Finite Group Databasebeta

← #14908122

Subgroups — #14908122

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2#13079103C211yesmaximal, characteristic, complemented
3#13077492C211yesmaximal, characteristic, complemented
4#13070680C212yesmaximal, complemented
5#13070673C212yesmaximal, complemented
6#13070654C212yesmaximal, complemented
7#13070649C212yesmaximal, complemented
8#13070374C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10C2×#10622147C211yesmaximal, characteristic, complemented
11C2×C11×#508C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C2×C11×#135C2211yescharacteristic
14#10623361—21no—
15#10623358—21no—
16C2×#67002—21no—
17C22×D88C2211yescharacteristic
18C11×#508—24no—
19C2×C11×Q32C2211yescharacteristic, complemented
20C2×C11×SD32C2211yescharacteristic, complemented
21C2×C11×SD32C2211yescharacteristic, complemented
22C2×C11×D16C2211yescharacteristic, complemented
23C22×C11×C16C2211yescharacteristic
24#10622845—21no—
25#10622806—24no—
26#10622804C2212yes—
27Q16×Dic11C2212yescomplemented
28C2×#66892C2212yes—
29#10622789—22no—
30#10622777—22no—
31#10622764C2212yes—
32D8×Dic11C2212yescomplemented
33C2×#66890C2212yes—
34C2×#66882C2211yescharacteristic
35#10622714C2211yescharacteristic
36C2×#66876C2211yescharacteristic
37#10622202C2212yescomplemented
38#10622200C2212yescomplemented
39#10622147C2212yes—
40#10622147C2212yes—
41Dic11⋊C16C2212yescomplemented
42Dic11⋊C16C2212yescomplemented
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C22×D44—21no—
46C11×#135—22no—
47C11×#135—22no—
48C11×#135—22no—
49C11×#135D414yescomplemented
50C2×C11×Q16C2311yescharacteristic
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C2×C11×D8C2311yescharacteristic
55C2×C11×D8C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57#67002—44no—
58#67000—22no—
59Q8×Dic11—22no—
60C2×#4325—22no—
61#66993—22no—
62#66990—42no—
63D4×Dic11—22no—
64D4×Dic11—42no—
65C2×#4323—22no—
66#66983—41no—
67#66983—41no—
68#66979—41no—
69#66979D411yescharacteristic
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—41no—
72C2×#4318D411yescharacteristic
73C2×D88—22no—
74C2×D88—22no—
75C2×D88—21no—
76C2×D88C2312yes—
77C11×Q32—22no—
78C11×SD32—22no—
79C11×SD32—22no—
80C11×D16—22no—
81C2×C11×C16—22no—
82C2×C11×C16C2311yescharacteristic
83C2×C11×C16C2311yescharacteristic
84#66899—22no—
85#66896—22no—
86#66892—24no—
87#66890—24no—
88#66882—21no—
89#66882C2312yes—
90#66879D412yes—
91C8×Dic11C2312yes—
92#66876—22no—
93C2×C11⋊C16C2312yes—
94#33589—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—24no—
97C11×#41—42no—
98C11×#41—42no—
99C11×#41—42no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C22×Dic11—42no—
112C22×Dic11—41no—
113C2×D44—22no—
114C2×D44—42no—
115C2×D44—41no—
116C2×D44—42no—
117C11×Q16—21no—
118C11×Q16—21no—
119C11×Q16—21no—
120C11×Q16C2×D412yes—
121C11×SD16—24no—
122C11×SD16—42no—
123C11×D8—21no—
124C11×D8—21no—
125C11×D8—21no—
126C11×D8C2×D412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11#4112yes—
130C2×C8×C11C2411yescharacteristic
131C22⋊Dic11—42no—
132C22⋊Dic11D812yes—
133#4325—44no—
134#4323—44no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137C4⋊Dic11—22no—
138C4⋊Dic11—42no—
139C4⋊Dic11—41no—
140C4⋊Dic11D811yescharacteristic
141C4⋊Dic11D811yescharacteristic
142C4×Dic11—42no—
143C4×Dic11C2×D412yes—
144#4318—22no—
145C2×C11⋊C8C2×D412yes—
146D88—22no—
147D88—22no—
148D88—42no—
149C11×C16—21no—
150C11×C16—21no—
151C11⋊C16—22no—
152C2×#509—111no—
153C2×#508D1111yescharacteristic, complemented
154#3155—111no—
155#2951—111no—
156#2211—112no—
157#2210—112no—
158#2207—112no—
159#2206—112no—
160#2151—111no—
161#2139—111no—
162C2×#357—111no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C2×D811yescharacteristic
166C22×D11—42no—
167C22×D11—82no—
168C22×D11—161no—
169C22×D11—161no—
170Q8×C11—22no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—41no—
174D4×C11—22no—
175D4×C11—44no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—82no—
180C2×C4×C11—41no—
181C2×C4×C11—44no—
182C2×C4×C11—41no—
183C2×C4×C11—82no—
184C2×C4×C11#12112yes—
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—162no—
189C22⋊D11—162no—
190C2×Dic11—42no—
191C2×Dic11—162no—
192C2×Dic11—161no—
193C2×Dic11C2×D812yes—
194C2×Dic11C2×D812yes—
195D44—42no—
196D44—42no—
197D44—82no—
198C8×C11#12112yes—
199C8×C11C22×D411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8—22no—
202C2×AGL(1,ℤ/8)—221no—
203C2×#135C2×D1111yescharacteristic
204C2×#135C2×D1111yescharacteristic
205C22×D8—111no—
206#535—221no—
207#520—221no—
208#509—224no—
209#508—24no—
210C2×Q32C2×D1111yescharacteristic, complemented
211C2×SD32—112no—
212C2×SD32C2×D1111yescharacteristic, complemented
213C2×SD32C2×D1111yescharacteristic, complemented
214C2×D16—112no—
215C2×D16C2×D1111yescharacteristic, complemented
216C2×M32—111no—
217C22×C16C2×D1111yescharacteristic
218#496—222no—
219#495—112no—
220#493—112no—
221#440—222no—
222C4×Q16—112no—
223C4×D8—112no—
224C2×#107—111no—
225#417—221no—
226#405—111no—
227C4⋊C16—112no—
228C4⋊C16—112no—
229#358—112no—
230#357—112no—
231#357—112no—
232#357—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#45912yes—
242C22×C11C22×D811yescharacteristic
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—82no—
246C2×D11—164no—
247C4×C11—42no—
248C4×C11—81no—
249C4×C11#45912yes—
250C4×C11C2×#12111yescharacteristic
251C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
252Dic11—22no—
253Dic11—22no—
254Dic11—82no—
255C2×#41—21no—
256C2×#41—21no—
257C22×D4—221no—
258AGL(1,ℤ/8)—444no—
259#135—22no—
260#135—22no—
261#135—22no—
262#135C22⋊D1114yescomplemented
263C2×Q16C22×D1111yescharacteristic
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—21no—
267C2×SD16—222no—
268C2×D8—112no—
269C2×D8—222no—
270C2×D8—221no—
271C2×D8—222no—
272C2×D8—222no—
273C2×D8C22×D1111yescharacteristic
274C2×D8C22×D1111yescharacteristic
275C2×M16—111no—
276C22×C8C22×D1111yescharacteristic
277#127—222no—
278#124—222no—
279#121—441no—
280#121—441no—
281#120—442no—
282C4×Q8—222no—
283C4×D4—222no—
284C4×D4—442no—
285#117—111no—
286#117—441no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—441no—
289Q32—22no—
290SD32—22no—
291SD32—22no—
292SD32—224no—
293D16—22no—
294D16—224no—
295M32—222no—
296C2×C16—22no—
297C2×C16—112no—
298C2×C16C22×D1111yescharacteristic
299C2×C16C22×D1111yescharacteristic
300#107—112no—
301#107—221no—
302#103—222no—
303#102—222no—
304#97—112no—
305C4×C8—112no—
306C2×C11—22no—
307C2×C11—82no—
308C2×C11—161no—
309C2×C11C2×#45911yescharacteristic
310C2×C11#341511yescharacteristic
311C2×C11#341611yescharacteristic
312D11—162no—
313C24—441no—
314#41—24no—
315#41—42no—
316#41—42no—
317#41—42no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—222no—
325C2×D4—442no—
326C2×D4—442no—
327C2×D4—441no—
328C2×D4—442no—
329C2×D4—442no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—442no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335Q16—21no—
336Q16—21no—
337Q16—21no—
338Q16C2×C22⋊D1112yes—
339SD16—24no—
340SD16—42no—
341SD16—444no—
342D8—21no—
343D8—21no—
344D8—21no—
345D8—222no—
346D8—222no—
347D8—444no—
348D8—442no—
349D8C2×C22⋊D1112yes—
350M16—222no—
351C2×C8—112no—
352C2×C8D4×D1111yescharacteristic
353C2×C8#434112yes—
354C2×C8C2×C22⋊D1112yes—
355C2×C8C23×D1111yescharacteristic
356C4⋊C4—111no—
357C4⋊C4—111no—
358C4⋊C4—222no—
359C4⋊C4—442no—
360C4⋊C4—441no—
361C22⋊C4—112no—
362C22⋊C4—442no—
363C22⋊C4—442no—
364C22⋊C4—442no—
365C42—112no—
366C42—442no—
367C16—21no—
368C16—21no—
369C16—222no—
370C11#3358911yescharacteristic, complemented, Sylow
371C23—41no—
372C23—41no—
373C23—442no—
374C23—882no—
375C23—1761no—
376C23—1761no—
377C23D8×D1111yescharacteristic
378Q8—22no—
379Q8—41no—
380Q8—41no—
381Q8—41no—
382D4—22no—
383D4—44no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—82no—
388D4—442no—
389D4—442no—
390D4—882no—
391D4—1762no—
392D4—1762no—
393C2×C4—41no—
394C2×C4—44no—
395C2×C4—41no—
396C2×C4—82no—
397C2×C4—112no—
398C2×C4—112no—
399C2×C4—442no—
400C2×C4—1762no—
401C2×C4—1761no—
402C2×C4D8×D1111yescharacteristic
403C2×C4#6696412yes—
404C2×C4#6699212yes—
405C2×C4C2×D4×D1111yescharacteristic
406C8—222no—
407C8#6699212yes—
408C8C2×#434111yescharacteristic
409C8C22×C22⋊D1111yescharacteristic
410C22—21no—
411C22—21no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—1764no—
422C22#1062276312yes—
423C22C2×D8×D1111yescharacteristic
424C4—42no—
425C4—81no—
426C4—222no—
427C4—222no—
428C4—882no—
429C4#1062276312yes—
430C4C2×#6696411yescharacteristic
431C4C2×#6699211yescharacteristic
432C2—22no—
433C2—82no—
434C2—161no—
435C2—1762no—
436C2C2×#1062276311yescharacteristic
437C2#1308175411yescharacteristic
438C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#508C2
socleC22×C11C22×D8
hypercenterC2×#508D11
hypocenterC11#33589
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. #13079103C2semidirect
3. #13077492C2semidirect
4. #13070680C2semidirect
5. #13070673C2semidirect
6. #13070654C2semidirect
7. #13070649C2semidirect
8. #13070374C2semidirect
9. #13070328C2semidirect
10. C2×#10622147C2semidirect
11. C2×C11×#508C2semidirect
19. C2×C11×Q32C22semidirect
20. C2×C11×SD32C22semidirect
21. C2×C11×SD32C22semidirect
22. C2×C11×D16C22semidirect
27. Q16×Dic11C22semidirect
32. D8×Dic11C22semidirect
37. #10622202C22semidirect
38. #10622200C22semidirect
41. Dic11⋊C16C22semidirect
42. Dic11⋊C16C22semidirect
49. C11×#135D4semidirect
153. C2×#508D11semidirect
210. C2×Q32C2×D11semidirect
212. C2×SD32C2×D11semidirect
213. C2×SD32C2×D11semidirect
215. C2×D16C2×D11semidirect
262. #135C22⋊D11semidirect
370. C11#33589semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
#130791032
#130774922
#130706802
#130706732
#130706542
#130706492
#130703742
#130703282
C2×#106221472
C2×C11×#5082
#3358911