Finite Group Databasebeta

← #15617451

Subgroups — #15617451

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66960C211yesmaximal, characteristic
2#13081817C212yesmaximal
3#13077215C218yesmaximal, complemented
4#13077210C218yesmaximal, complemented
5#13077206C211yesmaximal, characteristic, complemented
6#13077204C214yesmaximal, complemented
7C2×#10622611C212yesmaximal, complemented
8D11×#427C214yesmaximal, complemented
9C11×#2911C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2212yes—
13C2×#66979C2212yes—
14C23×C11⋊C8C2211yescharacteristic
15C2×#66960C4116yescomplemented
16C2×#66960C2214yes—
17C2×#66960C2214yes—
18C22×#4313C2212yes—
19C22×C8×D11C2212yes—
20#10623054C2218yes—
21#10623053—24no—
22#10623052—22no—
23D11×#117C2218yes—
24#10623047—22no—
25#10623035C2218yes—
26#10623017—24no—
27C4×#4339—24no—
28C11×#428C2218yescomplemented
29C11×#427C2214yes—
30#10622734C2218yescomplemented
31#10622719C2214yes—
32#10622611C2214yes—
33#10622611C2214yes—
34#10622611C2214yescomplemented
35#10622611C2214yescomplemented
36C2×#66872C2214yescomplemented
37C2×#66871C2214yescomplemented
38#10622494C22116yescomplemented
39#10622493C2218yescomplemented
40D11×#107C2218yescomplemented
41#10622474C22116yescomplemented
42#10622473C2218yescomplemented
43D11×#106C2218yescomplemented
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11D412yes—
46C2×#4339C2×C418yes—
47C2×#4339D414yes—
48C2×#4339Q818yes—
49C2×#4339C2314yes—
50C22×D44D411yescharacteristic
51C22×C4×D11C2312yes—
52C22×Dic22D411yescharacteristic
53C2×C11×M16C2×C418yescomplemented
54C2×C11×M16C2314yes—
55C22×C8×C11C2312yes—
56C11×#117—22no—
57C11×#117—22no—
58C11×#117C2314yes—
59C11×#117C2314yes—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63C2×C22⋊Dic11—22no—
64C4×C22⋊D11—216no—
65#66979—22no—
66#66979—22no—
67#66979C2314yes—
68#66979C2314yes—
69C2×C4⋊Dic11C2314yes—
70C2×C4×Dic11—22no—
71C22×C11⋊C8C2×C418yescomplemented
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2312yes—
76#66960C2×C4132yescomplemented
77#66960C2×C4132yescomplemented
78C2×#4313C2×C4116yescomplemented
79C2×#4313C2318yes—
80C2×C8×D11C2×C4116yescomplemented
81C2×C8×D11C2314yes—
82C2×C8×D11C2314yes—
83#66946—28no—
84#66945C23116yes—
85C4⋊C4×D11C23116yes—
86#66940—28no—
87(C22⋊D11)⋊C4—216no—
88C22⋊C4×D11—28no—
89#66930—28no—
90C4×D44—28no—
91#66925—28no—
92C42×D11—28no—
93C4×Dic22—28no—
94C11×#107C2318yes—
95C11×#106C2318yes—
96#66882C2318yes—
97#66881C2318yes—
98#66872C2318yes—
99#66872C2318yes—
100#66871C2318yes—
101#66871C2318yes—
102#60108—111nomaximal, Sylow
103C24×C11C2×D411yescharacteristic
104C23×D11C2×D412yes—
105C22×C4×C11—24no—
106C22×C4×C11C22×C414yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×Q814yes—
110C22×C4×C11C2412yes—
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11C4⋊C4116yes—
113C2×C22⋊D11C2×D418yes—
114C22×Dic11—24no—
115C22×Dic11C2×D412yes—
116#4339C4⋊C4132yes—
117#4339C22×C4116yes—
118#4339C2×Q8116yes—
119C2×D44C4⋊C418yes—
120C2×D44C2×D414yes—
121C2×C4×D11—216no—
122C2×C4×D11C22×C418yes—
123C2×C4×D11C2×D414yes—
124C2×C4×D11C2×Q818yes—
125C2×C4×D11C2414yes—
126C2×Dic22C4⋊C418yes—
127C2×Dic22C2×D414yes—
128C11×M16C22×C4116yes—
129C2×C8×C11C22×C418yes—
130C2×C8×C11C2414yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4C2418yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C42×C11—24no—
136C42×C11—24no—
137C22⋊Dic11—24no—
138C22⋊Dic11—24no—
139(C2×D11)⋊C4—216no—
140C4⋊Dic11—24no—
141C4⋊Dic11C2418yes—
142Dic11⋊C4—216no—
143C4×Dic11—216no—
144C4×Dic11—24no—
145C4×Dic11—24no—
146C2×C11⋊C8C22×C414yes—
147C2×C11⋊C8C22×C414yes—
148C2×C11⋊C8C22×C418yes—
149C2×C11⋊C8C22×C418yes—
150C2×C11⋊C8C2411yescharacteristic
151C2×C11⋊C8C2412yes—
152C2×C11⋊C8C2411yescharacteristic
153#4313C22×C4132yes—
154C8×D11C22×C4116yes—
155C8×D11C22×C4116yes—
156C22×#131—111no—
157#3428—112no—
158#2913—118no—
159#2912—118no—
160#2911—114no—
161#2911—111no—
162#2911D1111yescharacteristic, complemented
163C2×#427—114no—
164C2×#427—112no—
165C23×C11—42no—
166C23×C11C2×C4⋊C414yes—
167C23×C11C22×D411yescharacteristic
168C23×C11C22×D412yes—
169C22×D11—44no—
170C22×D11C2×C4⋊C418yes—
171C22×D11C22×D414yes—
172C2×C4×C11—28no—
173C2×C4×C11—84no—
174C2×C4×C11C2×C4⋊C414yes—
175C2×C4×C11C2×C4⋊C418yes—
176C2×C4×C11C23×C412yes—
177C2×C4×C11C23×C414yes—
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×Q812yes—
181C2×C4×C11C22×Q814yes—
182C2×C4×C11C2511yescharacteristic
183C22⋊D11C2×C4⋊C4132yes—
184C2×Dic11—28no—
185C2×Dic11—84no—
186C2×Dic11C2×C4⋊C418yes—
187C2×Dic11C22×D414yes—
188D44C2×C4⋊C4116yes—
189C4×D11—816no—
190C4×D11C2×C4⋊C4116yes—
191C4×D11C23×C418yes—
192C4×D11C22×Q818yes—
193Dic22C2×C4⋊C4116yes—
194C8×C11C23×C418yes—
195C11⋊C8C23×C412yes—
196C11⋊C8C23×C412yes—
197C11⋊C8C23×C414yes—
198C22×#41—111no—
199C2×#131—114no—
200C2×#131—114no—
201C2×#131—1116no—
202C22×M16—112no—
203C22×M16C2×D1111yescharacteristic
204C23×C8—111no—
205C23×C8—112no—
206#520—118no—
207#520—118no—
208#519—222no—
209#518—224no—
210#518—222no—
211C4×#41—224no—
212C4×#41—224no—
213C2×#117—112no—
214C2×#117—118no—
215C2×#117C2×D1112yes—
216#428—118no—
217#428—1116no—
218#428—1116no—
219#428C2×D1118yescomplemented
220#427—114no—
221#427—114no—
222#427—114no—
223#427—114no—
224#427—114no—
225#427—118no—
226#427—118no—
227#427C2×D1114yes—
228C2×#107—114no—
229C2×#107—118no—
230C2×#106—114no—
231C2×#106—118no—
232C22×C11—24no—
233C22×C11—22no—
234C22×C11—44no—
235C22×C11C22×C4⋊C412yes—
236C22×C11C22×C4⋊C414yes—
237C22×C11C23×D411yescharacteristic
238C2×D11—28no—
239C2×D11—48no—
240C2×D11C22×C4⋊C418yes—
241C4×C11—48no—
242C4×C11C22×C4⋊C414yes—
243C4×C11C22×C4⋊C412yes—
244C4×C11C24×C411yescharacteristic
245C4×C11C23×Q811yescharacteristic
246Dic11—48no—
247Dic11C22×C4⋊C418yes—
248C2×#41—118no—
249C2×#41—114no—
250C2×#41—118no—
251C2×#41—114no—
252C22×Q8—111no—
253C22×D4—112no—
254C22×D4—111no—
255C23×C4—112no—
256C23×C4C22×D1111yescharacteristic
257#131—1132no—
258#131—1132no—
259C2×M16—1116no—
260C2×M16—118no—
261C2×M16C4×D1118yescomplemented
262C2×M16C22×D1114yes—
263C22×C8—118no—
264C22×C8—111no—
265C22×C8—111no—
266C22×C8—112no—
267C22×C8—112no—
268C22×C8—1116no—
269C22×C8—114no—
270C22×C8—114no—
271C22×C8C22×D1112yes—
272C4×Q8—228no—
273C4×Q8—228no—
274C4×D4—228no—
275C4×D4—2216no—
276C4×D4—228no—
277C4×D4—2216no—
278#117—22no—
279#117—22no—
280#117—114no—
281#117—114no—
282#117—1116no—
283#117—228no—
284#117—228no—
285#117—222no—
286#117—222no—
287#117C22×D1114yes—
288#117C22×D1114yes—
289C2×C4⋊C4—114no—
290C2×C4⋊C4—1116no—
291C2×C4⋊C4C22×D1114yes—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—228no—
294C2×C22⋊C4—222no—
295C2×C42—22no—
296C2×C42—228no—
297C2×C42—222no—
298#107—118no—
299#107—118no—
300#107—118no—
301#107C22×D1118yes—
302#106—118no—
303#106—118no—
304#106—118no—
305#106C22×D1118yes—
306C2×C11—22no—
307C2×C11—24no—
308C2×C11C23×C4⋊C411yescharacteristic
309C2×C11#358412yes—
310D11—28no—
311C24—112no—
312C24D4×D1111yescharacteristic
313#41—1132no—
314#41—1116no—
315#41—1116no—
316C2×Q8—118no—
317C2×Q8—114no—
318C2×D4—1116no—
319C2×D4—118no—
320C2×D4—118no—
321C2×D4—114no—
322C22×C4—24no—
323C22×C4—112no—
324C22×C4—118no—
325C22×C4—114no—
326C22×C4—118no—
327C22×C4—114no—
328C22×C4—2216no—
329C22×C4—224no—
330C22×C4C2×C4×D1114yes—
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1112yes—
333C22×C4Q8×D1114yes—
334C22×C4C23×D1112yes—
335C22×C4C23×D1111yescharacteristic
336M16—1132no—
337M16C2×C4×D11116yes—
338C2×C8—114no—
339C2×C8—114no—
340C2×C8—118no—
341C2×C8—118no—
342C2×C8—111no—
343C2×C8—112no—
344C2×C8—111no—
345C2×C8—1116no—
346C2×C8—1116no—
347C2×C8C2×C4×D1118yes—
348C2×C8C23×D1114yes—
349C4⋊C4—24no—
350C4⋊C4—118no—
351C4⋊C4—2216no—
352C4⋊C4—224no—
353C4⋊C4C23×D1118yes—
354C22⋊C4—24no—
355C22⋊C4—24no—
356C22⋊C4—2216no—
357C22⋊C4—224no—
358C22⋊C4—224no—
359C42—24no—
360C42—24no—
361C42—2216no—
362C42—224no—
363C42—224no—
364C11#6010811yescharacteristic, complemented, Sylow
365C23—42no—
366C23—114no—
367C23—118no—
368C23—444no—
369C23C4⋊C4×D1114yes—
370C23C2×D4×D1111yescharacteristic
371C23C2×D4×D1112yes—
372Q8—1116no—
373D4—1132no—
374D4—1116no—
375C2×C4—28no—
376C2×C4—84no—
377C2×C4—118no—
378C2×C4—114no—
379C2×C4—1116no—
380C2×C4—118no—
381C2×C4—118no—
382C2×C4—228no—
383C2×C4—8816no—
384C2×C4—884no—
385C2×C4C4⋊C4×D1114yes—
386C2×C4C4⋊C4×D1118yes—
387C2×C4C22×C4×D1112yes—
388C2×C4C22×C4×D1114yes—
389C2×C4C2×D4×D1112yes—
390C2×C4C2×D4×D1111yescharacteristic
391C2×C4C2×Q8×D1112yes—
392C2×C4C2×Q8×D1114yes—
393C2×C4C24×D1111yescharacteristic
394C8—112no—
395C8—112no—
396C8—114no—
397C8C22×C4×D1118yes—
398C22—24no—
399C22—22no—
400C22—44no—
401C22—118no—
402C22—228no—
403C22—448no—
404C22C2×C4⋊C4×D1112yes—
405C22C2×C4⋊C4×D1114yes—
406C22C22×D4×D1111yescharacteristic
407C4—48no—
408C4—118no—
409C4—448no—
410C4C2×C4⋊C4×D1112yes—
411C4C2×C4⋊C4×D1114yes—
412C4C23×C4×D1111yescharacteristic
413C4C22×Q8×D1111yescharacteristic
414C2—22no—
415C2—24no—
416C2—228no—
417C2C22×C4⋊C4×D1111yescharacteristic
418C2#1308338912yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2911C2
socleC22×C11C23×D4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenter#2911D11
hypocenterC11#60108
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
3. #13077215C2semidirect
4. #13077210C2semidirect
5. #13077206C2semidirect
6. #13077204C2semidirect
7. C2×#10622611C2semidirect
8. D11×#427C2semidirect
9. C11×#2911C2semidirect
15. C2×#66960C4semidirect
28. C11×#428C22semidirect
30. #10622734C22semidirect
34. #10622611C22semidirect
35. #10622611C22semidirect
36. C2×#66872C22semidirect
37. C2×#66871C22semidirect
38. #10622494C22semidirect
39. #10622493C22semidirect
40. D11×#107C22semidirect
41. #10622474C22semidirect
42. #10622473C22semidirect
43. D11×#106C22semidirect
53. C2×C11×M16C2×C4semidirect
71. C22×C11⋊C8C2×C4semidirect
76. #66960C2×C4semidirect
77. #66960C2×C4semidirect
78. C2×#4313C2×C4semidirect
80. C2×C8×D11C2×C4semidirect
162. #2911D11semidirect
219. #428C2×D11semidirect
261. C2×M16C4×D11semidirect
364. C11#60108semidirect

Maximal subgroups

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

subgroupindex
C22×#669602
#130818172
#130772152
#130772102
#130772062
#130772042
C2×#106226112
D11×#4272
C11×#29112
#6010811