Finite Group Databasebeta

← C11×#34621 #14611814

Subgroups — C11×#34621 #14611814

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2651C214yesmaximal, complemented
2C11×#2648C214yesmaximal, complemented
3C11×#2647C211yesmaximal, characteristic, complemented
4C11×#2644C212yesmaximal, complemented
5C11×#2641C211yesmaximal, characteristic, complemented
6C11×#2629C211yesmaximal, characteristic, complemented
7C11×#2624C212yesmaximal, complemented
8C11×#2619C211yesmaximal, characteristic
9C11×#2395C214yesmaximal, complemented
10C11×#2392C214yesmaximal, complemented
11C4×C11×#127C211yesmaximal, characteristic, complemented
12C4×C11×#125C211yesmaximal, characteristic, complemented
13C4×C11×#121C212yesmaximal, complemented
14C11×#2293C212yesmaximal, complemented
15C4×C11×#117C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2214yes—
21C2×C4×D4×C11C2214yes—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C2×C11×#117C2214yes—
25C22×C42×C11C2211yescharacteristic
26C11×#400C2214yes—
27C11×#399C2214yes—
28C11×#398C2214yes—
29C11×#398C2214yes—
30C11×#397C2214yes—
31C11×#397C2214yes—
32C11×#397C2214yes—
33C11×#397C2214yes—
34C11×#396C2214yes—
35C11×#396C2214yes—
36C11×#394C2214yes—
37C11×#394C2214yes—
38C11×#394C2214yes—
39C11×#394C2214yes—
40C11×#394C2214yes—
41C11×#392C2214yes—
42C11×#390C2212yes—
43C11×#390C2212yes—
44C11×#390C2212yes—
45C11×#390C2212yes—
46C11×#390C2214yes—
47C11×#389C2212yes—
48C11×#389C2212yes—
49C11×#389C2212yes—
50C11×#389C2212yes—
51C11×#388C2214yes—
52C11×#388C2214yes—
53C11×#388C2214yes—
54C11×#387C2214yes—
55C11×#386C2214yes—
56C11×#384C2211yescharacteristic
57C11×#382C2211yescharacteristic
58C11×#380C2212yes—
59C4×C11×C4⋊C4C2214yes—
60C4×C11×C4⋊C4C2212yes—
61C4×C11×C4⋊C4C2212yes—
62C4×C11×C4⋊C4C2212yes—
63C4×C11×C22⋊C4C2212yes—
64C4×C11×C22⋊C4C2214yes—
65C4×C11×C22⋊C4C2212yes—
66C4×C11×C22⋊C4C2214yes—
67C11×#376C2211yescharacteristic
68C11×#376C2211yescharacteristic
69C43×C11C2211yescharacteristic
70C43×C11C2211yescharacteristic
71C22×D4×C11C2312yes—
72C22×D4×C11C2314yes—
73C22×D4×C11C2314yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C11×#127—24no—
79C11×#125—24no—
80C11×#121—28no—
81C4×D4×C11—28no—
82C4×D4×C11—48no—
83C4×D4×C11—48no—
84C11×#117—24no—
85C11×#117—24no—
86C11×#117—48no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C42×C11—24no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2312yes—
119C2×C42×C11C2312yes—
120C2×C42×C11C2314yes—
121C2×C42×C11C2312yes—
122C2×C42×C11C2312yes—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C11×#95C2312yes—
126C11×#95C2312yes—
127C11×#95C2312yes—
128C11×#95C2312yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136#34621C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11C2414yes—
138C24×C11C2411yescharacteristic
139C2×D4×C11—28no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—28no—
143C2×D4×C11—24no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—28no—
153C22×C4×C11—28no—
154C22×C4×C11—24no—
155C22×C4×C11—28no—
156C22×C4×C11—42no—
157C22×C4×C11#4114yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2414yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2411yescharacteristic
164C22×C4×C11C2414yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2412yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—44no—
178C11×C4⋊C4—44no—
179C11×C4⋊C4—44no—
180C11×C4⋊C4—44no—
181C11×C4⋊C4—44no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—44no—
187C11×C22⋊C4—44no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4—44no—
194C11×C22⋊C4—44no—
195C42×C11—22no—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—24no—
202C42×C11—28no—
203C42×C11—24no—
204C42×C11—42no—
205C42×C11—42no—
206C42×C11#4114yes—
207C42×C11#4114yes—
208#2651C2×C1114yescomplemented
209#2648C2×C1114yescomplemented
210#2647C2×C1111yescharacteristic, complemented
211#2644C2×C1112yescomplemented
212#2641C2×C1111yescharacteristic, complemented
213#2629C2×C1111yescharacteristic, complemented
214#2624C2×C1112yescomplemented
215#2619C2×C1111yescharacteristic
216#2395C2×C1114yescomplemented
217#2392C2×C1114yescomplemented
218C4×#127C2×C1111yescharacteristic, complemented
219C4×#125C2×C1111yescharacteristic, complemented
220C4×#121C2×C1112yescomplemented
221#2293C2×C1112yescomplemented
222C4×#117C2×C1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11C2×#4112yes—
235C23×C11C2511yescharacteristic
236D4×C11—416no—
237D4×C11—416no—
238D4×C11—48no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—44no—
268C2×C4×C11—44no—
269C2×C4×C11—416no—
270C2×C4×C11C2×#4112yes—
271C2×C4×C11C2×#4114yes—
272C2×C4×C11C2×#4112yes—
273C2×C4×C11C2×#4112yes—
274C2×C4×C11C2×#4112yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11H(5,𝔽2)14yes—
278C2×#127C22×C1111yescharacteristic
279C2×#125C22×C1111yescharacteristic
280C2×#121C22×C1112yes—
281C2×C4×D4C22×C1112yes—
282C2×C4×D4C22×C1114yes—
283C2×C4×D4C22×C1114yes—
284C2×#117C22×C1111yescharacteristic
285C2×#117C22×C1111yescharacteristic
286C2×#117C22×C1114yes—
287C22×C42C22×C1111yescharacteristic
288#400C22×C1114yes—
289#399C22×C1114yes—
290#398C22×C1114yes—
291#398C22×C1114yes—
292#397C22×C1114yes—
293#397C22×C1114yes—
294#397C22×C1114yes—
295#397C22×C1114yes—
296#396C22×C1114yes—
297#396C22×C1114yes—
298#394C22×C1114yes—
299#394C22×C1114yes—
300#394C22×C1114yes—
301#394C22×C1114yes—
302#394C22×C1114yes—
303#392C22×C1114yes—
304#390C22×C1112yes—
305#390C22×C1114yes—
306#390C22×C1112yes—
307#390C22×C1112yes—
308#390C22×C1112yes—
309#389C22×C1112yes—
310#389C22×C1112yes—
311#389C22×C1112yes—
312#389C22×C1112yes—
313#388C22×C1114yes—
314#388C22×C1114yes—
315#388C22×C1114yes—
316#387C22×C1114yes—
317#386C22×C1114yes—
318#384C22×C1111yescharacteristic
319#382C22×C1111yescharacteristic
320#380C22×C1112yes—
321C4×C4⋊C4C22×C1114yes—
322C4×C4⋊C4C22×C1112yes—
323C4×C4⋊C4C22×C1112yes—
324C4×C4⋊C4C22×C1112yes—
325C4×C22⋊C4C22×C1112yes—
326C4×C22⋊C4C22×C1114yes—
327C4×C22⋊C4C22×C1112yes—
328C4×C22⋊C4C22×C1114yes—
329#376C22×C1111yescharacteristic
330#376C22×C1111yescharacteristic
331C43C22×C1111yescharacteristic
332C43C22×C1111yescharacteristic
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11C22×#4111yescharacteristic
346C22×C11C22×#4111yescharacteristic
347C22×C11C22×#4111yescharacteristic
348C22×C11C2×H(5,𝔽2)12yes—
349C22×C11#58512yes—
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—24no—
353C4×C11—41no—
354C4×C11—44no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—44no—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11—44no—
361C4×C11#52914yes—
362C4×C11#54014yes—
363C22×D4C23×C1112yes—
364C22×D4C23×C1114yes—
365C22×D4C23×C1114yes—
366C23×C4C23×C1114yes—
367C23×C4C23×C1111yescharacteristic
368C23×C4C23×C1111yescharacteristic
369C23×C4C23×C1111yescharacteristic
370#127—24no—
371#125—24no—
372#121—28no—
373C4×D4—28no—
374C4×D4—48no—
375C4×D4—48no—
376#117—24no—
377#117—24no—
378#117—48no—
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1112yes—
381C2×C4⋊C4C23×C1112yes—
382C2×C4⋊C4C23×C1112yes—
383C2×C4⋊C4C23×C1112yes—
384C2×C4⋊C4C23×C1114yes—
385C2×C4⋊C4C23×C1114yes—
386C2×C4⋊C4C23×C1114yes—
387C2×C4⋊C4C23×C1114yes—
388C2×C4⋊C4C23×C1114yes—
389C2×C4⋊C4C23×C1114yes—
390C2×C22⋊C4C23×C1112yes—
391C2×C22⋊C4C23×C1112yes—
392C2×C22⋊C4C23×C1114yes—
393C2×C22⋊C4C23×C1114yes—
394C2×C22⋊C4C23×C1114yes—
395C2×C22⋊C4C23×C1114yes—
396C2×C22⋊C4C23×C1114yes—
397C2×C22⋊C4C23×C1114yes—
398C2×C22⋊C4C23×C1114yes—
399C2×C22⋊C4C23×C1114yes—
400C2×C22⋊C4C23×C1114yes—
401C2×C22⋊C4C23×C1114yes—
402C2×C22⋊C4C23×C1114yes—
403C2×C42—24no—
404C2×C42C23×C1112yes—
405C2×C42C23×C1114yes—
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408C2×C42C23×C1111yescharacteristic
409C2×C42C23×C1112yes—
410C2×C42C23×C1111yescharacteristic
411C2×C42C23×C1111yescharacteristic
412C2×C42C23×C1111yescharacteristic
413C2×C42C23×C1112yes—
414C2×C42C23×C1112yes—
415C2×C42C23×C1111yescharacteristic
416C2×C42C23×C1111yescharacteristic
417#95C23×C1112yes—
418#95C23×C1112yes—
419#95C23×C1112yes—
420#95C23×C1112yes—
421#95C23×C1114yes—
422#95C23×C1114yes—
423#95C23×C1114yes—
424#95C23×C1114yes—
425#95C23×C1114yes—
426#95C23×C1114yes—
427#95C23×C1114yes—
428C2×C11—42no—
429C2×C11—84no—
430C2×C11C2×#52911yescharacteristic
431C2×C11C2×#54011yescharacteristic
432C2×C11#345511yescharacteristic
433C2×C11#346012yes—
434C2×C11#346012yes—
435C24C24×C1114yes—
436C24C24×C1111yescharacteristic
437C2×D4—28no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—28no—
441C2×D4—24no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—42no—
455C22×C4C11×#4114yes—
456C22×C4C24×C1111yescharacteristic
457C22×C4C24×C1114yes—
458C22×C4C24×C1112yes—
459C22×C4C24×C1112yes—
460C22×C4C24×C1112yes—
461C22×C4C24×C1111yescharacteristic
462C22×C4C24×C1114yes—
463C22×C4C24×C1114yes—
464C22×C4C24×C1111yescharacteristic
465C22×C4C24×C1112yes—
466C22×C4C24×C1111yescharacteristic
467C22×C4C24×C1111yescharacteristic
468C22×C4C24×C1111yescharacteristic
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—28no—
474C4⋊C4—24no—
475C4⋊C4—44no—
476C4⋊C4—44no—
477C4⋊C4—44no—
478C4⋊C4—44no—
479C4⋊C4—44no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—28no—
483C22⋊C4—28no—
484C22⋊C4—44no—
485C22⋊C4—44no—
486C22⋊C4—44no—
487C22⋊C4—44no—
488C22⋊C4—44no—
489C22⋊C4—44no—
490C22⋊C4—44no—
491C22⋊C4—44no—
492C22⋊C4—44no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—24no—
500C42—28no—
501C42—24no—
502C42—42no—
503C42—42no—
504C42C11×#4114yes—
505C42C11×#4114yes—
506C11#3462111yescharacteristic, direct product factor, Sylow
507C23—21no—
508C23—21no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23C2×C11×#4112yes—
519C23C25×C1111yescharacteristic
520D4—416no—
521D4—416no—
522D4—48no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—416no—
554C2×C4C2×C11×#4112yes—
555C2×C4C2×C11×#4114yes—
556C2×C4C2×C11×#4112yes—
557C2×C4C2×C11×#4112yes—
558C2×C4C2×C11×#4112yes—
559C2×C4C2×C11×#4112yes—
560C2×C4C2×C11×#4112yes—
561C2×C4C11×H(5,𝔽2)14yes—
562C22—22no—
563C22—24no—
564C22—41no—
565C22—41no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22C22×C11×#4111yescharacteristic
575C22C22×C11×#4111yescharacteristic
576C22C22×C11×#4111yescharacteristic
577C22C2×C11×H(5,𝔽2)12yes—
578C22C11×#58512yes—
579C4—22no—
580C4—22no—
581C4—24no—
582C4—41no—
583C4—44no—
584C4—41no—
585C4—44no—
586C4—42no—
587C4—44no—
588C4—42no—
589C4—42no—
590C4C11×#52914yes—
591C4C11×#54014yes—
592C2—42no—
593C2—84no—
594C2C2×C11×#52911yescharacteristic
595C2C2×C11×#54011yescharacteristic
596C2C11×#345511yescharacteristic
597C2C11×#346012yes—
598C2C11×#346012yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2619C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2651C2semidirect
2. C11×#2648C2semidirect
3. C11×#2647C2semidirect
4. C11×#2644C2semidirect
5. C11×#2641C2semidirect
6. C11×#2629C2semidirect
7. C11×#2624C2semidirect
9. C11×#2395C2semidirect
10. C11×#2392C2semidirect
11. C4×C11×#127C2semidirect
12. C4×C11×#125C2semidirect
13. C4×C11×#121C2semidirect
14. C11×#2293C2semidirect
15. C4×C11×#117C2semidirect
136. #34621C11direct (N × H)
208. #2651C2×C11semidirect
209. #2648C2×C11semidirect
210. #2647C2×C11semidirect
211. #2644C2×C11semidirect
212. #2641C2×C11semidirect
213. #2629C2×C11semidirect
214. #2624C2×C11semidirect
216. #2395C2×C11semidirect
217. #2392C2×C11semidirect
218. C4×#127C2×C11semidirect
219. C4×#125C2×C11semidirect
220. C4×#121C2×C11semidirect
221. #2293C2×C11semidirect
222. C4×#117C2×C11semidirect
506. C11#34621direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26512
C11×#26482
C11×#26472
C11×#26442
C11×#26412
C11×#26292
C11×#26242
C11×#26192
C11×#23952
C11×#23922
C4×C11×#1272
C4×C11×#1252
C4×C11×#1212
C11×#22932
C4×C11×#1172
#3462111