Finite Group Databasebeta

← C11×#18906 #14596099

Subgroups — C11×#18906 #14596099

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic
4C2×C11×#462C211yesmaximal, characteristic, complemented
5C11×#1648C214yesmaximal, complemented
6C11×#1640C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C22×C11×Q16—21no—
11C11×#559C2212yes—
12C11×#557C2212yes—
13C11×#556—21no—
14C11×#556—22no—
15C11×#554—21no—
16C11×#552—22no—
17C11×#539—22no—
18C11×#536—21no—
19C11×#533C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#500C2212yes—
26C11×#498—21no—
27C11×#487—21no—
28C11×#486C2212yes—
29C11×#483—22no—
30C11×#480—22no—
31C11×#475C2214yes—
32C11×#474—22no—
33C11×#462—22no—
34C11×#462C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#332C2212yes—
40C11×#331C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×Q8⋊C8C2214yes—
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C2×C11×Q16—24no—
47C2×C11×Q16—44no—
48C22×C8×C11—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—22no—
61C11×#125—24no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C11×#121—21no—
74C11×#121D412yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×Q8×C11C2312yes—
82C4×Q8×C11C2312yes—
83C4×D4×C11—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11D412yes—
88C11×#117—22no—
89C11×#117—24no—
90C11×#117—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#107—24no—
99C11×#106—24no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#103—24no—
105C11×#103—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18906C1111yesmaximal, characteristic, direct product factor, Sylow
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—41no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D412yes—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C11×Q16—48no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—24no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#3507C2×C1111yescharacteristic
176#3229C2×C1111yescharacteristic, complemented
177#3226C2×C1111yescharacteristic
178C2×#462C2×C1111yescharacteristic, complemented
179#1648C2×C1114yescomplemented
180#1640C2×C1114yescomplemented
181#1540C2×C1111yescharacteristic
182#1481C2×C1111yescharacteristic, complemented
183#1479C2×C1111yescharacteristic, complemented
184C23×C11—22no—
185C23×C11#12011yescharacteristic
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—24no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—81no—
195Q8×C11—82no—
196D4×C11—42no—
197D4×C11—44no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—42no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—81no—
212C2×C4×C11—84no—
213C2×C4×C11—82no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#13512yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C8×C11—42no—
223C8×C11—42no—
224C8×C11—42no—
225C22×Q16—21no—
226#559C22×C1112yes—
227#557C22×C1112yes—
228#556—21no—
229#556—22no—
230#554—21no—
231#552—22no—
232#539—22no—
233#536—21no—
234#533C22×C1111yescharacteristic
235#532C22×C1111yescharacteristic
236C2×C4⋊Q8C22×C1111yescharacteristic
237#529—22no—
238#520—21no—
239C2×C4×Q8C22×C1111yescharacteristic
240#500C22×C1112yes—
241#498—21no—
242#487—21no—
243#486C22×C1112yes—
244#483—22no—
245#480—22no—
246#475C22×C1114yes—
247#474—22no—
248#462—22no—
249#462C22×C1114yes—
250#431C22×C1111yescharacteristic
251#431C22×C1111yescharacteristic
252C2×C4⋊C8C22×C1111yescharacteristic
253C2×#103—21no—
254#332C22×C1112yes—
255#331C22×C1112yes—
256Q8⋊C8C22×C1114yes—
257Q8⋊C8C22×C1114yes—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11#44912yes—
264C22×C11C2×#12011yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—82no—
274C4×C11#44912yes—
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11#57812yes—
278C2×#41—21no—
279C22×Q8—21no—
280C22×Q8D4×C1111yescharacteristic
281C2×Q16—24no—
282C2×Q16—44no—
283C22×C8—21no—
284C4⋊Q8—22no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8D4×C1111yescharacteristic
289C4⋊Q8D4×C1111yescharacteristic
290C4⋊Q8C23×C1112yes—
291C4⋊Q8C23×C1111yescharacteristic
292#127C23×C1111yescharacteristic
293#126—24no—
294#126—24no—
295#125—22no—
296#125—24no—
297#125—21no—
298#124—22no—
299#124—22no—
300#124—21no—
301#123—24no—
302#123—24no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8—21no—
307C22⋊Q8D4×C1112yes—
308#121—21no—
309#121D4×C1112yes—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8D4×C1112yes—
316C4×Q8C23×C1112yes—
317C4×Q8C23×C1112yes—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—21no—
322C4×D4D4×C1112yes—
323#117—22no—
324#117—24no—
325#117—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C42—21no—
332C2×C42C23×C1111yescharacteristic
333#107—24no—
334#106—24no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8C23×C1112yes—
338C4⋊C8C23×C1112yes—
339#103—24no—
340#103—24no—
341#102—24no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C4×C8—21no—
345C4×C8C23×C1112yes—
346C2×C11—22no—
347C2×C11—82no—
348C2×C11C2×#44911yescharacteristic
349C2×C11#301111yescharacteristic
350C2×C11#302211yescharacteristic
351#41—42no—
352#41—42no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—41no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8C2×D4×C1112yes—
363C2×Q8C2×D4×C1112yes—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×D4×C1112yes—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4C2×D4×C1111yescharacteristic
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376Q16—48no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C1112yes—
398C4⋊C4C2×D4×C1112yes—
399C4⋊C4C2×D4×C1112yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C42—24no—
407C42—22no—
408C42—22no—
409C42—22no—
410C42C2×D4×C1111yescharacteristic
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1111yescharacteristic
413C42C24×C1111yescharacteristic
414C11#1890611yescharacteristic, direct product factor, Sylow
415C23—22no—
416C23C11×#12011yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—24no—
420Q8—41no—
421Q8—41no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—81no—
426Q8—82no—
427D4—42no—
428D4—44no—
429D4—41no—
430D4—41no—
431D4—42no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—84no—
444C2×C4—82no—
445C2×C4C11×#12011yescharacteristic
446C2×C4C11×#12011yescharacteristic
447C2×C4C11×#12011yescharacteristic
448C2×C4C11×#13512yes—
449C2×C4C11×AGL(1,ℤ/8)12yes—
450C2×C4C22×D4×C1111yescharacteristic
451C2×C4C22×D4×C1111yescharacteristic
452C2×C4C22×D4×C1111yescharacteristic
453C8—42no—
454C8—42no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22C11×#44912yes—
462C22C2×C11×#12011yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4C11×#44912yes—
473C4C2×C11×#13511yescharacteristic
474C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
475C4C11×#57812yes—
476C2—22no—
477C2—82no—
478C2C2×C11×#44911yescharacteristic
479C2C11×#301111yescharacteristic
480C2C11×#302211yescharacteristic
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×#3229C2semidirect
4. C2×C11×#462C2semidirect
5. C11×#1648C2semidirect
6. C11×#1640C2semidirect
8. C11×#1481C2semidirect
9. C11×#1479C2semidirect
111. #18906C11direct (N × H)
176. #3229C2×C11semidirect
178. C2×#462C2×C11semidirect
179. #1648C2×C11semidirect
180. #1640C2×C11semidirect
182. #1481C2×C11semidirect
183. #1479C2×C11semidirect
414. C11#18906direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#32292
C11×#32262
C2×C11×#4622
C11×#16482
C11×#16402
C11×#15402
C11×#14812
C11×#14792
#1890611