Finite Group Databasebeta

← #14735005

Subgroups — #14735005

Order 2816.

936 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079806C212yesmaximal, complemented
2#13079080C211yesmaximal, characteristic
3#13067927C214yesmaximal, complemented
4#13067914C214yesmaximal, complemented
5#13067240C211yesmaximal, characteristic, complemented
6#13067218C212yesmaximal, complemented
7C2×C11×#563C211yesmaximal, characteristic, complemented
8C11×#563—24no—
9C11×#563—22no—
10C11×#563C2214yes—
11C2×C11×C4⋊Q8—21no—
12C2×C11×#126—22no—
13C2×C11×#125C2212yes—
14C2×C11×#124C2211yescharacteristic
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8—22no—
17C2×#66995—21no—
18C2×#66985—21no—
19#10623008C2211yescharacteristic
20#10622680C2214yescomplemented
21#10622679—24no—
22#10622678C2214yescomplemented
23#10622673C2212yes—
24#10622672—22no—
25#10622671C2212yes—
26#10622581—22no—
27#10622580—22no—
28#10622539C2212yes—
29C4×#4318C2211yescharacteristic
30#10622181C2218yescomplemented
31#10622178C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×#4339—21no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—24no—
39C11×#126—28no—
40C11×#126—28no—
41C11×#125—22no—
42C11×#125—22no—
43C11×#125D414yes—
44C11×#125C2314yes—
45C11×#124—22no—
46C11×#124D412yes—
47C11×#124C2312yes—
48C11×#123—24no—
49C11×#123—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63#66995—44no—
64C2×#4325—22no—
65C2×#4324—22no—
66#66985—44no—
67C2×#4323—22no—
68#66983—22no—
69C2×#4318—21no—
70#66928—21no—
71#66927C2311yescharacteristic
72C4×D44—22no—
73#66922C2311yescharacteristic
74C22⋊(C11⋊C8)—22no—
75#66873—24no—
76#66873—24no—
77#66872—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867C2312yes—
81#66867C2314yes—
82C4×C11⋊C8—21no—
83#18994—111nomaximal, Sylow
84C24×C11—21no—
85C2×Q8×C11—24no—
86C2×Q8×C11—21no—
87C2×Q8×C11—42no—
88C2×Q8×C11—82no—
89C2×Q8×C11C2×D412yes—
90C2×D4×C11—21no—
91C2×D4×C11—42no—
92C2×D4×C11C2×D412yes—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—82no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C2×C22⋊D11—41no—
101#4339—42no—
102#4339—42no—
103C2×D44—22no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—21no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4C2×D414yes—
115C11×C4⋊C4C2×D414yes—
116C11×C22⋊C4—28no—
117C11×C22⋊C4—24no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C42×C11—24no—
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D412yes—
123C42×C11C2411yescharacteristic
124#4326—44no—
125#4325—44no—
126#4324—44no—
127#4323—44no—
128(C2×D11)⋊C4—42no—
129C4⋊Dic11—22no—
130#4318—24no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—24no—
133C2×#563D1111yescharacteristic, complemented
134#3234—112no—
135#3153—111no—
136#1660—114no—
137#1657—114no—
138#1533—111no—
139#1528—112no—
140C23×C11—22no—
141C23×C11—44no—
142C23×C11—42no—
143C23×C11#12011yescharacteristic
144C22×D11—41no—
145Q8×C11—42no—
146Q8×C11—81no—
147Q8×C11—84no—
148D4×C11—42no—
149D4×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—84no—
159C2×C4×C11#12012yes—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11C22×D412yes—
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—82no—
164C2×Dic11—41no—
165D44—41no—
166D44—41no—
167D44—44no—
168C4×D11—82no—
169Dic22—41no—
170Dic22—41no—
171C11⋊C8—24no—
172C11⋊C8—44no—
173C2×#137—221no—
174C2×AGL(1,ℤ/8)—221no—
175#563—24no—
176#563—22no—
177#563C2×D1114yes—
178#532—111no—
179C2×C4⋊Q8—21no—
180C2×#126—22no—
181C2×#125C2×D1112yes—
182C2×#124C2×D1111yescharacteristic
183C2×#123—21no—
184C2×C22⋊Q8—22no—
185#501—114no—
186#497—112no—
187#496—112no—
188#495—222no—
189#490—114no—
190#481—222no—
191#480—222no—
192#478—224no—
193#432—112no—
194C4×M16—111no—
195#330—118no—
196#329—114no—
197C22×C11—22no—
198C22×C11—42no—
199C22×C11—44no—
200C22×C11—84no—
201C22×C11#45312yes—
202C22×C11C2×#12011yescharacteristic
203C2×D11—81no—
204C2×D11—82no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11—44no—
212Dic11—81no—
213C2×#41—221no—
214C22×Q8—21no—
215C22×Q8C22⋊D1111yescharacteristic
216C22×D4C22⋊D1111yescharacteristic
217C23×C4—21no—
218#137—444no—
219AGL(1,ℤ/8)—444no—
220C2×Q16—222no—
221C2×SD16—222no—
222C2×SD16—222no—
223C2×D8—222no—
224C2×M16—221no—
225C4⋊Q8—24no—
226C4⋊Q8—24no—
227C4⋊Q8—111no—
228#127—111no—
229#126—28no—
230#126—28no—
231#125—22no—
232#125—22no—
233#125C22⋊D1114yes—
234#125C22×D1114yes—
235#124—22no—
236#124—221no—
237#124C22⋊D1112yes—
238#124C22×D1112yes—
239#123—24no—
240#123—24no—
241C22⋊Q8—28no—
242C22⋊Q8—28no—
243#121—222no—
244C4×D4—222no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4C22⋊D1112yes—
249C2×C4⋊C4C22⋊D1112yes—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—22no—
253C2×C42—21no—
254C2×C42C22×D1111yescharacteristic
255#107—224no—
256#106—224no—
257C4⋊C8—222no—
258#102—224no—
259#102—224no—
260C22⋊C8—222no—
261#97—114no—
262#97—112no—
263C4×C8—221no—
264C2×C11—22no—
265C2×C11—82no—
266C2×C11C2×#45311yescharacteristic
267C2×C11#302012yes—
268D11—161no—
269C24—21no—
270#41—442no—
271#41—442no—
272C2×Q8—24no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—82no—
276C2×Q8—221no—
277C2×Q8C2×C22⋊D1112yes—
278C2×D4—21no—
279C2×D4—42no—
280C2×D4—222no—
281C2×D4—221no—
282C2×D4—441no—
283C2×D4C2×C22⋊D1112yes—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—82no—
289C22×C4—441no—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1112yes—
292Q16—444no—
293SD16—444no—
294SD16—444no—
295D8—444no—
296M16—224no—
297C2×C8—222no—
298C2×C8—224no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—222no—
307C4⋊C4C2×C22⋊D1114yes—
308C4⋊C4C2×C22⋊D1114yes—
309C22⋊C4—28no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—442no—
314C42—24no—
315C42C2×C22⋊D1111yescharacteristic
316C42C2×C22⋊D1112yes—
317C42C23×D1111yescharacteristic
318C11#1899411yescharacteristic, complemented, Sylow
319C23—22no—
320C23—44no—
321C23—42no—
322C23—441no—
323C23#6700611yescharacteristic
324Q8—42no—
325Q8—81no—
326Q8—84no—
327Q8—441no—
328Q8—441no—
329D4—42no—
330D4—81no—
331D4—441no—
332D4—441no—
333D4—444no—
334D4—882no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—84no—
344C2×C4—441no—
345C2×C4—882no—
346C2×C4#6700612yes—
347C2×C4#6700611yescharacteristic
348C2×C4C22×C22⋊D1112yes—
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—224no—
351C8—444no—
352C22—22no—
353C22—42no—
354C22—44no—
355C22—84no—
356C22—881no—
357C22—882no—
358C22#1062285412yes—
359C22C2×#6700611yescharacteristic
360C4—21no—
361C4—21no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—42no—
366C4—44no—
367C4—881no—
368C2—22no—
369C2—82no—
370C2—1761no—
371C2C2×#1062285411yescharacteristic
372C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#563C2
socleC22×C11C2×#120
prime radical#13079080C2
hypercenterC2×#563D11
hypocenterC11#18994
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
3. #13067927C2semidirect
4. #13067914C2semidirect
5. #13067240C2semidirect
6. #13067218C2semidirect
7. C2×C11×#563C2semidirect
20. #10622680C22semidirect
22. #10622678C22semidirect
30. #10622181C22semidirect
133. C2×#563D11semidirect
318. C11#18994semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130790802
#130679272
#130679142
#130672402
#130672182
C2×C11×#5632
#1899411