Finite Group Databasebeta

← C2×C11×#2081 #14600843

Subgroups — C2×C11×#2081 #14600843

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C2×C11×#418C211yesmaximal, characteristic
4C22×C11×#100C211yesmaximal, characteristic
5C11×#2081C218yesmaximal, direct product factor
6C2×C11×#344C211yesmaximal, characteristic, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C11×#430—22no—
17C11×#430C2214yescomplemented
18C2×C11×#108—22no—
19C11×#418—22no—
20C11×#418—22no—
21C11×#418C2214yes—
22C11×#418C2214yes—
23C2×C11×#102—22no—
24C2×C11×#102—22no—
25C2×C11×#100—22no—
26C2×C11×#100—22no—
27C2×C11×#100C2214yes—
28C11×#344C2214yescomplemented
29C11×#344C2214yescomplemented
30C11×H(3,ℤ/4)C2214yescomplemented
31C25×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11D412yes—
44C22×D4×C11D412yes—
45C22×D4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16D412yes—
67C2×C11×M16C2312yes—
68C2×C11×M16C2312yes—
69C2×C11×M16C2312yes—
70C2×C11×M16C2312yes—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11D412yes—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117C2312yes—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C11×#108—28no—
90C11×#102—28no—
91C11×#102—28no—
92C11×#100—28no—
93C2×#2081C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—41no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11—84no—
102C24×C11#4111yescharacteristic
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C2×D414yes—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4111yescharacteristic
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16—41no—
162C11×M16—41no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—41no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11C2×D414yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—41no—
186C42×C11—41no—
187C2×#430C2×C1111yescharacteristic, complemented
188C2×#418C2×C1111yescharacteristic
189C2×#418C2×C1111yescharacteristic
190C22×#100C2×C1111yescharacteristic
191#2081C2×C1118yesdirect product factor
192C2×#344C2×C1111yescharacteristic, complemented
193C2×#344C2×C1111yescharacteristic, complemented
194C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11#12311yescharacteristic
211C23×C11#12311yescharacteristic
212C23×C11#12411yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12611yescharacteristic
215C23×C11#12611yescharacteristic
216C23×C11C2×#4111yescharacteristic
217D4×C11—24no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—82no—
228C2×C4×C11—82no—
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12111yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12311yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12311yescharacteristic
242C2×C4×C11#12311yescharacteristic
243C2×C4×C11#12411yescharacteristic
244C2×C4×C11#12411yescharacteristic
245C2×C4×C11#12611yescharacteristic
246C2×C4×C11#12611yescharacteristic
247C2×C4×C11#12611yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C8×C11—24no—
258C8×C11—42no—
259C8×C11—42no—
260C8×C11—42no—
261C23×D4C22×C1111yescharacteristic
262C22×M16C22×C1111yescharacteristic
263C22×M16C22×C1111yescharacteristic
264C22×M16C22×C1111yescharacteristic
265C22×M16C22×C1111yescharacteristic
266C2×#117C22×C1111yescharacteristic
267C2×#117C22×C1111yescharacteristic
268#430—22no—
269#430C22×C1114yescomplemented
270C2×#108—22no—
271#418—22no—
272#418—22no—
273#418C22×C1114yes—
274#418C22×C1114yes—
275C2×#102—22no—
276C2×#102—22no—
277C2×#100—22no—
278C2×#100—22no—
279C2×#100C22×C1114yes—
280#344C22×C1114yescomplemented
281#344C22×C1114yescomplemented
282H(3,ℤ/4)C22×C1114yescomplemented
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—44no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11—84no—
295C22×C11—84no—
296C22×C11—84no—
297C22×C11—84no—
298C22×C11#39711yescharacteristic
299C22×C11#39711yescharacteristic
300C22×C11#39711yescharacteristic
301C22×C11#39711yescharacteristic
302C22×C11C2×#12311yescharacteristic
303C22×C11C2×#12411yescharacteristic
304C22×C11C2×#12611yescharacteristic
305C4×C11—82no—
306C4×C11—82no—
307C4×C11#39711yescharacteristic
308C4×C11#39711yescharacteristic
309C4×C11#39711yescharacteristic
310C4×C11#39711yescharacteristic
311C4×C11C2×#12111yescharacteristic
312C4×C11C2×#12311yescharacteristic
313C4×C11C2×#12311yescharacteristic
314C4×C11C2×#12611yescharacteristic
315C25—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4D4×C1112yes—
328C22×D4D4×C1112yes—
329C22×D4C23×C1112yes—
330C23×C4C23×C1111yescharacteristic
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16D4×C1112yes—
351C2×M16C23×C1112yes—
352C2×M16C23×C1112yes—
353C2×M16C23×C1112yes—
354C2×M16C23×C1112yes—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8D4×C1112yes—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117C23×C1112yes—
366#117C23×C1112yes—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42—21no—
372C2×C42—21no—
373#108—28no—
374#102—28no—
375#102—28no—
376#100—28no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—84no—
384C2×C11#208112yesdirect product factor
385C2×C11C2×#39711yescharacteristic
386C24—22no—
387C24—22no—
388C24—22no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—84no—
394C24C11×#4111yescharacteristic
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4C2×D4×C1114yes—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C11×#4111yescharacteristic
430C22×C4C11×#4111yescharacteristic
431C22×C4C11×#4111yescharacteristic
432C22×C4C11×#4111yescharacteristic
433C22×C4C11×#4111yescharacteristic
434C22×C4C11×#4111yescharacteristic
435C22×C4C11×#4111yescharacteristic
436C22×C4C11×#4111yescharacteristic
437C22×C4C11×#4111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—22no—
447M16—22no—
448M16—22no—
449M16—41no—
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—41no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8C2×D4×C1114yes—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—22no—
476C42—22no—
477C42—41no—
478C42—41no—
479C11C2×#208111yescharacteristic, direct product factor, Sylow
480C23—24no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23—84no—
494C23—84no—
495C23C11×#12311yescharacteristic
496C23C11×#12311yescharacteristic
497C23C11×#12411yescharacteristic
498C23C11×#12411yescharacteristic
499C23C11×#12611yescharacteristic
500C23C11×#12611yescharacteristic
501C23C2×C11×#4111yescharacteristic
502D4—24no—
503D4—24no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4C11×#12111yescharacteristic
515C2×C4C11×#12111yescharacteristic
516C2×C4C11×#12111yescharacteristic
517C2×C4C11×#12111yescharacteristic
518C2×C4C11×#12311yescharacteristic
519C2×C4C11×#12311yescharacteristic
520C2×C4C11×#12311yescharacteristic
521C2×C4C11×#12311yescharacteristic
522C2×C4C11×#12311yescharacteristic
523C2×C4C11×#12311yescharacteristic
524C2×C4C11×#12311yescharacteristic
525C2×C4C11×#12311yescharacteristic
526C2×C4C11×#12311yescharacteristic
527C2×C4C11×#12311yescharacteristic
528C2×C4C11×#12411yescharacteristic
529C2×C4C11×#12411yescharacteristic
530C2×C4C11×#12611yescharacteristic
531C2×C4C11×#12611yescharacteristic
532C2×C4C11×#12611yescharacteristic
533C2×C4C11×#12611yescharacteristic
534C2×C4C11×#12611yescharacteristic
535C2×C4C11×#12611yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C2×C11×#4111yescharacteristic
540C2×C4C2×C11×#4111yescharacteristic
541C2×C4C2×C11×#4111yescharacteristic
542C8—24no—
543C8—42no—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—44no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22C11×#39711yescharacteristic
562C22C11×#39711yescharacteristic
563C22C11×#39711yescharacteristic
564C22C11×#39711yescharacteristic
565C22C2×C11×#12311yescharacteristic
566C22C2×C11×#12411yescharacteristic
567C22C2×C11×#12611yescharacteristic
568C4—82no—
569C4—82no—
570C4C11×#39711yescharacteristic
571C4C11×#39711yescharacteristic
572C4C11×#39711yescharacteristic
573C4C11×#39711yescharacteristic
574C4C2×C11×#12111yescharacteristic
575C4C2×C11×#12311yescharacteristic
576C4C2×C11×#12311yescharacteristic
577C4C2×C11×#12611yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—84no—
585C2C11×#208112yesdirect product factor
586C2C2×C11×#39711yescharacteristic
subgroupG/H
center, socleC22×C11#397
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C11×#2081C2direct (N × H)
6. C2×C11×#344C2semidirect
7. C2×C11×#344C2semidirect
8. C2×C11×H(3,ℤ/4)C2semidirect
17. C11×#430C22semidirect
28. C11×#344C22semidirect
29. C11×#344C22semidirect
30. C11×H(3,ℤ/4)C22semidirect
93. C2×#2081C11direct (N × H)
187. C2×#430C2×C11semidirect
191. #2081C2×C11direct (N × H)
192. C2×#344C2×C11semidirect
193. C2×#344C2×C11semidirect
194. C2×H(3,ℤ/4)C2×C11semidirect
269. #430C22×C11semidirect
280. #344C22×C11semidirect
281. #344C22×C11semidirect
282. H(3,ℤ/4)C22×C11semidirect
384. C2×C11#2081direct (N × H)
479. C11C2×#2081direct (N × H)
585. C2C11×#2081direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#4182
C22×C11×#1002
C11×#20812
C2×C11×#3442
C2×C11×H(3,ℤ/4)2
C2×#208111