Finite Group Databasebeta

← #14909006

Subgroups — #14909006

Order 2816.

564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079354C211yesmaximal, characteristic, complemented
2#13077527C211yesmaximal, characteristic, complemented
3#13070831C212yesmaximal, complemented
4#13070788C212yesmaximal, complemented
5#13070693C212yesmaximal, complemented
6#13070564C212yesmaximal, complemented
7#13070516C214yesmaximal, complemented
8C11×#2165C211yesmaximal, characteristic, complemented
9#10623279C2211yescharacteristic
10#10623276—21no—
11#10623008—21no—
12C4×C11×M16C2211yescharacteristic
13#10622748—21no—
14#10622748C2212yes—
15#10622738C2211yescharacteristic
16C2×#66869—21no—
17#10622521C2214yes—
18#10622330—21no—
19#10622330C2212yes—
20#10622324—21no—
21#10622324C2212yescomplemented
22#10622313—21no—
23#10622313C2212yes—
24#10622308C2211yescharacteristic, complemented
25#10622307—21no—
26#10622293C2211yescharacteristic, complemented
27C11×#364C2212yescomplemented
28C11×#349C2212yes—
29C11×#347C2212yescomplemented
30#10622156C2214yes—
31#10622154C2214yescomplemented
32#10622151C2214yescomplemented
33C2×#4339—21no—
34C2×#4339—41no—
35C2×C11×M16D411yescharacteristic
36C2×C11×M16C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38#66983—22no—
39#66983—41no—
40C2×#4318—21no—
41#66962—22no—
42#66961—22no—
43#66960—42no—
44M16×D11—42no—
45#66957—21no—
46#66957C2312yes—
47C2×D88—21no—
48C2×D88C2312yes—
49#66954—22no—
50#66954—22no—
51#66928—41no—
52#66927—21no—
53C4×D44—22no—
54C4×D44—41no—
55#66922—21no—
56C11×M32C2314yes—
57C11×#97D411yescharacteristic
58C11×#97C2311yescharacteristic
59C4×C8×C11D411yescharacteristic
60C4×C8×C11C2311yescharacteristic
61#66885—22no—
62#66885—22no—
63#66883—21no—
64#66883C2312yes—
65#66881—21no—
66#66881C2312yes—
67#66869—22no—
68#66869—22no—
69#66864—24no—
70D176—24no—
71#33688—111nomaximal, Sylow
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—41no—
75C2×C22⋊D11—42no—
76#4339—22no—
77#4339—22no—
78#4339—41no—
79#4339—41no—
80#4339—84no—
81C2×D44—21no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×C4×D11—41no—
86C2×C4×D11—42no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C11×M16—22no—
90C11×M16—22no—
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2411yescharacteristic
95C42×C11—21no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100C4⋊Dic11—22no—
101C4⋊Dic11—41no—
102#4318—22no—
103#4318—41no—
104C2×C11⋊C8—41no—
105Dic44—21no—
106Dic44#4112yescomplemented
107D88—21no—
108D88—24no—
109D88—42no—
110D88#4112yescomplemented
111#4314—22no—
112#4314—22no—
113#4313—42no—
114#4313—42no—
115C8×D11—42no—
116C8×D11—42no—
117C11×C16—24no—
118#3184—111no—
119#2956—111no—
120#2238—112no—
121#2230—112no—
122#2213—112no—
123#2190—112no—
124AGL(1,ℤ/16)—114no—
125#2165D1111yescharacteristic, complemented
126C23×C11AGL(1,ℤ/8)11yescharacteristic
127C22×D11—41no—
128C22×D11—42no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C22⋊D11—42no—
137C22⋊D11—42no—
138C22⋊D11—84no—
139C2×Dic11—41no—
140C2×Dic11—42no—
141D44—22no—
142D44—41no—
143D44—42no—
144D44—42no—
145D44—82no—
146D44—82no—
147C4×D11—42no—
148C4×D11—42no—
149C4×D11—84no—
150Dic22—22no—
151Dic22—41no—
152Dic22—82no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11AGL(1,ℤ/8)12yes—
156C8×C11C2×#4112yes—
157C11⋊C8—42no—
158#575—111no—
159#568—221no—
160#532—221no—
161#509—114no—
162#498—111no—
163#493—111no—
164#486—221no—
165#469—112no—
166#469—221no—
167#444—112no—
168#444—221no—
169#443—112no—
170#443—221no—
171#442—112no—
172#442—221no—
173#430—111no—
174C2×#104—221no—
175C4×M16C2×D1111yescharacteristic
176#365—114no—
177#364C2×D1112yescomplemented
178#361—114no—
179#360—114no—
180#349C2×D1112yes—
181#347C2×D1112yescomplemented
182C22×C11—21no—
183C22×C11—41no—
184C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
185C2×D11—42no—
186C2×D11—82no—
187C2×D11—82no—
188C2×D11—82no—
189C2×D11—161no—
190C4×C11—22no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11#52511yescharacteristic
194C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
195Dic11—42no—
196Dic11—82no—
197C2×#41—221no—
198C2×#41—441no—
199#137—222no—
200AGL(1,ℤ/8)—222no—
201#135—112no—
202#135—221no—
203C2×D8—112no—
204C2×D8—221no—
205#131—222no—
206#131—222no—
207#131—442no—
208C2×M16—221no—
209C2×M16—442no—
210C2×M16D4411yescharacteristic
211C2×M16C22×D1111yescharacteristic
212C4⋊Q8—221no—
213#127—221no—
214#124—441no—
215#121—222no—
216#121—441no—
217C4×D4—222no—
218C4×D4—441no—
219C2×C42D4411yescharacteristic
220SD32—224no—
221D16—224no—
222M32C22×D1114yes—
223#108—112no—
224#108—221no—
225#106—112no—
226#106—221no—
227#104—222no—
228#104—222no—
229#102—222no—
230#102—222no—
231#97D4411yescharacteristic
232#97C22×D1111yescharacteristic
233C4×C8D4411yescharacteristic
234C4×C8C22×D1111yescharacteristic
235C2×C11—21no—
236C2×C11—41no—
237C2×C11#310911yescharacteristic
238D11—82no—
239D11—162no—
240#41—222no—
241#41—222no—
242#41—441no—
243#41—441no—
244#41—884no—
245C2×Q8—221no—
246C2×Q8—441no—
247C2×D4—221no—
248C2×D4—222no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—441no—
252C2×D4—442no—
253C22×C4—21no—
254C22×C4—441no—
255C22×C4—442no—
256C22×C4C2×D4411yescharacteristic
257Q16—112no—
258Q16—221no—
259SD16—222no—
260SD16—222no—
261D8—112no—
262D8—221no—
263D8—224no—
264D8—442no—
265M16—22no—
266M16—22no—
267M16—222no—
268M16—442no—
269M16—441no—
270M16—442no—
271C2×C8—442no—
272C2×C8—441no—
273C2×C8—442no—
274C2×C8C2×D4411yescharacteristic
275C2×C8C2×D4411yescharacteristic
276C2×C8C2×D4411yescharacteristic
277C2×C8C23×D1111yescharacteristic
278C4⋊C4—222no—
279C4⋊C4—441no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C42—21no—
283C42C2×D4411yescharacteristic
284C42C2×D4411yescharacteristic
285C16—24no—
286C11#3368811yescharacteristic, complemented, Sylow
287C23—441no—
288C23—442no—
289C23#6696111yescharacteristic
290Q8—222no—
291Q8—441no—
292Q8—882no—
293D4—222no—
294D4—441no—
295D4—442no—
296D4—442no—
297D4—442no—
298D4—442no—
299D4—882no—
300D4—882no—
301D4—884no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—442no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—884no—
312C2×C4#6696111yescharacteristic
313C2×C4C22×D4411yescharacteristic
314C8—21no—
315C8—21no—
316C8—442no—
317C8#6696112yes—
318C8#41×D1112yes—
319C22—21no—
320C22—41no—
321C22—442no—
322C22—882no—
323C22—882no—
324C22—882no—
325C22—1761no—
326C22C2×#6696111yescharacteristic
327C4—22no—
328C4—21no—
329C4—41no—
330C4—442no—
331C4—882no—
332C4#1062305511yescharacteristic
333C4C2×#6696111yescharacteristic
334C2—21no—
335C2—41no—
336C2—882no—
337C2—1762no—
338C2#1307870811yescharacteristic
subgroupG/H
centerC2#13078708
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2165C2
socleC2×C11#3109
hypercenter#2165D11
hypocenterC11#33688
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
1. #13079354C2semidirect
2. #13077527C2semidirect
3. #13070831C2semidirect
4. #13070788C2semidirect
5. #13070693C2semidirect
6. #13070564C2semidirect
7. #13070516C2semidirect
8. C11×#2165C2semidirect
21. #10622324C22semidirect
24. #10622308C22semidirect
26. #10622293C22semidirect
27. C11×#364C22semidirect
29. C11×#347C22semidirect
31. #10622154C22semidirect
32. #10622151C22semidirect
106. Dic44#41semidirect
110. D88#41semidirect
125. #2165D11semidirect
177. #364C2×D11semidirect
181. #347C2×D11semidirect
286. C11#33688semidirect

Maximal subgroups

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

subgroupindex
#130793542
#130775272
#130708312
#130707882
#130706932
#130705642
#130705162
C11×#21652
#3368811