Finite Group Databasebeta

← C11×#24255 #14601448

Subgroups — C11×#24255 #14601448

Order 2816.

1392 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#451C212yesmaximal, complemented
4C2×C11×#441C211yesmaximal, characteristic, complemented
5C11×#2536C211yesmaximal, characteristic
6C11×#2035C212yesmaximal, complemented
7C11×#2001C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic
10C11×#1805C211yesmaximal, characteristic, complemented
11C11×#1787C212yesmaximal, complemented
12C23×Q8×C11C2212yes—
13C22×C11×Q16C2212yes—
14C22×C11×Q16C2211yescharacteristic
15D4×Q8×C11—24no—
16D4×Q8×C11—24no—
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#462—24no—
27C11×#451—28no—
28C11×#441—24no—
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#398—21no—
41C11×#394—21no—
42C11×#388—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—24no—
50C22×Q8×C11—24no—
51C22×Q8×C11—42no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11D411yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11C2312yes—
59C2×C11×Q16—22no—
60C2×C11×Q16—22no—
61C2×C11×Q16—24no—
62C2×C11×Q16—24no—
63C2×C11×Q16—42no—
64C2×C11×Q16D414yescomplemented
65C22×C8×C11C2312yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—28no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8D414yes—
71C11×C22⋊Q8—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11D414yes—
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4D412yes—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#106—22no—
101C11×C4⋊C8—22no—
102C11×#103—22no—
103C11×#103—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—22no—
107C11×#103—42no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24255C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11C2×D412yes—
116C2×Q8×C11—28no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—44no—
131C2×Q8×C11—44no—
132C2×Q8×C11—48no—
133C2×Q8×C11—48no—
134C2×Q8×C11—48no—
135C2×Q8×C11—48no—
136C2×Q8×C11C2×D414yes—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D412yes—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11#4112yes—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—28no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C11×Q16—28no—
163C11×Q16—48no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—44no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C42×C11—24no—
191C42×C11—42no—
192C42×C11C2×D412yes—
193C42×C11C2×D412yes—
194C2×D4×Q8C2×C1111yescharacteristic
195C2×#462C2×C1111yescharacteristic, complemented
196C2×#451C2×C1112yescomplemented
197C2×#441C2×C1111yescharacteristic, complemented
198#2536C2×C1111yescharacteristic
199#2035C2×C1112yescomplemented
200#2001C2×C1112yescomplemented
201#1960C2×C1111yescharacteristic, complemented
202#1955C2×C1111yescharacteristic
203#1805C2×C1111yescharacteristic, complemented
204#1787C2×C1112yescomplemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11#13714yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—416no—
221Q8×C11—42no—
222Q8×C11—41no—
223Q8×C11—42no—
224Q8×C11—41no—
225Q8×C11#12114yes—
226D4×C11—28no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—416no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11#12012yes—
254C2×C4×C11#12012yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C8×C11—22no—
262C8×C11—41no—
263C8×C11—42no—
264C23×Q8C22×C1112yes—
265C22×Q16C22×C1112yes—
266C22×Q16C22×C1111yescharacteristic
267D4×Q8—24no—
268D4×Q8—24no—
269C2×C4⋊Q8—21no—
270C2×C4⋊Q8C22×C1111yescharacteristic
271C2×C22⋊Q8—22no—
272C2×C22⋊Q8C22×C1112yes—
273C2×C22⋊Q8C22×C1112yes—
274C2×C4×Q8C22×C1111yescharacteristic
275C2×C4×Q8C22×C1111yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C22×C1111yescharacteristic
278#462—24no—
279#451—28no—
280#441—24no—
281C2×#106C22×C1111yescharacteristic
282C2×C4⋊C8C22×C1111yescharacteristic
283C2×#103C22×C1112yes—
284C2×#103C22×C1111yescharacteristic
285C2×#103C22×C1111yescharacteristic
286C2×#103C22×C1112yes—
287C2×#103C22×C1112yes—
288C2×#103C22×C1112yes—
289C2×C22⋊C8C22×C1112yes—
290C2×C22⋊C8C22×C1112yes—
291C2×#97C22×C1111yescharacteristic
292#398—21no—
293#394—21no—
294#388—22no—
295#382C22×C1111yescharacteristic
296#380C22×C1112yes—
297#340C22×C1112yes—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C2×#12011yescharacteristic
306C22×C11D4211yescharacteristic
307C22×C11#54611yescharacteristic
308C22×C11C2×#13712yes—
309C22×C11#57812yes—
310C4×C11—24no—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—81no—
318C4×C11—82no—
319C4×C11C2×#12111yescharacteristic
320C4×C11#53511yescharacteristic
321C4×C11D4211yescharacteristic
322C4×C11#54611yescharacteristic
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—42no—
329C22×Q8—42no—
330C22×Q8C23×C1111yescharacteristic
331C22×Q8C23×C1112yes—
332C22×Q8C23×C1111yescharacteristic
333C22×D4D4×C1111yescharacteristic
334C23×C4—22no—
335C23×C4C23×C1112yes—
336C2×Q16—22no—
337C2×Q16—22no—
338C2×Q16—24no—
339C2×Q16—24no—
340C2×Q16—42no—
341C2×Q16D4×C1114yescomplemented
342C22×C8C23×C1112yes—
343C22×C8C23×C1111yescharacteristic
344C22×C8C23×C1111yescharacteristic
345C4⋊Q8—28no—
346C4⋊Q8—22no—
347C4⋊Q8D4×C1114yes—
348C22⋊Q8—216no—
349C22⋊Q8—24no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—42no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8D4×C1114yes—
357C4×D4—28no—
358C4×D4—22no—
359C4×D4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4D4×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C4⋊C4C23×C1112yes—
369C2×C4⋊C4C23×C1111yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4D4×C1112yes—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42C23×C1111yescharacteristic
377#106—22no—
378C4⋊C8—22no—
379#103—22no—
380#103—24no—
381#103—24no—
382#103—24no—
383#103—22no—
384#103—42no—
385C22⋊C8—24no—
386C22⋊C8—42no—
387#97—22no—
388#95—22no—
389#95—21no—
390#95—21no—
391C2×C11—44no—
392C2×C11#240811yescharacteristic
393C2×C11#300411yescharacteristic
394C2×C11#301111yescharacteristic
395C2×C11#327012yes—
396C2×C11#331212yes—
397C24C2×D4×C1112yes—
398C2×Q8—28no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—44no—
413C2×Q8—44no—
414C2×Q8—48no—
415C2×Q8—48no—
416C2×Q8—48no—
417C2×Q8—48no—
418C2×Q8C2×D4×C1114yes—
419C2×Q8C2×D4×C1112yes—
420C2×Q8C2×D4×C1112yes—
421C2×Q8C2×D4×C1112yes—
422C2×Q8C11×#4112yes—
423C2×D4—24no—
424C2×D4—22no—
425C22×C4—21no—
426C22×C4—28no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4C2×D4×C1112yes—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C24×C1111yescharacteristic
444Q16—28no—
445Q16—48no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—21no—
454C2×C8C2×D4×C1112yes—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—44no—
466C4⋊C4—42no—
467C4⋊C4C2×D4×C1112yes—
468C22⋊C4—28no—
469C22⋊C4—24no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C42—24no—
473C42—42no—
474C42C2×D4×C1112yes—
475C42C2×D4×C1112yes—
476C11#2425511yescharacteristic, direct product factor, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23C11×#13714yes—
484C23C22×D4×C1111yescharacteristic
485Q8—22no—
486Q8—22no—
487Q8—22no—
488Q8—22no—
489Q8—22no—
490Q8—24no—
491Q8—24no—
492Q8—416no—
493Q8—42no—
494Q8—41no—
495Q8—42no—
496Q8—41no—
497Q8C11×#12114yes—
498D4—28no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—416no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4C11×#12012yes—
526C2×C4C11×#12012yes—
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C22×D4×C1111yescharacteristic
529C2×C4C22×D4×C1111yescharacteristic
530C2×C4C2×C11×#4111yescharacteristic
531C2×C4C11×H(5,𝔽2)11yescharacteristic
532C2×C4C11×H(5,𝔽2)11yescharacteristic
533C8—22no—
534C8—41no—
535C8—42no—
536C22—24no—
537C22—24no—
538C22—24no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22C2×C11×#12011yescharacteristic
544C22D42×C1111yescharacteristic
545C22C11×#54611yescharacteristic
546C22C2×C11×#13712yes—
547C22C11×#57812yes—
548C4—24no—
549C4—22no—
550C4—22no—
551C4—42no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—82no—
557C4C2×C11×#12111yescharacteristic
558C4C11×#53511yescharacteristic
559C4D42×C1111yescharacteristic
560C4C11×#54611yescharacteristic
561C2—44no—
562C2C11×#240811yescharacteristic
563C2C11×#300411yescharacteristic
564C2C11×#301111yescharacteristic
565C2C11×#327012yes—
566C2C11×#331212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×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
2. C2×C11×#462C2semidirect
3. C2×C11×#451C2semidirect
4. C2×C11×#441C2semidirect
6. C11×#2035C2semidirect
7. C11×#2001C2semidirect
8. C11×#1960C2semidirect
10. C11×#1805C2semidirect
11. C11×#1787C2semidirect
64. C2×C11×Q16D4semidirect
114. #24255C11direct (N × H)
195. C2×#462C2×C11semidirect
196. C2×#451C2×C11semidirect
197. C2×#441C2×C11semidirect
199. #2035C2×C11semidirect
200. #2001C2×C11semidirect
201. #1960C2×C11semidirect
203. #1805C2×C11semidirect
204. #1787C2×C11semidirect
341. C2×Q16D4×C11semidirect
476. C11#24255direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4622
C2×C11×#4512
C2×C11×#4412
C11×#25362
C11×#20352
C11×#20012
C11×#19602
C11×#19552
C11×#18052
C11×#17872
#2425511