Finite Group Databasebeta

← C11×#33558 #14610751

Subgroups — C11×#33558 #14610751

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic, complemented
2C11×#3026C212yesmaximal, complemented
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C11×#2201C212yesmaximal, complemented
5C11×#2199C212yesmaximal, complemented
6C11×#2197C214yesmaximal, complemented
7C2×C11×#354C211yesmaximal, characteristic, complemented
8C11×#2121C212yesmaximal, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C2×C11×#137—21no—
11C11×#563C2211yescharacteristic, complemented
12C11×#562—21no—
13C11×H(3,𝔽4)C2211yescharacteristic, complemented
14C11×#555—21no—
15C11×#551—22no—
16C11×#551C2212yescomplemented
17C11×#546—22no—
18C11×#542—22no—
19C11×#538—22no—
20C11×#536—21no—
21C11×#534—22no—
22C11×#534C2212yes—
23C11×#529—21no—
24C2×C11×#124C2211yescharacteristic
25C11×#458—22no—
26C11×#458C2214yes—
27C11×B(4,𝔽2)—22no—
28C11×B(4,𝔽2)C2214yes—
29C11×#455—21no—
30C11×#455—21no—
31C11×#455C2212yes—
32C11×#455C2212yes—
33C2×C11×#104—21no—
34C2×C11×#100C2211yescharacteristic
35C2×C11×#99—22no—
36C2×C11×#99C2212yes—
37C11×#354C2212yescomplemented
38C11×#354C2212yescomplemented
39C11×#352C2214yescomplemented
40C11×AΣL(1,𝔽16)C2214yescomplemented
41C11×H(5,𝔽2)—22no—
42C11×H(5,𝔽2)—21no—
43C11×H(5,𝔽2)—42no—
44C11×H(5,𝔽2)C2312yes—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—41no—
48C22×Q8×C11D411yescharacteristic, complemented
49C22×D4×C11—22no—
50C22×D4×C11—41no—
51C22×D4×C11D412yescomplemented
52C22×D4×C11C2311yescharacteristic
53C11×#137—22no—
54C11×#137—22no—
55C11×#137—42no—
56C2×C11×Q16—41no—
57C2×C11×SD16—41no—
58C2×C11×M16—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—21no—
65C11×#124—21no—
66C11×#124—22no—
67C11×#124—21no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124—21no—
71C11×#124D411yescharacteristic, complemented
72C11×#124D411yescharacteristic, complemented
73C11×#124C2311yescharacteristic
74C11×#124C2311yescharacteristic
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—24no—
81C11×#123—42no—
82C11×#123D412yescomplemented
83C11×#123C2312yes—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×#121—21no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—44no—
95C11×#120—22no—
96C11×#120—22no—
97C11×#120—24no—
98C11×#120—42no—
99C11×#120D412yescomplemented
100C11×#120C2312yes—
101C4×Q8×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C11×#117—21no—
107C11×#117—22no—
108C11×#117—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4D412yescomplemented
113C2×C42×C11D411yescharacteristic, complemented
114C11×#104—22no—
115C11×#104—22no—
116C11×#100—21no—
117C11×#100C2312yes—
118C11×#99—22no—
119C11×#99—24no—
120C11×#99—24no—
121C11×#99C2314yes—
122#33558C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—22no—
124C24×C11C2×D412yes—
125C24×C11C2×D412yes—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—42no—
129C11×#41—41no—
130C11×#41—44no—
131C11×#41—42no—
132C11×#41—41no—
133C11×#41—81no—
134C11×#41—81no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×Q8×C11C2×D411yescharacteristic
142C2×Q8×C11C2×D411yescharacteristic
143C2×D4×C11—21no—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—44no—
159C2×D4×C11—42no—
160C2×D4×C11—41no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—44no—
164C2×D4×C11C2×D412yes—
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2411yescharacteristic
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—41no—
174C22×C4×C11—42no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C11×Q16—42no—
178C11×Q16—42no—
179C11×SD16—42no—
180C11×SD16—42no—
181C11×M16—22no—
182C11×M16—41no—
183C2×C8×C11—41no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—44no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—44no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—44no—
211C11×C22⋊C4C2×D412yes—
212C11×C22⋊C4C2×D412yes—
213C42×C11—21no—
214C42×C11—22no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219#3545C2×C1111yescharacteristic, complemented
220#3026C2×C1112yescomplemented
221C2×#455C2×C1111yescharacteristic, complemented
222#2201C2×C1112yescomplemented
223#2199C2×C1112yescomplemented
224#2197C2×C1114yescomplemented
225C2×#354C2×C1111yescharacteristic, complemented
226#2121C2×C1112yescomplemented
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—41no—
234C23×C11—82no—
235C23×C11—82no—
236C23×C11—162no—
237C23×C11#12012yes—
238C23×C11#12011yescharacteristic
239C23×C11C22×D412yes—
240Q8×C11—22no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—81no—
245Q8×C11—81no—
246Q8×C11—81no—
247D4×C11—22no—
248D4×C11—42no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—44no—
253D4×C11—44no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—42no—
258D4×C11—82no—
259D4×C11—82no—
260D4×C11—82no—
261D4×C11—81no—
262D4×C11—81no—
263D4×C11—164no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—24no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—44no—
282C2×C4×C11—82no—
283C2×C4×C11—81no—
284C2×C4×C11—82no—
285C2×C4×C11—82no—
286C2×C4×C11—162no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C8×C11—42no—
290C2×H(5,𝔽2)C22×C1111yescharacteristic
291C2×#137—21no—
292#563C22×C1111yescharacteristic, complemented
293#562—21no—
294H(3,𝔽4)C22×C1111yescharacteristic, complemented
295#555—21no—
296#551—22no—
297#551C22×C1112yescomplemented
298#546—22no—
299#542—22no—
300#538—22no—
301#536—21no—
302#534—22no—
303#534C22×C1112yes—
304#529—21no—
305C2×#124C22×C1111yescharacteristic
306#458—22no—
307#458C22×C1114yes—
308B(4,𝔽2)—22no—
309B(4,𝔽2)C22×C1114yes—
310#455—21no—
311#455—21no—
312#455C22×C1112yes—
313#455C22×C1112yes—
314C2×#104—21no—
315C2×#100C22×C1111yescharacteristic
316C2×#99—22no—
317C2×#99C22×C1112yes—
318#354C22×C1112yescomplemented
319#354C22×C1112yescomplemented
320#352C22×C1114yescomplemented
321AΣL(1,𝔽16)C22×C1114yescomplemented
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—41no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—84no—
335C22×C11—84no—
336C22×C11—162no—
337C22×C11B(4,𝔽2)11yescharacteristic
338C22×C11B(4,𝔽2)11yescharacteristic
339C22×C11C2×#12011yescharacteristic
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—84no—
351H(5,𝔽2)—22no—
352H(5,𝔽2)—21no—
353H(5,𝔽2)—42no—
354H(5,𝔽2)C23×C1112yes—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—41no—
358C22×Q8D4×C1111yescharacteristic, complemented
359C22×D4—22no—
360C22×D4—41no—
361C22×D4D4×C1112yescomplemented
362C22×D4C23×C1111yescharacteristic
363#137—22no—
364#137—22no—
365#137—42no—
366C2×Q16—41no—
367C2×SD16—41no—
368C2×M16—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371#126—22no—
372#126—22no—
373#126—22no—
374#125—21no—
375#124—21no—
376#124—22no—
377#124—21no—
378#124—22no—
379#124—22no—
380#124—21no—
381#124D4×C1111yescharacteristic, complemented
382#124D4×C1111yescharacteristic, complemented
383#124C23×C1111yescharacteristic
384#124C23×C1111yescharacteristic
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—24no—
391#123—42no—
392#123D4×C1112yescomplemented
393#123C23×C1112yes—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399#121—21no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—44no—
405#120—22no—
406#120—22no—
407#120—24no—
408#120—42no—
409#120D4×C1112yescomplemented
410#120C23×C1112yes—
411C4×Q8—21no—
412C4×D4—21no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416#117—21no—
417#117—22no—
418#117—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4D4×C1112yescomplemented
423C2×C42D4×C1111yescharacteristic, complemented
424#104—22no—
425#104—22no—
426#100—21no—
427#100C23×C1112yes—
428#99—22no—
429#99—24no—
430#99—24no—
431#99C23×C1114yes—
432C2×C11—21no—
433C2×C11—21no—
434C2×C11—21no—
435C2×C11—42no—
436C2×C11—42no—
437C2×C11—82no—
438C2×C11—82no—
439C2×C11C2×B(4,𝔽2)11yescharacteristic
440C24—22no—
441C24C2×D4×C1112yes—
442C24C2×D4×C1112yes—
443#41—22no—
444#41—22no—
445#41—42no—
446#41—41no—
447#41—44no—
448#41—42no—
449#41—41no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C2×D4×C1111yescharacteristic
459C2×Q8C2×D4×C1111yescharacteristic
460C2×D4—21no—
461C2×D4—24no—
462C2×D4—22no—
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—41no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4C2×D4×C1112yes—
482C2×D4C2×D4×C1111yescharacteristic
483C2×D4C24×C1111yescharacteristic
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4—42no—
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1112yes—
494Q16—42no—
495Q16—42no—
496SD16—42no—
497SD16—42no—
498M16—22no—
499M16—41no—
500C2×C8—41no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—44no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—24no—
525C22⋊C4—44no—
526C22⋊C4—42no—
527C22⋊C4—44no—
528C22⋊C4C2×D4×C1112yes—
529C22⋊C4C2×D4×C1112yes—
530C42—21no—
531C42—22no—
532C42—21no—
533C42—21no—
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C11#3355811yescharacteristic, direct product factor, Sylow
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—162no—
547C23C11×#12012yes—
548C23C11×#12011yescharacteristic
549C23C22×D4×C1112yes—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—81no—
555Q8—81no—
556Q8—81no—
557D4—22no—
558D4—41no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—44no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—81no—
572D4—81no—
573D4—164no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—82no—
593C2×C4—81no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—162no—
597C2×C4C11×#12011yescharacteristic
598C2×C4C22×D4×C1111yescharacteristic
599C8—42no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—84no—
613C22—84no—
614C22—162no—
615C22C11×B(4,𝔽2)11yescharacteristic
616C22C11×B(4,𝔽2)11yescharacteristic
617C22C2×C11×#12011yescharacteristic
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—42no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—84no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—82no—
635C2—82no—
636C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C11C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C11
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3545C2semidirect
2. C11×#3026C2semidirect
3. C2×C11×#455C2semidirect
4. C11×#2201C2semidirect
5. C11×#2199C2semidirect
6. C11×#2197C2semidirect
7. C2×C11×#354C2semidirect
8. C11×#2121C2semidirect
11. C11×#563C22semidirect
13. C11×H(3,𝔽4)C22semidirect
16. C11×#551C22semidirect
37. C11×#354C22semidirect
38. C11×#354C22semidirect
39. C11×#352C22semidirect
40. C11×AΣL(1,𝔽16)C22semidirect
48. C22×Q8×C11D4semidirect
51. C22×D4×C11D4semidirect
71. C11×#124D4semidirect
72. C11×#124D4semidirect
82. C11×#123D4semidirect
99. C11×#120D4semidirect
112. C2×C11×C22⋊C4D4semidirect
113. C2×C42×C11D4semidirect
122. #33558C11direct (N × H)
219. #3545C2×C11semidirect
220. #3026C2×C11semidirect
221. C2×#455C2×C11semidirect
222. #2201C2×C11semidirect
223. #2199C2×C11semidirect
224. #2197C2×C11semidirect
225. C2×#354C2×C11semidirect
226. #2121C2×C11semidirect
292. #563C22×C11semidirect
294. H(3,𝔽4)C22×C11semidirect
297. #551C22×C11semidirect
318. #354C22×C11semidirect
319. #354C22×C11semidirect
320. #352C22×C11semidirect
321. AΣL(1,𝔽16)C22×C11semidirect
358. C22×Q8D4×C11semidirect
361. C22×D4D4×C11semidirect
381. #124D4×C11semidirect
382. #124D4×C11semidirect
392. #123D4×C11semidirect
409. #120D4×C11semidirect
422. C2×C22⋊C4D4×C11semidirect
423. C2×C42D4×C11semidirect
536. C11#33558direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#30262
C2×C11×#4552
C11×#22012
C11×#21992
C11×#21972
C2×C11×#3542
C11×#21212
#3355811