Finite Group Databasebeta

← #14735794

Subgroups — #14735794

Order 2816.

1116 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 179 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#13079069C212yesmaximal, complemented
2#13078992C211yesmaximal, characteristic, complemented
3#13067909C218yesmaximal, complemented
4#13067211C211yesmaximal, characteristic, complemented
5#13067208C212yesmaximal, complemented
6C11×#3548C211yesmaximal, characteristic, complemented
7C11×#562C2214yescomplemented
8C11×#554—22no—
9C11×#550—22no—
10C11×#547—22no—
11C11×#540—22no—
12C11×#537—24no—
13C11×#533C2211yescharacteristic
14C11×#532C2212yes—
15C2×#67002—24no—
16C2×#66927C2211yescharacteristic
17#10622701—22no—
18#10622698—22no—
19#10622686—22no—
20#10622680C2214yes—
21#10622671C2218yes—
22#10622614—22no—
23C4×#4318C2212yes—
24C4×#4318C2211yescharacteristic
25#10622181C2214yescomplemented
26#10622178C2218yescomplemented
27C2×C11×#41—24no—
28C2×C11×#41D414yes—
29C22×D44—22no—
30C22×D44—21no—
31C11×C4⋊Q8D412yes—
32C11×C4⋊Q8D412yes—
33C11×#127—22no—
34C11×#127D412yes—
35C11×#125—22no—
36C11×#125C2312yes—
37C11×#124C2314yes—
38C11×#123—28no—
39C11×C22⋊Q8—24no—
40C11×C22⋊Q8—28no—
41C11×C22⋊Q8—22no—
42C11×#121—28no—
43C11×#121—24no—
44C11×#121—28no—
45C11×#121—22no—
46C11×#121—22no—
47C4×Q8×C11—22no—
48C4×D4×C11—24no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C11×#117D412yes—
52C2×C11×C4⋊C4—24no—
53C2×C42×C11C2311yescharacteristic
54#67002—416no—
55C2×#4325—28no—
56C2×#4323—28no—
57C2×#4318—22no—
58C2×#4318—21no—
59#66927—22no—
60#66927—21no—
61#66927C2312yes—
62#66873—28no—
63#66867C2314yes—
64#66867C2312yes—
65C4×C11⋊C8—22no—
66C4×C11⋊C8—21no—
67#19075—111nomaximal, Sylow
68C23×D11—41no—
69C11×#41—48no—
70C11×#41—88no—
71C2×Q8×C11—22no—
72C2×Q8×C11C2×D414yes—
73C2×D4×C11—28no—
74C2×D4×C11—24no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11C2×D414yes—
78C22×C4×C11—28no—
79C22×C4×C11—24no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×D44—22no—
83C2×D44—24no—
84C2×D44—48no—
85C2×D44—44no—
86C2×D44—42no—
87C2×D44—41no—
88C11×C4⋊C4—28no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4C2×D414yes—
94C11×C22⋊C4—28no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—24no—
97C11×C22⋊C4—24no—
98C42×C11—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D412yes—
101C42×C11C2411yescharacteristic
102#4325—416no—
103#4323—416no—
104#4318—28no—
105#4318—42no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—22no—
108#3548D1111yescharacteristic, complemented
109#3151—112no—
110#3138—111no—
111#1656—118no—
112#1526—111no—
113#1525—112no—
114C23×C11—24no—
115C23×C11#12011yescharacteristic
116C22×D11—42no—
117C22×D11—84no—
118C22×D11—82no—
119Q8×C11—44no—
120Q8×C11—44no—
121D4×C11—44no—
122D4×C11—44no—
123D4×C11—44no—
124D4×C11—84no—
125D4×C11—88no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—24no—
129C2×C4×C11—24no—
130C2×C4×C11—48no—
131C2×C4×C11—88no—
132C2×C4×C11#12012yes—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11C22×D411yescharacteristic
135C2×C4×C11C22×D412yes—
136D44—48no—
137D44—44no—
138D44—84no—
139D44—82no—
140C11⋊C8—28no—
141C11⋊C8—42no—
142C2×AGL(1,ℤ/8)—224no—
143#562C2×D1114yescomplemented
144#554—22no—
145#550—22no—
146#547—22no—
147#540—22no—
148#537—24no—
149#533C2×D1111yescharacteristic
150#532C2×D1112yes—
151C2×#127—111no—
152#496—118no—
153#493—222no—
154#492—222no—
155#490—114no—
156#486—222no—
157#418—222no—
158C4×M16—111no—
159C4×M16—112no—
160#330—114no—
161#329—118no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—44no—
165C22×C11—44no—
166C22×C11—44no—
167C22×C11C2×#12011yescharacteristic
168C2×D11—84no—
169C2×D11—82no—
170C2×D11—164no—
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—44no—
174C4×C11—44no—
175C4×C11#45314yes—
176C4×C11#45412yes—
177C2×#41—24no—
178C2×#41C22⋊D1114yes—
179C22×D4—222no—
180C22×D4—221no—
181AGL(1,ℤ/8)—4416no—
182C2×SD16—228no—
183C2×D8—228no—
184C2×M16—222no—
185C2×M16—221no—
186C4⋊Q8C22⋊D1112yes—
187C4⋊Q8C22⋊D1112yes—
188#127—22no—
189#127—112no—
190#127—221no—
191#127—222no—
192#127C22⋊D1112yes—
193#125—22no—
194#125C22×D1112yes—
195#124C22×D1114yes—
196#123—28no—
197C22⋊Q8—24no—
198C22⋊Q8—28no—
199C22⋊Q8—22no—
200#121—28no—
201#121—24no—
202#121—28no—
203#121—22no—
204#121—22no—
205C4×Q8—22no—
206C4×D4—24no—
207C4×D4—22no—
208C4×D4—22no—
209#117C22⋊D1112yes—
210C2×C4⋊C4—24no—
211C2×C42C22×D1111yescharacteristic
212#102—228no—
213#97—112no—
214#97—114no—
215C4×C8—221no—
216C4×C8—222no—
217C2×C11—41no—
218C2×C11—84no—
219C2×C11C2×#45312yes—
220C2×C11C2×#45411yescharacteristic
221D11—162no—
222C24—441no—
223#41—48no—
224#41—88no—
225C2×Q8—22no—
226C2×Q8C2×C22⋊D1114yes—
227C2×D4—28no—
228C2×D4—24no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—222no—
232C2×D4—224no—
233C2×D4—448no—
234C2×D4—444no—
235C2×D4—442no—
236C2×D4—441no—
237C2×D4C2×C22⋊D1114yes—
238C22×C4—28no—
239C22×C4—24no—
240C22×C4C2×C22⋊D1111yescharacteristic
241C22×C4C2×C22⋊D1112yes—
242SD16—4416no—
243D8—4416no—
244M16—228no—
245M16—442no—
246C2×C8—224no—
247C2×C8—222no—
248C4⋊C4—28no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4C2×C22⋊D1114yes—
254C22⋊C4—28no—
255C22⋊C4—22no—
256C22⋊C4—24no—
257C22⋊C4—24no—
258C42—22no—
259C42C2×C22⋊D1111yescharacteristic
260C42C2×C22⋊D1112yes—
261C42C23×D1111yescharacteristic
262C11#1907511yescharacteristic, complemented, Sylow
263C23—24no—
264C23—442no—
265C23—884no—
266C23—882no—
267C23#6700611yescharacteristic
268Q8—44no—
269Q8—44no—
270D4—44no—
271D4—44no—
272D4—44no—
273D4—84no—
274D4—88no—
275D4—448no—
276D4—444no—
277D4—884no—
278D4—882no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—48no—
284C2×C4—88no—
285C2×C4#6700612yes—
286C2×C4#6700611yescharacteristic
287C2×C4C22×C22⋊D1111yescharacteristic
288C2×C4C22×C22⋊D1112yes—
289C8—228no—
290C8—442no—
291C22—22no—
292C22—21no—
293C22—44no—
294C22—44no—
295C22—44no—
296C22—884no—
297C22—882no—
298C22—1764no—
299C22C2×#6700611yescharacteristic
300C4—22no—
301C4—21no—
302C4—44no—
303C4—44no—
304C4#1062285414yes—
305C4#1062285812yes—
306C2—41no—
307C2—84no—
308C2—1762no—
309C2C2×#1062285412yes—
310C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3548C2
socleC22×C11C2×#120
hypercenter#3548D11
hypocenterC11#19075
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13079069C2semidirect
2. #13078992C2semidirect
3. #13067909C2semidirect
4. #13067211C2semidirect
5. #13067208C2semidirect
6. C11×#3548C2semidirect
7. C11×#562C22semidirect
25. #10622181C22semidirect
26. #10622178C22semidirect
108. #3548D11semidirect
143. #562C2×D11semidirect
262. C11#19075semidirect

Maximal subgroups

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

subgroupindex
#130790692
#130789922
#130679092
#130672112
#130672082
C11×#35482
#1907511