Finite Group Databasebeta

← #14644423

Subgroups — #14644423

Order 2816.

562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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#13071080C211yesmaximal, characteristic
2#13068362C211yesmaximal, characteristic, complemented
3C2×#10622121C212yesmaximal
4#13066455C212yesmaximal, complemented
5C11×#1767C211yesmaximal, characteristic, complemented
6C2×C4×D44C2211yescharacteristic
7C2×#66925—21no—
8C2×C11×C4⋊C8C2212yes—
9C2×C11×#97—21no—
10C43×C11C2211yescharacteristic
11#10622553—22no—
12#10622552C412yes—
13C4×(C2×D11)⋊C4—21no—
14C4×C4⋊Dic11C2211yescharacteristic
15#10622541C412yes—
16C2×C4×C11⋊C8C2212yes—
17C11×#336—21no—
18#10622162—22no—
19#10622121C418yescomplemented
20C22×D44C2×C411yescharacteristic
21C22×C4×D11—21no—
22C22×C8×C11—22no—
23C2×C42×C11C2×C412yes—
24C2×C42×C11D412yes—
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11C2311yescharacteristic
28C2×(C2×D11)⋊C4—21no—
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31C2×C4⋊Dic11C2×C412yes—
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×Dic11⋊C4—22no—
34C2×C4×Dic11—21no—
35C22×C11⋊C8—22no—
36C4×D44—22no—
37C4×D44C2×C414yes—
38#66925—44no—
39C11×C4⋊C8—22no—
40C11×C4⋊C8C2×C414yes—
41C11×#97—42no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C4×C11⋊C8—22no—
45C4×C11⋊C8C2×C414yes—
46#8179—111nomaximal, Sylow
47C23×D11—21no—
48C22×C4×C11C22⋊C412yes—
49C22×C4×C11C22⋊C412yes—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×Dic11—21no—
54C22×Dic11—22no—
55C2×D44—21no—
56C2×D44—24no—
57C2×D44C4212yes—
58C2×C4×D11—24no—
59C2×C4×D11—42no—
60C2×C4×D11—41no—
61C2×C4×D11—41no—
62C2×C8×C11—24no—
63C2×C8×C11—42no—
64C2×C8×C11—42no—
65C42×C11—24no—
66C42×C11—21no—
67C42×C11—22no—
68C42×C11—21no—
69C42×C11—42no—
70C42×C11C22×C412yes—
71C42×C11#4112yes—
72(C2×D11)⋊C4—24no—
73(C2×D11)⋊C4—44no—
74(C2×D11)⋊C4—44no—
75C4⋊Dic11—21no—
76C4⋊Dic11—24no—
77C4⋊Dic11C4212yes—
78Dic11⋊C4—44no—
79C4×Dic11—42no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—44no—
82#2293—111no—
83#1767D1111yescharacteristic, complemented
84#1744—111no—
85C2×D4⋊C8—112no—
86#1279—112no—
87C23×C11C2×C22⋊C411yescharacteristic
88C22×D11—22no—
89C22×D11—42no—
90C22×D11—41no—
91C22×D11—41no—
92C22×D11—42no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11C2×C4211yescharacteristic
101C2×C4×C11#11711yescharacteristic
102C2×C4×C11C4×D412yes—
103C2×C4×C11C4×D412yes—
104C2×C4×C11#13114yes—
105C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×C4×C11#13711yescharacteristic
108C2×Dic11—22no—
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114D44—24no—
115D44—42no—
116C4×D11—44no—
117C4×D11—44no—
118C8×C11—44no—
119C11⋊C8—44no—
120C2×C4×D4—111no—
121C2×#117—221no—
122C2×C4⋊C8C2×D1112yes—
123C2×#97—21no—
124C2×C4×C8—112no—
125#390—112no—
126#389—112no—
127#388—222no—
128C4×C4⋊C4—111no—
129C4×C22⋊C4—221no—
130C43C2×D1111yescharacteristic
131#336—21no—
132#336—222no—
133D4⋊C8—118no—
134C22×C11C4×C22⋊C411yescharacteristic
135C22×C11#40812yes—
136C22×C11#41711yescharacteristic
137C22×C11#41811yescharacteristic
138C22×C11#42112yes—
139C2×D11—42no—
140C2×D11—42no—
141C2×D11—42no—
142C2×D11—82no—
143C2×D11—82no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11#40512yes—
148C4×C11#43312yes—
149C4×C11#44012yes—
150C4×C11#44212yes—
151Dic11—42no—
152Dic11—82no—
153C22×D4—111no—
154C23×C4—221no—
155C22×C8—22no—
156C22×C8—222no—
157C4×D4—114no—
158C4×D4—222no—
159#117—444no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4—222no—
163C2×C22⋊C4—221no—
164C2×C22⋊C4—222no—
165C2×C22⋊C4—222no—
166C2×C42—221no—
167C2×C42C4×D1112yes—
168C2×C42D4412yes—
169C2×C42C22⋊D1111yescharacteristic
170C2×C42C22⋊D1111yescharacteristic
171C2×C42C22×D1111yescharacteristic
172C4⋊C8—22no—
173C4⋊C8C4×D1114yes—
174#97—42no—
175C4×C8—114no—
176C4×C8—222no—
177#95—222no—
178#95—221no—
179C2×C11#149512yes—
180C2×C11#149612yes—
181C2×C11#175011yescharacteristic
182C2×C11#175911yescharacteristic
183C2×C11#176211yescharacteristic
184D11—82no—
185C24—221no—
186C2×D4—112no—
187C2×D4—221no—
188C2×D4—224no—
189C22×C4—221no—
190C22×C4—224no—
191C22×C4—222no—
192C22×C4—441no—
193C22×C4—441no—
194C22×C4—442no—
195C22×C4(C2×D11)⋊C412yes—
196C22×C4(C2×D11)⋊C412yes—
197C22×C4C2×C4×D1111yescharacteristic
198C22×C4C2×D4411yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200C2×C8—24no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—224no—
204C2×C8—444no—
205C4⋊C4—112no—
206C4⋊C4—221no—
207C4⋊C4—224no—
208C4⋊C4—444no—
209C22⋊C4—224no—
210C22⋊C4—444no—
211C22⋊C4—444no—
212C42—24no—
213C42—21no—
214C42—21no—
215C42—22no—
216C42—42no—
217C42—442no—
218C42C2×C4×D1112yes—
219C42#433912yes—
220C11#817911yescharacteristic, complemented, Sylow
221C23—222no—
222C23—442no—
223C23—442no—
224C23—441no—
225C23—441no—
226C23C2×(C2×D11)⋊C411yescharacteristic
227D4—224no—
228D4—442no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—222no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—444no—
240C2×C4—444no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4C42×D1111yescharacteristic
245C2×C4#6692511yescharacteristic
246C2×C4C4×D4412yes—
247C2×C4#6696014yes—
248C2×C4C4×C22⋊D1112yes—
249C2×C4#6698511yescharacteristic
250C2×C4#6699511yescharacteristic
251C2×C4#6700212yes—
252C8—44no—
253C8—444no—
254C22—442no—
255C22—442no—
256C22—442no—
257C22—882no—
258C22—882no—
259C22C4×(C2×D11)⋊C411yescharacteristic
260C22#1062257911yescharacteristic
261C22#1062261411yescharacteristic
262C22#1062274212yes—
263C22#1062275212yes—
264C4—22no—
265C4—42no—
266C4—42no—
267C4—442no—
268C4—882no—
269C4#1062232112yes—
270C4#1062232212yes—
271C4#1062262712yes—
272C4#1062263912yes—
273C2—882no—
274C2#1306707912yes—
275C2#1306708412yes—
276C2#1306838511yescharacteristic
277C2#1306842911yescharacteristic
278C2#1306844411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1767C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1767D11
hypocenterC11#8179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #13068362C2semidirect
4. #13066455C2semidirect
5. C11×#1767C2semidirect
19. #10622121C4semidirect
83. #1767D11semidirect
220. C11#8179semidirect

Maximal subgroups

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

subgroupindex
#130710802
#130683622
C2×#106221212
#130664552
C11×#17672
#817911