Finite Group Databasebeta

← #14664856

Subgroups — #14664856

Order 2816.

412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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#13070227C211yesmaximal, characteristic
3#13066627C214yesmaximal, complemented
4C11×#1807C211yesmaximal, characteristic
5C23×C8×C11C2211yescharacteristic
6C2×#66977—21no—
7C22×Dic44C411yescharacteristic, complemented
8C2×C11×#106—21no—
9C11×#380—21no—
10#10622729—21no—
11#10622729—21no—
12#10622729C412yescomplemented
13#10622729C2212yes—
14C2×#66882C411yescharacteristic, complemented
15C2×#66880—21no—
16C2×#66876—21no—
17C11×#340C2212yes—
18C22⋊(C11⋊C16)—21no—
19C22⋊(C11⋊C16)C2212yes—
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×C11×C4⋊C4—22no—
30C2×C11×C22⋊C4—41no—
31C2×C22⋊Dic11—41no—
32C2×C4⋊Dic11—21no—
33#66977—22no—
34#66977—22no—
35#66977—41no—
36#66977—41no—
37C2×Dic11⋊C4—41no—
38C2×Dic44—21no—
39C2×Dic44—42no—
40C2×Dic44C2×C412yes—
41C11×#106—42no—
42C11×#95—41no—
43#66882—21no—
44#66882C2×C412yes—
45#66880—22no—
46#66880—22no—
47#66876—42no—
48C2×C11⋊C16—22no—
49#11889—111nomaximal, Sylow
50C24×C11D811yescharacteristic
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—42no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11D811yescharacteristic
57C22×C4×C11SD1611yescharacteristic
58C22×C4×C11SD1611yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—41no—
61C22×Dic11—41no—
62C2×Dic22—22no—
63C2×Dic22—42no—
64C2×Dic22—42no—
65C2×Dic22—41no—
66C2×C8×C11—22no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11C22⋊C411yescharacteristic
73C2×C8×C11C22⋊C411yescharacteristic
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C22⋊C4—82no—
79C22⋊Dic11—42no—
80C22⋊Dic11—42no—
81C4⋊Dic11—22no—
82C4⋊Dic11—41no—
83Dic11⋊C4—42no—
84Dic11⋊C4—42no—
85Dic44—42no—
86Dic44—42no—
87C11⋊C16—42no—
88C2×#467—111no—
89#2112—111no—
90#1807D1111yescharacteristic
91#1348—114no—
92C23×C11—22no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11#10211yescharacteristic
96C23×C11#10211yescharacteristic
97C23×C11C2×D811yescharacteristic
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11—82no—
110C2×C4×C11#10211yescharacteristic
111C2×C4×C11#10211yescharacteristic
112C2×C4×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11C2×SD1611yescharacteristic
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—82no—
117C2×Dic11—82no—
118Dic22—42no—
119Dic22—42no—
120Dic22—82no—
121C8×C11—21no—
122C8×C11—21no—
123C8×C11—21no—
124C8×C11#9912yes—
125C22×Q16—111no—
126C23×C8C2×D1111yescharacteristic
127C2×C22⋊Q8—221no—
128C2×M32—221no—
129#467—112no—
130#467—112no—
131#467—221no—
132#467—221no—
133C2×#107—111no—
134C2×#106—21no—
135C2×#103—221no—
136#380—21no—
137C22⋊C16—112no—
138C22⋊C16—221no—
139#340C2×D1112yes—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—44no—
148C22×C11#36012yes—
149C22×C11C2×#10211yescharacteristic
150C22×C11#51012yes—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—162no—
155C4×C11C2×#9911yescharacteristic
156C4×C11#42111yescharacteristic
157Dic11—82no—
158Dic11—82no—
159C22×Q8—221no—
160C23×C4C22⋊D1111yescharacteristic
161C2×Q16—112no—
162C2×Q16—221no—
163C2×Q16—442no—
164C22×C8—42no—
165C22×C8C4×D1111yescharacteristic
166C22×C8C4×D1111yescharacteristic
167C22×C8D4411yescharacteristic
168C22×C8D4411yescharacteristic
169C22×C8C22⋊D1111yescharacteristic
170C22×C8C22×D1111yescharacteristic
171C22⋊Q8—222no—
172C22⋊Q8—222no—
173C22⋊Q8—441no—
174C22⋊Q8—441no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—441no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—441no—
180M32—442no—
181C2×C16—222no—
182#107—112no—
183#107—221no—
184#106—42no—
185#103—222no—
186#103—222no—
187#95—41no—
188C2×C11—22no—
189C2×C11—22no—
190C2×C11—41no—
191C2×C11#151911yescharacteristic
192C2×C11#214111yescharacteristic
193C2×C11C2×#36011yescharacteristic
194C24#432311yescharacteristic
195C2×Q8—222no—
196C2×Q8—442no—
197C2×Q8—442no—
198C2×Q8—441no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—42no—
202C22×C4—441no—
203C22×C4—441no—
204C22×C4(C2×D11)⋊C411yescharacteristic
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4#432311yescharacteristic
207C22×C4#432511yescharacteristic
208C22×C4#432511yescharacteristic
209C22×C4C2×C22⋊D1111yescharacteristic
210Q16—442no—
211Q16—442no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8(C2×D11)⋊C411yescharacteristic
219C2×C8(C2×D11)⋊C411yescharacteristic
220C2×C8C2×C4×D1111yescharacteristic
221C2×C8C2×D4411yescharacteristic
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—222no—
225C4⋊C4—441no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C22⋊C4—82no—
229C22⋊C4—442no—
230C22⋊C4—442no—
231C16—442no—
232C11#1188911yescharacteristic, complemented, Sylow
233C23—22no—
234C23—22no—
235C23—41no—
236C23#6687311yescharacteristic
237C23#6687311yescharacteristic
238C23C2×#432311yescharacteristic
239Q8—442no—
240Q8—442no—
241Q8—882no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—882no—
257C2×C4—882no—
258C2×C4#6687311yescharacteristic
259C2×C4#6687311yescharacteristic
260C2×C4C2×(C2×D11)⋊C411yescharacteristic
261C2×C4C2×#432511yescharacteristic
262C8—21no—
263C8—21no—
264C8—21no—
265C8#6687012yes—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—44no—
274C22#1062212612yes—
275C22C2×#6687311yescharacteristic
276C22#1062280812yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—162no—
281C4—882no—
282C4—882no—
283C4C2×#6687011yescharacteristic
284C4#1062261811yescharacteristic
285C2—22no—
286C2—22no—
287C2—41no—
288C2#1306718311yescharacteristic
289C2#1307033511yescharacteristic
290C2C2×#1062212611yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1807C2
socleC22×C11C2×#102
prime radicalC24×C11D8
cosocleC22×C8×C11C23
hypercenter#1807D11
hypocenterC11#11889
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #1807

Complements

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

NH ≅ G/Ntype
3. #13066627C2semidirect
7. C22×Dic44C4semidirect
12. #10622729C4semidirect
14. C2×#66882C4semidirect
232. C11#11889semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
#130702272
#130666272
C11×#18072
#1188911