Finite Group Databasebeta

← #14666516

Subgroups — #14666516

Order 2816.

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

normal subgroups only

This group has 500 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#13076640C211yesmaximal, characteristic
2#13069783C211yesmaximal, characteristic, complemented
3#13067541C212yesmaximal, complemented
4#13066614C212yesmaximal, complemented
5C11×#1317C211yesmaximal, characteristic, complemented
6C2×#66983—21no—
7#10623014C2211yescharacteristic
8C11×#381C2211yescharacteristic
9#10622824—21no—
10#10622573—21no—
11#10622573C2212yes—
12#10622344—22no—
13#10622287—22no—
14#10622284—22no—
15C11×#323C2212yes—
16#10622165—21no—
17#10622164C2211yescharacteristic
18#10622105—22no—
19C23×C4×C11D411yescharacteristic
20C22×C22⋊D11—22no—
21C22×D44—21no—
22C22×D44—21no—
23C22×D44D412yes—
24C2×C11×C22⋊C4D411yescharacteristic
25C2×C11×C22⋊C4C2311yescharacteristic
26C2×C22⋊Dic11—21no—
27C2×C22⋊Dic11—21no—
28#66983—42no—
29#66983—42no—
30C2×(C2×D11)⋊C4—22no—
31C2×(C2×D11)⋊C4—22no—
32C2×(C2×D11)⋊C4—22no—
33C2×C4⋊Dic11—21no—
34#66977—22no—
35C2×#4314—42no—
36#66931—42no—
37C11×C22⋊C8—22no—
38C11×#95—22no—
39C11⋊#95—21no—
40C11⋊#95—42no—
41C11⋊#95D412yes—
42#66885—42no—
43#12206—111nomaximal, Sylow
44C24×C11C2×D411yescharacteristic
45C23×D11—22no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11—41no—
50C22×C4×C11—41no—
51C22×C4×C11SD1612yescomplemented
52C22×C4×C11C2×D412yes—
53C2×C22⋊D11—42no—
54C2×C22⋊D11—42no—
55C2×C22⋊D11—82no—
56C2×C22⋊D11—82no—
57C22×Dic11—22no—
58C22×Dic11—22no—
59C22×Dic11—41no—
60C2×D44—42no—
61C2×D44—42no—
62C2×D44—82no—
63C2×D44—81no—
64C2×D44—81no—
65C2×D44—82no—
66C2×D44—81no—
67C2×Dic22—22no—
68C2×C8×C11—42no—
69C11×C22⋊C4—41no—
70C11×C22⋊C4—41no—
71C22⋊Dic11—41no—
72C22⋊Dic11—41no—
73C22⋊Dic11—41no—
74C22⋊Dic11—41no—
75(C2×D11)⋊C4—44no—
76(C2×D11)⋊C4—82no—
77(C2×D11)⋊C4—82no—
78C4⋊Dic11—22no—
79C4⋊Dic11—42no—
80Dic11⋊C4—42no—
81#4314—84no—
82#2815—111no—
83#2030—111no—
84#1596—112no—
85#1343—112no—
86#1317D1111yescharacteristic, complemented
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—42no—
90C23×C11#12011yescharacteristic
91C23×C11C2×SD1611yescharacteristic
92C23×C11AGL(1,ℤ/8)11yescharacteristic
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C22×D11—42no—
99C22×D11—42no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—41no—
108C2×C4×C11—81no—
109C22⋊D11—84no—
110C22⋊D11—84no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—82no—
116C2×Dic11—81no—
117C2×Dic11—82no—
118D44—44no—
119D44—82no—
120D44—84no—
121D44—84no—
122Dic22—82no—
123C8×C11—82no—
124#543—111no—
125C2×#121—221no—
126#450—222no—
127#397—222no—
128#392—112no—
129#392—222no—
130#392—221no—
131#381—221no—
132#381C2×D1111yescharacteristic
133#342—111no—
134#342—221no—
135#328—222no—
136#323C2×D1112yes—
137C22×C11—22no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—42no—
143C22×C11—81no—
144C22×C11#45011yescharacteristic
145C22×C11#45511yescharacteristic
146C22×C11B(4,𝔽2)11yescharacteristic
147C2×D11—82no—
148C2×D11—82no—
149C2×D11—82no—
150C2×D11—82no—
151C2×D11—82no—
152C2×D11—82no—
153C2×D11—82no—
154C4×C11—42no—
155C4×C11—42no—
156C4×C11—81no—
157Dic11—82no—
158Dic11—82no—
159Dic11—161no—
160C22×D4—112no—
161C22×D4—221no—
162C22×D4—221no—
163C22×D4—222no—
164C23×C4D4411yescharacteristic
165C2×SD16—442no—
166C22⋊Q8—222no—
167C22⋊Q8—442no—
168#121—442no—
169#121—442no—
170C2×C4⋊C4—221no—
171C2×C22⋊C4—222no—
172C2×C22⋊C4—221no—
173C2×C22⋊C4—221no—
174C2×C22⋊C4—222no—
175C2×C22⋊C4—222no—
176C2×C22⋊C4D4411yescharacteristic
177C2×C22⋊C4C22×D1111yescharacteristic
178#102—442no—
179C22⋊C8—22no—
180#95—22no—
181#95—112no—
182#95—221no—
183#95—442no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11—41no—
187C2×C11—41no—
188C2×C11#160111yescharacteristic
189C2×C11#220012yes—
190D11—162no—
191C24—222no—
192C24C2×D4411yescharacteristic
193C2×Q8—222no—
194C2×D4—442no—
195C2×D4—442no—
196C2×D4—442no—
197C2×D4—442no—
198C2×D4—882no—
199C2×D4—881no—
200C2×D4—881no—
201C2×D4—882no—
202C2×D4—881no—
203C2×D4—882no—
204C2×D4—882no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—441no—
213C22×C4#431412yescomplemented
214C22×C4D4×D1112yes—
215SD16—884no—
216C2×C8—42no—
217C4⋊C4—222no—
218C4⋊C4—442no—
219C4⋊C4—442no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—444no—
223C22⋊C4—441no—
224C22⋊C4—441no—
225C22⋊C4—441no—
226C22⋊C4—441no—
227C22⋊C4—882no—
228C22⋊C4—882no—
229C11#1220611yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—42no—
233C23—442no—
234C23—442no—
235C23—442no—
236C23—442no—
237C23—442no—
238C23—442no—
239C23—442no—
240C23#6693511yescharacteristic
241C23C2×#431411yescharacteristic
242C23#6696111yescharacteristic
243Q8—882no—
244D4—444no—
245D4—882no—
246D4—884no—
247D4—884no—
248D4—884no—
249D4—884no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—442no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—882no—
264C2×C4—881no—
265C2×C4—882no—
266C8—82no—
267C22—22no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—81no—
274C22—882no—
275C22—882no—
276C22—882no—
277C22—882no—
278C22—882no—
279C22—882no—
280C22—882no—
281C22#1062234411yescharacteristic
282C22#1062235411yescharacteristic
283C22#1062235911yescharacteristic
284C4—42no—
285C4—42no—
286C4—81no—
287C4—882no—
288C4—882no—
289C4—1761no—
290C2—21no—
291C2—21no—
292C2—41no—
293C2—41no—
294C2—1762no—
295C2#1306757011yescharacteristic
296C2#1307062412yes—
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11B(4,𝔽2)
prime radical#13076640C2
hypercenter#1317D11
hypocenterC11#12206
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #13069783C2semidirect
3. #13067541C2semidirect
4. #13066614C2semidirect
5. C11×#1317C2semidirect
51. C22×C4×C11SD16semidirect
86. #1317D11semidirect
213. C22×C4#4314semidirect
229. C11#12206semidirect

Maximal subgroups

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

subgroupindex
#130766402
#130697832
#130675412
#130666142
C11×#13172
#1220611