Finite Group Databasebeta

← #14666768

Subgroups — #14666768

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#13069961C211yesmaximal, characteristic, complemented
3#13067558C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1325C211yesmaximal, characteristic, complemented
6C2×#66948—22no—
7#10623031C2211yescharacteristic
8C2×C4×D44—21no—
9C11×#384C2211yescharacteristic
10#10622604—21no—
11#10622604C2212yes—
12#10622600—22no—
13#10622577—21no—
14#10622344—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×D44—21no—
20C22×D44—21no—
21C22×D44D412yes—
22C22×C4×D11—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×(C2×D11)⋊C4—22no—
28C2×(C2×D11)⋊C4—22no—
29C2×(C2×D11)⋊C4—22no—
30#66979—21no—
31C2×C4⋊Dic11—21no—
32#66977—22no—
33C2×#4318—21no—
34C2×#4314—42no—
35#66948—48no—
36#66943—41no—
37#66941—41no—
38C4×D44—42no—
39C4×D44—42no—
40C11×C22⋊C8—22no—
41C11⋊#95—21no—
42C11⋊#95D412yes—
43#66885—42no—
44#66872—41no—
45#66871—41no—
46#12246—111nomaximal, Sylow
47C23×D11—22no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C2×D44—24no—
54C2×D44—42no—
55C2×D44—42no—
56C2×D44—42no—
57C2×D44—44no—
58C2×D44—44no—
59C2×D44—81no—
60C2×C4×D11—44no—
61C2×C4×D11—44no—
62C2×C4×D11—44no—
63C2×Dic22—22no—
64C2×C8×C11—42no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—44no—
67C11×C4⋊C4—41no—
68C42×C11—21no—
69C42×C11SD1612yescomplemented
70C22⋊Dic11—41no—
71(C2×D11)⋊C4—44no—
72(C2×D11)⋊C4—44no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77C4⋊Dic11—22no—
78C4⋊Dic11—42no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81#4318—22no—
82#4318—41no—
83C2×C11⋊C8—41no—
84#4314—84no—
85#2537—111no—
86#2060—111no—
87#1599—112no—
88#1345—112no—
89#1325D1111yescharacteristic, complemented
90C23×C11#12011yescharacteristic
91C22×D11—24no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11C2×SD1611yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114D44—48no—
115D44—44no—
116D44—82no—
117D44—84no—
118C4×D11—88no—
119Dic22—82no—
120C8×C11—82no—
121C11⋊C8—42no—
122#544—111no—
123C2×#121—222no—
124C2×C4×D4—221no—
125#450—222no—
126#428—221no—
127#394—112no—
128#394—221no—
129#384C2×D1111yescharacteristic
130#380—222no—
131#343—111no—
132#339—221no—
133#328—222no—
134#324C2×D1112yes—
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—
152Dic11—82no—
153Dic11—81no—
154Dic11—81no—
155C22×D4—112no—
156C22×D4—221no—
157C22×D4—221no—
158C23×C4—222no—
159C2×SD16—442no—
160C2×M16—221no—
161C4⋊Q8—441no—
162#125—441no—
163C22⋊Q8—222no—
164#121—448no—
165C4×D4—442no—
166C4×D4—442no—
167#117—221no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4D4411yescharacteristic
171C2×C4⋊C4C22×D1111yescharacteristic
172C2×C22⋊C4—222no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4—222no—
175C2×C42D4411yescharacteristic
176#107—441no—
177#106—441no—
178#102—442no—
179C22⋊C8—22no—
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—222no—
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×C4C2×D4411yescharacteristic
204C22×C4D4×D1112yes—
205SD16—884no—
206M16—222no—
207M16—441no—
208C2×C8—42no—
209C2×C8—441no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—44no—
213C4⋊C4—222no—
214C4⋊C4—221no—
215C4⋊C4—221no—
216C4⋊C4—442no—
217C4⋊C4—442no—
218C22⋊C4—444no—
219C22⋊C4—444no—
220C22⋊C4—441no—
221C22⋊C4—442no—
222C22⋊C4—442no—
223C42—21no—
224C42—441no—
225C42#431412yescomplemented
226C11#1224611yescharacteristic, complemented, Sylow
227C23—224no—
228C23—442no—
229C23—442no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23—442no—
234C23#6693511yescharacteristic
235Q8—882no—
236D4—448no—
237D4—444no—
238D4—882no—
239D4—884no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—442no—
250C2×C4—442no—
251C2×C4—442no—
252C2×C4—441no—
253C2×C4—441no—
254C2×C4—888no—
255C2×C4C2×#431411yescharacteristic
256C2×C4#6696111yescharacteristic
257C8—82no—
258C8—442no—
259C22—21no—
260C22—21no—
261C22—444no—
262C22—444no—
263C22—444no—
264C22—882no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22#1062234411yescharacteristic
269C22#1062235411yescharacteristic
270C22#1062236511yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—81no—
276C4—882no—
277C4—881no—
278C4—881no—
279C2—21no—
280C2—21no—
281C2—884no—
282C2#1306758711yescharacteristic
283C2#1307060211yescharacteristic
284C2#1307064411yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11B(4,𝔽2)
prime radical#13073532C2
hypercenter#1325D11
hypocenterC11#12246
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #13069961C2semidirect
3. #13067558C2semidirect
4. #13066620C2semidirect
5. C11×#1325C2semidirect
69. C42×C11SD16semidirect
89. #1325D11semidirect
225. C42#4314semidirect
226. C11#12246semidirect

Maximal subgroups

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

subgroupindex
#130735322
#130699612
#130675582
#130666202
C11×#13252
#1224611