Finite Group Databasebeta

← #14909771

Subgroups — #14909771

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
2C2×#10622308C211yesmaximal, characteristic, complemented
3#13070882C212yesmaximal, complemented
4#13070858C212yesmaximal, complemented
5#13070657C212yesmaximal, complemented
6#13070652C212yesmaximal, complemented
7#13070547C212yesmaximal, complemented
8#13070530C212yesmaximal, complemented
9C11×#2163C211yesmaximal, characteristic, complemented
10C22×D88—21no—
11C22×D88C2212yes—
12#10623010—21no—
13C2×#66927—21no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622729C2211yescharacteristic
16#10622728C2211yescharacteristic
17#10622727—21no—
18C2×#66864C2214yescomplemented
19C2×D176C2214yescomplemented
20C4×Dic44C2211yescharacteristic, complemented
21#10622310—21no—
22#10622309C2211yescharacteristic, complemented
23#10622308—21no—
24#10622308—21no—
25#10622308C2212yes—
26#10622308C2212yes—
27C4×D88C2211yescharacteristic, complemented
28C4×#4314—21no—
29#10622296C2211yescharacteristic, complemented
30C11×C4⋊C16C2212yescomplemented
31C11×C22⋊C16C2212yes—
32C11×#346C2212yescomplemented
33#10622147C2214yescomplemented
34#10622147C2214yescomplemented
35C22×D44—22no—
36C22×D44—41no—
37C22×D44—41no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11C2311yescharacteristic
40C2×C42×C11D411yescharacteristic
41#66983—21no—
42#66982—41no—
43C4×C22⋊D11—41no—
44#66977—21no—
45C2×Dic44C2311yescharacteristic
46C2×D88—22no—
47C2×D88—22no—
48C2×D88—22no—
49C2×D88—44no—
50C2×D88—44no—
51C2×D88C2311yescharacteristic
52C2×D88C2314yes—
53C2×#4314—21no—
54#66929—41no—
55#66928—21no—
56#66927—22no—
57#66927—22no—
58#66927—41no—
59#66927—41no—
60C4×D44—21no—
61#66925—41no—
62#66923—21no—
63C4×Dic22—21no—
64C2×C11×C16C2314yes—
65C4×C8×C11D411yescharacteristic
66C4×C8×C11D411yescharacteristic
67C4×C8×C11C2311yescharacteristic
68C4×C8×C11C2311yescharacteristic
69#66885—21no—
70#66885—21no—
71#66882C2311yescharacteristic
72#66882C2311yescharacteristic
73#66881—21no—
74#66880—21no—
75#66880—21no—
76#66864—44no—
77D176—44no—
78#33783—111nomaximal, Sylow
79C23×D11—42no—
80C22×C4×C11D811yescharacteristic
81C22×C4×C11D811yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C2×D44—21no—
85C2×D44—24no—
86C2×D44—44no—
87C2×D44—44no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—84no—
94C2×D44—84no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C42×C11D811yescharacteristic
104C42×C11D811yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114Dic11⋊C4—41no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119Dic44—22no—
120D88—22no—
121D88—24no—
122D88—24no—
123D88—44no—
124D88—44no—
125D88—44no—
126#4314—42no—
127C11×C16—24no—
128#3168—111no—
129C2×#493—111no—
130#2250—112no—
131#2244—112no—
132#2207—112no—
133#2206—112no—
134#2187—112no—
135#2184—112no—
136#2163D1111yescharacteristic, complemented
137C23×C11C2×D811yescharacteristic
138C22×D11—41no—
139C22×D11—44no—
140C22×D11—84no—
141C22×D11—84no—
142C22×D11—84no—
143C2×C4×C11—22no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11C2×D811yescharacteristic
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C22⋊D11—82no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157D44—44no—
158D44—41no—
159D44—41no—
160D44—44no—
161D44—84no—
162D44—84no—
163D44—84no—
164D44—84no—
165D44—84no—
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—112no—
174C22×D8—221no—
175C2×#127—221no—
176#529—221no—
177C2×SD32—114no—
178C2×D16—114no—
179#499—111no—
180#495—111no—
181#493—112no—
182#493—112no—
183#493—221no—
184#493—221no—
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⋊C16C2×D1112yescomplemented
194#357—114no—
195#357—114no—
196C22⋊C16C2×D1112yes—
197#346C2×D1112yescomplemented
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#50912yes—
201C22×C11C22×D811yescharacteristic
202C2×D11—84no—
203C2×D11—84no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—84no—
207C2×D11—81no—
208C2×D11—168no—
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—222no—
220C22×D4—441no—
221C22×D4—441no—
222C2×Q16—111no—
223C2×SD16—221no—
224C2×D8—114no—
225C2×D8—111no—
226C2×D8—222no—
227C2×D8—222no—
228C2×D8—222no—
229C2×D8—444no—
230C2×D8—444no—
231C22×C8D4411yescharacteristic
232C22×C8C22×D1111yescharacteristic
233#127—222no—
234#127—222no—
235#127—441no—
236#127—441no—
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×C42D4411yescharacteristic
248SD32—444no—
249D16—444no—
250C2×C16C22×D1114yes—
251#107—111no—
252#107—111no—
253#106—221no—
254#103—221no—
255#103—221no—
256#102—221no—
257#102—221no—
258C4×C8D4411yescharacteristic
259C4×C8D4411yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11#320511yescharacteristic
264C2×C11C2×#50911yescharacteristic
265C2×C11C2×#50911yescharacteristic
266D11—161no—
267D11—164no—
268C24—442no—
269C2×Q8—221no—
270C2×D4—221no—
271C2×D4—224no—
272C2×D4—444no—
273C2×D4—444no—
274C2×D4—441no—
275C2×D4—442no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—884no—
281C2×D4—884no—
282C22×C4—441no—
283C22×C4D8811yescharacteristic
284C22×C4D8811yescharacteristic
285C22×C4C2×D4411yescharacteristic
286Q16—222no—
287SD16—442no—
288D8—222no—
289D8—224no—
290D8—224no—
291D8—444no—
292D8—444no—
293D8—444no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×D4411yescharacteristic
297C2×C8C2×D4411yescharacteristic
298C2×C8C2×D4411yescharacteristic
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—
312C42D8811yescharacteristic
313C42D8811yescharacteristic
314C42C2×D4411yescharacteristic
315C42C2×D4411yescharacteristic
316C16—24no—
317C11#3378311yescharacteristic, complemented, Sylow
318C23—441no—
319C23—444no—
320C23—884no—
321C23—884no—
322C23—884no—
323C23C2×D8811yescharacteristic
324Q8—441no—
325Q8—441no—
326D4—444no—
327D4—441no—
328D4—444no—
329D4—441no—
330D4—884no—
331D4—884no—
332D4—884no—
333D4—884no—
334D4—882no—
335D4—884no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—882no—
344C2×C4C2×D8811yescharacteristic
345C2×C4C2×D8811yescharacteristic
346C2×C4C2×D8811yescharacteristic
347C2×C4C2×D8811yescharacteristic
348C2×C4C2×D8811yescharacteristic
349C2×C4C22×D4411yescharacteristic
350C8—21no—
351C8—21no—
352C8#6696112yes—
353C8#6704212yes—
354C22—21no—
355C22—21no—
356C22—881no—
357C22—884no—
358C22—884no—
359C22—881no—
360C22—884no—
361C22—881no—
362C22—1768no—
363C22#1062252112yes—
364C22C22×D8811yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—881no—
370C4—881no—
371C4—881no—
372C4#1062252112yes—
373C4#1062305611yescharacteristic
374C4C2×#6696111yescharacteristic
375C2—22no—
376C2—1764no—
377C2—1761no—
378C2#1307953611yescharacteristic
379C2C2×#1062252111yescharacteristic
380C2C2×#1062252111yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
hypercenter#2163D11
hypocenterC11#33783
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. C2×#10622308C2semidirect
3. #13070882C2semidirect
4. #13070858C2semidirect
5. #13070657C2semidirect
6. #13070652C2semidirect
7. #13070547C2semidirect
8. #13070530C2semidirect
9. C11×#2163C2semidirect
18. C2×#66864C22semidirect
19. C2×D176C22semidirect
20. C4×Dic44C22semidirect
22. #10622309C22semidirect
27. C4×D88C22semidirect
29. #10622296C22semidirect
30. C11×C4⋊C16C22semidirect
32. C11×#346C22semidirect
33. #10622147C22semidirect
34. #10622147C22semidirect
136. #2163D11semidirect
193. C4⋊C16C2×D11semidirect
197. #346C2×D11semidirect
317. C11#33783semidirect

Maximal subgroups

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

subgroupindex
#130791862
C2×#106223082
#130708822
#130708582
#130706572
#130706522
#130705472
#130705302
C11×#21632
#3378311