Finite Group Databasebeta

← C11×#18202 #14595395

Subgroups — C11×#18202 #14595395

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C2×C11×#480C212yesmaximal, complemented
3C11×#2486C211yesmaximal, characteristic, complemented
4C11×#1610C214yesmaximal, complemented
5C11×#1607C214yesmaximal, complemented
6C11×#1519C212yesmaximal, complemented
7C11×#1459C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537C2212yes—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C2×C11×#123—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C11×#480—24no—
22C11×#480C2218yescomplemented
23C2×C11×#107—22no—
24C2×C11×#102—22no—
25C2×C11×C22⋊C8C2212yescomplemented
26C11×#398C2212yescomplemented
27C11×#397C2212yescomplemented
28C11×#389—21no—
29C11×#381—21no—
30C11×#380—21no—
31C11×#380C2211yescharacteristic, complemented
32C11×#327C2218yescomplemented
33C11×#324C2212yescomplemented
34C11×#323C2212yescomplemented
35C11×H(5,𝔽2)—44no—
36C11×H(5,𝔽2)—44no—
37C2×C11×#41—24no—
38C2×C11×#41—22no—
39C22×D4×C11—24no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11D411yescharacteristic
44C22×D4×C11D412yes—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C8×C11—22no—
49C11×C4⋊Q8—21no—
50C11×#127—21no—
51C11×#124—22no—
52C11×#123—24no—
53C11×#123—24no—
54C11×#123—44no—
55C11×C22⋊Q8—24no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121D414yes—
64C11×#121C2314yes—
65C11×#120—24no—
66C11×#120—24no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D412yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4C2311yescharacteristic
86C2×C42×C11D411yescharacteristic
87C11×#107—28no—
88C11×#102—28no—
89C11×C22⋊C8—22no—
90C11×C22⋊C8C2314yes—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95C2312yes—
94#18202C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C11×#41—44no—
100C11×#41—416no—
101C11×#41—44no—
102C2×Q8×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—44no—
113C2×D4×C11—416no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11—82no—
119C2×D4×C11D814yes—
120C2×D4×C11C2×D414yes—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2411yescharacteristic
140C2×C8×C11—24no—
141C2×C8×C11—44no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4C2×D414yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—44no—
160C42×C11—21no—
161C42×C11—21no—
162#3496C2×C1111yescharacteristic
163C2×#480C2×C1112yescomplemented
164#2486C2×C1111yescharacteristic, complemented
165#1610C2×C1114yescomplemented
166#1607C2×C1114yescomplemented
167#1519C2×C1112yescomplemented
168#1459C2×C1111yescharacteristic, complemented
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—24no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—44no—
177C23×C11—44no—
178C23×C11—82no—
179C23×C11—82no—
180C23×C11—82no—
181C23×C11—82no—
182C23×C11#12012yes—
183C23×C11C2×D812yes—
184C23×C11C2×D812yes—
185C23×C11AGL(1,ℤ/8)12yes—
186C23×C11C22×D411yescharacteristic
187Q8×C11—44no—
188D4×C11—28no—
189D4×C11—44no—
190D4×C11—44no—
191D4×C11—48no—
192D4×C11—44no—
193D4×C11—44no—
194D4×C11—48no—
195D4×C11—44no—
196D4×C11—82no—
197D4×C11—82no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—48no—
208C2×C4×C11—44no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—81no—
220C2×C4×C11—84no—
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C2×D812yes—
224C2×C4×C11C22×D412yes—
225C8×C11—44no—
226C2×H(5,𝔽2)—21no—
227#547—22no—
228#546—24no—
229D42—22no—
230#537C22×C1112yes—
231#534—21no—
232#534C22×C1112yes—
233#532—21no—
234C2×#123—21no—
235C2×#121—21no—
236C2×#121C22×C1112yes—
237C2×C4×D4C22×C1111yescharacteristic
238C22×C4⋊C4C22×C1111yescharacteristic, complemented
239#480—24no—
240#480C22×C1118yescomplemented
241C2×#107—22no—
242C2×#102—22no—
243C2×C22⋊C8C22×C1112yescomplemented
244#398C22×C1112yescomplemented
245#397C22×C1112yescomplemented
246#389—21no—
247#381—21no—
248#380—21no—
249#380C22×C1111yescharacteristic, complemented
250#327C22×C1118yescomplemented
251#324C22×C1112yescomplemented
252#323C22×C1112yescomplemented
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—21no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—81no—
267C22×C11—164no—
268C22×C11—164no—
269C22×C11#44714yes—
270C22×C11C2×#12011yescharacteristic
271C22×C11C22×D811yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C4×C11—22no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—44no—
277C4×C11—41no—
278C4×C11—41no—
279C4×C11—82no—
280C4×C11—82no—
281C4×C11#45812yes—
282H(5,𝔽2)—44no—
283H(5,𝔽2)—44no—
284C2×#41—24no—
285C2×#41—22no—
286C22×D4—24no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4D4×C1111yescharacteristic
291C22×D4D4×C1112yes—
292C23×C4—21no—
293C23×C4D4×C1111yescharacteristic
294C23×C4C23×C1111yescharacteristic
295C22×C8—22no—
296C4⋊Q8—21no—
297#127—21no—
298#124—22no—
299#123—24no—
300#123—24no—
301#123—44no—
302C22⋊Q8—24no—
303#121—22no—
304#121—22no—
305#121—24no—
306#121—22no—
307#121—22no—
308#121—22no—
309#121—22no—
310#121D4×C1114yes—
311#121C23×C1114yes—
312#120—24no—
313#120—24no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C1112yes—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4D4×C1111yescharacteristic
332C2×C22⋊C4C23×C1111yescharacteristic
333C2×C42D4×C1111yescharacteristic
334#107—28no—
335#102—28no—
336C22⋊C8—22no—
337C22⋊C8C23×C1114yes—
338#95—22no—
339#95—22no—
340#95C23×C1112yes—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—24no—
344C2×C11—42no—
345C2×C11—84no—
346C2×C11C2×#44711yescharacteristic
347C2×C11#302211yescharacteristic
348C2×C11C2×#45811yescharacteristic
349C24—22no—
350C24—22no—
351C24C2×D4×C1111yescharacteristic
352C24C2×D4×C1111yescharacteristic
353#41—44no—
354#41—416no—
355#41—44no—
356C2×Q8—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—44no—
367C2×D4—416no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—44no—
372C2×D4—82no—
373C2×D4C11×D814yes—
374C2×D4C2×D4×C1114yes—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1112yes—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1112yes—
393C22×C4C24×C1111yescharacteristic
394C2×C8—24no—
395C2×C8—44no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—24no—
401C4⋊C4—42no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—44no—
405C4⋊C4C2×D4×C1114yes—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—22no—
409C22⋊C4—24no—
410C22⋊C4—24no—
411C22⋊C4—22no—
412C22⋊C4—42no—
413C22⋊C4—44no—
414C42—21no—
415C42—21no—
416C11#1820211yescharacteristic, direct product factor, Sylow
417C23—21no—
418C23—21no—
419C23—24no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—44no—
425C23—44no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23—82no—
430C23C11×#12012yes—
431C23C2×C11×D812yes—
432C23C2×C11×D812yes—
433C23C11×AGL(1,ℤ/8)12yes—
434C23C22×D4×C1111yescharacteristic
435Q8—44no—
436D4—28no—
437D4—44no—
438D4—44no—
439D4—48no—
440D4—44no—
441D4—44no—
442D4—48no—
443D4—44no—
444D4—82no—
445D4—82no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—48no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4C11×#12011yescharacteristic
470C2×C4C11×#12011yescharacteristic
471C2×C4C2×C11×D812yes—
472C2×C4C22×D4×C1112yes—
473C8—44no—
474C22—21no—
475C22—22no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—81no—
488C22—164no—
489C22—164no—
490C22C11×#44714yes—
491C22C2×C11×#12011yescharacteristic
492C22C22×C11×D811yescharacteristic
493C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
494C4—22no—
495C4—22no—
496C4—21no—
497C4—44no—
498C4—41no—
499C4—41no—
500C4—82no—
501C4—82no—
502C4C11×#45812yes—
503C2—21no—
504C2—21no—
505C2—24no—
506C2—42no—
507C2—84no—
508C2C2×C11×#44711yescharacteristic
509C2C11×#302211yescharacteristic
510C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#480C2semidirect
3. C11×#2486C2semidirect
4. C11×#1610C2semidirect
5. C11×#1607C2semidirect
6. C11×#1519C2semidirect
7. C11×#1459C2semidirect
20. C22×C11×C4⋊C4C22semidirect
22. C11×#480C22semidirect
25. C2×C11×C22⋊C8C22semidirect
26. C11×#398C22semidirect
27. C11×#397C22semidirect
31. C11×#380C22semidirect
32. C11×#327C22semidirect
33. C11×#324C22semidirect
34. C11×#323C22semidirect
94. #18202C11direct (N × H)
163. C2×#480C2×C11semidirect
164. #2486C2×C11semidirect
165. #1610C2×C11semidirect
166. #1607C2×C11semidirect
167. #1519C2×C11semidirect
168. #1459C2×C11semidirect
238. C22×C4⋊C4C22×C11semidirect
240. #480C22×C11semidirect
243. C2×C22⋊C8C22×C11semidirect
244. #398C22×C11semidirect
245. #397C22×C11semidirect
249. #380C22×C11semidirect
250. #327C22×C11semidirect
251. #324C22×C11semidirect
252. #323C22×C11semidirect
416. C11#18202direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C2×C11×#4802
C11×#24862
C11×#16102
C11×#16072
C11×#15192
C11×#14592
#1820211