Finite Group Databasebeta

← #14664852

Subgroups — #14664852

Order 2816.

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

normal subgroups only

This group has 464 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×#10622728C211yesmaximal, characteristic
2#13070227C211yesmaximal, characteristic, complemented
3#13066624C214yesmaximal, complemented
4C11×#1807C211yesmaximal, characteristic, complemented
5C23×C8×C11C2211yescharacteristic
6C2×#66983—21no—
7C22×D88C411yescharacteristic, complemented
8C2×C11×#106—21no—
9C11×#380—21no—
10#10622728—21no—
11#10622728—21no—
12#10622728C412yescomplemented
13#10622728C2212yes—
14C2×#66885—21no—
15C2×#66882C411yescharacteristic, complemented
16C2×#66876—21no—
17C11×#340C2212yescomplemented
18C22⋊(C11⋊C16)—21no—
19C22⋊(C11⋊C16)C2212yescomplemented
20C23×C4×C11D411yescharacteristic
21C22×C22⋊D11—41no—
22C22×D44—21no—
23C22×C8×C11—42no—
24C22×C8×C11C2×C411yescharacteristic
25C22×C8×C11C2×C411yescharacteristic
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C2×C11×C4⋊C4—22no—
31C2×C11×C22⋊C4—41no—
32#66983—22no—
33#66983—22no—
34#66983—41no—
35#66983—41no—
36C2×(C2×D11)⋊C4—41no—
37C2×C4⋊Dic11—21no—
38C2×D88—21no—
39C2×D88—42no—
40C2×D88C2×C412yes—
41C11×#106—42no—
42C11×#95—41no—
43#66885—22no—
44#66885—22no—
45#66882—21no—
46#66882C2×C412yes—
47#66876—42no—
48C2×C11⋊C16—22no—
49#11888—111nomaximal, Sylow
50C24×C11D811yescharacteristic
51C23×D11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11—42no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11D811yescharacteristic
58C22×C4×C11SD1611yescharacteristic
59C22×C4×C11SD1611yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—42no—
62C2×C22⋊D11—42no—
63C2×C22⋊D11—84no—
64C22×Dic11—41no—
65C2×D44—22no—
66C2×D44—42no—
67C2×D44—42no—
68C2×D44—41no—
69C2×C8×C11—22no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11C22⋊C411yescharacteristic
76C2×C8×C11C22⋊C411yescharacteristic
77C2×C8×C11C22×C411yescharacteristic
78C2×C8×C11C2×D411yescharacteristic
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—82no—
82(C2×D11)⋊C4—42no—
83(C2×D11)⋊C4—42no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86D88—42no—
87D88—42no—
88C11⋊C16—42no—
89C2×#466—111no—
90#2112—111no—
91#1807D1111yescharacteristic, complemented
92#1347—114no—
93C23×C11—22no—
94C23×C11—22no—
95C23×C11—41no—
96C23×C11#10211yescharacteristic
97C23×C11#10211yescharacteristic
98C23×C11C2×D811yescharacteristic
99C22×D11—42no—
100C22×D11—82no—
101C22×D11—82no—
102C22×D11—82no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×C4×C11—82no—
115C2×C4×C11#10211yescharacteristic
116C2×C4×C11#10211yescharacteristic
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C22⋊D11—84no—
120C22⋊D11—84no—
121C2×Dic11—42no—
122C2×Dic11—82no—
123D44—42no—
124D44—42no—
125D44—82no—
126C8×C11—21no—
127C8×C11—21no—
128C8×C11—21no—
129C8×C11#9912yes—
130C22×D8—111no—
131C23×C8C2×D1111yescharacteristic
132C2×#121—221no—
133C2×M32—221no—
134#466—112no—
135#466—112no—
136#466—221no—
137#466—221no—
138C2×#107—111no—
139C2×#106—21no—
140C2×#102—221no—
141#380—21no—
142C22⋊C16—112no—
143C22⋊C16—221no—
144#340C2×D1112yescomplemented
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—44no—
153C22×C11#36012yes—
154C22×C11C2×#10211yescharacteristic
155C22×C11#50912yes—
156C2×D11—82no—
157C2×D11—82no—
158C2×D11—82no—
159C2×D11—164no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—162no—
164C4×C11C2×#9911yescharacteristic
165C4×C11#42111yescharacteristic
166Dic11—82no—
167C22×D4—221no—
168C22×D4—441no—
169C23×C4C22⋊D1111yescharacteristic
170C2×D8—112no—
171C2×D8—221no—
172C2×D8—442no—
173C22×C8—42no—
174C22×C8C4×D1111yescharacteristic
175C22×C8C4×D1111yescharacteristic
176C22×C8D4411yescharacteristic
177C22×C8D4411yescharacteristic
178C22×C8C22⋊D1111yescharacteristic
179C22×C8C22×D1111yescharacteristic
180#121—222no—
181#121—222no—
182#121—441no—
183#121—441no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—221no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—441no—
188M32—442no—
189C2×C16—222no—
190#107—112no—
191#107—221no—
192#106—42no—
193#102—222no—
194#102—222no—
195#95—41no—
196C2×C11—22no—
197C2×C11—22no—
198C2×C11—41no—
199C2×C11#151911yescharacteristic
200C2×C11#214011yescharacteristic
201C2×C11C2×#36011yescharacteristic
202D11—162no—
203C24—441no—
204C24#432311yescharacteristic
205C2×D4—222no—
206C2×D4—442no—
207C2×D4—442no—
208C2×D4—442no—
209C2×D4—442no—
210C2×D4—441no—
211C2×D4—884no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—441no—
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4(C2×D11)⋊C411yescharacteristic
218C22×C4#432311yescharacteristic
219C22×C4#432511yescharacteristic
220C22×C4#432511yescharacteristic
221C22×C4C2×C22⋊D1111yescharacteristic
222D8—442no—
223D8—442no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8(C2×D11)⋊C411yescharacteristic
231C2×C8(C2×D11)⋊C411yescharacteristic
232C2×C8C2×C4×D1111yescharacteristic
233C2×C8C2×D4411yescharacteristic
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—222no—
237C4⋊C4—441no—
238C22⋊C4—82no—
239C22⋊C4—442no—
240C22⋊C4—442no—
241C16—442no—
242C11#1188811yescharacteristic, complemented, Sylow
243C23—22no—
244C23—22no—
245C23—41no—
246C23—442no—
247C23—882no—
248C23—882no—
249C23—882no—
250C23#6687311yescharacteristic
251C23#6687311yescharacteristic
252C23C2×#432311yescharacteristic
253D4—442no—
254D4—442no—
255D4—882no—
256D4—884no—
257D4—884no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—442no—
271C2×C4—882no—
272C2×C4#6687311yescharacteristic
273C2×C4#6687311yescharacteristic
274C2×C4C2×(C2×D11)⋊C411yescharacteristic
275C2×C4C2×#432511yescharacteristic
276C8—21no—
277C8—21no—
278C8—21no—
279C8#6687012yes—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—44no—
288C22—882no—
289C22—882no—
290C22—882no—
291C22—1764no—
292C22#1062212612yes—
293C22C2×#6687311yescharacteristic
294C22#1062280612yes—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—162no—
299C4—882no—
300C4C2×#6687011yescharacteristic
301C4#1062261811yescharacteristic
302C2—22no—
303C2—22no—
304C2—41no—
305C2—1762no—
306C2#1306718311yescharacteristic
307C2#1307033111yescharacteristic
308C2C2×#1062212611yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1807C2
socleC22×C11C2×#102
prime radicalC2×#10622728C2
cosocleC22×C8×C11C23
hypercenter#1807D11
hypocenterC11#11888
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
2. #13070227C2semidirect
3. #13066624C2semidirect
4. C11×#1807C2semidirect
7. C22×D88C4semidirect
12. #10622728C4semidirect
15. C2×#66882C4semidirect
17. C11×#340C22semidirect
19. C22⋊(C11⋊C16)C22semidirect
91. #1807D11semidirect
144. #340C2×D11semidirect
242. C11#11888semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
#130702272
#130666242
C11×#18072
#1188811