Finite Group Databasebeta

← #14729853

Subgroups — #14729853

Order 2816.

1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#10623244C211yesmaximal, characteristic, complemented
2#13078734C212yesmaximal, complemented
3#13067735C214yesmaximal, complemented
4#13067673C214yesmaximal, complemented
5#13067330C211yesmaximal, characteristic, complemented
6#13067064C212yesmaximal, complemented
7C11×#3151C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×#66989—22no—
12C2×#66988—22no—
13C2×D4×Dic11—22no—
14#10623244—22no—
15#10623244—24no—
16#10623244C2214yes—
17C2×C4×Dic22C2212yes—
18C11×#496—22no—
19C11×#493C2212yes—
20C11×#492C2212yes—
21C4×C11×M16C2211yescharacteristic
22#10622704C2214yescomplemented
23#10622688C2214yescomplemented
24#10622653—22no—
25#10622646—22no—
26#10622631—24no—
27#10622539C2212yes—
28#10622182C2214yes—
29#10622094C2218yescomplemented
30C2×C11×#41—21no—
31C22×D4×C11—22no—
32C22×D4×C11D412yes—
33C23×Dic11—22no—
34C22×Dic22D412yes—
35C11×AGL(1,ℤ/8)—48no—
36C2×C11×SD16—24no—
37C2×C11×D8—24no—
38C2×C11×M16—21no—
39C11×C4⋊Q8C2311yescharacteristic
40C11×#127—22no—
41C11×#127D412yes—
42C11×#127C2311yescharacteristic
43C11×#127C2312yes—
44C11×#124—21no—
45C11×#121—22no—
46C4×D4×C11—22no—
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—22no—
50#66989—28no—
51#66989—28no—
52#66988—28no—
53#66988—28no—
54D4×Dic11—28no—
55D4×Dic11—28no—
56C2×#4324—24no—
57C2×C4⋊Dic11D412yes—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C4×Dic22—22no—
61C4×Dic22—22no—
62C4×Dic22D414yes—
63C4×Dic22C2314yes—
64C11×#97—21no—
65C4×C8×C11C2312yes—
66#66896—24no—
67C22⋊(C11⋊C8)—22no—
68#66874—24no—
69#66871—24no—
70C4⋊(C11⋊C8)C2314yes—
71#66867—22no—
72#18526—111nomaximal, Sylow
73C24×C11—22no—
74C11×#41—44no—
75C2×Q8×C11—21no—
76C2×D4×C11—24no—
77C2×D4×C11—22no—
78C2×D4×C11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—48no—
82C2×D4×C11—44no—
83C2×D4×C11—41no—
84C2×D4×C11C2×D414yes—
85C22×C4×C11—41no—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—28no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—84no—
92C2×Dic22—22no—
93C2×Dic22—44no—
94C2×Dic22C2×D414yes—
95C11×SD16—48no—
96C11×D8—48no—
97C11×M16—24no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C22⋊C4—42no—
101C42×C11C2×D412yes—
102C42×C11C2×D411yescharacteristic
103C42×C11C2411yescharacteristic
104C22⋊Dic11—216no—
105C22⋊Dic11—28no—
106#4324—48no—
107C4⋊Dic11—22no—
108C4⋊Dic11C2×D414yes—
109Dic11⋊C4—24no—
110Dic11⋊C4—24no—
111C4×Dic11—24no—
112C4×Dic11—24no—
113C2×C11⋊C8—24no—
114C2×#559—111no—
115#3151D1111yescharacteristic
116#3112—112no—
117#1630—114no—
118#1620—114no—
119#1555—111no—
120#1491—112no—
121C23×C11—24no—
122C23×C11—48no—
123C23×C11—44no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126Q8×C11—42no—
127D4×C11—44no—
128D4×C11—48no—
129D4×C11—42no—
130D4×C11—48no—
131D4×C11—44no—
132D4×C11—82no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—41no—
137C2×C4×C11—82no—
138C2×C4×C11#12012yes—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11C22×D412yes—
141C2×C4×C11C22×D411yescharacteristic
142C2×Dic11—24no—
143C2×Dic11—24no—
144C2×Dic11—44no—
145C2×Dic11—44no—
146C2×Dic11—88no—
147Dic22—24no—
148Dic22—24no—
149Dic22—44no—
150C8×C11—24no—
151C11⋊C8—44no—
152C2×AGL(1,ℤ/8)—22no—
153#559—114no—
154#559—224no—
155#559—222no—
156#532C2×D1111yescharacteristic
157C2×#127C2×D1111yescharacteristic
158C2×#124—222no—
159C2×#123—222no—
160C2×C4×Q8—112no—
161C2×C4×D4—222no—
162#496—22no—
163#493C2×D1112yes—
164#492C2×D1112yes—
165#480—222no—
166#477—114no—
167#460—114no—
168#448—222no—
169#440—224no—
170#432—112no—
171C4×M16C2×D1111yescharacteristic
172#331—114no—
173Q8⋊C8—118no—
174C22×C11—22no—
175C22×C11—48no—
176C22×C11—44no—
177C22×C11—88no—
178C22×C11—82no—
179C22×C11—81no—
180C22×C11#45312yes—
181C22×C11C2×#12011yescharacteristic
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11#57514yes—
187Dic11—44no—
188Dic11—44no—
189C2×#41—21no—
190C22×Q8—112no—
191C22×D4—22no—
192C22×D4C22⋊D1112yes—
193C23×C4—222no—
194AGL(1,ℤ/8)—48no—
195C2×SD16—24no—
196C2×SD16—224no—
197C2×D8—24no—
198C2×M16—21no—
199C4⋊Q8C22×D1111yescharacteristic
200#127—22no—
201#127C22⋊D1112yes—
202#127C22×D1111yescharacteristic
203#127C22×D1112yes—
204#124—21no—
205#124—228no—
206#124—228no—
207#123—228no—
208#123—228no—
209#121—22no—
210C4×Q8—114no—
211C4×Q8—114no—
212C4×Q8—222no—
213C4×Q8—222no—
214C4×D4—22no—
215C4×D4—228no—
216C4×D4—228no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—222no—
219C2×C22⋊C4—224no—
220C2×C22⋊C4—222no—
221C2×C42—222no—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224C4⋊C8—114no—
225#103—224no—
226#102—224no—
227C22⋊C8—222no—
228#97—21no—
229#97—222no—
230C4×C8C22×D1112yes—
231C2×C11—22no—
232C2×C11—84no—
233C2×C11—161no—
234C2×C11#300512yes—
235C2×C11C2×#45311yescharacteristic
236C24—22no—
237#41—44no—
238C2×Q8—21no—
239C2×Q8—114no—
240C2×Q8—222no—
241C2×Q8—444no—
242C2×D4—24no—
243C2×D4—22no—
244C2×D4—24no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—41no—
250C2×D4C2×C22⋊D1114yes—
251C22×C4—41no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4—228no—
255C22×C4—884no—
256C22×C4D4×D1112yes—
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—48no—
259SD16—448no—
260D8—48no—
261M16—24no—
262C2×C8—22no—
263C2×C8—224no—
264C4⋊C4—22no—
265C4⋊C4—114no—
266C4⋊C4—222no—
267C4⋊C4—224no—
268C4⋊C4—224no—
269C22⋊C4—42no—
270C22⋊C4—2216no—
271C22⋊C4—228no—
272C42—224no—
273C42—224no—
274C42D4×D1112yes—
275C42C2×C22⋊D1111yescharacteristic
276C42C23×D1111yescharacteristic
277C11#1852611yescharacteristic, complemented, Sylow
278C23—24no—
279C23—48no—
280C23—44no—
281C23—41no—
282C23#6699011yescharacteristic
283Q8—42no—
284Q8—224no—
285Q8—224no—
286Q8—444no—
287D4—44no—
288D4—48no—
289D4—42no—
290D4—48no—
291D4—44no—
292D4—82no—
293D4—82no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—224no—
299C2×C4—224no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—888no—
303C2×C4#6699012yes—
304C2×C4#6699011yescharacteristic
305C2×C4C2×D4×D1112yes—
306C2×C4C22×C22⋊D1111yescharacteristic
307C8—24no—
308C8—444no—
309C22—22no—
310C22—48no—
311C22—44no—
312C22—88no—
313C22—82no—
314C22—81no—
315C22#1062269012yes—
316C22C2×#6699011yescharacteristic
317C4—22no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—444no—
322C4—444no—
323C4#1062330414yes—
324C2—22no—
325C2—84no—
326C2—161no—
327C2#1307785512yes—
328C2C2×#1062269011yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3151C2
socleC22×C11C2×#120
hypercenter#3151D11
hypocenterC11#18526
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. #13078734C2semidirect
3. #13067735C2semidirect
4. #13067673C2semidirect
5. #13067330C2semidirect
6. #13067064C2semidirect
22. #10622704C22semidirect
23. #10622688C22semidirect
29. #10622094C22semidirect
277. C11#18526semidirect

Maximal subgroups

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

subgroupindex
C2×#106232442
#130787342
#130677352
#130676732
#130673302
#130670642
C11×#31512
#1852611