Finite Group Databasebeta

← #14735692

Subgroups — #14735692

Order 2816.

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

normal subgroups only

This group has 920 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#13079627C212yesmaximal, complemented
2#13079138C211yesmaximal, characteristic, complemented
3#13067933C218yesmaximal, complemented
4#13067254C211yesmaximal, characteristic, complemented
5#13067227C212yesmaximal, complemented
6C11×#3548C211yesmaximal, characteristic
7C11×#562C2214yes—
8C11×#554—22no—
9C11×#550—22no—
10C11×#547—22no—
11C11×#540—22no—
12C11×#537—24no—
13C11×#533C2211yescharacteristic
14C11×#532C2212yes—
15#10623001C2211yescharacteristic
16#10622852—24no—
17#10622703—22no—
18#10622693—22no—
19#10622688—22no—
20#10622678C2214yes—
21#10622673C2214yes—
22#10622668C2214yes—
23#10622611—22no—
24#10622539C2212yes—
25C2×#66867C2211yescharacteristic
26#10622181C2214yes—
27#10622178C2218yes—
28C2×C11×#41—24no—
29C2×C11×#41D414yes—
30C11×C4⋊Q8D412yes—
31C11×C4⋊Q8D412yes—
32C11×#127—22no—
33C11×#127D412yes—
34C11×#125—22no—
35C11×#125C2312yes—
36C11×#124C2314yes—
37C11×#123—28no—
38C11×C22⋊Q8—24no—
39C11×C22⋊Q8—28no—
40C11×C22⋊Q8—22no—
41C11×#121—28no—
42C11×#121—24no—
43C11×#121—28no—
44C11×#121—22no—
45C11×#121—22no—
46C4×Q8×C11—22no—
47C4×D4×C11—24no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C11×#117D412yes—
51C2×C11×C4⋊C4—24no—
52C2×C42×C11C2311yescharacteristic
53C2×#4326—24no—
54C2×#4324—24no—
55#66979—21no—
56#66977—22no—
57C22×C11⋊C8—21no—
58#66923—21no—
59#66922C2312yes—
60C4×Dic22—22no—
61#66899—24no—
62#66896—24no—
63C22⋊(C11⋊C8)—22no—
64#66872—24no—
65#66871—24no—
66C4⋊(C11⋊C8)—22no—
67#66867—21no—
68#66867C2312yes—
69#66867C2314yes—
70#19065—111nomaximal, Sylow
71C11×#41—84no—
72C11×#41—88no—
73C2×Q8×C11—22no—
74C2×Q8×C11C2×D414yes—
75C2×D4×C11—28no—
76C2×D4×C11—24no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11C2×D414yes—
80C22×C4×C11—28no—
81C22×C4×C11—24no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C2×Dic22—22no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4C2×D414yes—
91C11×C22⋊C4—28no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—24no—
94C11×C22⋊C4—24no—
95C42×C11—22no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D412yes—
98C42×C11C2411yescharacteristic
99C22⋊Dic11—41no—
100#4326—84no—
101#4324—84no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104Dic11⋊C4—42no—
105C4×Dic11—41no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—24no—
109#3548D1111yescharacteristic
110#3216—112no—
111#3162—111no—
112#1661—118no—
113#1537—111no—
114#1530—112no—
115C23×C11—24no—
116C23×C11#12011yescharacteristic
117Q8×C11—44no—
118Q8×C11—44no—
119D4×C11—44no—
120D4×C11—44no—
121D4×C11—44no—
122D4×C11—84no—
123D4×C11—88no—
124C2×C4×C11—22no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—42no—
128C2×C4×C11—48no—
129C2×C4×C11—88no—
130C2×C4×C11#12012yes—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11C22×D411yescharacteristic
133C2×C4×C11C22×D412yes—
134C2×Dic11—42no—
135Dic22—42no—
136Dic22—42no—
137C11⋊C8—24no—
138C11⋊C8—44no—
139#562C2×D1114yes—
140#554—22no—
141#550—22no—
142#547—22no—
143#540—22no—
144#537—24no—
145#533—111no—
146#533C2×D1111yescharacteristic
147#532C2×D1112yes—
148#501—114no—
149#501—222no—
150#497—114no—
151#489—114no—
152#462—222no—
153#460—222no—
154#452—224no—
155#432—112no—
156#427—222no—
157C2×#97—111no—
158#330—114no—
159#329—118no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—44no—
163C22×C11—44no—
164C22×C11—44no—
165C22×C11C2×#12011yescharacteristic
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—44no—
170C4×C11—44no—
171C4×C11#45612yes—
172Dic11—82no—
173C2×#41—24no—
174C2×#41C22⋊D1114yes—
175C2×Q16—224no—
176C2×SD16—224no—
177C22×C8—221no—
178C4⋊Q8—112no—
179C4⋊Q8C22⋊D1112yes—
180C4⋊Q8C22⋊D1112yes—
181#127—22no—
182#127C22⋊D1112yes—
183#125—22no—
184#125—221no—
185#125C22×D1112yes—
186#124C22×D1114yes—
187#123—28no—
188C22⋊Q8—24no—
189C22⋊Q8—28no—
190C22⋊Q8—22no—
191C22⋊Q8—222no—
192#121—28no—
193#121—24no—
194#121—28no—
195#121—22no—
196#121—22no—
197C4×Q8—22no—
198C4×Q8—222no—
199C4×D4—24no—
200C4×D4—22no—
201C4×D4—22no—
202#117—221no—
203#117C22⋊D1112yes—
204C2×C4⋊C4—24no—
205C2×C42C22×D1111yescharacteristic
206#107—224no—
207#106—224no—
208C4⋊C8—222no—
209#103—224no—
210#102—224no—
211C22⋊C8—222no—
212#97—112no—
213#97—114no—
214#97—221no—
215C2×C11—41no—
216C2×C11—84no—
217C2×C11C2×#45611yescharacteristic
218C2×C11#301912yes—
219#41—84no—
220#41—88no—
221C2×Q8—22no—
222C2×Q8—222no—
223C2×Q8C2×C22⋊D1114yes—
224C2×D4—28no—
225C2×D4—24no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4C2×C22⋊D1114yes—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4C2×C22⋊D1111yescharacteristic
232C22×C4C2×C22⋊D1112yes—
233Q16—884no—
234SD16—884no—
235C2×C8—224no—
236C2×C8—222no—
237C2×C8—224no—
238C4⋊C4—28no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—222no—
244C4⋊C4—222no—
245C4⋊C4—442no—
246C4⋊C4C2×C22⋊D1114yes—
247C22⋊C4—28no—
248C22⋊C4—22no—
249C22⋊C4—24no—
250C22⋊C4—24no—
251C22⋊C4—441no—
252C42—22no—
253C42—441no—
254C42C2×C22⋊D1111yescharacteristic
255C42C2×C22⋊D1112yes—
256C42C23×D1111yescharacteristic
257C11#1906511yescharacteristic, complemented, Sylow
258C23—24no—
259C23#6700611yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—442no—
263Q8—442no—
264D4—44no—
265D4—44no—
266D4—44no—
267D4—84no—
268D4—88no—
269C2×C4—22no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—48no—
274C2×C4—88no—
275C2×C4—442no—
276C2×C4#6700612yes—
277C2×C4#6700611yescharacteristic
278C2×C4C22×C22⋊D1111yescharacteristic
279C2×C4C22×C22⋊D1112yes—
280C8—224no—
281C8—444no—
282C22—21no—
283C22—22no—
284C22—44no—
285C22—44no—
286C22—44no—
287C22C2×#6700611yescharacteristic
288C4—21no—
289C4—22no—
290C4—22no—
291C4—44no—
292C4—44no—
293C4—882no—
294C4#1062285912yes—
295C2—41no—
296C2—84no—
297C2C2×#1062285911yescharacteristic
298C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3548C2
socleC22×C11C2×#120
hypercenter#3548D11
hypocenterC11#19065
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. #13079627C2semidirect
2. #13079138C2semidirect
3. #13067933C2semidirect
4. #13067254C2semidirect
5. #13067227C2semidirect
257. C11#19065semidirect

Maximal subgroups

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

subgroupindex
#130796272
#130791382
#130679332
#130672542
#130672272
C11×#35482
#1906511