Finite Group Databasebeta

← #14907250

Subgroups — #14907250

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic
2#13077534C211yesmaximal, characteristic, complemented
3#13077469C211yesmaximal, characteristic, complemented
4#13070516C218yesmaximal, complemented
5#13070389C211yesmaximal, characteristic, complemented
6C2×#10622154C211yesmaximal, characteristic, complemented
7#13070353C211yesmaximal, characteristic, complemented
8C11×#2110C211yesmaximal, characteristic, complemented
9#10623276—21no—
10C2×#66957C2211yescharacteristic
11C22×D88C2211yescharacteristic
12#10623052—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×M32C2211yescharacteristic
15C11×#405C2211yescharacteristic
16#10622744—21no—
17C2×#66883C2211yescharacteristic
18#10622719C2211yescharacteristic
19#10622618—21no—
20#10622521C414yescomplemented
21#10622521C2214yes—
22C2×#66864C412yescomplemented
23C2×D176C412yescomplemented
24#10622330C2214yescomplemented
25#10622324C2214yescomplemented
26#10622313—22no—
27C4×D88—22no—
28C11×#347C2214yescomplemented
29#10622156C2214yescomplemented
30#10622154C2214yescomplemented
31#10622151C2214yescomplemented
32C2×#4339—21no—
33C22×D44—21no—
34C2×C11×M16D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C11×#117D411yescharacteristic
37#66979—21no—
38C2×#4318—21no—
39#66960—42no—
40M16×D11—42no—
41C2×Dic44C2×C411yescharacteristic, complemented
42#66957—21no—
43#66957—21no—
44#66957C2×C412yescomplemented
45#66957C2312yes—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88C2×C412yes—
50C2×D88C2×C412yes—
51C2×D88C2×C411yescharacteristic, complemented
52C2×D88C2312yes—
53C2×#4314—21no—
54#66954—24no—
55#66946—42no—
56C22⋊C4×D11—42no—
57C4×D44—24no—
58C11×M32—21no—
59C11×M32C2×C412yescomplemented
60C11×M32C2312yes—
61C11×M32C2312yes—
62C2×C11×C16—21no—
63C2×C11×C16C2×C412yescomplemented
64C11×#97C2312yes—
65C4×C8×C11D412yes—
66#66885—24no—
67#66883—21no—
68#66883C2312yes—
69#66882—21no—
70#66881C2312yes—
71#66869—24no—
72#66864C2×C418yescomplemented
73D176C2×C418yescomplemented
74#33471—111nomaximal, Sylow
75C23×D11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C2×C22⋊D11—41no—
78#4339—22no—
79#4339—22no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×C4×D11—44no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C11×M16—21no—
93C11×M16—21no—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C22⋊C4—21no—
103C42×C11C2×D412yes—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—44no—
106C4⋊Dic11—22no—
107C4×Dic11—41no—
108#4318—22no—
109#4318—41no—
110C2×C11⋊C8—41no—
111Dic44—21no—
112Dic44C22×C412yes—
113D88—22no—
114D88—22no—
115D88—21no—
116D88—22no—
117D88C22×C412yes—
118D88C22×C414yes—
119#4314—22no—
120#4314—22no—
121#4313—44no—
122C8×D11—44no—
123C11×C16—22no—
124C11×C16C22×C414yes—
125C2×#509—111no—
126#2957—111no—
127#2948—111no—
128AGL(1,ℤ/16)—118no—
129#2155—111no—
130C2×#361—111no—
131#2145—111no—
132#2110D1111yescharacteristic, complemented
133C23×C11AGL(1,ℤ/8)11yescharacteristic
134C22×D11—42no—
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—162no—
139C2×C4×C11—22no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C22⋊D11—42no—
147C22⋊D11—42no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150D44—22no—
151D44—24no—
152D44—42no—
153D44—42no—
154D44—42no—
155D44—41no—
156C4×D11—42no—
157C4×D11—42no—
158C4×D11—164no—
159Dic22—22no—
160Dic22—41no—
161C8×C11—22no—
162C8×C11C4×D411yescharacteristic
163C8×C11C4×D411yescharacteristic
164C8×C11C23×C411yescharacteristic
165C8×C11C2×#4111yescharacteristic
166C11⋊C8—42no—
167C2×#135—111no—
168C22×D8—111no—
169#568—221no—
170#518—221no—
171#509—114no—
172#509—114no—
173C2×SD32—112no—
174C2×D16—112no—
175C2×M32C2×D1111yescharacteristic
176C2×M32C2×D1111yescharacteristic
177#444—114no—
178#443—222no—
179#442—114no—
180C4×D8—222no—
181C2×#108—111no—
182#427—111no—
183#421—221no—
184#418—221no—
185#405C2×D1111yescharacteristic
186#365—114no—
187#361—114no—
188#360—114no—
189#347C2×D1114yescomplemented
190C22×C11—41no—
191C22×C11#44211yescharacteristic
192C22×C11#44211yescharacteristic
193C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
194C2×D11—44no—
195C2×D11—42no—
196C2×D11—84no—
197C2×D11—161no—
198C2×D11—162no—
199C2×D11—162no—
200C4×C11—42no—
201C4×C11#44211yescharacteristic
202C4×C11#44211yescharacteristic
203C4×C11C2×C4×D411yescharacteristic
204C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
205Dic11—42no—
206Dic11—82no—
207C2×#41—221no—
208C22×D4—221no—
209#135—112no—
210#135—112no—
211#135—221no—
212#135—221no—
213C2×Q16—111no—
214C2×SD16—221no—
215C2×D8—112no—
216C2×D8—112no—
217C2×D8—111no—
218C2×D8—112no—
219C2×D8—221no—
220C2×D8—221no—
221C2×D8—221no—
222#131—224no—
223#131—442no—
224C2×M16—221no—
225C2×M16—442no—
226C2×M16D4411yescharacteristic
227C22×C8C22×D1111yescharacteristic
228C4×D4—224no—
229C4×D4—442no—
230#117—221no—
231#117D4411yescharacteristic
232C2×C22⋊C4—442no—
233SD32—118no—
234D16—118no—
235M32—21no—
236M32C4×D1112yescomplemented
237M32C22×D1112yes—
238M32C22×D1112yes—
239C2×C16—21no—
240C2×C16C4×D1112yescomplemented
241#108—112no—
242#108—221no—
243#107—221no—
244#106—112no—
245#104—224no—
246#102—224no—
247#97C22×D1112yes—
248C4×C8D4412yes—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11C2×#44211yescharacteristic
253D11—84no—
254D11—82no—
255C24—441no—
256#41—222no—
257#41—222no—
258#41—441no—
259#41—441no—
260C2×Q8—221no—
261C2×D4—222no—
262C2×D4—222no—
263C2×D4—221no—
264C2×D4—222no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C22×C4—444no—
270C22×C4—441no—
271C22×C4C2×D4411yescharacteristic
272Q16—112no—
273Q16—221no—
274SD16—222no—
275SD16—222no—
276D8—112no—
277D8—114no—
278D8—222no—
279D8—222no—
280D8—221no—
281D8—222no—
282M16—21no—
283M16—21no—
284M16—222no—
285M16—444no—
286M16—441no—
287C2×C8—444no—
288C2×C8—441no—
289C2×C8C2×C4×D1111yescharacteristic
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8C2×D4412yes—
292C2×C8C2×D4411yescharacteristic
293C2×C8#433911yescharacteristic
294C2×C8#433911yescharacteristic
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—222no—
298C22⋊C4—21no—
299C22⋊C4—444no—
300C22⋊C4—441no—
301C42—441no—
302C42C2×D4412yes—
303C16—22no—
304C16C2×C4×D1114yes—
305C11#3347111yescharacteristic, complemented, Sylow
306C23—442no—
307C23—441no—
308C23—442no—
309C23—442no—
310C23—1762no—
311C23#6696111yescharacteristic
312Q8—222no—
313Q8—441no—
314D4—224no—
315D4—222no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—442no—
320D4—442no—
321D4—441no—
322C2×C4—22no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—1764no—
328C2×C4C4×D4411yescharacteristic
329C2×C4C4×D4411yescharacteristic
330C2×C4#6696111yescharacteristic
331C2×C4#6696111yescharacteristic
332C2×C4#6696111yescharacteristic
333C2×C4C22×D4411yescharacteristic
334C8—22no—
335C8—442no—
336C8C4×D4411yescharacteristic
337C8C4×D4411yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#433911yescharacteristic
340C22—41no—
341C22—442no—
342C22—444no—
343C22—884no—
344C22—1762no—
345C22—1762no—
346C22—1761no—
347C22#1062232411yescharacteristic
348C22#1062232411yescharacteristic
349C22C2×#6696111yescharacteristic
350C4—42no—
351C4—442no—
352C4—882no—
353C4#1062232411yescharacteristic
354C4#1062232411yescharacteristic
355C4C2×C4×D4411yescharacteristic
356C4C2×#6696111yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—884no—
361C2—882no—
362C2C2×#1062232411yescharacteristic
subgroupG/H
centerC2C2×#10622324
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2110C2
socleC2×C11C2×#442
prime radicalC2×#10622521C2
cosocleC2×C8×C11C24
hypercenter#2110D11
hypocenterC11#33471
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2110

Complements

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

NH ≅ G/Ntype
2. #13077534C2semidirect
3. #13077469C2semidirect
4. #13070516C2semidirect
5. #13070389C2semidirect
6. C2×#10622154C2semidirect
7. #13070353C2semidirect
8. C11×#2110C2semidirect
20. #10622521C4semidirect
22. C2×#66864C4semidirect
23. C2×D176C4semidirect
24. #10622330C22semidirect
25. #10622324C22semidirect
28. C11×#347C22semidirect
29. #10622156C22semidirect
30. #10622154C22semidirect
31. #10622151C22semidirect
41. C2×Dic44C2×C4semidirect
44. #66957C2×C4semidirect
51. C2×D88C2×C4semidirect
59. C11×M32C2×C4semidirect
63. C2×C11×C16C2×C4semidirect
72. #66864C2×C4semidirect
73. D176C2×C4semidirect
132. #2110D11semidirect
189. #347C2×D11semidirect
236. M32C4×D11semidirect
240. C2×C16C4×D11semidirect
305. C11#33471semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
#130775342
#130774692
#130705162
#130703892
C2×#106221542
#130703532
C11×#21102
#3347111