Finite Group Databasebeta

← C11×#19081 #14596274

Subgroups — C11×#19081 #14596274

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3165C211yesmaximal, characteristic, complemented
3C11×#3141C211yesmaximal, characteristic
4C11×#3139C211yesmaximal, characteristic, complemented
5C11×#1664C218yesmaximal, complemented
6C11×#1526C211yesmaximal, characteristic, complemented
7C11×#1526C211yesmaximal, characteristic, complemented
8C11×#1525C211yesmaximal, characteristic
9C11×#563C2214yes—
10C11×#559—21no—
11Q82×C11—21no—
12C11×#556—21no—
13C11×#556—21no—
14D4×Q8×C11—21no—
15D4×Q8×C11—21no—
16C11×#542—22no—
17C11×#542—22no—
18C11×#536—22no—
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C2×C11×C4⋊Q8C2211yescharacteristic
23C11×#501C2214yes—
24C11×#500—21no—
25C11×#498—21no—
26C11×#491C2214yes—
27C11×#489C2214yes—
28C11×#487—21no—
29C11×#487—21no—
30C11×#487—21no—
31C11×#486—21no—
32C11×#428—22no—
33C11×#419—22no—
34C11×#417—22no—
35C4×C11×M16C2211yescharacteristic
36C4×C11×M16C2211yescharacteristic
37C4×C11×M16C2211yescharacteristic
38C11×#330C2214yes—
39C11×#330C2214yes—
40C11×#329C2214yes—
41C2×C11×#41D412yes—
42C22×Q8×C11—22no—
43C22×Q8×C11—21no—
44C2×C11×M16—21no—
45C2×C11×M16—21no—
46C2×C11×M16—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—24no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×#127D411yescharacteristic
60C11×#126—24no—
61C11×#126—24no—
62C11×#125C2312yes—
63C11×#125C2312yes—
64C11×#124—24no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124C2312yes—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×#121—21no—
79C11×#121—21no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C11×#117—22no—
91C11×#117D412yes—
92C11×#117D412yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C42×C11C2311yescharacteristic
96C11×#107—24no—
97C11×#106—24no—
98C11×#103—24no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#102—24no—
102C11×#97C2312yes—
103C11×#97C2312yes—
104C11×#97C2312yes—
105C4×C8×C11—21no—
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108#19081C1111yesmaximal, characteristic, direct product factor, Sylow
109C11×#41—44no—
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—44no—
117C2×Q8×C11—41no—
118C2×Q8×C11—84no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C11×M16—24no—
131C11×M16—42no—
132C11×M16—42no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2411yescharacteristic
170#3550C2×C1111yescharacteristic
171#3165C2×C1111yescharacteristic, complemented
172#3141C2×C1111yescharacteristic
173#3139C2×C1111yescharacteristic, complemented
174#1664C2×C1118yescomplemented
175#1526C2×C1111yescharacteristic, complemented
176#1526C2×C1111yescharacteristic, complemented
177#1525C2×C1111yescharacteristic
178C23×C11—22no—
179C23×C11#12011yescharacteristic
180Q8×C11—42no—
181Q8×C11—44no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—42no—
185Q8×C11—42no—
186Q8×C11—84no—
187Q8×C11—82no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—82no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—84no—
203C2×C4×C11—82no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C8×C11—24no—
211C8×C11—42no—
212C8×C11—42no—
213#563C22×C1114yes—
214#559—21no—
215Q82—21no—
216#556—21no—
217#556—21no—
218D4×Q8—21no—
219D4×Q8—21no—
220#542—22no—
221#542—22no—
222#536—22no—
223#533C22×C1111yescharacteristic
224#533C22×C1111yescharacteristic
225#532C22×C1111yescharacteristic
226C2×C4⋊Q8C22×C1111yescharacteristic
227#501C22×C1114yes—
228#500—21no—
229#498—21no—
230#491C22×C1114yes—
231#489C22×C1114yes—
232#487—21no—
233#487—21no—
234#487—21no—
235#486—21no—
236#428—22no—
237#419—22no—
238#417—22no—
239C4×M16C22×C1111yescharacteristic
240C4×M16C22×C1111yescharacteristic
241C4×M16C22×C1111yescharacteristic
242#330C22×C1114yes—
243#330C22×C1114yes—
244#329C22×C1114yes—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11C2×#12011yescharacteristic
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—82no—
261C4×C11#45412yes—
262C4×C11#45512yes—
263C4×C11#45612yes—
264C2×#41D4×C1112yes—
265C22×Q8—22no—
266C22×Q8—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C4⋊Q8—22no—
271C4⋊Q8—22no—
272C4⋊Q8—24no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8D4×C1111yescharacteristic
277C4⋊Q8D4×C1111yescharacteristic
278C4⋊Q8D4×C1111yescharacteristic
279C4⋊Q8D4×C1111yescharacteristic
280C4⋊Q8D4×C1111yescharacteristic
281C4⋊Q8C23×C1112yes—
282#127D4×C1111yescharacteristic
283#126—24no—
284#126—24no—
285#125C23×C1112yes—
286#125C23×C1112yes—
287#124—24no—
288#124—22no—
289#124—22no—
290#124C23×C1112yes—
291#123—24no—
292#123—24no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—24no—
300C22⋊Q8—24no—
301#121—21no—
302#121—21no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—21no—
312C4×D4—21no—
313#117—22no—
314#117D4×C1112yes—
315#117D4×C1112yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C42C23×C1111yescharacteristic
319#107—24no—
320#106—24no—
321#103—24no—
322#103—24no—
323#103—24no—
324#102—24no—
325#97C23×C1112yes—
326#97C23×C1112yes—
327#97C23×C1112yes—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8—21no—
331C2×C11—41no—
332C2×C11—82no—
333C2×C11C2×#45511yescharacteristic
334C2×C11C2×#45411yescharacteristic
335C2×C11C2×#45611yescharacteristic
336#41—44no—
337C2×Q8—24no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—44no—
344C2×Q8—41no—
345C2×Q8—84no—
346C2×Q8C2×D4×C1112yes—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×D4×C1112yes—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357M16—24no—
358M16—42no—
359M16—42no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C4⋊C4—24no—
364C4⋊C4—24no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C1112yes—
380C4⋊C4C2×D4×C1112yes—
381C4⋊C4C2×D4×C1112yes—
382C4⋊C4C2×D4×C1112yes—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C42—24no—
391C42—22no—
392C42—22no—
393C42C2×D4×C1111yescharacteristic
394C42C2×D4×C1111yescharacteristic
395C42C2×D4×C1111yescharacteristic
396C42C24×C1111yescharacteristic
397C11#1908111yescharacteristic, direct product factor, Sylow
398C23—22no—
399C23C11×#12011yescharacteristic
400Q8—42no—
401Q8—44no—
402Q8—42no—
403Q8—42no—
404Q8—42no—
405Q8—42no—
406Q8—84no—
407Q8—82no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4C11×#12011yescharacteristic
425C2×C4C11×#12011yescharacteristic
426C2×C4C11×#12011yescharacteristic
427C2×C4C22×D4×C1111yescharacteristic
428C2×C4C22×D4×C1111yescharacteristic
429C2×C4C22×D4×C1111yescharacteristic
430C8—24no—
431C8—42no—
432C8—42no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×C11×#12011yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4C11×#45412yes—
450C4C11×#45512yes—
451C4C11×#45612yes—
452C2—41no—
453C2—82no—
454C2C2×C11×#45511yescharacteristic
455C2C2×C11×#45411yescharacteristic
456C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3165C2semidirect
4. C11×#3139C2semidirect
5. C11×#1664C2semidirect
6. C11×#1526C2semidirect
7. C11×#1526C2semidirect
108. #19081C11direct (N × H)
171. #3165C2×C11semidirect
173. #3139C2×C11semidirect
174. #1664C2×C11semidirect
175. #1526C2×C11semidirect
176. #1526C2×C11semidirect
397. C11#19081direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#31652
C11×#31412
C11×#31392
C11×#16642
C11×#15262
C11×#15252
#1908111