Finite Group Databasebeta

← #14907246

Subgroups — #14907246

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#13077534C211yesmaximal, characteristic, complemented
3#13070512C218yesmaximal, complemented
4#13070388C211yesmaximal, characteristic, complemented
5C2×#10622201C211yesmaximal, characteristic, complemented
6#13070351C211yesmaximal, characteristic, complemented
7#13070221C211yesmaximal, characteristic, complemented
8C11×#2948C211yesmaximal, characteristic, complemented
9C22×C11×D8C2211yescharacteristic
10C11×#518—21no—
11#10623276—21no—
12C2×#66957C2211yescharacteristic
13C11×#442C2214yescomplemented
14C4×C11×D8—22no—
15C11×#427C2211yescharacteristic
16C11×#418—21no—
17C11×#405C2211yescharacteristic
18C2×#66891C412yescomplemented
19#10622760C414yescomplemented
20#10622760C2214yes—
21C2×#66890C412yescomplemented
22C2×#66883C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622618—21no—
26#10622330C2214yescomplemented
27#10622313—22no—
28#10622201C2214yescomplemented
29#10622126C2214yescomplemented
30#10622125C2214yescomplemented
31#10622104C2214yescomplemented
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×M16D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C4×D4×C11—24no—
43C4×D4×C11—42no—
44C11×#117—21no—
45C11×#117D411yescharacteristic
46C2×C11×C22⋊C4—42no—
47C2×#4318—21no—
48#66960—42no—
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—24no—
58C11×#107—21no—
59C11×#106C2312yes—
60C11×#102—24no—
61C11×#97C2312yes—
62C4×C8×C11D412yes—
63#66891C2×C418yescomplemented
64#66890C2×C418yescomplemented
65#66883—21no—
66#66883C2312yes—
67#66876—21no—
68#66876C2×C412yescomplemented
69#66876C2312yes—
70#66876C2312yes—
71C2×C11⋊C16—21no—
72C2×C11⋊C16C2×C412yescomplemented
73#66869—24no—
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×C11—44no—
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
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—21no—
97C11×M16—21no—
98C2×C8×C11C22×C411yescharacteristic
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D412yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11#4111yescharacteristic
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—22no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—44no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D412yes—
112#4318—22no—
113#4318—41no—
114C2×C11⋊C8—41no—
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#2948D1111yescharacteristic, complemented
128AGL(1,ℤ/16)—118no—
129#2155—111no—
130C2×#361—111no—
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×C11—22no—
144C2×C4×C11—42no—
145C2×C4×C11—164no—
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C22⋊D11—42no—
153C22⋊D11—42no—
154C2×Dic11—41no—
155D44—22no—
156D44—41no—
157C4×D11—42no—
158C4×D11—42no—
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×D8C2×D1111yescharacteristic
169#568—221no—
170#518—21no—
171#509—114no—
172#509—114no—
173C2×SD32—112no—
174C2×D16—112no—
175C2×M32—111no—
176C2×M32—111no—
177#444—114no—
178#443—222no—
179#442C2×D1114yescomplemented
180C4×D8—22no—
181C2×#108—111no—
182#427C2×D1111yescharacteristic
183#421—221no—
184#418—21no—
185#405C2×D1111yescharacteristic
186#365—114no—
187#361—114no—
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—42no—
201C4×C11—82no—
202C4×C11#44211yescharacteristic
203C4×C11#44211yescharacteristic
204C4×C11C2×C4×D411yescharacteristic
205C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
206Dic11—42no—
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—221no—
225C2×M16—442no—
226C2×M16C22⋊D1111yescharacteristic
227C22×C8C22×D1111yescharacteristic
228C4×D4—24no—
229C4×D4—42no—
230#117—21no—
231#117C22⋊D1111yescharacteristic
232C2×C22⋊C4—42no—
233SD32—118no—
234D16—118no—
235M32—112no—
236M32—112no—
237M32—112no—
238M32—221no—
239C2×C16—112no—
240C2×C16—221no—
241#108—112no—
242#108—221no—
243#107—21no—
244#106C22×D1112yes—
245#104—224no—
246#102—24no—
247#97C22×D1112yes—
248C4×C8C22⋊D1112yes—
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—44no—
270C22×C4—441no—
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—112no—
273Q16—221no—
274SD16—222no—
275SD16—222no—
276D8—22no—
277D8—22no—
278D8—22no—
279D8—112no—
280D8—221no—
281D8C2×C4×D1114yes—
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×C8#433911yescharacteristic
292C2×C8#433911yescharacteristic
293C2×C8C2×C22⋊D1112yes—
294C2×C8C2×C22⋊D1111yescharacteristic
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—22no—
298C22⋊C4—21no—
299C22⋊C4—44no—
300C22⋊C4—41no—
301C42—41no—
302C42C2×C22⋊D1112yes—
303C16—114no—
304C16—222no—
305C11#3347111yescharacteristic, complemented, Sylow
306C23—42no—
307C23—42no—
308C23—42no—
309C23—162no—
310C23—441no—
311C23#6698511yescharacteristic
312Q8—222no—
313Q8—441no—
314D4—24no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—222no—
319D4—442no—
320D4—442no—
321D4—441no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—164no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4C4×C22⋊D1111yescharacteristic
329C2×C4C4×C22⋊D1111yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4#6700211yescharacteristic
332C2×C4#6700211yescharacteristic
333C2×C4C22×C22⋊D1111yescharacteristic
334C8—22no—
335C8—442no—
336C8C4×C22⋊D1111yescharacteristic
337C8C4×C22⋊D1111yescharacteristic
338C8C22×C4×D1111yescharacteristic
339C8C2×#433911yescharacteristic
340C22—41no—
341C22—44no—
342C22—84no—
343C22—162no—
344C22—162no—
345C22—442no—
346C22—1761no—
347C22#1062262711yescharacteristic
348C22#1062262711yescharacteristic
349C22C2×#6698511yescharacteristic
350C4—42no—
351C4—82no—
352C4—442no—
353C4#1062262711yescharacteristic
354C4#1062262711yescharacteristic
355C4C2×C4×C22⋊D1111yescharacteristic
356C4C2×#6700211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—84no—
361C2—882no—
362C2C2×#1062262711yescharacteristic
subgroupG/H
centerC2C2×#10622627
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2948C2
socleC2×C11C2×#442
prime radicalC2×#10622760C2
cosocleC2×C8×C11C24
hypercenter#2948D11
hypocenterC11#33471
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #13077534C2semidirect
3. #13070512C2semidirect
4. #13070388C2semidirect
5. C2×#10622201C2semidirect
6. #13070351C2semidirect
7. #13070221C2semidirect
8. C11×#2948C2semidirect
13. C11×#442C22semidirect
18. C2×#66891C4semidirect
19. #10622760C4semidirect
21. C2×#66890C4semidirect
26. #10622330C22semidirect
28. #10622201C22semidirect
29. #10622126C22semidirect
30. #10622125C22semidirect
31. #10622104C22semidirect
50. C2×Dic44C2×C4semidirect
53. #66957C2×C4semidirect
55. C2×D88C2×C4semidirect
63. #66891C2×C4semidirect
64. #66890C2×C4semidirect
68. #66876C2×C4semidirect
72. C2×C11⋊C16C2×C4semidirect
127. #2948D11semidirect
179. #442C2×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
#130775342
#130705122
#130703882
C2×#106222012
#130703512
#130702212
C11×#29482
#3347111