Finite Group Databasebeta

← #14907251

Subgroups — #14907251

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×#10622760C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic, complemented
3#13077468C211yesmaximal, characteristic, complemented
4#13070517C218yesmaximal, complemented
5#13070390C211yesmaximal, characteristic, complemented
6#13070353C211yesmaximal, characteristic, complemented
7#13070220C211yesmaximal, characteristic, complemented
8C2×C11×#361C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10#10623329—21no—
11#10623276—21no—
12C2×#66957C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15#10622828—21no—
16#10622765C2214yescomplemented
17D8×Dic11—22no—
18C2×#66891C412yescomplemented
19#10622760C414yescomplemented
20#10622760C2214yes—
21C2×#66890C412yescomplemented
22#10622752—21no—
23#10622719C2211yescharacteristic
24#10622714C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622508—22no—
27#10622507C2214yescomplemented
28C11×#361C2214yescomplemented
29#10622156C2214yescomplemented
30#10622150C2214yescomplemented
31#10622132C2214yescomplemented
32C22×D4×C11—21no—
33C2×#4339—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8C2×C412yes—
38C2×C11×D8C2×C412yes—
39C2×C11×D8C2312yes—
40C2×C11×M16—21no—
41C22×C8×C11C2311yescharacteristic
42C2×C22⋊Dic11—42no—
43D4×Dic11—24no—
44D4×Dic11—42no—
45#66979—21no—
46#66979D411yescharacteristic
47C2×#4318D411yescharacteristic
48#66960—24no—
49M16×D11—42no—
50C2×Dic44C2×C411yescharacteristic, complemented
51#66957—21no—
52#66957—21no—
53#66957C2×C412yescomplemented
54#66957C2312yes—
55C2×D88C2×C411yescharacteristic, complemented
56C2×#4314—21no—
57#66954—42no—
58C11×M32—21no—
59C11×M32C2312yes—
60C2×C11×C16—21no—
61C11×#108—21no—
62C11×#108C2312yes—
63#66896—24no—
64#66891C2×C418yescomplemented
65#66890C2×C418yescomplemented
66#66889—24no—
67#66882—21no—
68#66881C2312yes—
69#66879C2312yes—
70C8×Dic11D412yes—
71#66876C2×C412yescomplemented
72#66876C2312yes—
73C2×C11⋊C16C2×C412yescomplemented
74#33471—111nomaximal, Sylow
75C24×C11—41no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—44no—
85#4339—22no—
86#4339—22no—
87#4339—41no—
88#4339—41no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C11×D8—22no—
93C11×D8—22no—
94C11×D8—22no—
95C11×D8C22×C414yes—
96C11×M16—22no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C2×C8×C11C2411yescharacteristic
105C22⋊Dic11—21no—
106C22⋊Dic11—44no—
107C22⋊Dic11—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4×Dic11—41no—
111C4×Dic11C2×D412yes—
112#4318—21no—
113#4318—21no—
114C2×C11⋊C8C2×D412yes—
115Dic44—21no—
116Dic44C22×C412yes—
117D88—21no—
118D88C22×C412yes—
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×#361D1111yescharacteristic, complemented
131#2145—111no—
132#2110—111no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—162no—
137C23×C11AGL(1,ℤ/8)11yescharacteristic
138C22×D11—41no—
139D4×C11—24no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C22⋊D11—42no—
150C22⋊D11—42no—
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—164no—
155D44—22no—
156D44—41no—
157C4×D11—42no—
158C4×D11—42no—
159Dic22—22no—
160Dic22—41no—
161C8×C11—42no—
162C8×C11C4×D411yescharacteristic
163C8×C11C4×D411yescharacteristic
164C8×C11C23×C411yescharacteristic
165C8×C11C2×#4111yescharacteristic
166C11⋊C8—22no—
167C2×#135—111no—
168C22×D8C2×D1111yescharacteristic
169#568—221no—
170#518—221no—
171#509—114no—
172#509—114no—
173C2×SD32—112no—
174C2×D16—112no—
175C2×M32—111no—
176C2×M32C2×D1111yescharacteristic
177#444—114no—
178#443—222no—
179#442—114no—
180C4×D8—222no—
181C2×#108C2×D1111yescharacteristic
182#427—111no—
183#421—221no—
184#418—221no—
185#405—111no—
186#365—114no—
187#361C2×D1114yescomplemented
188#360—114no—
189#347—114no—
190C22×C11—41no—
191C22×C11—44no—
192C22×C11—84no—
193C22×C11—162no—
194C22×C11—162no—
195C22×C11#44211yescharacteristic
196C22×C11#44211yescharacteristic
197C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
198C2×D11—42no—
199C2×D11—161no—
200C4×C11#44211yescharacteristic
201C4×C11#44211yescharacteristic
202C4×C11C2×C4×D411yescharacteristic
203C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
204Dic11—42no—
205Dic11—42no—
206Dic11—82no—
207C2×#41—221no—
208C22×D4—21no—
209#135—112no—
210#135—112no—
211#135—221no—
212#135—221no—
213C2×Q16—111no—
214C2×SD16—221no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—111no—
219C2×D8C4×D1112yes—
220C2×D8C4×D1112yes—
221C2×D8C22×D1112yes—
222#131—224no—
223#131—442no—
224C2×M16—21no—
225C2×M16—111no—
226C2×M16—442no—
227C22×C8C22×D1111yescharacteristic
228C4×D4—224no—
229C4×D4—442no—
230#117—111no—
231#117—221no—
232C2×C22⋊C4—442no—
233SD32—118no—
234D16—118no—
235M32—21no—
236M32—112no—
237M32—112no—
238M32C22×D1112yes—
239C2×C16—21no—
240C2×C16—112no—
241#108—21no—
242#108C22×D1112yes—
243#107—221no—
244#106—112no—
245#104—224no—
246#102—224no—
247#97—112no—
248C4×C8—112no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—84no—
253C2×C11C2×#44211yescharacteristic
254D11—82no—
255C24—41no—
256#41—222no—
257#41—222no—
258#41—441no—
259#41—441no—
260C2×Q8—221no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—221no—
268C2×D4—441no—
269C22×C4—444no—
270C22×C4—441no—
271C22×C4D4×D1111yescharacteristic
272Q16—112no—
273Q16—221no—
274SD16—222no—
275SD16—222no—
276D8—22no—
277D8—22no—
278D8—22no—
279D8—112no—
280D8—221no—
281D8C2×C4×D1114yes—
282M16—22no—
283M16—41no—
284M16—221no—
285M16—221no—
286M16—444no—
287C2×C8—41no—
288C2×C8—112no—
289C2×C8—444no—
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8C2×C4×D1111yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8#434111yescharacteristic
294C2×C8#434111yescharacteristic
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—221no—
297C4⋊C4—222no—
298C22⋊C4—221no—
299C22⋊C4—444no—
300C22⋊C4—441no—
301C42—112no—
302C42—441no—
303C16—22no—
304C16—114no—
305C11#3347111yescharacteristic, complemented, Sylow
306C23—42no—
307C23—42no—
308C23—42no—
309C23—162no—
310C23—441no—
311C23#6696711yescharacteristic
312Q8—222no—
313Q8—441no—
314D4—24no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—222no—
319D4—442no—
320D4—442no—
321D4—441no—
322C2×C4—222no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—1764no—
328C2×C4(C22⋊D11)⋊C411yescharacteristic
329C2×C4(C22⋊D11)⋊C411yescharacteristic
330C2×C4#6696411yescharacteristic
331C2×C4#6696411yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C8—42no—
335C8—222no—
336C8(C22⋊D11)⋊C411yescharacteristic
337C8(C22⋊D11)⋊C411yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#434111yescharacteristic
340C22—41no—
341C22—44no—
342C22—84no—
343C22—162no—
344C22—162no—
345C22—442no—
346C22—1761no—
347C22#1062239811yescharacteristic
348C22#1062239811yescharacteristic
349C22C2×#6696711yescharacteristic
350C4—442no—
351C4—442no—
352C4—882no—
353C4#1062239811yescharacteristic
354C4#1062239811yescharacteristic
355C4C2×(C22⋊D11)⋊C411yescharacteristic
356C4C2×#6696411yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—84no—
361C2—882no—
362C2C2×#1062239811yescharacteristic
subgroupG/H
centerC2C2×#10622398
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#361C2
socleC2×C11C2×#442
prime radicalC2×#10622760C2
cosocleC2×C8×C11C24
hypercenterC2×#361D11
hypocenterC11#33471
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. #13077532C2semidirect
3. #13077468C2semidirect
4. #13070517C2semidirect
5. #13070390C2semidirect
6. #13070353C2semidirect
7. #13070220C2semidirect
8. C2×C11×#361C2semidirect
16. #10622765C22semidirect
18. C2×#66891C4semidirect
19. #10622760C4semidirect
21. C2×#66890C4semidirect
27. #10622507C22semidirect
28. C11×#361C22semidirect
29. #10622156C22semidirect
30. #10622150C22semidirect
31. #10622132C22semidirect
50. C2×Dic44C2×C4semidirect
53. #66957C2×C4semidirect
55. C2×D88C2×C4semidirect
64. #66891C2×C4semidirect
65. #66890C2×C4semidirect
71. #66876C2×C4semidirect
73. C2×C11⋊C16C2×C4semidirect
130. C2×#361D11semidirect
187. #361C2×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×#106227602
#130775322
#130774682
#130705172
#130703902
#130703532
#130702202
C2×C11×#3612
#3347111