Finite Group Databasebeta

← #14908050

Subgroups — #14908050

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C212yesmaximal, complemented
2#13079045C211yesmaximal, characteristic, complemented
3C4×D8×D11C211yesmaximal, characteristic, complemented
4#13070674C212yesmaximal, complemented
5#13070673C212yesmaximal, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070652C211yesmaximal, characteristic, complemented
8#13070651C211yesmaximal, characteristic, complemented
9#13070370C211yesmaximal, characteristic, complemented
10#13070327C212yesmaximal, complemented
11C11×#2208C211yesmaximal, characteristic, complemented
12C2×#66972—21no—
13C2×#66972C2212yes—
14C2×D8×D11C2211yescharacteristic
15#10623256—21no—
16C4×D4×D11—21no—
17C2×C11×SD32C2212yes—
18C11×#494C2211yescharacteristic, complemented
19C4×C11×D8C2211yescharacteristic
20#10622804—21no—
21#10622804C2212yescomplemented
22C2×#66892C2212yes—
23D8×Dic11C2211yescharacteristic
24C2×#66890C2212yes—
25#10622698—21no—
26C4×#4323—21no—
27#10622527—28no—
28C2×D176C2212yes—
29C2×#66862C2212yes—
30D11×#107C2211yescharacteristic
31#10622485C2211yescharacteristic
32D11×#102—21no—
33#10622369—21no—
34#10622308C2211yescharacteristic, complemented
35C4×D88C2211yescharacteristic
36C4×C8×D11C2211yescharacteristic
37C11×C4⋊C16C2211yescharacteristic, complemented
38C11×#358C2212yescomplemented
39#10622202C2212yescomplemented
40#10622147C2212yescomplemented
41Dic11⋊C16C2212yescomplemented
42#10622129C2212yescomplemented
43C4⋊(C11⋊C16)C2211yescharacteristic, complemented
44C2×#4343—22no—
45C2×D4×D11—21no—
46C22×C4×D11—41no—
47C2×C11×Q16—21no—
48C2×C11×Q16C2312yes—
49C2×C11×D8C2311yescharacteristic
50C11×C4⋊Q8—21no—
51C4×D4×C11—21no—
52#67000—22no—
53C2×#4325—22no—
54C2×#4325—22no—
55D4×Dic11—21no—
56C2×#4323—21no—
57C4×C22⋊D11—41no—
58#66972—24no—
59#66972—24no—
60#66972—44no—
61D8×D11—22no—
62D8×D11D414yescomplemented
63C2×D88—21no—
64C2×D88C2312yes—
65C2×D88C2311yescharacteristic
66C2×C8×D11D411yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66948—41no—
69#66948—41no—
70#66946—21no—
71#66946—41no—
72#66946—41no—
73C4⋊C4×D11—21no—
74(C22⋊D11)⋊C4—41no—
75C22⋊C4×D11—41no—
76#66927—21no—
77C4×D44—21no—
78C42×D11D411yescharacteristic
79C11×SD32—24no—
80C2×C11×C16C2312yes—
81C11×#107C2311yescharacteristic
82C11×#102—21no—
83C4×C8×C11C2311yescharacteristic
84#66896—21no—
85#66892—24no—
86#66890—24no—
87#66885—21no—
88#66882C2311yescharacteristic
89C8×Dic11D411yescharacteristic
90C8×Dic11C2311yescharacteristic
91C2×C11⋊C16C2312yes—
92#66873—21no—
93#66871—21no—
94C4×C11⋊C8D411yescharacteristic
95D176—24no—
96#66862—24no—
97#33580—111nomaximal, Sylow
98C23×D11—41no—
99C2×Q8×C11—22no—
100C2×D4×C11—21no—
101C22×C4×C11—41no—
102C2×C22⋊D11—41no—
103C22×Dic11—41no—
104#4343—44no—
105#4343—44no—
106D4×D11—24no—
107D4×D11—42no—
108C2×D44—21no—
109C2×D44—22no—
110C2×D44—42no—
111C2×D44—41no—
112C2×D44—41no—
113C2×C4×D11—41no—
114C2×C4×D11—42no—
115C2×C4×D11—41no—
116C2×C4×D11—41no—
117C2×C4×D11—84no—
118C2×C4×D11D811yescharacteristic
119C2×C4×D11D811yescharacteristic
120C2×C4×D11C2×D411yescharacteristic
121C11×Q16—22no—
122C11×Q16—22no—
123C11×Q16—42no—
124C11×D8—21no—
125C11×D8C2×D412yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11C2×D411yescharacteristic
133C22⋊Dic11—41no—
134#4325—44no—
135#4325—44no—
136#4323—24no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—41no—
141C4⋊Dic11—21no—
142Dic11⋊C4—41no—
143C4×Dic11D811yescharacteristic
144C4×Dic11D811yescharacteristic
145C4×Dic11C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148D88—22no—
149D88—21no—
150D88—22no—
151D88—42no—
152D88C2×D412yes—
153C8×D11—22no—
154C8×D11C2×D412yes—
155C8×D11#4112yes—
156C11×C16—22no—
157C11⋊C16—22no—
158C2×#509—112no—
159#3147—111no—
160C2×C4×D8—111no—
161#2210—112no—
162#2210—112no—
163#2208—111no—
164#2208D1111yescharacteristic, complemented
165#2206—111no—
166#2206—111no—
167#2150—111no—
168#2139—112no—
169C23×C11—41no—
170C22×D11—41no—
171C22×D11—44no—
172C22×D11—42no—
173C22×D11—82no—
174C22×D11—82no—
175C22×D11C2×D811yescharacteristic
176Q8×C11—42no—
177Q8×C11—42no—
178D4×C11—22no—
179D4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—82no—
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—44no—
187C2×Dic11—41no—
188C2×Dic11—82no—
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191C2×Dic11C2×D811yescharacteristic
192D44—22no—
193D44—42no—
194D44—41no—
195D44—42no—
196D44—82no—
197D44—84no—
198D44—82no—
199C4×D11—22no—
200C4×D11—41no—
201C4×D11—82no—
202C4×D11—82no—
203C4×D11—82no—
204C4×D11—84no—
205C4×D11#12112yes—
206C4×D11AGL(1,ℤ/8)12yes—
207C8×C11—21no—
208C8×C11C22×D411yescharacteristic
209C8×C11C2×#4111yescharacteristic
210C11⋊C8—21no—
211C11⋊C8#12112yes—
212C2×#135—112no—
213C2×#135—221no—
214C22×D8—111no—
215#532—221no—
216C2×C4×D4—221no—
217#509—228no—
218C2×SD32—112no—
219C2×SD32C2×D1112yes—
220C2×D16—112no—
221C2×D16—112no—
222C2×M32—112no—
223#495—112no—
224#495—221no—
225#494C2×D1111yescharacteristic, complemented
226#493—111no—
227#492—221no—
228C4×D8—111no—
229C4×D8—111no—
230C4×D8—111no—
231C4×D8—221no—
232C4×D8—221no—
233C4×D8C2×D1111yescharacteristic
234C2×#107—111no—
235C2×#102—221no—
236C2×C4×C8—111no—
237C4⋊C16—112no—
238C4⋊C16—111no—
239C4⋊C16C2×D1111yescharacteristic, complemented
240#358—112no—
241#358C2×D1112yescomplemented
242#357—112no—
243#357—112no—
244C22×C11—42no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11C22×D811yescharacteristic
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—42no—
251C2×D11—88no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11#45912yes—
258C4×C11—21no—
259C4×C11—81no—
260C4×C11—82no—
261C4×C11#50912yescomplemented
262C4×C11C2×#12111yescharacteristic
263C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
264Dic11—21no—
265Dic11—21no—
266Dic11—81no—
267Dic11#45912yes—
268C2×#41—222no—
269C22×D4—221no—
270C23×C4—441no—
271#135—224no—
272#135—224no—
273#135—444no—
274C2×Q16—21no—
275C2×Q16C22×D1112yes—
276C2×SD16—222no—
277C2×SD16—222no—
278C2×D8—114no—
279C2×D8—111no—
280C2×D8—112no—
281C2×D8—222no—
282C2×D8—221no—
283C2×D8—221no—
284C2×D8C22×D1111yescharacteristic
285C22×C8—111no—
286C22×C8—111no—
287C4⋊Q8—21no—
288#127—221no—
289#124—222no—
290#121—441no—
291#121—441no—
292C4×D4—21no—
293C4×D4—221no—
294C4×D4—221no—
295C4×D4—221no—
296C4×D4—441no—
297C4×D4—441no—
298C4×D4—441no—
299C4×D4—441no—
300C2×C4⋊C4—221no—
301C2×C22⋊C4—441no—
302C2×C42—111no—
303SD32—24no—
304SD32—224no—
305D16—224no—
306D16—224no—
307M32—224no—
308C2×C16—112no—
309C2×C16C22×D1112yes—
310#107—111no—
311#107—221no—
312#107C22×D1111yescharacteristic
313#102—21no—
314#102—221no—
315#102—221no—
316#102—221no—
317C4×C8—111no—
318C4×C8—111no—
319C4×C8—111no—
320C4×C8C22×D1111yescharacteristic
321C2×C11—82no—
322C2×C11C2×#45911yescharacteristic
323C2×C11C2×#50911yescharacteristic
324C2×C11#341411yescharacteristic
325D11—22no—
326D11—82no—
327D11—162no—
328C24—441no—
329#41—444no—
330#41—444no—
331C2×Q8—22no—
332C2×D4—21no—
333C2×D4—224no—
334C2×D4—221no—
335C2×D4—222no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C22×C4—41no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—441no—
346C22×C4—442no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—884no—
351Q16—22no—
352Q16—22no—
353Q16—42no—
354SD16—444no—
355SD16—444no—
356D8—21no—
357D8—112no—
358D8—224no—
359D8—222no—
360D8—221no—
361D8—222no—
362D8—442no—
363D8D4×D1112yes—
364C2×C8—111no—
365C2×C8—112no—
366C2×C8—112no—
367C2×C8—111no—
368C2×C8—222no—
369C2×C8D4×D1111yescharacteristic
370C2×C8C23×D1111yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—221no—
375C4⋊C4—441no—
376C22⋊C4—41no—
377C22⋊C4—441no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C42—111no—
383C42—111no—
384C42—111no—
385C42D4×D1111yescharacteristic
386C16—22no—
387C16—222no—
388C11#3358011yescharacteristic, complemented, Sylow
389C23—41no—
390C23—111no—
391C23—444no—
392C23—441no—
393C23—442no—
394C23—882no—
395C23—882no—
396Q8—42no—
397Q8—42no—
398D4—22no—
399D4—41no—
400D4—222no—
401D4—444no—
402D4—441no—
403D4—442no—
404D4—442no—
405D4—882no—
406D4—884no—
407D4—882no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—111no—
412C2×C4—112no—
413C2×C4—112no—
414C2×C4—111no—
415C2×C4—111no—
416C2×C4—222no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—884no—
420C2×C4—882no—
421C2×C4—882no—
422C2×C4—882no—
423C2×C4—882no—
424C2×C4D8×D1111yescharacteristic
425C2×C4D8×D1111yescharacteristic
426C2×C4C2×D4×D1111yescharacteristic
427C8—21no—
428C8—112no—
429C8—221no—
430C8C2×D4×D1111yescharacteristic
431C8#41×D1111yescharacteristic
432C22—42no—
433C22—81no—
434C22—81no—
435C22—112no—
436C22—221no—
437C22—221no—
438C22—442no—
439C22—888no—
440C22—881no—
441C22—881no—
442C22—882no—
443C22—882no—
444C22—882no—
445C22C2×D8×D1111yescharacteristic
446C4—21no—
447C4—82no—
448C4—81no—
449C4—112no—
450C4—221no—
451C4—221no—
452C4—881no—
453C4#1062252712yescomplemented
454C4D11×#12111yescharacteristic
455C4D11×AGL(1,ℤ/8)11yescharacteristic
456C2—82no—
457C2—222no—
458C2—882no—
459C2—1762no—
460C2D11×#45911yescharacteristic
461C2C2×#1062252711yescharacteristic
462C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2208C2
socleC22×C11C22×D8
hypercenter#2208D11
hypocenterC11#33580
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. #13079045C2semidirect
3. C4×D8×D11C2semidirect
4. #13070674C2semidirect
5. #13070673C2semidirect
6. #13070658C2semidirect
7. #13070652C2semidirect
8. #13070651C2semidirect
9. #13070370C2semidirect
10. #13070327C2semidirect
11. C11×#2208C2semidirect
18. C11×#494C22semidirect
21. #10622804C22semidirect
34. #10622308C22semidirect
37. C11×C4⋊C16C22semidirect
38. C11×#358C22semidirect
39. #10622202C22semidirect
40. #10622147C22semidirect
41. Dic11⋊C16C22semidirect
42. #10622129C22semidirect
43. C4⋊(C11⋊C16)C22semidirect
62. D8×D11D4semidirect
164. #2208D11semidirect
225. #494C2×D11semidirect
239. C4⋊C16C2×D11semidirect
241. #358C2×D11semidirect
261. C4×C11#509semidirect
388. C11#33580semidirect
453. C4#10622527semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
#130790452
C4×D8×D112
#130706742
#130706732
#130706582
#130706522
#130706512
#130703702
#130703272
C11×#22082
#3358011