Finite Group Databasebeta

← #14907248

Subgroups — #14907248

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×#10622806C211yesmaximal, characteristic
2#13077469C211yesmaximal, characteristic, complemented
3#13070514C218yesmaximal, complemented
4#13070390C211yesmaximal, characteristic, complemented
5C2×#10622133C211yesmaximal, characteristic, complemented
6#13070352C211yesmaximal, characteristic, complemented
7#13070221C211yesmaximal, characteristic, complemented
8C11×#2957C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C11×#568—21no—
11C22×D88C2211yescharacteristic
12#10623052—21no—
13C11×#444C2214yescomplemented
14C11×#443—22no—
15C2×C11×#108C2211yescharacteristic
16C11×#421—21no—
17C11×#405C2211yescharacteristic
18#10622806C414yescomplemented
19#10622806C2214yes—
20C2×#66892C412yescomplemented
21C2×#66890C412yescomplemented
22#10622744—21no—
23#10622719C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622324C2214yescomplemented
27C4×D88—22no—
28#10622204C2214yescomplemented
29#10622133C2214yescomplemented
30#10622132C2214yescomplemented
31#10622104C2214yescomplemented
32C2×C11×#41—21no—
33C22×D44—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135C2×C412yescomplemented
37C11×#135C2312yes—
38C2×C11×Q16C2×C411yescharacteristic, complemented
39C2×C11×SD16—21no—
40C2×C11×D8C2×C411yescharacteristic, complemented
41C11×#131—24no—
42C11×#131—42no—
43C2×C11×M16—21no—
44C2×C11×M16—42no—
45C2×C11×M16D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#117D411yescharacteristic
48#66979—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88—21no—
52C2×D88C2×C412yes—
53C2×D88C2×C412yes—
54C2×D88C2312yes—
55#66946—42no—
56C22⋊C4×D11—42no—
57C4×D44—24no—
58C11×#108—21no—
59C11×#108C2312yes—
60C11×#104—24no—
61C11×#97C2312yes—
62C4×C8×C11D412yes—
63#66892C2×C418yescomplemented
64#66890C2×C418yescomplemented
65#66885—24no—
66#66882—21no—
67#66881C2312yes—
68#66876—21no—
69#66876C2×C412yescomplemented
70#66876C2312yes—
71#66876C2312yes—
72C2×C11⋊C16—21no—
73C2×C11⋊C16C2×C412yescomplemented
74#33471—111nomaximal, Sylow
75C23×D11—41no—
76C11×#41—22no—
77C11×#41—22no—
78C11×#41—41no—
79C11×#41—41no—
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×C4×D11—44no—
92C11×Q16—21no—
93C11×Q16C22×C412yes—
94C11×SD16—22no—
95C11×SD16—22no—
96C11×D8—21no—
97C11×D8C22×C412yes—
98C11×M16—21no—
99C11×M16—21no—
100C11×M16—22no—
101C11×M16—44no—
102C11×M16—41no—
103C2×C8×C11—44no—
104C2×C8×C11—41no—
105C2×C8×C11C22×C411yescharacteristic
106C2×C8×C11C22×C411yescharacteristic
107C2×C8×C11C2×D412yes—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11#4111yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C22⋊C4—21no—
114C42×C11C2×D412yes—
115C22⋊Dic11—41no—
116(C2×D11)⋊C4—44no—
117C4⋊Dic11—22no—
118C4×Dic11—41no—
119D88—22no—
120D88—22no—
121D88—22no—
122D88C22×C414yes—
123C11⋊C16—22no—
124C11⋊C16C22×C414yes—
125C2×#509—111no—
126#2957D1111yescharacteristic, complemented
127#2948—111no—
128AGL(1,ℤ/16)—118no—
129#2155—111no—
130C2×#361—111no—
131#2145—111no—
132#2110—111no—
133C23×C11—41no—
134C23×C11AGL(1,ℤ/8)11yescharacteristic
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—162no—
139Q8×C11—22no—
140Q8×C11—41no—
141D4×C11—22no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×Dic11—42no—
156D44—24no—
157D44—42no—
158D44—42no—
159D44—42no—
160C4×D11—164no—
161C8×C11—22no—
162C8×C11—42no—
163C8×C11C4×D411yescharacteristic
164C8×C11C4×D411yescharacteristic
165C8×C11C23×C411yescharacteristic
166C8×C11C2×#4111yescharacteristic
167C2×#135C2×D1111yescharacteristic
168C22×D8—111no—
169#568—21no—
170#518—221no—
171#509—114no—
172#509—114no—
173C2×SD32—112no—
174C2×D16—112no—
175C2×M32—111no—
176C2×M32—111no—
177#444C2×D1114yescomplemented
178#443—22no—
179#442—114no—
180C4×D8—222no—
181C2×#108C2×D1111yescharacteristic
182#427—111no—
183#421—21no—
184#418—221no—
185#405C2×D1111yescharacteristic
186#365—114no—
187#361—114no—
188#360—114no—
189#347—114no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—161no—
193C22×C11#44211yescharacteristic
194C22×C11#44211yescharacteristic
195C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
196C2×D11—44no—
197C2×D11—84no—
198C2×D11—162no—
199C2×D11—162no—
200C4×C11—42no—
201C4×C11—42no—
202C4×C11#44211yescharacteristic
203C4×C11#44211yescharacteristic
204C4×C11C2×C4×D411yescharacteristic
205C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×D4—221no—
209#135—21no—
210#135—21no—
211#135C4×D1112yescomplemented
212#135C22×D1112yes—
213C2×Q16C4×D1111yescharacteristic, complemented
214C2×SD16—21no—
215C2×D8—112no—
216C2×D8—112no—
217C2×D8—112no—
218C2×D8—221no—
219C2×D8—221no—
220C2×D8—221no—
221C2×D8C4×D1111yescharacteristic, complemented
222#131—24no—
223#131—42no—
224C2×M16—21no—
225C2×M16—42no—
226C2×M16C22⋊D1111yescharacteristic
227C22×C8C22×D1111yescharacteristic
228C4×D4—224no—
229C4×D4—442no—
230#117—221no—
231#117C22⋊D1111yescharacteristic
232C2×C22⋊C4—442no—
233SD32—118no—
234D16—118no—
235M32—112no—
236M32—112no—
237M32—112no—
238M32—221no—
239C2×C16—112no—
240C2×C16—221no—
241#108—21no—
242#108C22×D1112yes—
243#107—221no—
244#106—112no—
245#104—24no—
246#102—224no—
247#97C22×D1112yes—
248C4×C8C22⋊D1112yes—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—82no—
253C2×C11C2×#44211yescharacteristic
254D11—84no—
255C24—441no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—222no—
264C2×D4—222no—
265C2×D4—222no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C22×C4—41no—
270C22×C4—444no—
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—21no—
273Q16C2×C4×D1112yes—
274SD16—22no—
275SD16—22no—
276D8—21no—
277D8—114no—
278D8—222no—
279D8—222no—
280D8—222no—
281D8C2×C4×D1112yes—
282M16—21no—
283M16—21no—
284M16—22no—
285M16—44no—
286M16—41no—
287C2×C8—44no—
288C2×C8—41no—
289C2×C8C2×C4×D1111yescharacteristic
290C2×C8C2×C4×D1111yescharacteristic
291C2×C8#433911yescharacteristic
292C2×C8#433911yescharacteristic
293C2×C8C2×C22⋊D1112yes—
294C2×C8C2×C22⋊D1111yescharacteristic
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—222no—
298C22⋊C4—21no—
299C22⋊C4—444no—
300C22⋊C4—441no—
301C42—441no—
302C42C2×C22⋊D1112yes—
303C16—114no—
304C16—222no—
305C11#3347111yescharacteristic, complemented, Sylow
306C23—41no—
307C23—442no—
308C23—442no—
309C23—442no—
310C23—1762no—
311C23#6700211yescharacteristic
312Q8—22no—
313Q8—41no—
314D4—22no—
315D4—42no—
316D4—42no—
317D4—41no—
318D4—224no—
319D4—442no—
320D4—442no—
321D4—442no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—442no—
327C2×C4—1764no—
328C2×C4C4×C22⋊D1111yescharacteristic
329C2×C4C4×C22⋊D1111yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4#6698511yescharacteristic
332C2×C4#6700211yescharacteristic
333C2×C4C22×C22⋊D1111yescharacteristic
334C8—22no—
335C8—42no—
336C8C4×C22⋊D1111yescharacteristic
337C8C4×C22⋊D1111yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#433911yescharacteristic
340C22—41no—
341C22—42no—
342C22—161no—
343C22—444no—
344C22—884no—
345C22—1762no—
346C22—1762no—
347C22#1062262711yescharacteristic
348C22#1062262711yescharacteristic
349C22C2×#6700211yescharacteristic
350C4—42no—
351C4—42no—
352C4—882no—
353C4#1062262711yescharacteristic
354C4#1062262711yescharacteristic
355C4C2×C4×C22⋊D1111yescharacteristic
356C4C2×#6698511yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—884no—
362C2C2×#1062262711yescharacteristic
subgroupG/H
centerC2C2×#10622627
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2957C2
socleC2×C11C2×#442
prime radicalC2×#10622806C2
cosocleC2×C8×C11C24
hypercenter#2957D11
hypocenterC11#33471
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #13077469C2semidirect
3. #13070514C2semidirect
4. #13070390C2semidirect
5. C2×#10622133C2semidirect
6. #13070352C2semidirect
7. #13070221C2semidirect
8. C11×#2957C2semidirect
13. C11×#444C22semidirect
18. #10622806C4semidirect
20. C2×#66892C4semidirect
21. C2×#66890C4semidirect
26. #10622324C22semidirect
28. #10622204C22semidirect
29. #10622133C22semidirect
30. #10622132C22semidirect
31. #10622104C22semidirect
36. C11×#135C2×C4semidirect
38. C2×C11×Q16C2×C4semidirect
40. C2×C11×D8C2×C4semidirect
63. #66892C2×C4semidirect
64. #66890C2×C4semidirect
69. #66876C2×C4semidirect
73. C2×C11⋊C16C2×C4semidirect
126. #2957D11semidirect
177. #444C2×D11semidirect
211. #135C4×D11semidirect
213. C2×Q16C4×D11semidirect
221. C2×D8C4×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×#106228062
#130774692
#130705142
#130703902
C2×#106221332
#130703522
#130702212
C11×#29572
#3347111