Finite Group Databasebeta

← C11×#13349 #14590542

Subgroups — C11×#13349 #14590542

Order 2816.

780 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#458C211yesmaximal, characteristic
2C2×C11×#455C211yesmaximal, characteristic
3C11×#2717C211yesmaximal, characteristic, complemented
4C2×C11×#354C211yesmaximal, characteristic, complemented
5C2×C11×#352C211yesmaximal, characteristic, complemented
6C11×#1790C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)C2211yescharacteristic
9C2×C11×#137—21no—
10C2×C11×#124C2211yescharacteristic
11C2×C11×#123—21no—
12C2×C11×#123C2211yescharacteristic
13C11×#458—22no—
14C11×#458—22no—
15C11×#455—22no—
16C11×#455—22no—
17C2×C11×#104—21no—
18C2×C11×#100C2211yescharacteristic
19C2×C11×#99—21no—
20C2×C11×#99—21no—
21C2×C11×#99C2211yescharacteristic
22C2×C11×#99C2211yescharacteristic
23C11×#397—21no—
24C11×#397—21no—
25C11×#395—21no—
26C11×#387—21no—
27C11×#386—21no—
28C11×#386C2211yescharacteristic
29C11×#385—21no—
30C11×#380—21no—
31C11×#354—22no—
32C11×#352—22no—
33C11×H(5,𝔽2)—21no—
34C11×H(5,𝔽2)—21no—
35C11×H(5,𝔽2)—21no—
36C11×H(5,𝔽2)—42no—
37C11×H(5,𝔽2)D412yes—
38C2×C11×#41—21no—
39C2×C11×#41—41no—
40C22×Q8×C11D411yescharacteristic
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—41no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C11×#137—24no—
48C11×#137—42no—
49C2×C11×Q16—41no—
50C2×C11×SD16—41no—
51C2×C11×M16—21no—
52C11×#124—21no—
53C11×#124—21no—
54C11×#124—21no—
55C11×#124—21no—
56C11×#123—24no—
57C11×#123—21no—
58C11×#123—21no—
59C11×#123—21no—
60C11×#123—21no—
61C11×#123—42no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—41no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—41no—
74C2×C11×C22⋊C4—41no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C11×#104—24no—
79C11×#100—21no—
80C11×#100D412yes—
81C11×#99—24no—
82C11×#99—21no—
83C11×#99—21no—
84C11×#99—21no—
85C11×#99—42no—
86C11×#99D412yes—
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—41no—
94#13349C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—21no—
96C24×C11—21no—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—42no—
102C11×#41—41no—
103C11×#41—42no—
104C11×#41—42no—
105C11×#41—42no—
106C11×#41—41no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11C2×D411yescharacteristic
131C2×D4×C11C2×D411yescharacteristic
132C2×D4×C11C2×D411yescharacteristic
133C2×D4×C11#4111yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—41no—
145C22×C4×C11—42no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11C2×D411yescharacteristic
152C11×Q16—44no—
153C11×SD16—44no—
154C11×M16—22no—
155C11×M16—41no—
156C2×C8×C11—41no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—81no—
162C11×C4⋊C4—81no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—82no—
179C42×C11—21no—
180C42×C11—21no—
181C2×#458C2×C1111yescharacteristic
182C2×#455C2×C1111yescharacteristic
183#2717C2×C1111yescharacteristic, complemented
184C2×#354C2×C1111yescharacteristic, complemented
185C2×#352C2×C1111yescharacteristic, complemented
186#1790C2×C1111yescharacteristic
187#1390C2×C1111yescharacteristic, complemented
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—81no—
202C23×C11—81no—
203C23×C11—81no—
204C23×C11—81no—
205C23×C11#12011yescharacteristic
206C23×C11#12011yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11#12111yescharacteristic
209C23×C11#12711yescharacteristic
210Q8×C11—22no—
211Q8×C11—41no—
212Q8×C11—42no—
213Q8×C11—81no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—81no—
257C2×C4×C11—81no—
258C2×C4×C11—81no—
259C2×C4×C11—81no—
260C2×C4×C11—81no—
261C2×C4×C11—81no—
262C2×C4×C11—81no—
263C2×C4×C11#12011yescharacteristic
264C2×C4×C11#12111yescharacteristic
265C8×C11—42no—
266C2×H(5,𝔽2)C22×C1111yescharacteristic
267C2×#137—21no—
268C2×#124C22×C1111yescharacteristic
269C2×#123—21no—
270C2×#123C22×C1111yescharacteristic
271#458—22no—
272#458—22no—
273#455—22no—
274#455—22no—
275C2×#104—21no—
276C2×#100C22×C1111yescharacteristic
277C2×#99—21no—
278C2×#99—21no—
279C2×#99C22×C1111yescharacteristic
280C2×#99C22×C1111yescharacteristic
281#397—21no—
282#397—21no—
283#395—21no—
284#387—21no—
285#386—21no—
286#386C22×C1111yescharacteristic
287#385—21no—
288#380—21no—
289#354—22no—
290#352—22no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—161no—
313C22×C11—161no—
314C22×C11#39211yescharacteristic
315C22×C11B(4,𝔽2)11yescharacteristic
316C22×C11B(4,𝔽2)11yescharacteristic
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11—81no—
324C4×C11—82no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11—161no—
328H(5,𝔽2)—21no—
329H(5,𝔽2)—21no—
330H(5,𝔽2)—21no—
331H(5,𝔽2)—42no—
332H(5,𝔽2)D4×C1112yes—
333C2×#41—21no—
334C2×#41—41no—
335C22×Q8D4×C1111yescharacteristic
336C22×D4—21no—
337C22×D4—21no—
338C22×D4—41no—
339C22×D4C23×C1111yescharacteristic
340C23×C4D4×C1111yescharacteristic
341C23×C4D4×C1111yescharacteristic
342#137—24no—
343#137—42no—
344C2×Q16—41no—
345C2×SD16—41no—
346C2×M16—21no—
347#124—21no—
348#124—21no—
349#124—21no—
350#124—21no—
351#123—24no—
352#123—21no—
353#123—21no—
354#123—21no—
355#123—21no—
356#123—42no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—41no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4D4×C1111yescharacteristic
371C2×C22⋊C4D4×C1111yescharacteristic
372C2×C42D4×C1111yescharacteristic
373#104—24no—
374#100—21no—
375#100D4×C1112yes—
376#99—24no—
377#99—21no—
378#99—21no—
379#99—21no—
380#99—42no—
381#99D4×C1112yes—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—41no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—41no—
392C2×C11—41no—
393C2×C11—41no—
394C2×C11—41no—
395C2×C11—82no—
396C2×C11#202111yescharacteristic
397C2×C11#219711yescharacteristic
398C2×C11#220111yescharacteristic
399C24—21no—
400C24—21no—
401C24C2×D4×C1111yescharacteristic
402C24C2×D4×C1111yescharacteristic
403#41—22no—
404#41—22no—
405#41—42no—
406#41—41no—
407#41—42no—
408#41—42no—
409#41—42no—
410#41—41no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4C2×D4×C1111yescharacteristic
435C2×D4C2×D4×C1111yescharacteristic
436C2×D4C2×D4×C1111yescharacteristic
437C2×D4C11×#4111yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4C2×D4×C1111yescharacteristic
456Q16—44no—
457SD16—44no—
458M16—22no—
459M16—41no—
460C2×C8—41no—
461C4⋊C4—42no—
462C4⋊C4—44no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C22⋊C4—21no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—42no—
471C22⋊C4—41no—
472C22⋊C4—44no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—82no—
483C42—21no—
484C42—21no—
485C11#1334911yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—81no—
500C23—81no—
501C23—81no—
502C23—81no—
503C23C11×#12011yescharacteristic
504C23C11×#12011yescharacteristic
505C23C11×#12111yescharacteristic
506C23C11×#12111yescharacteristic
507C23C11×#12711yescharacteristic
508Q8—22no—
509Q8—41no—
510Q8—42no—
511Q8—81no—
512D4—22no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—42no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4C11×#12011yescharacteristic
562C2×C4C11×#12111yescharacteristic
563C8—42no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—82no—
582C22—82no—
583C22—81no—
584C22—81no—
585C22—161no—
586C22—161no—
587C22C11×#39211yescharacteristic
588C22C11×B(4,𝔽2)11yescharacteristic
589C22C11×B(4,𝔽2)11yescharacteristic
590C4—21no—
591C4—21no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—82no—
598C4—81no—
599C4—81no—
600C4—161no—
601C2—21no—
602C2—21no—
603C2—41no—
604C2—41no—
605C2—41no—
606C2—41no—
607C2—82no—
608C2C11×#202111yescharacteristic
609C2C11×#219711yescharacteristic
610C2C11×#220111yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C11
prime radicalC2×C11×H(5,𝔽2)C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2717C2semidirect
4. C2×C11×#354C2semidirect
5. C2×C11×#352C2semidirect
7. C11×#1390C2semidirect
94. #13349C11direct (N × H)
183. #2717C2×C11semidirect
184. C2×#354C2×C11semidirect
185. C2×#352C2×C11semidirect
187. #1390C2×C11semidirect
485. C11#13349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4582
C2×C11×#4552
C11×#27172
C2×C11×#3542
C2×C11×#3522
C11×#17902
C11×#13902
#1334911