Finite Group Databasebeta

← C11×#19076 #14596269

Subgroups — C11×#19076 #14596269

Order 2816.

1000 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic
2C11×#3165C211yesmaximal, characteristic, complemented
3C11×#3152C211yesmaximal, characteristic, complemented
4C11×#3141C211yesmaximal, characteristic, complemented
5C11×#1661C218yesmaximal, complemented
6C11×#1526C211yesmaximal, characteristic, complemented
7C11×#1525C211yesmaximal, characteristic, complemented
8C11×#1525C211yesmaximal, characteristic, complemented
9C2×C11×#137—22no—
10C11×#562C2214yes—
11C11×#554—21no—
12C11×#554—21no—
13C11×#550—21no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#547—21no—
17C11×#540—22no—
18C11×#537—22no—
19C11×#537—22no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#501C2214yes—
25C11×#500—21no—
26C11×#498—21no—
27C11×#497C2214yes—
28C11×#494—21no—
29C11×#492—21no—
30C11×#489C2214yes—
31C11×#487—21no—
32C11×#486—21no—
33C11×#428—22no—
34C11×#417—22no—
35C4×C11×M16C2211yescharacteristic
36C4×C11×M16C2211yescharacteristic
37C4×C11×M16C2211yescharacteristic
38C11×#330C2214yes—
39C11×#329C2214yes—
40C11×#329C2214yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D412yes—
44C2×C11×#41D412yes—
45C22×Q8×C11—21no—
46C11×#137—48no—
47C2×C11×Q16—24no—
48C2×C11×SD16—24no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2312yes—
60C11×#127—22no—
61C11×#127D411yescharacteristic
62C11×#127D411yescharacteristic
63C11×#125—22no—
64C11×#125C2312yes—
65C11×#124C2312yes—
66C11×#124C2312yes—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×#121—24no—
76C11×#121—24no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—24no—
80C11×#121—24no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11—21no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C11×#117D412yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C42×C11C2311yescharacteristic
99C11×#107—24no—
100C11×#106—24no—
101C11×#103—24no—
102C11×#102—24no—
103C11×#97C2312yes—
104C11×#97C2312yes—
105C11×#97C2312yes—
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108C4×C8×C11—21no—
109#19076C1111yesmaximal, characteristic, direct product factor, Sylow
110C11×#41—44no—
111C11×#41—44no—
112C11×#41—84no—
113C11×#41—84no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—44no—
118C2×Q8×C11—41no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—41no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C11×Q16—48no—
140C11×SD16—48no—
141C11×M16—24no—
142C11×M16—24no—
143C11×M16—42no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#3548C2×C1111yescharacteristic
176#3165C2×C1111yescharacteristic, complemented
177#3152C2×C1111yescharacteristic, complemented
178#3141C2×C1111yescharacteristic, complemented
179#1661C2×C1118yescomplemented
180#1526C2×C1111yescharacteristic, complemented
181#1525C2×C1111yescharacteristic, complemented
182#1525C2×C1111yescharacteristic, complemented
183C23×C11—22no—
184C23×C11—22no—
185C23×C11#12011yescharacteristic
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—44no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—82no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—84no—
201D4×C11—84no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—84no—
213C2×C4×C11—84no—
214C2×C4×C11—82no—
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C8×C11—24no—
222C8×C11—24no—
223C8×C11—42no—
224C2×#137—22no—
225#562C22×C1114yes—
226#554—21no—
227#554—21no—
228#550—21no—
229#550—21no—
230#547—21no—
231#547—21no—
232#540—22no—
233#537—22no—
234#537—22no—
235#533C22×C1111yescharacteristic
236#532C22×C1111yescharacteristic
237#532C22×C1111yescharacteristic
238C2×C4⋊Q8C22×C1111yescharacteristic
239#501C22×C1114yes—
240#500—21no—
241#498—21no—
242#497C22×C1114yes—
243#494—21no—
244#492—21no—
245#489C22×C1114yes—
246#487—21no—
247#486—21no—
248#428—22no—
249#417—22no—
250C4×M16C22×C1111yescharacteristic
251C4×M16C22×C1111yescharacteristic
252C4×M16C22×C1111yescharacteristic
253#330C22×C1114yes—
254#329C22×C1114yes—
255#329C22×C1114yes—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11C2×#12011yescharacteristic
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—82no—
274C4×C11#45312yes—
275C4×C11#45512yes—
276C4×C11#45612yes—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41D4×C1112yes—
280C2×#41D4×C1112yes—
281C22×Q8—21no—
282#137—48no—
283C2×Q16—24no—
284C2×SD16—24no—
285C2×M16—21no—
286C2×M16—21no—
287C2×M16—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8D4×C1111yescharacteristic
292C4⋊Q8D4×C1111yescharacteristic
293C4⋊Q8D4×C1111yescharacteristic
294C4⋊Q8D4×C1111yescharacteristic
295C4⋊Q8C23×C1112yes—
296#127—22no—
297#127D4×C1111yescharacteristic
298#127D4×C1111yescharacteristic
299#125—22no—
300#125C23×C1112yes—
301#124C23×C1112yes—
302#124C23×C1112yes—
303#123—24no—
304#123—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311#121—24no—
312#121—24no—
313#121—22no—
314#121—22no—
315#121—24no—
316#121—24no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329#117D4×C1112yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C42C23×C1111yescharacteristic
335#107—24no—
336#106—24no—
337#103—24no—
338#102—24no—
339#97C23×C1112yes—
340#97C23×C1112yes—
341#97C23×C1112yes—
342C4×C8—21no—
343C4×C8—21no—
344C4×C8—21no—
345C2×C11—41no—
346C2×C11—82no—
347C2×C11—82no—
348C2×C11C2×#45311yescharacteristic
349C2×C11C2×#45511yescharacteristic
350C2×C11C2×#45611yescharacteristic
351#41—44no—
352#41—44no—
353#41—84no—
354#41—84no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—44no—
359C2×Q8—41no—
360C2×Q8C2×D4×C1112yes—
361C2×Q8C2×D4×C1112yes—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×D4×C1112yes—
371C2×D4C2×D4×C1112yes—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380Q16—48no—
381SD16—48no—
382M16—24no—
383M16—24no—
384M16—42no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C2×D4×C1112yes—
403C4⋊C4C2×D4×C1112yes—
404C22⋊C4—24no—
405C22⋊C4—24no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C42—22no—
412C42C2×D4×C1111yescharacteristic
413C42C2×D4×C1111yescharacteristic
414C42C2×D4×C1111yescharacteristic
415C42C24×C1111yescharacteristic
416C11#1907611yescharacteristic, direct product factor, Sylow
417C23—22no—
418C23—22no—
419C23C11×#12011yescharacteristic
420Q8—42no—
421Q8—42no—
422Q8—44no—
423Q8—42no—
424Q8—42no—
425Q8—82no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—82no—
433D4—82no—
434D4—84no—
435D4—84no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4—84no—
448C2×C4—82no—
449C2×C4C11×#12011yescharacteristic
450C2×C4C11×#12011yescharacteristic
451C2×C4C11×#12011yescharacteristic
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C2×C4C22×D4×C1111yescharacteristic
455C8—24no—
456C8—24no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×C11×#12011yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4C11×#45312yes—
477C4C11×#45512yes—
478C4C11×#45612yes—
479C2—41no—
480C2—82no—
481C2—82no—
482C2C2×C11×#45311yescharacteristic
483C2C2×C11×#45511yescharacteristic
484C2C2×C11×#45611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3548C2
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
3. C11×#3152C2semidirect
4. C11×#3141C2semidirect
5. C11×#1661C2semidirect
6. C11×#1526C2semidirect
7. C11×#1525C2semidirect
8. C11×#1525C2semidirect
109. #19076C11direct (N × H)
176. #3165C2×C11semidirect
177. #3152C2×C11semidirect
178. #3141C2×C11semidirect
179. #1661C2×C11semidirect
180. #1526C2×C11semidirect
181. #1525C2×C11semidirect
182. #1525C2×C11semidirect
416. C11#19076direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#31652
C11×#31522
C11×#31412
C11×#16612
C11×#15262
C11×#15252
#1907611