Finite Group Databasebeta

← C2×C11×#3353 #14638439

Subgroups — C2×C11×#3353 #14638439

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic, complemented
2C2×C11×#547C211yesmaximal, characteristic
3C11×#3353C2116yesmaximal, direct product factor
4C2×C11×#500C211yesmaximal, characteristic, complemented
5C2×C11×#484C212yesmaximal, complemented
6C2×C11×#482C212yesmaximal, complemented
7C2×C11×#475C211yesmaximal, characteristic, complemented
8C2×C11×#474C211yesmaximal, characteristic, complemented
9C2×C11×#468C212yesmaximal, complemented
10C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C2×C11×#428C212yesmaximal, complemented
13C22×C11×#41—21no—
14C22×C11×SD16C2211yescharacteristic
15C22×C11×M16C2212yes—
16C11×#556—24no—
17C11×#556C2218yescomplemented
18C11×#547—24no—
19C11×#547C2218yes—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#126—22no—
23C2×C11×#124—21no—
24C2×C11×#123—22no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×#121C2212yes—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2212yes—
33C22×C11×C4⋊C4C2212yes—
34C11×#500C2218yescomplemented
35C11×#484C22116yescomplemented
36C11×#482C22116yescomplemented
37C11×#475C2218yescomplemented
38C11×#474C2218yescomplemented
39C11×#468C22116yescomplemented
40C4×C11×SD16C2218yescomplemented
41C11×#436C2218yescomplemented
42C11×#428C22116yescomplemented
43C2×C11×#107C2212yes—
44C2×C11×#107C2212yes—
45C2×C11×#107C2212yes—
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2212yes—
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2212yes—
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2212yes—
53C2×C11×C22⋊C8C2212yes—
54C2×C4×C8×C11C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—22no—
64C23×C4×C11—21no—
65C23×C4×C11C2312yes—
66C2×C11×SD16—24no—
67C2×C11×SD16C2314yes—
68C2×C11×M16—28no—
69C2×C11×M16C2318yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2312yes—
72C22×C8×C11C2311yescharacteristic
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C11×C4⋊Q8C2314yes—
77C11×#126—216no—
78C11×#124—28no—
79C11×#123—216no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—28no—
82C11×C22⋊Q8C2318yes—
83C11×#121—24no—
84C11×#121C2318yes—
85C4×Q8×C11—28no—
86C4×Q8×C11—22no—
87C4×Q8×C11C2314yes—
88C4×D4×C11—22no—
89C4×D4×C11D414yes—
90C4×D4×C11C2314yes—
91C4×D4×C11C2314yes—
92C11×#117—24no—
93C11×#117C2318yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2318yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4D412yes—
111C2×C42×C11—22no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C11×#107C2318yes—
115C11×#107C2318yes—
116C11×#107C2318yes—
117C11×#106C2314yes—
118C11×#106C2318yes—
119C11×C4⋊C8C2314yes—
120C11×#103C2314yes—
121C11×#103C2318yes—
122C11×#102C2314yes—
123C11×#102C2318yes—
124C11×C22⋊C8C2318yes—
125C4×C8×C11C2314yes—
126C2×#3353C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—21no—
128C24×C11C2×D412yes—
129C11×#41—432no—
130C2×Q8×C11—21no—
131C2×Q8×C11—24no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—44no—
136C2×Q8×C11—44no—
137C2×Q8×C11C2412yes—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—48no—
144C2×D4×C11C2×D414yes—
145C2×D4×C11C2412yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—28no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11—48no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2414yes—
162C22×C4×C11C2411yescharacteristic
163C11×SD16—28no—
164C11×M16—216no—
165C2×C8×C11—24no—
166C2×C8×C11—22no—
167C2×C8×C11#4114yescomplemented
168C2×C8×C11C2412yes—
169C2×C8×C11C2414yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4C2×D414yes—
181C11×C4⋊C4C2412yes—
182C11×C4⋊C4C2414yes—
183C11×C4⋊C4C2412yes—
184C11×C4⋊C4C2414yes—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4C2×D418yes—
190C42×C11—28no—
191C42×C11—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194C2×#556C2×C1111yescharacteristic, complemented
195C2×#547C2×C1111yescharacteristic
196#3353C2×C11116yesdirect product factor
197C2×#500C2×C1111yescharacteristic, complemented
198C2×#484C2×C1112yescomplemented
199C2×#482C2×C1112yescomplemented
200C2×#475C2×C1111yescharacteristic, complemented
201C2×#474C2×C1111yescharacteristic, complemented
202C2×#468C2×C1112yescomplemented
203C2×C4×SD16C2×C1111yescharacteristic, complemented
204C2×#436C2×C1111yescharacteristic, complemented
205C2×#428C2×C1112yescomplemented
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C22×D414yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—42no—
218Q8×C11—48no—
219Q8×C11—48no—
220D4×C11—28no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—416no—
224D4×C11—42no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—28no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—416no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—48no—
242C2×C4×C11AGL(1,ℤ/8)14yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C112−1+412yes—
249C2×C4×C11C2511yescharacteristic
250C8×C11—24no—
251C8×C11—22no—
252C8×C11C2×#4114yescomplemented
253C22×#41—21no—
254C22×SD16C22×C1111yescharacteristic
255C22×M16C22×C1112yes—
256#556—24no—
257#556C22×C1118yescomplemented
258#547—24no—
259#547C22×C1118yes—
260C2×C4⋊Q8C22×C1111yescharacteristic
261C2×C4⋊Q8C22×C1111yescharacteristic
262C2×#126—22no—
263C2×#124—21no—
264C2×#123—22no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8C22×C1112yes—
267C2×#121C22×C1112yes—
268C2×C4×Q8—21no—
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×D4C22×C1111yescharacteristic
271C2×C4×D4C22×C1111yescharacteristic
272C2×#117C22×C1112yes—
273C22×C4⋊C4C22×C1112yes—
274#500C22×C1118yescomplemented
275#484C22×C11116yescomplemented
276#482C22×C11116yescomplemented
277#475C22×C1118yescomplemented
278#474C22×C1118yescomplemented
279#468C22×C11116yescomplemented
280C4×SD16C22×C1118yescomplemented
281#436C22×C1118yescomplemented
282#428C22×C11116yescomplemented
283C2×#107C22×C1112yes—
284C2×#107C22×C1112yes—
285C2×#107C22×C1112yes—
286C2×#106C22×C1112yes—
287C2×#106C22×C1111yescharacteristic
288C2×C4⋊C8C22×C1111yescharacteristic
289C2×#103C22×C1112yes—
290C2×#103C22×C1111yescharacteristic
291C2×#102C22×C1111yescharacteristic
292C2×#102C22×C1112yes—
293C2×C22⋊C8C22×C1112yes—
294C2×C4×C8C22×C1111yescharacteristic
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—48no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—84no—
303C22×C11#54712yes—
304C22×C11C2×AGL(1,ℤ/8)12yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11—44no—
313C4×C11—42no—
314C4×C11#54712yes—
315C4×C11C2×AGL(1,ℤ/8)14yes—
316C4×C11C22×#4111yescharacteristic
317C4×C11C2×2−1+411yescharacteristic
318C2×#41—28no—
319C2×#41—48no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8C23×C1111yescharacteristic
323C22×D4—22no—
324C22×D4D4×C1111yescharacteristic
325C22×D4C23×C1111yescharacteristic
326C23×C4—22no—
327C23×C4—21no—
328C23×C4C23×C1112yes—
329C2×SD16—24no—
330C2×SD16C23×C1114yes—
331C2×M16—28no—
332C2×M16C23×C1118yes—
333C22×C8C23×C1112yes—
334C22×C8C23×C1111yescharacteristic
335C22×C8C23×C1111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C23×C1114yes—
339C4⋊Q8C23×C1114yes—
340#126—216no—
341#124—28no—
342#123—216no—
343C22⋊Q8—24no—
344C22⋊Q8—28no—
345C22⋊Q8C23×C1118yes—
346#121—24no—
347#121C23×C1118yes—
348C4×Q8—28no—
349C4×Q8—22no—
350C4×Q8C23×C1114yes—
351C4×D4—22no—
352C4×D4D4×C1114yes—
353C4×D4C23×C1114yes—
354C4×D4C23×C1114yes—
355#117—24no—
356#117C23×C1118yes—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1112yes—
366C2×C4⋊C4C23×C1118yes—
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1112yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C1112yes—
374C2×C42—22no—
375C2×C42—21no—
376C2×C42C23×C1111yescharacteristic
377#107C23×C1118yes—
378#107C23×C1118yes—
379#107C23×C1118yes—
380#106C23×C1114yes—
381#106C23×C1118yes—
382C4⋊C8C23×C1114yes—
383#103C23×C1114yes—
384#103C23×C1118yes—
385#102C23×C1114yes—
386#102C23×C1118yes—
387C22⋊C8C23×C1118yes—
388C4×C8C23×C1114yes—
389C2×C11—44no—
390C2×C11—82no—
391C2×C11#335314yesdirect product factor
392C2×C11C2×#54711yescharacteristic
393C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C11C2×#57811yescharacteristic
395C24—21no—
396C24C2×D4×C1112yes—
397#41—432no—
398C2×Q8—21no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8—44no—
405C2×Q8C24×C1112yes—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—48no—
412C2×D4C2×D4×C1114yes—
413C2×D4C24×C1112yes—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—28no—
422C22×C4—24no—
423C22×C4—48no—
424C22×C4—44no—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1114yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C24×C1114yes—
430C22×C4C24×C1111yescharacteristic
431SD16—28no—
432M16—216no—
433C2×C8—24no—
434C2×C8—22no—
435C2×C8C11×#4114yescomplemented
436C2×C8C24×C1112yes—
437C2×C8C24×C1114yes—
438C2×C8C24×C1112yes—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—28no—
442C4⋊C4—28no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4C2×D4×C1114yes—
449C4⋊C4C24×C1112yes—
450C4⋊C4C24×C1114yes—
451C4⋊C4C24×C1112yes—
452C4⋊C4C24×C1114yes—
453C22⋊C4—28no—
454C22⋊C4—28no—
455C22⋊C4—24no—
456C22⋊C4—28no—
457C22⋊C4C2×D4×C1118yes—
458C42—28no—
459C42—24no—
460C42C2×D4×C1112yes—
461C42C24×C1112yes—
462C11C2×#335311yescharacteristic, direct product factor, Sylow
463C23—24no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×D4×C1114yes—
471C23C22×D4×C1111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—48no—
476Q8—48no—
477D4—28no—
478D4—22no—
479D4—22no—
480D4—416no—
481D4—42no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—28no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—416no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4C11×AGL(1,ℤ/8)14yes—
500C2×C4C22×D4×C1114yes—
501C2×C4C22×D4×C1112yes—
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C22×D4×C1112yes—
504C2×C4C2×C11×#4112yes—
505C2×C4C11×2−1+412yes—
506C2×C4C25×C1111yescharacteristic
507C8—24no—
508C8—22no—
509C8C2×C11×#4114yescomplemented
510C22—24no—
511C22—24no—
512C22—24no—
513C22—48no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—84no—
518C22C11×#54712yes—
519C22C2×C11×AGL(1,ℤ/8)12yes—
520C22C11×#57812yes—
521C22C23×D4×C1111yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—42no—
526C4—44no—
527C4—44no—
528C4—42no—
529C4C11×#54712yes—
530C4C2×C11×AGL(1,ℤ/8)14yes—
531C4C22×C11×#4111yescharacteristic
532C4C2×C11×2−1+411yescharacteristic
533C2—44no—
534C2—82no—
535C2C11×#335314yesdirect product factor
536C2C2×C11×#54711yescharacteristic
537C2C22×C11×AGL(1,ℤ/8)11yescharacteristic
538C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#556C2semidirect
3. C11×#3353C2direct (N × H)
4. C2×C11×#500C2semidirect
5. C2×C11×#484C2semidirect
6. C2×C11×#482C2semidirect
7. C2×C11×#475C2semidirect
8. C2×C11×#474C2semidirect
9. C2×C11×#468C2semidirect
10. C2×C4×C11×SD16C2semidirect
11. C2×C11×#436C2semidirect
12. C2×C11×#428C2semidirect
17. C11×#556C22semidirect
34. C11×#500C22semidirect
35. C11×#484C22semidirect
36. C11×#482C22semidirect
37. C11×#475C22semidirect
38. C11×#474C22semidirect
39. C11×#468C22semidirect
40. C4×C11×SD16C22semidirect
41. C11×#436C22semidirect
42. C11×#428C22semidirect
126. C2×#3353C11direct (N × H)
167. C2×C8×C11#41semidirect
194. C2×#556C2×C11semidirect
196. #3353C2×C11direct (N × H)
197. C2×#500C2×C11semidirect
198. C2×#484C2×C11semidirect
199. C2×#482C2×C11semidirect
200. C2×#475C2×C11semidirect
201. C2×#474C2×C11semidirect
202. C2×#468C2×C11semidirect
203. C2×C4×SD16C2×C11semidirect
204. C2×#436C2×C11semidirect
205. C2×#428C2×C11semidirect
252. C8×C11C2×#41semidirect
257. #556C22×C11semidirect
274. #500C22×C11semidirect
275. #484C22×C11semidirect
276. #482C22×C11semidirect
277. #475C22×C11semidirect
278. #474C22×C11semidirect
279. #468C22×C11semidirect
280. C4×SD16C22×C11semidirect
281. #436C22×C11semidirect
282. #428C22×C11semidirect
391. C2×C11#3353direct (N × H)
435. C2×C8C11×#41semidirect
462. C11C2×#3353direct (N × H)
509. C8C2×C11×#41semidirect
535. C2C11×#3353direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#5472
C11×#33532
C2×C11×#5002
C2×C11×#4842
C2×C11×#4822
C2×C11×#4752
C2×C11×#4742
C2×C11×#4682
C2×C4×C11×SD162
C2×C11×#4362
C2×C11×#4282
C2×#335311