Finite Group Databasebeta

← #14664889

Subgroups — #14664889

Order 2816.

390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#10622729C211yesmaximal, characteristic
2#13068654C211yesmaximal, characteristic
3#13066635C214yesmaximal, complemented
4C11×#2112C211yesmaximal, characteristic
5C23×C8×C11C2211yescharacteristic
6C2×#66977—21no—
7C22×Dic44C411yescharacteristic
8C2×C11×M32—21no—
9#10622820—21no—
10#10622729—21no—
11#10622729—21no—
12#10622729C412yes—
13#10622729C2212yes—
14C2×#66883—21no—
15C2×#66882C411yescharacteristic
16C2×#66880—21no—
17C11×C22⋊C16—21no—
18C11×C22⋊C16C2212yes—
19#10622190C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C22×C8×C11—42no—
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11C2×C411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C2×C22⋊Dic11—41no—
30C2×C4⋊Dic11—21no—
31#66977—22no—
32#66977—22no—
33#66977—41no—
34#66977—41no—
35C2×Dic11⋊C4—41no—
36C2×#4318—22no—
37C2×Dic44—21no—
38C2×Dic44—42no—
39C2×Dic44C2×C412yes—
40C11×M32—42no—
41C2×C11×C16—22no—
42C22⋊(C11⋊C8)—41no—
43C22⋊(C11⋊C8)—41no—
44#66883—42no—
45#66882—21no—
46#66882C2×C412yes—
47#66880—22no—
48#66880—22no—
49#11896—111nomaximal, Sylow
50C24×C11SD1611yescharacteristic
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C22⋊C411yescharacteristic
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11D811yescharacteristic
56C22×C4×C11D811yescharacteristic
57C22×C4×C11SD1611yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—41no—
60C22×Dic11—41no—
61C2×Dic22—22no—
62C2×Dic22—42no—
63C2×Dic22—42no—
64C2×Dic22—41no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—22no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11C22⋊C411yescharacteristic
72C2×C8×C11C22⋊C411yescharacteristic
73C2×C8×C11C22×C411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C22⋊Dic11—42no—
76C22⋊Dic11—42no—
77C4⋊Dic11—22no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80Dic11⋊C4—42no—
81#4318—42no—
82#4318—42no—
83C2×C11⋊C8—42no—
84Dic44—42no—
85Dic44—42no—
86C11×C16—42no—
87C2×#467—111no—
88#2112D1111yescharacteristic
89#1810—111no—
90#1350—114no—
91C23×C11—22no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11#10211yescharacteristic
95C23×C11#10211yescharacteristic
96C23×C11C2×SD1611yescharacteristic
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11#10211yescharacteristic
107C2×C4×C11#10211yescharacteristic
108C2×C4×C11C2×C22⋊C411yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—82no—
113C2×Dic11—82no—
114Dic22—42no—
115Dic22—42no—
116Dic22—82no—
117C8×C11—21no—
118C8×C11—21no—
119C8×C11—21no—
120C8×C11#9912yes—
121C11⋊C8—82no—
122C22×Q16—111no—
123C23×C8C2×D1111yescharacteristic
124C2×C22⋊Q8—221no—
125C2×M32—21no—
126#467—112no—
127#467—112no—
128#467—221no—
129#467—221no—
130C2×#108—221no—
131C2×#107—111no—
132C2×#103—221no—
133#407—221no—
134C22⋊C16—21no—
135C22⋊C16C2×D1112yes—
136#341—112no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—44no—
146C22×C11#36212yes—
147C22×C11C2×#10211yescharacteristic
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11C2×#9911yescharacteristic
152C4×C11#42111yescharacteristic
153Dic11—82no—
154Dic11—82no—
155C22×Q8—221no—
156C23×C4D4411yescharacteristic
157C2×Q16—112no—
158C2×Q16—221no—
159C2×Q16—442no—
160C2×M16—222no—
161C22×C8—42no—
162C22×C8C4×D1111yescharacteristic
163C22×C8C4×D1111yescharacteristic
164C22×C8D4411yescharacteristic
165C22×C8C22⋊D1111yescharacteristic
166C22×C8C22⋊D1111yescharacteristic
167C22×C8C22×D1111yescharacteristic
168C22⋊Q8—222no—
169C22⋊Q8—222no—
170C22⋊Q8—441no—
171C22⋊Q8—441no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—441no—
174C2×C22⋊C4—441no—
175M32—42no—
176C2×C16—22no—
177#108—442no—
178#107—112no—
179#107—221no—
180#103—222no—
181#103—222no—
182C22⋊C8—441no—
183C22⋊C8—441no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11—41no—
187C2×C11#151911yescharacteristic
188C2×C11#214311yescharacteristic
189C2×C11C2×#36211yescharacteristic
190C24#431411yescharacteristic
191C2×Q8—222no—
192C2×Q8—442no—
193C2×Q8—442no—
194C2×Q8—441no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—441no—
198C22×C4—441no—
199C22×C4#431411yescharacteristic
200C22×C4D8811yescharacteristic
201C22×C4D8811yescharacteristic
202C22×C4(C2×D11)⋊C411yescharacteristic
203C22×C4(C2×D11)⋊C411yescharacteristic
204C22×C4C2×D4411yescharacteristic
205Q16—442no—
206Q16—442no—
207M16—442no—
208M16—442no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—442no—
216C2×C8(C2×D11)⋊C411yescharacteristic
217C2×C8(C2×D11)⋊C411yescharacteristic
218C2×C8C2×C4×D1111yescharacteristic
219C2×C8C2×C22⋊D1111yescharacteristic
220C4⋊C4—222no—
221C4⋊C4—441no—
222C4⋊C4—442no—
223C4⋊C4—442no—
224C22⋊C4—442no—
225C22⋊C4—442no—
226C16—42no—
227C11#1189611yescharacteristic, complemented, Sylow
228C23—22no—
229C23—41no—
230C23—41no—
231C23#6688511yescharacteristic
232C23#6688511yescharacteristic
233C23C2×#431411yescharacteristic
234Q8—442no—
235Q8—442no—
236Q8—882no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—882no—
249C2×C4—882no—
250C2×C4#6688511yescharacteristic
251C2×C4#6688511yescharacteristic
252C2×C4C2×D8811yescharacteristic
253C2×C4C2×(C2×D11)⋊C411yescharacteristic
254C8—21no—
255C8—21no—
256C8—21no—
257C8—882no—
258C8#6687012yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22#1062215512yes—
269C22C2×#6688511yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—882no—
274C4—882no—
275C4C2×#6687011yescharacteristic
276C4#1062275211yescharacteristic
277C2—22no—
278C2—41no—
279C2—41no—
280C2#1306718511yescharacteristic
281C2#1307034511yescharacteristic
282C2C2×#1062215511yescharacteristic
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2112C2
socleC22×C11C2×#102
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenter#2112D11
hypocenterC11#11896
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
3. #13066635C2semidirect
227. C11#11896semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
#130686542
#130666352
C11×#21122
#1189611