Finite Group Databasebeta

← D11×#2233 #14908555

Subgroups — D11×#2233 #14908555

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#466C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3#13070803C212yesmaximal, complemented
4#13070802C211yesmaximal, characteristic, complemented
5#13070801C211yesmaximal, characteristic, complemented
6#13070800C212yesmaximal, complemented
7#13070799C211yesmaximal, characteristic, complemented
8D11×#367C212yesmaximal, complemented
9D11×#357C212yesmaximal, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2233C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×#121—21no—
15C2×C4⋊C4×D11—21no—
16C11×#466C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic, complemented
18#10622770C2211yescharacteristic
19#10622728C2211yescharacteristic
20C2×#66882C2211yescharacteristic, complemented
21#10622651—21no—
22C2×#66871—21no—
23C2×C16×D11C2212yes—
24#10622496C2211yescharacteristic
25D11×#107—21no—
26D11×#107—21no—
27D11×#107C2211yescharacteristic
28D11×#107C2212yes—
29D11×#107C2212yescomplemented
30#10622388—21no—
31D11×#102—21no—
32C11×#367C2212yescomplemented
33C11×#357C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic, complemented
35#10622200C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic, complemented
37#10622147C2212yescomplemented
38(C2×D11)⋊C16C2212yescomplemented
39#10622143C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622128C2212yescomplemented
43C2×D4×D11—21no—
44C2×D4×D11—41no—
45C22×C4×D11—41no—
46C22×C4×D11D411yescharacteristic
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#121—21no—
50C2×C11×C4⋊C4—21no—
51#66992—41no—
52#66991—21no—
53C2×#4323—21no—
54#66983—21no—
55C2×C4⋊Dic11—21no—
56C2×Dic11⋊C4—41no—
57C22×C11⋊C8D411yescharacteristic
58D8×D11—24no—
59C2×D88C2311yescharacteristic
60C2×C8×D11—24no—
61C2×C8×D11D411yescharacteristic
62C2×C8×D11D411yescharacteristic
63C2×C8×D11C2311yescharacteristic
64C2×C8×D11C2311yescharacteristic
65#66948—21no—
66C4⋊C4×D11—22no—
67C4⋊C4×D11—22no—
68C4⋊C4×D11—21no—
69C4⋊C4×D11—41no—
70C4⋊C4×D11—41no—
71#66937—41no—
72C22⋊C4×D11—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#107C2311yescharacteristic
77C11×#102—21no—
78#66896—21no—
79#66885—21no—
80#66882—21no—
81#66882C2311yescharacteristic
82#66882C2312yes—
83C2×C11⋊C16C2312yes—
84#66873—21no—
85#66871—22no—
86#66871—22no—
87#66871—21no—
88C16×D11—24no—
89C2×#2233—111nomaximal, Sylow
90C23×D11—41no—
91C23×D11D811yescharacteristic
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C22×Dic11—41no—
100C22×Dic11D811yescharacteristic
101D4×D11—42no—
102D4×D11—42no—
103D4×D11—84no—
104C2×D44—21no—
105C2×D44—41no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—41no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—84no—
112C2×C4×D11D811yescharacteristic
113C2×C4×D11D811yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C2×C4×D11C2×D411yescharacteristic
116C11×D8—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—41no—
125#4323—42no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—42no—
133Dic11⋊C4—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137D88—22no—
138C8×D11—22no—
139C8×D11—22no—
140C8×D11—22no—
141C8×D11#4114yes—
142C11×C16—22no—
143C11⋊C16—22no—
144C2×#466—111no—
145C22×#107—111no—
146#2233—111no—
147#2233—111no—
148#2233—112no—
149#2233—112no—
150#2233—111no—
151#2233D1111yescharacteristic, direct product factor
152C2×#367—112no—
153C2×#357—112no—
154C2×C22⋊C16—111no—
155C23×C11—41no—
156C23×C11C2×D811yescharacteristic
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—41no—
160C22×D11—82no—
161C22×D11—82no—
162C22×D11—82no—
163C22×D11SD3214yes—
164C22×D11C2×D811yescharacteristic
165C22×D11C2×D811yescharacteristic
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—82no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—82no—
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C22⋊D11—82no—
177C22⋊D11—82no—
178C22⋊D11—82no—
179C2×Dic11—22no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—82no—
183C2×Dic11C2×D811yescharacteristic
184C2×Dic11C2×D811yescharacteristic
185D44—41no—
186D44—41no—
187D44—82no—
188C4×D11—22no—
189C4×D11—21no—
190C4×D11—21no—
191C4×D11—22no—
192C4×D11—84no—
193C4×D11—82no—
194C4×D11—84no—
195C4×D11#12312yes—
196C4×D11#13712yes—
197C8×C11—21no—
198C8×C11C2×#4112yes—
199C11⋊C8—21no—
200C11⋊C8#12312yes—
201C22×D8—111no—
202C23×C8—111no—
203C2×#121—221no—
204C22×C4⋊C4—221no—
205C22×C16—112no—
206#466—111no—
207#466—111no—
208#466—111no—
209#466—221no—
210#466—221no—
211#466C2×D1111yescharacteristic
212C2×#107—111no—
213C2×#107—112no—
214C2×#107—111no—
215C2×#107—112no—
216C2×#107—221no—
217C2×#107—221no—
218C2×#107—221no—
219C2×#107C2×D1111yescharacteristic, complemented
220C2×#102—221no—
221#367—112no—
222#367—112no—
223#367—112no—
224#367C2×D1112yescomplemented
225#357—112no—
226#357—112no—
227#357—112no—
228#357C2×D1112yescomplemented
229C22⋊C16—111no—
230C22⋊C16—112no—
231C22⋊C16C2×D1111yescharacteristic, complemented
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11C2×SD3212yes—
238C22×C11C22×D811yescharacteristic
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—28no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C2×D11—164no—
246C2×D11#48012yes—
247C2×D11C2×SD3212yes—
248C2×D11C2×SD3212yes—
249C2×D11#50912yes—
250C4×C11—21no—
251C4×C11—81no—
252C4×C11—82no—
253C4×C11C2×#12311yescharacteristic
254C4×C11C2×#13711yescharacteristic
255Dic11—21no—
256Dic11—81no—
257Dic11—82no—
258Dic11#48012yes—
259C22×D4—221no—
260C22×D4—441no—
261C23×C4—111no—
262C23×C4—441no—
263C2×D8—111no—
264C2×D8—224no—
265C2×D8—221no—
266C2×D8C22×D1111yescharacteristic
267C22×C8—111no—
268C22×C8—111no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—111no—
272C22×C8—224no—
273C22×C8C22×D1111yescharacteristic
274#121—21no—
275#121—221no—
276#121—221no—
277#121—221no—
278#121—441no—
279#121—441no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—441no—
286C2×C4⋊C4—441no—
287C2×C4⋊C4—441no—
288C2×C22⋊C4—441no—
289C2×C16—112no—
290C2×C16—224no—
291C2×C16C22×D1112yes—
292#107—21no—
293#107—112no—
294#107—111no—
295#107—222no—
296#107—222no—
297#107—221no—
298#107—221no—
299#107C22×D1112yes—
300#107C22×D1111yescharacteristic
301#102—21no—
302#102—221no—
303#102—221no—
304#102—221no—
305C2×C11—22no—
306C2×C11—161no—
307C2×C11C2×#48011yescharacteristic
308C2×C11C22×SD3211yescharacteristic
309C2×C11C2×#50911yescharacteristic
310D11—22no—
311D11—161no—
312D11#223314yesdirect product factor
313C24—111no—
314C24—441no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—221no—
318C2×D4—441no—
319C2×D4—442no—
320C2×D4—442no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—884no—
325C22×C4—41no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—222no—
332C22×C4—222no—
333C22×C4—441no—
334C22×C4—442no—
335C22×C4—442no—
336C22×C4—441no—
337C22×C4—884no—
338C22×C4D4×D1111yescharacteristic
339D8—22no—
340D8—222no—
341D8—442no—
342C2×C8—22no—
343C2×C8—111no—
344C2×C8—114no—
345C2×C8—111no—
346C2×C8—222no—
347C2×C8—222no—
348C2×C8—222no—
349C2×C8—222no—
350C2×C8D4×D1111yescharacteristic
351C2×C8C23×D1111yescharacteristic
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—41no—
355C4⋊C4—221no—
356C4⋊C4—222no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C22⋊C4—41no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C16—22no—
366C16—222no—
367C11C2×#223311yescharacteristic, complemented, Sylow
368C23—41no—
369C23—111no—
370C23—111no—
371C23—114no—
372C23—222no—
373C23—222no—
374C23—441no—
375C23—882no—
376C23—882no—
377C23—882no—
378C23D8×D1111yescharacteristic
379D4—41no—
380D4—41no—
381D4—82no—
382D4—441no—
383D4—441no—
384D4—882no—
385D4—882no—
386D4—882no—
387D4—882no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—111no—
394C2×C4—112no—
395C2×C4—112no—
396C2×C4—111no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—441no—
403C2×C4—442no—
404C2×C4—884no—
405C2×C4—882no—
406C2×C4—884no—
407C2×C4—882no—
408C2×C4D8×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C8—21no—
411C8—112no—
412C8—221no—
413C8#41×D1112yes—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—112no—
420C22—112no—
421C22—112no—
422C22—112no—
423C22—228no—
424C22—221no—
425C22—221no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22—1764no—
430C22D11×SD3212yes—
431C22C2×D8×D1111yescharacteristic
432C4—21no—
433C4—81no—
434C4—82no—
435C4—112no—
436C4—221no—
437C4—881no—
438C4—882no—
439C4D11×#12311yescharacteristic
440C4D11×#13711yescharacteristic
441C2—22no—
442C2—114no—
443C2—161no—
444C2—222no—
445C2—1761no—
446C2D11×#48011yescharacteristic
447C2C2×D11×SD3211yescharacteristic
448C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2233D11
hypocenterC11C2×#2233
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
3. #13070803C2semidirect
4. #13070802C2semidirect
5. #13070801C2semidirect
6. #13070800C2semidirect
7. #13070799C2semidirect
8. D11×#367C2semidirect
9. D11×#357C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2233C2semidirect
17. C2×C11×#107C22semidirect
20. C2×#66882C22semidirect
29. D11×#107C22semidirect
32. C11×#367C22semidirect
33. C11×#357C22semidirect
34. C11×C22⋊C16C22semidirect
35. #10622200C22semidirect
36. C22⋊(C11⋊C16)C22semidirect
37. #10622147C22semidirect
38. (C2×D11)⋊C16C22semidirect
39. #10622143C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622128C22semidirect
151. #2233D11direct (N × H)
219. C2×#107C2×D11semidirect
224. #367C2×D11semidirect
228. #357C2×D11semidirect
231. C22⋊C16C2×D11semidirect
312. D11#2233direct (N × H)
367. C11C2×#2233semidirect

Maximal subgroups

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

subgroupindex
D11×#4662
C2×D11×#1072
#130708032
#130708022
#130708012
#130708002
#130707992
D11×#3672
D11×#3572
D11×C22⋊C162
C11×#22332
C2×#223311