Finite Group Databasebeta

← #14666765

Subgroups — #14666765

Order 2816.

558 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073532C211yesmaximal, characteristic
2#13067556C212yesmaximal, complemented
3#13066618C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2060C211yesmaximal, characteristic, complemented
6C11×#544C2211yescharacteristic
7C2×#66948—22no—
8C2×C4×D44—21no—
9C11×#428—21no—
10C11×#384C2211yescharacteristic
11#10622659—22no—
12#10622604—21no—
13#10622604C2212yes—
14#10622600—22no—
15C11×#343C2211yescharacteristic
16C11×#339—21no—
17#10622176—22no—
18#10622166C2212yes—
19C22×D44—21no—
20C22×D44—21no—
21C22×D44D412yes—
22C22×C4×D11—22no—
23C2×C11×M16—21no—
24C11×C4⋊Q8—41no—
25C11×#125—41no—
26C11×C22⋊Q8—22no—
27C11×#117—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×#4325—42no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11—21no—
37#66948—48no—
38C4×D44—42no—
39C4×D44—42no—
40C11×#107—41no—
41C11×#106—41no—
42C11⋊#95—21no—
43C11⋊#95D412yes—
44C22⋊(C11⋊C8)—22no—
45#66873—42no—
46#12246—111nomaximal, Sylow
47C23×D11—22no—
48C2×Q8×C11—22no—
49C22×C4×C11—21no—
50C22×C4×C11—21no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C22×Dic11—22no—
54C2×D44—24no—
55C2×D44—42no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—44no—
59C2×D44—44no—
60C2×D44—81no—
61C2×C4×D11—44no—
62C2×C4×D11—44no—
63C2×C4×D11—44no—
64C11×M16—22no—
65C11×M16—41no—
66C2×C8×C11—41no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—44no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C22⋊C4—41no—
75C42×C11—21no—
76C42×C11—41no—
77C42×C11SD1612yescomplemented
78#4325—84no—
79(C2×D11)⋊C4—44no—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4—42no—
82(C2×D11)⋊C4—42no—
83C4⋊Dic11—42no—
84C2×C11⋊C8—42no—
85#2537—111no—
86#2060D1111yescharacteristic, complemented
87#1599—112no—
88#1345—112no—
89#1325—111no—
90C23×C11#12011yescharacteristic
91C22×D11—24no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98Q8×C11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11C2×SD1611yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115D44—48no—
116D44—44no—
117D44—82no—
118D44—84no—
119C4×D11—88no—
120C8×C11—42no—
121C11⋊C8—82no—
122#544C2×D1111yescharacteristic
123C2×#121—222no—
124C2×C4×D4—221no—
125#450—222no—
126#428—21no—
127#394—112no—
128#394—221no—
129#384C2×D1111yescharacteristic
130#380—222no—
131#343C2×D1111yescharacteristic
132#339—21no—
133#328—222no—
134#324—112no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11#45011yescharacteristic
138C22×C11#45611yescharacteristic
139C22×C11B(4,𝔽2)11yescharacteristic
140C2×D11—44no—
141C2×D11—44no—
142C2×D11—44no—
143C2×D11—82no—
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C4×C11—24no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—42no—
151C4×C11—81no—
152C4×C11—81no—
153C4×C11—81no—
154Dic11—82no—
155C22×D4—112no—
156C22×D4—221no—
157C22×D4—221no—
158C23×C4—222no—
159C2×SD16—442no—
160C2×M16—21no—
161C4⋊Q8—41no—
162#125—41no—
163C22⋊Q8—22no—
164#121—448no—
165C4×D4—442no—
166C4×D4—442no—
167#117—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4C22⋊D1111yescharacteristic
171C2×C4⋊C4C22×D1111yescharacteristic
172C2×C22⋊C4—222no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4—222no—
175C2×C42C22⋊D1111yescharacteristic
176#107—41no—
177#106—41no—
178#102—442no—
179C22⋊C8—222no—
180#95—112no—
181#95—221no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11#160411yescharacteristic
185C2×C11#219611yescharacteristic
186C2×C11#220411yescharacteristic
187D11—84no—
188C24—222no—
189C2×Q8—22no—
190C2×D4—224no—
191C2×D4—442no—
192C2×D4—442no—
193C2×D4—442no—
194C2×D4—444no—
195C2×D4—444no—
196C2×D4—881no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—222no—
200C22×C4—444no—
201C22×C4—444no—
202C22×C4—444no—
203C22×C4D4×D1112yes—
204C22×C4C2×C22⋊D1111yescharacteristic
205SD16—884no—
206M16—22no—
207M16—41no—
208C2×C8—41no—
209C2×C8—442no—
210C4⋊C4—22no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—44no—
216C4⋊C4—42no—
217C4⋊C4—442no—
218C22⋊C4—41no—
219C22⋊C4—444no—
220C22⋊C4—444no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C42—21no—
224C42—41no—
225C42#432512yescomplemented
226C11#1224611yescharacteristic, complemented, Sylow
227C23—224no—
228C23—442no—
229C23—442no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23—442no—
234C23#6699011yescharacteristic
235Q8—82no—
236D4—448no—
237D4—444no—
238D4—882no—
239D4—884no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—888no—
255C2×C4C2×#432511yescharacteristic
256C2×C4#6700211yescharacteristic
257C8—42no—
258C8—882no—
259C22—21no—
260C22—21no—
261C22—444no—
262C22—444no—
263C22—444no—
264C22—882no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22#1062264511yescharacteristic
269C22#1062265911yescharacteristic
270C22#1062270811yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—81no—
276C4—81no—
277C4—81no—
278C4—882no—
279C2—21no—
280C2—21no—
281C2—884no—
282C2#1306758411yescharacteristic
283C2#1307059911yescharacteristic
284C2#1307064111yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2060C2
socleC22×C11B(4,𝔽2)
prime radical#13073532C2
hypercenter#2060D11
hypocenterC11#12246
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
2. #13067556C2semidirect
3. #13066618C2semidirect
4. #13066562C2semidirect
5. C11×#2060C2semidirect
77. C42×C11SD16semidirect
86. #2060D11semidirect
225. C42#4325semidirect
226. C11#12246semidirect

Maximal subgroups

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

subgroupindex
#130735322
#130675562
#130666182
#130665622
C11×#20602
#1224611