q8×C11#4118yescomplemented
138C2×Q8×C11C24124yes—
139C2×Q8×C11C24112yes—
140C2×Q8×C11C2414yes—
141C2×D4×C11—224no—
142C2×D4×C11—212no—
143C2×D4×C11#4118yescomplemented
144C2×D4×C11C24124yes—
145C2×D4×C11C24112yes—
146C2×D4×C11C2414yes—
147C22×C4×C11—224no—
148C22×C4×C11—224no—
149C22×C4×C11—212no—
150C22×C4×C11—212no—
151C22×C4×C11—28no—
152C22×C4×C11—212no—
153C22×C4×C11C2412yes—
154C22×C4×C11C2418yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2413yes—
157C22×C4×C11C2413yes—
158C22×C4×C11C2416yes—
159C22×C4×C11C2416yes—
160C22×C4×C11C24124yes—
161C22×C4×C11C24124yes—
162C22×C4×C11C24112yes—
163C22×C4×C11C24112yes—
164C22×C4×C11C24112yes—
165C22×C4×C11C2413yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C11×C4⋊C4C24112yes—
169C11×C4⋊C4C24124yes—
170C11×C4⋊C4C24148yes—
171C11×C4⋊C4C2414yes—
172C11×C4⋊C4C24124yes—
173C11×C4⋊C4C24112yes—
174C11×C4⋊C4C24112yes—
175C11×C4⋊C4C24124yes—
176C11×C4⋊C4C24124yes—
177C11×C4⋊C4C24124yes—
178C11×C22⋊C4C2418yes—
179C11×C22⋊C4C24124yes—
180C11×C22⋊C4C24124yes—
181C11×C22⋊C4C24124yes—
182C11×C22⋊C4C24148yes—
183C42×C11C24112yes—
184C42×C11C2414yes—
185C42×C11C24112yes—
186C42×C11C24124yes—
187C42×C11C24124yes—
188C42×C11C24112yes—
189C42×C11C24124yes—
190#3482C2×C11132yesdirect product factor
191C2×#557C2×C1111yescharacteristic, complemented
192C2×#556C2×C1113yescomplemented
193C2×#552C2×C1116yescomplemented
194C2×D4×Q8C2×C1111yescharacteristic, complemented
195C2×#548C2×C1112yescomplemented
196C2×#547C2×C1113yescomplemented
197C2×#533C2×C1113yescomplemented
198C2×#529C2×C1116yescomplemented
199C2×C4×#41C2×C1111yescharacteristic, complemented
200C2×C4×#41C2×C1113yescomplemented
201C22×C4×Q8C2×C1112yescomplemented
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—26no—
205C23×C11—26no—
206C23×C11—26no—
207C23×C11C2×#4118yes—
208C23×C11C2516yes—
209C23×C11C2514yes—
210C23×C11C2511yescharacteristic
211Q8×C11—248no—
212Q8×C11—224no—
213Q8×C11C2×#41116yescomplemented
214D4×C11—248no—
215D4×C11—224no—
216D4×C11C2×#41116yescomplemented
217C2×C4×C11—26no—
218C2×C4×C11—22no—
219C2×C4×C11—212no—
220C2×C4×C11—212no—
221C2×C4×C11—248no—
222C2×C4×C11—24no—
223C2×C4×C11—26no—
224C2×C4×C11—248no—
225C2×C4×C11—224no—
226C2×C4×C11—224no—
227C2×C4×C11—216no—
228C2×C4×C11—224no—
229C2×C4×C11C2×#41112yes—
230C2×C4×C11C2×#4114yes—
231C2×C4×C112−1+414yes—
232C2×C4×C11C2514yes—
233C2×C4×C11C2512yes—
234C2×C4×C11C2516yes—
235C2×C4×C11C2516yes—
236C2×C4×C11C25112yes—
237C2×C4×C11C25112yes—
238C2×C4×C11C2516yes—
239C2×C4×C11C2512yes—
240C2×C4×C11C2512yes—
241C22×#41C22×C1113yes—
242C22×#41C22×C1111yescharacteristic
243C23×Q8C22×C1112yes—
244#557C22×C11116yescomplemented
245#556C22×C11148yescomplemented
246#552C22×C11196yescomplemented
247D4×Q8C22×C11116yescomplemented
248#548C22×C11132yescomplemented
249#547C22×C11148yescomplemented
250#533C22×C11148yescomplemented
251C2×C4⋊Q8C22×C1113yes—
252C2×C4⋊Q8C22×C1113yes—
253#529C22×C11196yescomplemented
254C2×#126C22×C11112yes—
255C2×#125C22×C1116yes—
256C2×#125C22×C1116yes—
257C2×#124C22×C1116yes—
258C2×#123C22×C11112yes—
259C2×C22⋊Q8C22×C1116yes—
260C2×C22⋊Q8C22×C1116yes—
261C2×C22⋊Q8C22×C1116yes—
262C2×#121C22×C1116yes—
263C4×#41C22×C11148yescomplemented
264C4×#41C22×C11116yescomplemented
265C2×C4×Q8C22×C1111yescharacteristic
266C2×C4×Q8C22×C1116yes—
267C2×C4×Q8C22×C1112yes—
268C2×C4×Q8C22×C1116yes—
269C2×C4×Q8C22×C1113yes—
270C2×C4×Q8C22×C1111yescharacteristic
271C2×C4×Q8C22×C1113yes—
272C2×C4×Q8C22×C11132yescomplemented
273C2×C4×D4C22×C1111yescharacteristic
274C2×C4×D4C22×C1116yes—
275C2×C4×D4C22×C1113yes—
276C2×C4×D4C22×C1113yes—
277C2×C4×D4C22×C1113yes—
278C2×C4×D4C22×C1116yes—
279C2×#117C22×C1113yes—
280C2×#117C22×C1116yes—
281C2×#117C22×C1113yes—
282C2×#117C22×C1116yes—
283C22×C4⋊C4C22×C1116yes—
284C22×C42C22×C1116yes—
285C22×C42C22×C1113yes—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—216no—
289C22×C11—26no—
290C22×C11—26no—
291C22×C11—26no—
292C22×C11—412no—
293C22×C11C22×#4118yes—
294C22×C11C22×#4112yes—
295C22×C11C22×#4112yes—
296C22×C11C2×2−1+412yes—
297C22×C11C2611yescharacteristic
298C4×C11—26no—
299C4×C11—22no—
300C4×C11—212no—
301C4×C11—212no—
302C4×C11—24no—
303C4×C11—26no—
304C4×C11C22×#41112yes—
305C4×C11C22×#4114yes—
306C4×C11C2×2−1+414yes—
307C2×#41—28no—
308C2×#41—224no—
309C2×#41C23×C11124yes—
310C2×#41C23×C1118yes—
311C22×Q8—216no—
312C22×Q8C23×C1116yes—
313C22×Q8C23×C1113yes—
314C22×Q8C23×C11116yes—
315C22×Q8C23×C1111yescharacteristic
316C22×D4C23×C1116yes—
317C22×D4C23×C1113yes—
318C22×D4C23×C1111yescharacteristic
319C23×C4C23×C1116yes—
320C23×C4C23×C1116yes—
321C23×C4C23×C1113yes—
322C23×C4C23×C1113yes—
323C23×C4C23×C1113yes—
324C23×C4C23×C1112yes—
325C4⋊Q8C23×C11124yes—
326C4⋊Q8C23×C11124yes—
327#126C23×C11196yes—
328#125C23×C11148yes—
329#125C23×C11148yes—
330#124C23×C11148yes—
331#123C23×C11196yes—
332C22⋊Q8C23×C11148yes—
333C22⋊Q8C23×C11148yes—
334C22⋊Q8C23×C11148yes—
335#121C23×C11148yes—
336C4×Q8C23×C1118yes—
337C4×Q8C23×C11148yes—
338C4×Q8C23×C11116yes—
339C4×Q8C23×C11148yes—
340C4×Q8C23×C11124yes—
341C4×Q8C23×C1118yes—
342C4×Q8C23×C11124yes—
343C4×D4C23×C1118yes—
344C4×D4C23×C11124yes—
345C4×D4C23×C11148yes—
346C4×D4C23×C11124yes—
347C4×D4C23×C11124yes—
348C4×D4C23×C11148yes—
349#117C23×C11124yes—
350#117C23×C11148yes—
351#117C23×C11124yes—
352#117C23×C11148yes—
353C2×C4⋊C4C23×C1113yes—
354C2×C4⋊C4C23×C1116yes—
355C2×C4⋊C4C23×C11112yes—
356C2×C4⋊C4C23×C11148yes—
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C4⋊C4C23×C1116yes—
359C2×C4⋊C4C23×C1113yes—
360C2×C4⋊C4C23×C1113yes—
361C2×C4⋊C4C23×C1116yes—
362C2×C4⋊C4C23×C1116yes—
363C2×C4⋊C4C23×C1116yes—
364C2×C22⋊C4C23×C1112yes—
365C2×C22⋊C4C23×C1116yes—
366C2×C22⋊C4C23×C1116yes—
367C2×C22⋊C4C23×C1116yes—
368C2×C22⋊C4C23×C11112yes—
369C2×C42C23×C1113yes—
370C2×C42C23×C1116yes—
371C2×C42C23×C1116yes—
372C2×C42C23×C1113yes—
373C2×C42C23×C1116yes—
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1113yes—
376C2×C42C23×C11148yes—
377C2×C42C23×C11124yes—
378C2×C11—28no—
379C2×C11—46no—
380C2×C11#348214yesdirect product factor
381C2×C11C23×#4111yescharacteristic
382C2×C11C23×#4111yescharacteristic
383C2×C11C22×2−1+411yescharacteristic
384C24C24×C1113yes—
385C24C24×C1112yes—
386#41—232no—
387#41—296no—
388C2×Q8—264no—
389C2×Q8—224no—
390C2×Q8—212no—
391C2×Q8C11×#4118yescomplemented
392C2×Q8C24×C11124yes—
393C2×Q8C24×C11112yes—
394C2×Q8C24×C1114yes—
395C2×D4—224no—
396C2×D4—212no—
397C2×D4C11×#4118yescomplemented
398C2×D4C24×C11124yes—
399C2×D4C24×C11112yes—
400C2×D4C24×C1114yes—
401C22×C4—224no—
402C22×C4—224no—
403C22×C4—212no—
404C22×C4—212no—
405C22×C4—28no—
406C22×C4—212no—
407C22×C4C24×C1112yes—
408C22×C4C24×C1118yes—
409C22×C4C24×C1111yescharacteristic
410C22×C4C24×C1113yes—
411C22×C4C24×C1113yes—
412C22×C4C24×C1116yes—
413C22×C4C24×C1116yes—
414C22×C4C24×C11124yes—
415C22×C4C24×C11124yes—
416C22×C4C24×C11112yes—
417C22×C4C24×C11112yes—
418C22×C4C24×C11112yes—
419C22×C4C24×C1113yes—
420C22×C4C24×C1111yescharacteristic
421C22×C4C24×C1111yescharacteristic
422C4⋊C4C24×C11112yes—
423C4⋊C4C24×C11124yes—
424C4⋊C4C24×C11148yes—
425C4⋊C4C24×C1114yes—
426C4⋊C4C24×C11124yes—
427C4⋊C4C24×C11112yes—
428C4⋊C4C24×C11112yes—
429C4⋊C4C24×C11124yes—
430C4⋊C4C24×C11124yes—
431C4⋊C4C24×C11124yes—
432C22⋊C4C24×C1118yes—
433C22⋊C4C24×C11124yes—
434C22⋊C4C24×C11124yes—
435C22⋊C4C24×C11124yes—
436C22⋊C4C24×C11148yes—
437C42C24×C11112yes—
438C42C24×C1114yes—
439C42C24×C11112yes—
440C42C24×C11124yes—
441C42C24×C11124yes—
442C42C24×C11112yes—
443C42C24×C11124yes—
444C11C2×#348211yescharacteristic, direct product factor, Sylow
445C23—24no—
446C23—24no—
447C23—26no—
448C23—26no—
449C23—26no—
450C23C2×C11×#4118yes—
451C23C25×C1116yes—
452C23C25×C1114yes—
453C23C25×C1111yescharacteristic
454Q8—248no—
455Q8—224no—
456Q8C2×C11×#41116yescomplemented
457D4—248no—
458D4—224no—
459D4C2×C11×#41116yescomplemented
460C2×C4—26no—
461C2×C4—22no—
462C2×C4—212no—
463C2×C4—212no—
464C2×C4—248no—
465C2×C4—24no—
466C2×C4—26no—
467C2×C4—248no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—216no—
471C2×C4—224no—
472C2×C4C2×C11×#41112yes—
473C2×C4C2×C11×#4114yes—
474C2×C4C11×2−1+414yes—
475C2×C4C25×C1114yes—
476C2×C4C25×C1112yes—
477C2×C4C25×C1116yes—
478C2×C4C25×C1116yes—
479C2×C4C25×C11112yes—
480C2×C4C25×C11112yes—
481C2×C4C25×C1116yes—
482C2×C4C25×C1112yes—
483C2×C4C25×C1112yes—
484C22—216no—
485C22—24no—
486C22—24no—
487C22—26no—
488C22—26no—
489C22—26no—
490C22—412no—
491C22C22×C11×#4118yes—
492C22C22×C11×#4112yes—
493C22C22×C11×#4112yes—
494C22C2×C11×2−1+412yes—
495C22C26×C1111yescharacteristic
496C4—26no—
497C4—22no—
498C4—212no—
499C4—212no—
500C4—24no—
501C4—26no—
502C4C22×C11×#41112yes—
503C4C22×C11×#4114yes—
504C4C2×C11×2−1+414yes—
505C2—28no—
506C2—46no—
507C2C11×#348214yesdirect product factor
508C2C23×C11×#4111yescharacteristic
509C2C23×C11×#4111yescharacteristic
510C2C22×C11×2−1+411yescharacteristic
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×#3482C2direct (N × H)
2. C2×C11×#557C2semidirect
3. C2×C11×#556C2semidirect
4. C2×C11×#552C2semidirect
5. C2×D4×Q8×C11C2semidirect
6. C2×C11×#548C2semidirect
7. C2×C11×#547C2semidirect
8. C2×C11×#533C2semidirect
9. C2×C11×#529C2semidirect
10. C2×C4×C11×#41C2semidirect
11. C2×C4×C11×#41C2semidirect
12. C22×C4×Q8×C11C2semidirect
16. C11×#557C22semidirect
17. C11×#556C22semidirect
18. C11×#552C22semidirect
19. D4×Q8×C11C22semidirect
20. C11×#548C22semidirect
21. C11×#547C22semidirect
22. C11×#533C22semidirect
25. C11×#529C22semidirect
35. C4×C11×#41C22semidirect
36. C4×C11×#41C22semidirect
44. C2×C4×Q8×C11C22semidirect
129. C2×#3482C11direct (N × H)
137. C2×Q8×C11#41semidirect
143. C2×D4×C11#41semidirect
190. #3482C2×C11direct (N × H)
191. C2×#557C2×C11semidirect
192. C2×#556C2×C11semidirect
193. C2×#552C2×C11semidirect
194. C2×D4×Q8C2×C11semidirect
195. C2×#548C2×C11semidirect
196. C2×#547C2×C11semidirect
197. C2×#533C2×C11semidirect
198. C2×#529C2×C11semidirect
199. C2×C4×#41C2×C11semidirect
200. C2×C4×#41C2×C11semidirect
201. C22×C4×Q8C2×C11semidirect
213. Q8×C11C2×#41semidirect
216. D4×C11C2×#41semidirect
244. #557C22×C11semidirect
245. #556C22×C11semidirect
246. #552C22×C11semidirect
247. D4×Q8C22×C11semidirect
248. #548C22×C11semidirect
249. #547C22×C11semidirect
250. #533C22×C11semidirect
253. #529C22×C11semidirect
263. C4×#41C22×C11semidirect
264. C4×#41C22×C11semidirect
272. C2×C4×Q8C22×C11semidirect
380. C2×C11#3482direct (N × H)
391. C2×Q8C11×#41semidirect
397. C2×D4C11×#41semidirect
444. C11C2×#3482direct (N × H)
456. Q8C2×C11×#41semidirect
459. D4C2×C11×#41semidirect
507. C2C11×#3482direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34822
C2×C11×#5572
C2×C11×#5562
C2×C11×#5522
C2×D4×Q8×C112
C2×C11×#5482
C2×C11×#5472
C2×C11×#5332
C2×C11×#5292
C2×C4×C11×#412
C22×C4×Q8×C112
C2×#348211