Finite Group Databasebeta

← C11×#24780 #14601973

Subgroups — C11×#24780 #14601973

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#466C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C22×C11×#107C211yesmaximal, characteristic, complemented
5C11×#2416C212yesmaximal, complemented
6C11×#2067C212yesmaximal, complemented
7C11×#2033C212yesmaximal, complemented
8C11×#1970C211yesmaximal, characteristic, complemented
9C11×#1942C211yesmaximal, characteristic, complemented
10C11×#1874C212yesmaximal, complemented
11C11×#1808C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#121—22no—
16C2×C11×#121C2212yes—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C11×#466—24no—
21C11×#466—24no—
22C8×D4×C11—24no—
23C2×C11×#107—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2212yes—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—22no—
36C11×#394—22no—
37C11×#390C2212yes—
38C11×#389C2212yes—
39C11×#386—22no—
40C11×#380C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C2×C11×D8—22no—
51C2×C11×D8—22no—
52C2×C11×D8—22no—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11—22no—
56C22×C8×C11—22no—
57C22×C8×C11—22no—
58C22×C8×C11D414yescomplemented
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—24no—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—42no—
67C11×#121—48no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—42no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×#107—22no—
87C11×#107—22no—
88C11×#107—24no—
89C11×#107D414yescomplemented
90C11×C4⋊C8—22no—
91C11×#102—24no—
92C11×#102—24no—
93C11×#102—42no—
94C11×C22⋊C8—22no—
95C11×C22⋊C8—22no—
96C4×C8×C11—22no—
97C11×#95—22no—
98C11×#95—22no—
99#24780C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—22no—
101C24×C11C2×D411yescharacteristic
102C24×C11C2×D411yescharacteristic
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—44no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—82no—
117C2×D4×C11D814yescomplemented
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—44no—
132C22×C4×C11—44no—
133C22×C4×C11—82no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C11×D8—44no—
142C2×C8×C11—28no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—44no—
152C2×C8×C11C2×D412yes—
153C2×C8×C11C2×D412yes—
154C2×C8×C11C2×D412yes—
155C2×C8×C11#4112yes—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164C11×C4⋊C4C2×D414yes—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—44no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—82no—
172C42×C11—21no—
173C42×C11—21no—
174C2×#466C2×C1111yescharacteristic, complemented
175C2×#466C2×C1111yescharacteristic, complemented
176C2×C8×D4C2×C1111yescharacteristic, complemented
177C22×#107C2×C1111yescharacteristic, complemented
178#2416C2×C1112yescomplemented
179#2067C2×C1112yescomplemented
180#2033C2×C1112yescomplemented
181#1970C2×C1111yescharacteristic, complemented
182#1942C2×C1111yescharacteristic, complemented
183#1874C2×C1112yescomplemented
184#1808C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11#12112yes—
203C23×C11C2×D812yes—
204C23×C11C2×D812yes—
205C23×C11#13512yes—
206C23×C11C22×D411yescharacteristic
207D4×C11—28no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—88no—
213D4×C11—88no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—88no—
242C2×C4×C11#12112yes—
243C2×C4×C11C2×D812yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C8×C11—22no—
251C8×C11—41no—
252C8×C11—41no—
253C8×C11#12114yescomplemented
254C22×D8C22×C1111yescharacteristic
255C23×C8C22×C1111yescharacteristic
256C23×C8C22×C1111yescharacteristic
257C2×#121—22no—
258C2×#121C22×C1112yes—
259C2×#121C22×C1112yes—
260C2×C4×D4C22×C1111yescharacteristic
261C22×C4⋊C4C22×C1112yes—
262#466—24no—
263#466—24no—
264C8×D4—24no—
265C2×#107—24no—
266C2×#107C22×C1111yescharacteristic
267C2×#107C22×C1111yescharacteristic
268C2×#107C22×C1112yes—
269C2×#107C22×C1111yescharacteristic
270C2×C4⋊C8C22×C1111yescharacteristic
271C2×#102C22×C1112yes—
272C2×#102C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×C22⋊C8C22×C1111yescharacteristic
275C2×C22⋊C8C22×C1111yescharacteristic
276C2×C4×C8C22×C1111yescharacteristic
277#396—22no—
278#394—22no—
279#390C22×C1112yes—
280#389C22×C1112yes—
281#386—22no—
282#380C22×C1112yes—
283#340C22×C1112yes—
284#340C22×C1112yes—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11#46614yescomplemented
306C22×C11C2×#12111yescharacteristic
307C22×C11D4211yescharacteristic
308C22×C11#54711yescharacteristic
309C22×C11C22×D811yescharacteristic
310C22×C11C2×#13511yescharacteristic
311C22×C11#57611yescharacteristic
312C22×C11#57811yescharacteristic
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—41no—
316C4×C11—44no—
317C4×C11—41no—
318C4×C11—82no—
319C4×C11—82no—
320C4×C11C2×#12111yescharacteristic
321C4×C11#53711yescharacteristic
322C4×C11#54811yescharacteristic
323C4×C11#55311yescharacteristic
324C22×D4—22no—
325C22×D4—22no—
326C22×D4D4×C1111yescharacteristic
327C22×D4C23×C1112yes—
328C23×C4—22no—
329C23×C4C23×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8D4×C1114yescomplemented
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343C22×C8C23×C1111yescharacteristic
344#121—24no—
345#121—24no—
346#121—24no—
347#121—42no—
348#121—48no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4D4×C1111yescharacteristic
356C2×C4⋊C4C23×C1112yes—
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1112yes—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4D4×C1111yescharacteristic
365C2×C22⋊C4D4×C1111yescharacteristic
366C2×C42C23×C1111yescharacteristic
367#107—22no—
368#107—22no—
369#107—24no—
370#107D4×C1114yescomplemented
371C4⋊C8—22no—
372#102—24no—
373#102—24no—
374#102—42no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C4×C8—22no—
378#95—22no—
379#95—22no—
380C2×C11—24no—
381C2×C11—42no—
382C2×C11—162no—
383C2×C11#241611yescharacteristic
384C2×C11C2×#46611yescharacteristic
385C2×C11#306111yescharacteristic
386C2×C11D4×D811yescharacteristic
387C2×C11#328511yescharacteristic
388C2×C11#333411yescharacteristic
389C2×C11#333911yescharacteristic
390C24—22no—
391C24C2×D4×C1111yescharacteristic
392C24C2×D4×C1111yescharacteristic
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—82no—
407C2×D4C11×D814yescomplemented
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—82no—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C11×#4112yes—
430C22×C4C24×C1111yescharacteristic
431D8—44no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—28no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—44no—
442C2×C8C2×D4×C1112yes—
443C2×C8C2×D4×C1112yes—
444C2×C8C2×D4×C1112yes—
445C2×C8C11×#4112yes—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4C2×D4×C1114yes—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—44no—
461C22⋊C4—82no—
462C42—21no—
463C42—21no—
464C11#2478011yescharacteristic, direct product factor, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23C11×#12112yes—
483C23C2×C11×D812yes—
484C23C2×C11×D812yes—
485C23C11×#13512yes—
486C23C22×D4×C1111yescharacteristic
487D4—28no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—42no—
492D4—88no—
493D4—88no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—88no—
522C2×C4C11×#12112yes—
523C2×C4C2×C11×D812yes—
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C22×D4×C1111yescharacteristic
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C2×C11×#4111yescharacteristic
528C2×C4C11×H(5,𝔽2)11yescharacteristic
529C2×C4C11×2−1+411yescharacteristic
530C8—22no—
531C8—41no—
532C8—41no—
533C8C11×#12114yescomplemented
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22C11×#46614yescomplemented
555C22C2×C11×#12111yescharacteristic
556C22D42×C1111yescharacteristic
557C22C11×#54711yescharacteristic
558C22C22×C11×D811yescharacteristic
559C22C2×C11×#13511yescharacteristic
560C22C11×#57611yescharacteristic
561C22C11×#57811yescharacteristic
562C4—22no—
563C4—22no—
564C4—41no—
565C4—44no—
566C4—41no—
567C4—82no—
568C4—82no—
569C4C2×C11×#12111yescharacteristic
570C4C11×#53711yescharacteristic
571C4C11×#54811yescharacteristic
572C4C11×#55311yescharacteristic
573C2—24no—
574C2—42no—
575C2—162no—
576C2C11×#241611yescharacteristic
577C2C2×C11×#46611yescharacteristic
578C2C11×#306111yescharacteristic
579C2D4×C11×D811yescharacteristic
580C2C11×#328511yescharacteristic
581C2C11×#333411yescharacteristic
582C2C11×#333911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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
1. C2×C11×#466C2semidirect
2. C2×C11×#466C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C22×C11×#107C2semidirect
5. C11×#2416C2semidirect
6. C11×#2067C2semidirect
7. C11×#2033C2semidirect
8. C11×#1970C2semidirect
9. C11×#1942C2semidirect
10. C11×#1874C2semidirect
11. C11×#1808C2semidirect
58. C22×C8×C11D4semidirect
89. C11×#107D4semidirect
99. #24780C11direct (N × H)
117. C2×D4×C11D8semidirect
174. C2×#466C2×C11semidirect
175. C2×#466C2×C11semidirect
176. C2×C8×D4C2×C11semidirect
177. C22×#107C2×C11semidirect
178. #2416C2×C11semidirect
179. #2067C2×C11semidirect
180. #2033C2×C11semidirect
181. #1970C2×C11semidirect
182. #1942C2×C11semidirect
183. #1874C2×C11semidirect
184. #1808C2×C11semidirect
253. C8×C11#121semidirect
305. C22×C11#466semidirect
339. C22×C8D4×C11semidirect
370. #107D4×C11semidirect
407. C2×D4C11×D8semidirect
464. C11#24780direct (N × H)
533. C8C11×#121semidirect
554. C22C11×#466semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4662
C2×C8×D4×C112
C22×C11×#1072
C11×#24162
C11×#20672
C11×#20332
C11×#19702
C11×#19422
C11×#18742
C11×#18082
#2478011