Finite Group Databasebeta

← #14909769

Subgroups — #14909769

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070880C212yesmaximal, complemented
3#13070857C212yesmaximal, complemented
4#13070653C212yesmaximal, complemented
5#13070648C212yesmaximal, complemented
6#13070545C212yesmaximal, complemented
7#13070528C212yesmaximal, complemented
8#13070419C211yesmaximal, characteristic, complemented
9C2×C11×#493C211yesmaximal, characteristic, complemented
10C22×C11×D8—21no—
11C22×C11×D8C2212yes—
12C2×C11×#127—21no—
13#10623010—21no—
14C11×#493—21no—
15C11×#493—21no—
16C11×#493C2212yes—
17C11×#493C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66891C2214yescomplemented
20C2×#66890C2214yescomplemented
21#10622729C2211yescharacteristic
22#10622728C2211yescharacteristic
23#10622727—21no—
24C4×Dic44C2211yescharacteristic, complemented
25#10622310—21no—
26#10622309C2211yescharacteristic, complemented
27C4×D88C2211yescharacteristic, complemented
28C4×#4314—21no—
29#10622296C2211yescharacteristic, complemented
30#10622200C2214yescomplemented
31#10622200C2214yescomplemented
32C22⋊(C11⋊C16)C2212yes—
33C4⋊(C11⋊C16)C2212yescomplemented
34#10622099C2212yescomplemented
35C22×D4×C11—22no—
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C2×C11×D8—22no—
39C2×C11×D8—22no—
40C2×C11×D8—22no—
41C2×C11×D8—44no—
42C2×C11×D8—44no—
43C2×C11×D8C2314yes—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C11×#127—22no—
47C11×#127—22no—
48C11×#127—41no—
49C11×#127—41no—
50C2×C42×C11D411yescharacteristic
51#66983—21no—
52#66982—41no—
53C4×C22⋊D11—41no—
54#66977—21no—
55C2×Dic44C2311yescharacteristic
56C2×D88C2311yescharacteristic
57C2×#4314—21no—
58#66929—41no—
59#66928—21no—
60C4×D44—21no—
61#66925—41no—
62#66923—21no—
63C4×Dic22—21no—
64C4×C8×C11D411yescharacteristic
65C4×C8×C11D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68#66891—44no—
69#66890—44no—
70#66885—21no—
71#66885—21no—
72#66882C2311yescharacteristic
73#66882C2311yescharacteristic
74#66881—21no—
75#66880—21no—
76#66880—21no—
77C2×C11⋊C16C2314yes—
78#33783—111nomaximal, Sylow
79C24×C11—42no—
80C2×D4×C11—24no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—84no—
89C2×D4×C11—84no—
90C22×C4×C11D811yescharacteristic
91C22×C4×C11D811yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×D8—24no—
98C11×D8—24no—
99C11×D8—44no—
100C11×D8—44no—
101C11×D8—44no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C42×C11D811yescharacteristic
109C42×C11D811yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C22⋊Dic11—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124Dic44—22no—
125D88—22no—
126#4314—42no—
127C11⋊C16—24no—
128#3168—111no—
129C2×#493D1111yescharacteristic, complemented
130#2250—112no—
131#2244—112no—
132#2207—112no—
133#2206—112no—
134#2187—112no—
135#2184—112no—
136#2163—111no—
137C23×C11—44no—
138C23×C11—84no—
139C23×C11—84no—
140C23×C11—84no—
141C23×C11C2×D811yescharacteristic
142C22×D11—41no—
143D4×C11—44no—
144D4×C11—44no—
145D4×C11—84no—
146D4×C11—84no—
147D4×C11—84no—
148D4×C11—84no—
149D4×C11—84no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164D44—41no—
165D44—41no—
166C4×D11—82no—
167Dic22—41no—
168Dic22—41no—
169C8×C11—21no—
170C8×C11—21no—
171C8×C11AGL(1,ℤ/8)12yes—
172C8×C11H(5,𝔽2)12yes—
173C22×D8—21no—
174C22×D8C2×D1112yes—
175C2×#127—21no—
176#529—221no—
177C2×SD32—114no—
178C2×D16—114no—
179#499—111no—
180#495—111no—
181#493—21no—
182#493—21no—
183#493C2×D1112yes—
184#493C2×D1112yes—
185#488—221no—
186#467—111no—
187#466—111no—
188#465—221no—
189C4×Q16—111no—
190C4×SD16—221no—
191C4×D8—111no—
192C2×C4×C8C2×D1111yescharacteristic
193C4⋊C16—112no—
194#357—114no—
195#357—114no—
196C22⋊C16—112no—
197#346—112no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—84no—
201C22×C11—84no—
202C22×C11—84no—
203C22×C11—168no—
204C22×C11#50912yes—
205C22×C11C22×D811yescharacteristic
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11#50912yes—
214C4×C11#53511yescharacteristic
215C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219C22×D4—22no—
220C22×D4—41no—
221C22×D4—41no—
222C2×Q16—111no—
223C2×SD16—221no—
224C2×D8—22no—
225C2×D8—22no—
226C2×D8—22no—
227C2×D8—44no—
228C2×D8—44no—
229C2×D8—111no—
230C2×D8C22×D1114yes—
231C22×C8C22⋊D1111yescharacteristic
232C22×C8C22×D1111yescharacteristic
233#127—22no—
234#127—22no—
235#127—41no—
236#127—41no—
237#126—441no—
238#125—221no—
239#124—221no—
240#123—441no—
241C22⋊Q8—221no—
242#121—221no—
243C4×Q8—221no—
244C4×D4—221no—
245C4×D4—441no—
246#117—441no—
247C2×C42C22⋊D1111yescharacteristic
248SD32—444no—
249D16—444no—
250C2×C16—114no—
251#107—111no—
252#107—111no—
253#106—221no—
254#103—221no—
255#103—221no—
256#102—221no—
257#102—221no—
258C4×C8C22⋊D1111yescharacteristic
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11—164no—
264C2×C11#320511yescharacteristic
265C2×C11C2×#50911yescharacteristic
266C2×C11C2×#50911yescharacteristic
267D11—161no—
268C24—42no—
269C2×Q8—221no—
270C2×D4—24no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—84no—
279C2×D4—84no—
280C2×D4—221no—
281C2×D4—441no—
282C22×C4—441no—
283C22×C4#432311yescharacteristic
284C22×C4#432311yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286Q16—222no—
287SD16—442no—
288D8—24no—
289D8—24no—
290D8—44no—
291D8—44no—
292D8—44no—
293D8—222no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—441no—
312C42#432311yescharacteristic
313C42#432311yescharacteristic
314C42C2×C22⋊D1111yescharacteristic
315C42C2×C22⋊D1111yescharacteristic
316C16—224no—
317C11#3378311yescharacteristic, complemented, Sylow
318C23—44no—
319C23—84no—
320C23—84no—
321C23—84no—
322C23—441no—
323C23C2×#432311yescharacteristic
324Q8—441no—
325Q8—441no—
326D4—44no—
327D4—44no—
328D4—84no—
329D4—84no—
330D4—84no—
331D4—84no—
332D4—84no—
333D4—441no—
334D4—441no—
335D4—882no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—882no—
344C2×C4C2×#432311yescharacteristic
345C2×C4C2×#432311yescharacteristic
346C2×C4C2×#432311yescharacteristic
347C2×C4C2×#432311yescharacteristic
348C2×C4C2×#432311yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8#6698512yes—
353C8#6703712yes—
354C22—21no—
355C22—21no—
356C22—84no—
357C22—84no—
358C22—84no—
359C22—168no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22#1062276012yes—
364C22C22×#432311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—881no—
370C4—881no—
371C4—881no—
372C4#1062276012yes—
373C4C2×#6698511yescharacteristic
374C4#1062333611yescharacteristic
375C2—22no—
376C2—164no—
377C2—1761no—
378C2#1307953411yescharacteristic
379C2C2×#1062276011yescharacteristic
380C2C2×#1062276011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#493C2
socleC22×C11C22×D8
hypercenterC2×#493D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070880C2semidirect
3. #13070857C2semidirect
4. #13070653C2semidirect
5. #13070648C2semidirect
6. #13070545C2semidirect
7. #13070528C2semidirect
8. #13070419C2semidirect
9. C2×C11×#493C2semidirect
19. C2×#66891C22semidirect
20. C2×#66890C22semidirect
24. C4×Dic44C22semidirect
26. #10622309C22semidirect
27. C4×D88C22semidirect
29. #10622296C22semidirect
30. #10622200C22semidirect
31. #10622200C22semidirect
33. C4⋊(C11⋊C16)C22semidirect
34. #10622099C22semidirect
129. C2×#493D11semidirect
317. C11#33783semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708802
#130708572
#130706532
#130706482
#130705452
#130705282
#130704192
C2×C11×#4932
#3378311