Finite Group Databasebeta

← #15618111

Subgroups — #15618111

Order 2816.

2612 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083328C212yesmaximal, complemented
2#13077533C216yesmaximal, complemented
3#13077526C216yesmaximal, complemented
4#13077519C216yesmaximal, complemented
5C2×#10622809C216yesmaximal, complemented
6#13077227C211yesmaximal, characteristic, complemented
7#13077163C212yesmaximal, complemented
8#131×Dic11C211yesmaximal, characteristic, complemented
9C11×#3584C211yesmaximal, characteristic
10C11×#585C2212yes—
11C11×#578C414yescomplemented
12C11×#577C418yescomplemented
13C11×#576C414yescomplemented
14C11×#575C2216yes—
15C2×C11×#135C2216yes—
16C2×C11×#131C2211yescharacteristic
17#41×Dic11C2211yescharacteristic
18#10623350—28no—
19#10623350C2212yes—
20#10623350C22112yescomplemented
21C2×#67001—28no—
22C2×#67001C2211yescharacteristic
23C2×#67001C22112yescomplemented
24#10622849C22112yescomplemented
25C2×#66901C22112yescomplemented
26#10622810C22124yescomplemented
27#10622809C2214yescomplemented
28#10622809C22112yescomplemented
29#10622809C22112yescomplemented
30#10622809C22112yescomplemented
31#10622738C2216yescomplemented
32#10622735C2213yescomplemented
33M16×Dic11C2213yescomplemented
34C2×#66883C2216yescomplemented
35#10622714C2213yescomplemented
36C2×C8×Dic11C2213yescomplemented
37C11×2−1+4—22no—
38C11×2−1+4C2×C418yes—
39C11×H(5,𝔽2)—26no—
40C11×H(5,𝔽2)C2×C418yes—
41C2×C11×#41—28no—
42C2×C11×#41C23112yes—
43C2×C11×#41C2311yescharacteristic
44C11×#137C2×C4124yescomplemented
45C11×AGL(1,ℤ/8)C2×C4124yescomplemented
46C11×#135C2×C4112yescomplemented
47C11×#135C2×C4112yescomplemented
48C11×#135C2314yes—
49C11×#135C23112yes—
50C2×C11×Q16C2×C416yescomplemented
51C2×C11×SD16C2×C4112yescomplemented
52C2×C11×D8C2×C416yescomplemented
53C11×#131C2×C414yes—
54C11×#131C2×C414yes—
55C2×C11×M16C2313yes—
56C22×C8×C11C2313yes—
57#67001—28no—
58#67001—224no—
59#67001—212no—
60#67001—212no—
61#67001D414yes—
62#67001D414yes—
63#67001C2318yes—
64#67001C23124yes—
65Q8×Dic11—21no—
66D4×Dic11—23no—
67#66979C2313yes—
68C2×C4×Dic11C2313yes—
69C2×#4318—224no—
70C2×#4318—212no—
71C2×#4318C23112yes—
72C2×#4318C2313yes—
73C22×C11⋊C8—212no—
74C22×C11⋊C8C2313yes—
75#66901C2318yes—
76#66901C23124yes—
77#66883C2314yes—
78#66883C23112yes—
79#66879C2316yes—
80C8×Dic11C2313yes—
81C8×Dic11C2313yes—
82C8×Dic11C2311yescharacteristic
83C8×Dic11C2313yes—
84#60183—111nomaximal, Sylow
85C11×#41—28no—
86C11×#41—224no—
87C11×#41—212no—
88C11×#41—212no—
89C11×#41C22×C4124yes—
90C11×#41C22×C414yes—
91C11×#41C2×D414yes—
92C11×#41C2418yes—
93C2×Q8×C11—28no—
94C2×Q8×C11C22×C4112yes—
95C2×Q8×C11#4111yescharacteristic
96C2×D4×C11—212no—
97C2×D4×C11—224no—
98C2×D4×C11C22×C4112yes—
99C2×D4×C11#4113yes—
100C22×C4×C11—212no—
101C22×C4×C11C2413yes—
102C22×Dic11—23no—
103C11×Q16C22×C414yes—
104C11×Q16C22×C4112yes—
105C11×SD16C22×C418yes—
106C11×SD16C22×C4124yes—
107C11×D8C22×C414yes—
108C11×D8C22×C4112yes—
109C11×M16C22×C4112yes—
110C2×C8×C11C22×C416yes—
111C2×C8×C11C22×C416yes—
112C2×C8×C11C2411yescharacteristic
113C2×C8×C11C2413yes—
114C22⋊Dic11—23no—
115C4⋊Dic11—23no—
116C4×Dic11—23no—
117C4×Dic11C2411yescharacteristic
118C4×Dic11C2413yes—
119#4318—224no—
120#4318—28no—
121#4318—212no—
122#4318C2×D4112yes—
123#4318C2418yes—
124C2×C11⋊C8—28no—
125C2×C11⋊C8—224no—
126C2×C11⋊C8—212no—
127C2×C11⋊C8C2×D416yes—
128C2×C11⋊C8C2×D416yes—
129C2×C11⋊C8C2411yescharacteristic
130C2×C11⋊C8C2413yes—
131#3584D1111yescharacteristic
132#3573—112no—
133#2957—116no—
134#2956—116no—
135#2955—116no—
136C2×#443—116no—
137#2916—111no—
138#2901—112no—
139C4×#131—111no—
140C23×C11—212no—
141C23×C11C2×#4113yes—
142Q8×C11—212no—
143Q8×C11C4×D414yes—
144Q8×C11C23×C418yes—
145D4×C11—224no—
146D4×C11—28no—
147D4×C11—212no—
148D4×C11C4×D4112yes—
149D4×C11C23×C418yes—
150C2×C4×C11—212no—
151C2×C4×C11—224no—
152C2×C4×C11—28no—
153C2×C4×C11C23×C416yes—
154C2×C4×C11C22×D416yes—
155C2×C4×C11C2×#4113yes—
156C2×C4×C11C2511yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—23no—
159C2×Dic11—46no—
160C8×C11C23×C411yescharacteristic
161C8×C11C23×C411yescharacteristic
162C8×C11C23×C416yes—
163C11⋊C8—28no—
164C11⋊C8C22×D411yescharacteristic
165C11⋊C8C22×D416yes—
166C11⋊C8C22×D411yescharacteristic
167#585C2×D1112yes—
168#578Dic1114yescomplemented
169#577Dic1118yescomplemented
170#576Dic1114yescomplemented
171#575C2×D1116yes—
172C2×#135C2×D1116yes—
173#568—112no—
174#568—1112no—
175#568—228no—
176C2×#131—111no—
177C2×#131—1112no—
178C2×#131—228no—
179C2×#131C2×D1111yescharacteristic
180C4×#41—111no—
181#444—1124no—
182#443—114no—
183#443—1112no—
184#443—1112no—
185#443—1112no—
186#430—116no—
187C2×#108—116no—
188#421—1112no—
189C2×#104—1112no—
190#405—113no—
191#405—113no—
192C4×M16—113no—
193C2×C4×C8—113no—
194C22×C11—28no—
195C22×C11—43no—
196C22×C11—812no—
197C22×C11C2×C4×D416yes—
198C22×C11C22×#4111yescharacteristic
199C4×C11—28no—
200C4×C11C2×C4×D416yes—
201C4×C11C24×C411yescharacteristic
202C4×C11C23×D411yescharacteristic
203Dic11—22no—
204Dic11—43no—
2052−1+4—22no—
2062−1+4C2×Dic1118yes—
207H(5,𝔽2)—26no—
208H(5,𝔽2)C2×Dic1118yes—
209C2×#41—28no—
210C2×#41C22×D11112yes—
211C2×#41C22×D1111yescharacteristic
212#137C2×Dic11124yescomplemented
213AGL(1,ℤ/8)C2×Dic11124yescomplemented
214#135C2×Dic11112yescomplemented
215#135C2×Dic11112yescomplemented
216#135C22×D1114yes—
217#135C22×D11112yes—
218C2×Q16C2×Dic1116yescomplemented
219C2×SD16C2×Dic11112yescomplemented
220C2×D8C2×Dic1116yescomplemented
221#131—114no—
222#131—114no—
223#131—118no—
224#131—1124no—
225#131—2212no—
226#131—2212no—
227#131—2224no—
228#131—228no—
229#131C2×Dic1114yes—
230#131C2×Dic1114yes—
231C2×M16—113no—
232C2×M16—1112no—
233C2×M16—2212no—
234C2×M16—2224no—
235C2×M16C22×D1113yes—
236C22×C8—113no—
237C22×C8—2212no—
238C22×C8C22×D1113yes—
239C4×Q8—221no—
240C4×D4—223no—
241#117—113no—
242C2×C42—113no—
243#108—114no—
244#108—1112no—
245#104—118no—
246#104—1124no—
247#97—116no—
248C4×C8—111no—
249C4×C8—113no—
250C4×C8—113no—
251C4×C8—113no—
252C2×C11—21no—
253C2×C11—26no—
254C2×C11—48no—
255C2×C11C22×C4×D411yescharacteristic
256#41—28no—
257#41—224no—
258#41—212no—
259#41—212no—
260#41D4×D1114yes—
261#41C22×Dic11124yes—
262#41C22×Dic1114yes—
263#41C23×D1118yes—
264C2×Q8—28no—
265C2×Q8#434111yescharacteristic
266C2×Q8C22×Dic11112yes—
267C2×D4—212no—
268C2×D4—224no—
269C2×D4#434113yes—
270C2×D4C22×Dic11112yes—
271C22×C4—212no—
272C22×C4—223no—
273C22×C4C23×D1113yes—
274Q16C22×Dic1114yes—
275Q16C22×Dic11112yes—
276SD16C22×Dic1118yes—
277SD16C22×Dic11124yes—
278D8C22×Dic1114yes—
279D8C22×Dic11112yes—
280M16—1112no—
281M16—118no—
282M16—228no—
283M16—2224no—
284M16—2212no—
285M16C22×Dic11112yes—
286C2×C8—116no—
287C2×C8—116no—
288C2×C8—111no—
289C2×C8—113no—
290C2×C8—228no—
291C2×C8—2224no—
292C2×C8—2212no—
293C2×C8C22×Dic1116yes—
294C2×C8C22×Dic1116yes—
295C2×C8C23×D1111yescharacteristic
296C2×C8C23×D1113yes—
297C4⋊C4—223no—
298C22⋊C4—223no—
299C42—111no—
300C42—113no—
301C42—223no—
302C11#6018311yescharacteristic, complemented, Sylow
303C23—212no—
304C23C2×#434113yes—
305Q8—212no—
306Q8D4×Dic1114yes—
307Q8C23×Dic1118yes—
308D4—224no—
309D4—28no—
310D4—212no—
311D4D4×Dic11112yes—
312D4C23×Dic1118yes—
313C2×C4—212no—
314C2×C4—224no—
315C2×C4—28no—
316C2×C4—221no—
317C2×C4—223no—
318C2×C4—446no—
319C2×C4C2×D4×D1116yes—
320C2×C4C2×#434113yes—
321C2×C4C23×Dic1116yes—
322C2×C4C24×D1111yescharacteristic
323C8—111no—
324C8—111no—
325C8—116no—
326C8—228no—
327C8C23×Dic1111yescharacteristic
328C8C23×Dic1111yescharacteristic
329C8C23×Dic1116yes—
330C22—28no—
331C22—43no—
332C22—812no—
333C22C2×D4×Dic1116yes—
334C22C22×#434111yescharacteristic
335C4—28no—
336C4—222no—
337C4—443no—
338C4C2×D4×Dic1116yes—
339C4C22×D4×D1111yescharacteristic
340C4C24×Dic1111yescharacteristic
341C2—21no—
342C2—26no—
343C2—48no—
344C2C22×D4×Dic1111yescharacteristic
subgroupG/H
centerC4C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3584C2
socleC2×C11C22×C4×D4
cosocleC2×C4×C11C25
hypercenter#3584D11
hypocenterC11#60183
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×#41 ◁ #3584

Complements

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

NH ≅ G/Ntype
1. #13083328C2semidirect
2. #13077533C2semidirect
3. #13077526C2semidirect
4. #13077519C2semidirect
5. C2×#10622809C2semidirect
6. #13077227C2semidirect
7. #13077163C2semidirect
8. #131×Dic11C2semidirect
11. C11×#578C4semidirect
12. C11×#577C4semidirect
13. C11×#576C4semidirect
20. #10623350C22semidirect
23. C2×#67001C22semidirect
24. #10622849C22semidirect
25. C2×#66901C22semidirect
26. #10622810C22semidirect
27. #10622809C22semidirect
28. #10622809C22semidirect
29. #10622809C22semidirect
30. #10622809C22semidirect
31. #10622738C22semidirect
32. #10622735C22semidirect
33. M16×Dic11C22semidirect
34. C2×#66883C22semidirect
35. #10622714C22semidirect
36. C2×C8×Dic11C22semidirect
44. C11×#137C2×C4semidirect
45. C11×AGL(1,ℤ/8)C2×C4semidirect
46. C11×#135C2×C4semidirect
47. C11×#135C2×C4semidirect
50. C2×C11×Q16C2×C4semidirect
51. C2×C11×SD16C2×C4semidirect
52. C2×C11×D8C2×C4semidirect
168. #578Dic11semidirect
169. #577Dic11semidirect
170. #576Dic11semidirect
212. #137C2×Dic11semidirect
213. AGL(1,ℤ/8)C2×Dic11semidirect
214. #135C2×Dic11semidirect
215. #135C2×Dic11semidirect
218. C2×Q16C2×Dic11semidirect
219. C2×SD16C2×Dic11semidirect
220. C2×D8C2×Dic11semidirect
302. C11#60183semidirect

Maximal subgroups

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

subgroupindex
#130833282
#130775332
#130775262
#130775192
C2×#106228092
#130772272
#130771632
#131×Dic112
C11×#35842
#6018311