Finite Group Databasebeta

← C11×#12186 #14589379

Subgroups — C11×#12186 #14589379

Order 2816.

682 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C11×#2668C211yesmaximal, characteristic, complemented
2C11×#2021C211yesmaximal, characteristic, complemented
3C11×#1613C211yesmaximal, characteristic, complemented
4C11×#1595C211yesmaximal, characteristic, complemented
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1316C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#120—21no—
11C2×C11×#120—21no—
12C11×#481—21no—
13C11×#447—21no—
14C2×C11×#99—21no—
15C11×#399C2211yescharacteristic
16C11×#397—21no—
17C11×#394—21no—
18C11×#392C2211yescharacteristic
19C11×#386—21no—
20C11×#386—21no—
21C11×#379C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C25×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—41no—
33C22×D4×C11D411yescharacteristic, complemented
34C23×C4×C11—21no—
35C2×C11×D8—41no—
36C11×#123—41no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—44no—
40C11×#120—42no—
41C11×#120—41no—
42C11×#120—44no—
43C11×#120—42no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic, complemented
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—41no—
55C2×C11×C22⋊C4D411yescharacteristic
56C2×C11×C22⋊C4C2311yescharacteristic
57C11×#106—41no—
58C11×#102—41no—
59C11×#102—41no—
60C11×#99—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95D411yescharacteristic, complemented
66C11×#95D411yescharacteristic, complemented
67#12186C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—21no—
69C24×C11—21no—
70C24×C11—21no—
71C24×C11—21no—
72C24×C11—21no—
73C24×C11—41no—
74C24×C11—41no—
75C24×C11—42no—
76C24×C11—81no—
77C24×C11C2×D411yescharacteristic
78C2×D4×C11—24no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—44no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—81no—
96C2×D4×C11—81no—
97C2×D4×C11—81no—
98C2×D4×C11—81no—
99C2×D4×C11—82no—
100C2×D4×C11—82no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11—81no—
109C22×C4×C11—81no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C11×D8—82no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—44no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—81no—
132C11×C22⋊C4—81no—
133#2668C2×C1111yescharacteristic, complemented
134#2021C2×C1111yescharacteristic, complemented
135#1613C2×C1111yescharacteristic, complemented
136#1595C2×C1111yescharacteristic, complemented
137#1352C2×C1111yescharacteristic, complemented
138#1343C2×C1111yescharacteristic, complemented
139#1316C2×C1111yescharacteristic, complemented
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—81no—
165C23×C11—82no—
166C23×C11—81no—
167C23×C11—82no—
168C23×C11—84no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11#12011yescharacteristic
173C23×C11#13511yescharacteristic
174C23×C11AGL(1,ℤ/8)11yescharacteristic
175D4×C11—42no—
176D4×C11—84no—
177D4×C11—81no—
178D4×C11—81no—
179D4×C11—81no—
180D4×C11—81no—
181D4×C11—81no—
182D4×C11—82no—
183D4×C11—82no—
184D4×C11—84no—
185D4×C11—88no—
186D4×C11—81no—
187D4×C11—81no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—84no—
209C2×C4×C11—81no—
210C2×C4×C11—81no—
211C8×C11—81no—
212C8×C11—81no—
213#534C22×C1111yescharacteristic
214C2×#121—21no—
215C2×#120—21no—
216C2×#120—21no—
217#481—21no—
218#447—21no—
219C2×#99—21no—
220#399C22×C1111yescharacteristic
221#397—21no—
222#394—21no—
223#392C22×C1111yescharacteristic
224#386—21no—
225#386—21no—
226#379C22×C1111yescharacteristic
227#342C22×C1111yescharacteristic
228#327—21no—
229#327—21no—
230#323C22×C1111yescharacteristic
231#323C22×C1111yescharacteristic
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—44no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11—82no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—82no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—161no—
264C22×C11#44911yescharacteristic
265C22×C11#45311yescharacteristic
266C22×C11B(4,𝔽2)11yescharacteristic
267C4×C11—42no—
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11—81no—
274C4×C11—81no—
275C25D4×C1111yescharacteristic
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—41no—
281C22×D4D4×C1111yescharacteristic, complemented
282C23×C4—21no—
283C2×D8—41no—
284#123—41no—
285#121—21no—
286#121—21no—
287#121—44no—
288#120—42no—
289#120—41no—
290#120—44no—
291#120—42no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4D4×C1111yescharacteristic, complemented
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4D4×C1111yescharacteristic
304C2×C22⋊C4C23×C1111yescharacteristic
305#106—41no—
306#102—41no—
307#102—41no—
308#99—42no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311#95—21no—
312#95—21no—
313#95D4×C1111yescharacteristic, complemented
314#95D4×C1111yescharacteristic, complemented
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—41no—
318C2×C11—41no—
319C2×C11—82no—
320C2×C11—82no—
321C2×C11—161no—
322C2×C11#160011yescharacteristic
323C2×C11#219611yescharacteristic
324C2×C11#220011yescharacteristic
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—41no—
331C24—41no—
332C24—42no—
333C24—81no—
334C24C2×D4×C1111yescharacteristic
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—41no—
345C2×D4—42no—
346C2×D4—44no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—81no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4—81no—
356C2×D4—82no—
357C2×D4—82no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—41no—
365C22×C4—81no—
366C22×C4—81no—
367C22×C4C2×D4×C1111yescharacteristic
368C22×C4C2×D4×C1111yescharacteristic
369D8—82no—
370C2×C8—41no—
371C2×C8—41no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—42no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—44no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—81no—
389C22⋊C4—81no—
390C11#1218611yescharacteristic, direct product factor, Sylow
391C23—21no—
392C23—21no—
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—81no—
416C23—82no—
417C23—81no—
418C23—82no—
419C23—84no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23C11×#12011yescharacteristic
424C23C11×#13511yescharacteristic
425C23C11×AGL(1,ℤ/8)11yescharacteristic
426D4—42no—
427D4—84no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—82no—
434D4—82no—
435D4—84no—
436D4—88no—
437D4—81no—
438D4—81no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—84no—
460C2×C4—81no—
461C2×C4—81no—
462C8—81no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—161no—
496C22C11×#44911yescharacteristic
497C22C11×#45311yescharacteristic
498C22C11×B(4,𝔽2)11yescharacteristic
499C4—42no—
500C4—41no—
501C4—41no—
502C4—81no—
503C4—81no—
504C4—82no—
505C4—81no—
506C4—81no—
507C2—21no—
508C2—21no—
509C2—41no—
510C2—41no—
511C2—82no—
512C2—82no—
513C2—161no—
514C2C11×#160011yescharacteristic
515C2C11×#219611yescharacteristic
516C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2668C2semidirect
2. C11×#2021C2semidirect
3. C11×#1613C2semidirect
4. C11×#1595C2semidirect
5. C11×#1352C2semidirect
6. C11×#1343C2semidirect
7. C11×#1316C2semidirect
33. C22×D4×C11D4semidirect
45. C2×C11×C4⋊C4D4semidirect
65. C11×#95D4semidirect
66. C11×#95D4semidirect
67. #12186C11direct (N × H)
133. #2668C2×C11semidirect
134. #2021C2×C11semidirect
135. #1613C2×C11semidirect
136. #1595C2×C11semidirect
137. #1352C2×C11semidirect
138. #1343C2×C11semidirect
139. #1316C2×C11semidirect
281. C22×D4D4×C11semidirect
293. C2×C4⋊C4D4×C11semidirect
313. #95D4×C11semidirect
314. #95D4×C11semidirect
390. C11#12186direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26682
C11×#20212
C11×#16132
C11×#15952
C11×#13522
C11×#13432
C11×#13162
#1218611