Finite Group Databasebeta

← #14737669

Subgroups — #14737669

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622308C211yesmaximal, characteristic, complemented
2#13078097C212yesmaximal, complemented
3C8×#4339C211yesmaximal, characteristic, complemented
4#13067977C214yesmaximal, complemented
5#13067972C214yesmaximal, complemented
6#13067285C212yesmaximal, complemented
7C11×#1567C211yesmaximal, characteristic, complemented
8C2×#66961—22no—
9C22×D88—22no—
10C2×#66927C2212yes—
11C4×#4339C2211yescharacteristic
12C11×#423C2212yes—
13C2×C4×C8×C11C2211yescharacteristic
14#10622744—22no—
15C8×C22⋊D11—22no—
16#10622538C2211yescharacteristic
17#10622461—22no—
18#10622461C2214yescomplemented
19#10622456—22no—
20#10622456C2214yescomplemented
21#10622308—21no—
22#10622308—21no—
23#10622308C2214yes—
24C8×D44C2212yescomplemented
25#10622298—21no—
26C4×C8×D11—21no—
27C8×Dic22C2212yescomplemented
28C11×#335C2214yescomplemented
29#10622123C2218yescomplemented
30C2×#4339D411yescharacteristic
31C22×D44—22no—
32C22×D44—22no—
33C22×D44—22no—
34C2×C11×M16—22no—
35C22×C8×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C4×C22⋊D11—21no—
38C4×C22⋊D11—21no—
39#66979D411yescharacteristic
40#66961—48no—
41C2×D88—24no—
42C2×D88—24no—
43C2×D88—24no—
44C2×D88—48no—
45C2×#4314—24no—
46C2×C8×D11—22no—
47#66927—22no—
48#66927—22no—
49#66927—22no—
50#66927C2314yes—
51C4×D44D411yescharacteristic
52C4×D44C2311yescharacteristic
53#66925—21no—
54C42×D11—21no—
55C4×Dic22D411yescharacteristic
56C4×Dic22C2311yescharacteristic
57C11×C4⋊C8—22no—
58C11×C4⋊C8C2314yes—
59C4×C8×C11D411yescharacteristic
60C4×C8×C11D411yescharacteristic
61C4×C8×C11C2312yes—
62C22⋊(C11⋊C8)—21no—
63#66885—24no—
64#66885—24no—
65(C2×D11)⋊C8—22no—
66Dic11⋊C8—22no—
67C8×Dic11—22no—
68C4⋊(C11⋊C8)C2312yes—
69C4×C11⋊C8—21no—
70#19267—111nomaximal, Sylow
71C23×D11—42no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—21no—
76#4339—22no—
77#4339D814yescomplemented
78C2×D44—24no—
79C2×D44—24no—
80C2×D44—24no—
81C2×D44—48no—
82C2×D44—42no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—44no—
86C2×D44—44no—
87C2×D44—84no—
88C2×D44C2×D411yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×Dic22C2×D411yescharacteristic
93C11×M16—44no—
94C2×C8×C11—24no—
95C2×C8×C11—24no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D412yes—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11C2411yescharacteristic
102C22⋊Dic11—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11C2×D411yescharacteristic
106C4⋊Dic11C2×D411yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C2×C11⋊C8—22no—
113D88—48no—
114D88—48no—
115D88—48no—
116#4314—48no—
117C8×D11—44no—
118C2×#493—111no—
119#3038—112no—
120C8×#41—111no—
121#1668—114no—
122#1667—114no—
123#1567D1111yescharacteristic, complemented
124#1545—112no—
125C23×C11#12111yescharacteristic
126C22×D11—21no—
127C22×D11—44no—
128C22×D11—84no—
129C22×D11—84no—
130C22×D11—84no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11C2×D812yes—
137C2×C4×C11#13512yes—
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C2×#4111yescharacteristic
141C22⋊D11—24no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145D44—21no—
146D44—44no—
147D44—44no—
148D44—48no—
149D44—84no—
150D44—84no—
151D44—84no—
152D44—84no—
153D44C2×D812yescomplemented
154C4×D11—24no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—21no—
158Dic22C2×D812yescomplemented
159C8×C11—22no—
160C8×C11—44no—
161C8×C11AGL(1,ℤ/8)14yescomplemented
162C11⋊C8—42no—
163C2×AGL(1,ℤ/8)—222no—
164C22×D8—222no—
165C2×#127—112no—
166C4×#41—111no—
167#493—114no—
168#493—221no—
169#493—221no—
170#460—114no—
171#460—222no—
172#459—114no—
173#459—222no—
174C8×Q8—112no—
175C8×D4—112no—
176C8×D4—222no—
177#431—111no—
178#431—221no—
179#423C2×D1112yes—
180#418—222no—
181C2×C4×C8—221no—
182C2×C4×C8C2×D1111yescharacteristic
183#335C2×D1114yescomplemented
184#331—118no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#46612yes—
188C22×C11C2×#12111yescharacteristic
189C2×D11—22no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—84no—
193C2×D11—84no—
194C2×D11—84no—
195C2×D11—168no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11#46612yes—
199C4×C11#47212yes—
200C4×C11C22×D811yescharacteristic
201C4×C11C2×#13511yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)12yes—
203Dic11—22no—
204Dic11—41no—
205Dic11—41no—
206C2×#41—111no—
207C22×D4—222no—
208C22×D4—222no—
209C22×D4—222no—
210AGL(1,ℤ/8)—448no—
211C2×SD16—224no—
212C2×D8—224no—
213C2×D8—224no—
214C2×D8—224no—
215C2×D8—448no—
216C2×M16—22no—
217C22×C8—222no—
218C22×C8D4412yes—
219#127—114no—
220#127—222no—
221#127—222no—
222#127—222no—
223C4×Q8—111no—
224C4×Q8—111no—
225C4×D4—111no—
226C4×D4—111no—
227C4×D4—221no—
228C4×D4—221no—
229#117—111no—
230#117—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—22no—
234C4⋊C8—112no—
235C4⋊C8—222no—
236C4⋊C8C22×D1114yes—
237#102—224no—
238#102—224no—
239C22⋊C8—221no—
240C22⋊C8—222no—
241C4×C8—222no—
242C4×C8—221no—
243C4×C8D4411yescharacteristic
244C4×C8D4411yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11—22no—
247C2×C11#303811yescharacteristic
248C2×C11C2×#46611yescharacteristic
249C2×C11C2×#47211yescharacteristic
250D11—42no—
251D11—164no—
252C24—442no—
253#41—114no—
254#41—222no—
255C2×Q8—111no—
256C2×D4—111no—
257C2×D4—221no—
258C2×D4—224no—
259C2×D4—224no—
260C2×D4—224no—
261C2×D4—448no—
262C2×D4—442no—
263C2×D4—442no—
264C2×D4—442no—
265C2×D4—444no—
266C2×D4—444no—
267C2×D4—884no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4C2×D4411yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4#434311yescharacteristic
274SD16—448no—
275D8—448no—
276D8—448no—
277D8—448no—
278M16—44no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—222no—
282C2×C8—444no—
283C2×C8C2×D4412yes—
284C2×C8C2×D4412yes—
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—221no—
293C42—221no—
294C42—221no—
295C42C2×D4411yescharacteristic
296C42D4×D1111yescharacteristic
297C42#434311yescharacteristic
298C42C23×D1111yescharacteristic
299C11#1926711yescharacteristic, complemented, Sylow
300C23—221no—
301C23—444no—
302C23—884no—
303C23—884no—
304C23—884no—
305C23#6694811yescharacteristic
306Q8—112no—
307Q8—221no—
308D4—112no—
309D4—224no—
310D4—221no—
311D4—448no—
312D4—444no—
313D4—444no—
314D4—884no—
315D4—884no—
316D4—884no—
317D4—884no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—221no—
321C2×C4—224no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4#6694811yescharacteristic
327C2×C4#6694811yescharacteristic
328C2×C4#6694811yescharacteristic
329C2×C4D8×D1112yes—
330C2×C4#6697212yes—
331C2×C4C22×D4411yescharacteristic
332C2×C4C2×D4×D1111yescharacteristic
333C2×C4C2×#434311yescharacteristic
334C8—22no—
335C8—44no—
336C8—442no—
337C8#6696114yescomplemented
338C22—21no—
339C22—21no—
340C22—222no—
341C22—441no—
342C22—441no—
343C22—884no—
344C22—884no—
345C22—884no—
346C22—1768no—
347C22#1062249612yes—
348C22C2×#6694811yescharacteristic
349C4—21no—
350C4—21no—
351C4—222no—
352C4—441no—
353C4—441no—
354C4#1062249612yes—
355C4#1062251012yes—
356C4C2×#6696112yes—
357C4C2×D8×D1111yescharacteristic
358C4C2×#6697211yescharacteristic
359C2—22no—
360C2—442no—
361C2—1764no—
362C2#1307809711yescharacteristic
363C2C2×#1062249611yescharacteristic
364C2C2×#1062251011yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1567C2
socleC22×C11C2×#121
hypercenter#1567D11
hypocenterC11#19267
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
1. C2×#10622308C2semidirect
2. #13078097C2semidirect
3. C8×#4339C2semidirect
4. #13067977C2semidirect
5. #13067972C2semidirect
6. #13067285C2semidirect
7. C11×#1567C2semidirect
18. #10622461C22semidirect
20. #10622456C22semidirect
24. C8×D44C22semidirect
27. C8×Dic22C22semidirect
28. C11×#335C22semidirect
29. #10622123C22semidirect
77. #4339D8semidirect
123. #1567D11semidirect
153. D44C2×D8semidirect
158. Dic22C2×D8semidirect
161. C8×C11AGL(1,ℤ/8)semidirect
183. #335C2×D11semidirect
299. C11#19267semidirect
337. C8#66961semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
#130780972
C8×#43392
#130679772
#130679722
#130672852
C11×#15672
#1926711