Finite Group Databasebeta

← C11×#18210 #14595403

Subgroups — C11×#18210 #14595403

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic, complemented
2C11×#3100C212yesmaximal, complemented
3C11×#2535C211yesmaximal, characteristic, complemented
4C11×#1607C214yesmaximal, complemented
5C11×#1595C214yesmaximal, complemented
6C11×#1517C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537—21no—
13C11×#534C2214yes—
14C11×#532C2212yes—
15C2×C11×#121—22no—
16C2×C11×#121—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic, complemented
19C11×#480C2214yescomplemented
20C11×#474—22no—
21C11×#459—22no—
22C11×#447C2214yescomplemented
23C4×C11×D8—24no—
24C11×#431C2212yescomplemented
25C11×#397C2212yescomplemented
26C11×#392C2212yescomplemented
27C11×#386—22no—
28C11×#382C2211yescharacteristic, complemented
29C11×#380—21no—
30C11×#327C2218yescomplemented
31C11×#323C2214yescomplemented
32C11×H(5,𝔽2)—44no—
33C11×H(5,𝔽2)—44no—
34C2×C11×#41—24no—
35C2×C11×#41—22no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11D411yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11D412yes—
44C2×C11×D8—24no—
45C11×C4⋊Q8D412yescomplemented
46C11×#127D412yescomplemented
47C11×#124—22no—
48C11×#123—28no—
49C11×C22⋊Q8—24no—
50C11×#121—24no—
51C11×#121—24no—
52C11×#121—24no—
53C11×#121—22no—
54C11×#121—24no—
55C11×#121—44no—
56C11×#121C2314yes—
57C11×#120—28no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yescomplemented
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4C2312yes—
73C2×C42×C11C2311yescharacteristic
74C11×#107—24no—
75C11×C4⋊C8—22no—
76C11×#102—24no—
77C11×#102—24no—
78C11×C22⋊C8C2314yes—
79C4×C8×C11—22no—
80C11×#95—22no—
81C11×#95—21no—
82C11×#95C2312yes—
83#18210C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—24no—
85C24×C11—21no—
86C24×C11C2×D412yes—
87C11×#41—416no—
88C11×#41—44no—
89C11×#41—44no—
90C2×Q8×C11—22no—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—42no—
100C2×D4×C11—416no—
101C2×D4×C11—48no—
102C2×D4×C11—48no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C2×D4×C11—84no—
106C2×D4×C11—82no—
107C2×D4×C11D814yescomplemented
108C2×D4×C11C2×D414yes—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—82no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C11×D8—48no—
124C2×C8×C11—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4C2×D414yes—
131C11×C22⋊C4—28no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—44no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—82no—
139C42×C11C2×D412yes—
140C42×C11C2×D412yes—
141#3496C2×C1111yescharacteristic, complemented
142#3100C2×C1112yescomplemented
143#2535C2×C1111yescharacteristic, complemented
144#1607C2×C1114yescomplemented
145#1595C2×C1114yescomplemented
146#1517C2×C1112yescomplemented
147#1460C2×C1111yescharacteristic, complemented
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—48no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—84no—
162C23×C11—84no—
163C23×C11C2×D814yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—44no—
166D4×C11—24no—
167D4×C11—28no—
168D4×C11—44no—
169D4×C11—42no—
170D4×C11—44no—
171D4×C11—416no—
172D4×C11—44no—
173D4×C11—44no—
174D4×C11—44no—
175D4×C11—84no—
176D4×C11—88no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—44no—
182C2×C4×C11—48no—
183C2×C4×C11—48no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—82no—
192C2×C4×C11—84no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12012yes—
196C2×C4×C11C2×D812yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11C22×D412yes—
199C8×C11—44no—
200C2×H(5,𝔽2)—21no—
201#547—22no—
202#546—24no—
203D42—22no—
204#537—21no—
205#534C22×C1114yes—
206#532C22×C1112yes—
207C2×#121—22no—
208C2×#121—21no—
209C2×C4×D4C22×C1111yescharacteristic
210C2×C4×D4C22×C1111yescharacteristic, complemented
211#480C22×C1114yescomplemented
212#474—22no—
213#459—22no—
214#447C22×C1114yescomplemented
215C4×D8—24no—
216#431C22×C1112yescomplemented
217#397C22×C1112yescomplemented
218#392C22×C1112yescomplemented
219#386—22no—
220#382C22×C1111yescharacteristic, complemented
221#380—21no—
222#327C22×C1118yescomplemented
223#323C22×C1114yescomplemented
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—24no—
227C22×C11—44no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—44no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—168no—
242C22×C11C2×#12011yescharacteristic
243C22×C11C22×D811yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—22no—
248C4×C11—44no—
249C4×C11—42no—
250C4×C11—82no—
251C4×C11—81no—
252C4×C11#44714yes—
253H(5,𝔽2)—44no—
254H(5,𝔽2)—44no—
255C2×#41—24no—
256C2×#41—22no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4D4×C1111yescharacteristic
262C22×D4C23×C1111yescharacteristic
263C23×C4—21no—
264C23×C4D4×C1112yes—
265C2×D8—24no—
266C4⋊Q8D4×C1112yescomplemented
267#127D4×C1112yescomplemented
268#124—22no—
269#123—28no—
270C22⋊Q8—24no—
271#121—24no—
272#121—24no—
273#121—24no—
274#121—22no—
275#121—24no—
276#121—44no—
277#121C23×C1114yes—
278#120—28no—
279C4×D4—22no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—22no—
283C4×D4—22no—
284C4×D4D4×C1114yescomplemented
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4D4×C1111yescharacteristic
288C2×C4⋊C4C23×C1111yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4C23×C1112yes—
294C2×C42C23×C1111yescharacteristic
295#107—24no—
296C4⋊C8—22no—
297#102—24no—
298#102—24no—
299C22⋊C8C23×C1114yes—
300C4×C8—22no—
301#95—22no—
302#95—21no—
303#95C23×C1112yes—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—44no—
307C2×C11—82no—
308C2×C11—84no—
309C2×C11C2×#44711yescharacteristic
310C2×C11#301911yescharacteristic
311C2×C11#302511yescharacteristic
312C24—24no—
313C24—21no—
314C24C2×D4×C1112yes—
315#41—416no—
316#41—44no—
317#41—44no—
318C2×Q8—22no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—24no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—42no—
328C2×D4—416no—
329C2×D4—48no—
330C2×D4—48no—
331C2×D4—44no—
332C2×D4—44no—
333C2×D4—84no—
334C2×D4—82no—
335C2×D4C11×D814yescomplemented
336C2×D4C2×D4×C1114yes—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—82no—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C24×C1111yescharacteristic
351D8—48no—
352C2×C8—24no—
353C4⋊C4—24no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—42no—
358C4⋊C4C2×D4×C1114yes—
359C22⋊C4—28no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—44no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—82no—
367C42C2×D4×C1112yes—
368C42C2×D4×C1112yes—
369C11#1821011yescharacteristic, direct product factor, Sylow
370C23—22no—
371C23—22no—
372C23—22no—
373C23—24no—
374C23—42no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—48no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—84no—
384C23—84no—
385C23C2×C11×D814yes—
386C23C22×D4×C1111yescharacteristic
387Q8—44no—
388D4—24no—
389D4—28no—
390D4—44no—
391D4—42no—
392D4—44no—
393D4—416no—
394D4—44no—
395D4—44no—
396D4—44no—
397D4—84no—
398D4—88no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—48no—
405C2×C4—48no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—84no—
415C2×C4C11×#12011yescharacteristic
416C2×C4C11×#12011yescharacteristic
417C2×C4C11×#12012yes—
418C2×C4C2×C11×D812yes—
419C2×C4C11×AGL(1,ℤ/8)12yes—
420C2×C4C22×D4×C1112yes—
421C8—44no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—44no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—44no—
431C22—44no—
432C22—42no—
433C22—44no—
434C22—82no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—168no—
440C22C2×C11×#12011yescharacteristic
441C22C22×C11×D811yescharacteristic
442C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
443C4—21no—
444C4—21no—
445C4—22no—
446C4—44no—
447C4—42no—
448C4—82no—
449C4—81no—
450C4C11×#44714yes—
451C2—21no—
452C2—21no—
453C2—44no—
454C2—82no—
455C2—84no—
456C2C2×C11×#44711yescharacteristic
457C2C11×#301911yescharacteristic
458C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3496C2semidirect
2. C11×#3100C2semidirect
3. C11×#2535C2semidirect
4. C11×#1607C2semidirect
5. C11×#1595C2semidirect
6. C11×#1517C2semidirect
7. C11×#1460C2semidirect
18. C2×C4×D4×C11C22semidirect
19. C11×#480C22semidirect
22. C11×#447C22semidirect
24. C11×#431C22semidirect
25. C11×#397C22semidirect
26. C11×#392C22semidirect
28. C11×#382C22semidirect
30. C11×#327C22semidirect
31. C11×#323C22semidirect
45. C11×C4⋊Q8D4semidirect
46. C11×#127D4semidirect
63. C4×D4×C11D4semidirect
83. #18210C11direct (N × H)
107. C2×D4×C11D8semidirect
141. #3496C2×C11semidirect
142. #3100C2×C11semidirect
143. #2535C2×C11semidirect
144. #1607C2×C11semidirect
145. #1595C2×C11semidirect
146. #1517C2×C11semidirect
147. #1460C2×C11semidirect
210. C2×C4×D4C22×C11semidirect
211. #480C22×C11semidirect
214. #447C22×C11semidirect
216. #431C22×C11semidirect
217. #397C22×C11semidirect
218. #392C22×C11semidirect
220. #382C22×C11semidirect
222. #327C22×C11semidirect
223. #323C22×C11semidirect
266. C4⋊Q8D4×C11semidirect
267. #127D4×C11semidirect
284. C4×D4D4×C11semidirect
335. C2×D4C11×D8semidirect
369. C11#18210direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#31002
C11×#25352
C11×#16072
C11×#15952
C11×#15172
C11×#14602
#1821011