Finite Group Databasebeta

← #14647131

Subgroups — #14647131

Order 2816.

540 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066455C214yesmaximal, complemented
4C11×#1797C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66979—21no—
7C2×C11×C4⋊C8C2212yes—
8C2×C11×C22⋊C8—21no—
9#10622825—21no—
10#10622825C412yes—
11C2×C22⋊(C11⋊C8)—21no—
12#10622549—21no—
13#10622548C411yescharacteristic
14#10622548C411yescharacteristic
15C4×C4⋊Dic11—21no—
16C4×C4⋊Dic11C2212yes—
17C2×C4×C11⋊C8C2212yes—
18C11×#336—21no—
19#10622162—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×C8×C11—22no—
24C2×C42×C11—24no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—22no—
30#66979—42no—
31#66979—42no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C412yes—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4×Dic11—22no—
39C22×C11⋊C8—22no—
40C11×C4⋊C8—24no—
41C11×C22⋊C8—42no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—24no—
45C4×C11⋊C8—24no—
46#8709—111nomaximal, Sylow
47C24×C11C22⋊C411yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—41no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11D812yes—
60C22×C4×C11SD1612yes—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—22no—
65C22×Dic11—22no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C2×C8×C11—42no—
69C42×C11—22no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11#4114yes—
73C22⋊Dic11—44no—
74C4⋊Dic11—24no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4×Dic11—42no—
81C4×Dic11—42no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—42no—
84C2×C11⋊C8—42no—
85#2285—111no—
86#1797D1111yescharacteristic
87C4×C22⋊C8—111no—
88#1279—114no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11#10212yes—
96C23×C11C2×C22⋊C411yescharacteristic
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—24no—
104C2×C4×C11—24no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—44no—
109C2×C4×C11—44no—
110C2×C4×C11#10212yes—
111C2×C4×C11#10412yes—
112C2×C4×C11#11712yes—
113C2×C4×C11#12312yes—
114C2×C4×C11#12312yes—
115C2×C4×C11#13112yes—
116C2×C4×C11#13112yes—
117C2×C4×C11C2×D811yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11#13712yes—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C8×C11—82no—
127C11⋊C8—44no—
128C2×#117—221no—
129C22×C42C2×D1111yescharacteristic
130C2×C4⋊C8C2×D1112yes—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—221no—
133C2×C4×C8—112no—
134#384—111no—
135#384—111no—
136#382—221no—
137#380—112no—
138#380—221no—
139C4×C4⋊C4—112no—
140C4×C4⋊C4—221no—
141#336—21no—
142#336—221no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11#38111yescharacteristic
151C22×C11#40811yescharacteristic
152C22×C11#40811yescharacteristic
153C22×C11C2×#10211yescharacteristic
154C22×C11#41911yescharacteristic
155C22×C11C2×#10411yescharacteristic
156C22×C11#42111yescharacteristic
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11#43314yes—
162C4×C11#48012yes—
163C4×C11#48312yes—
164Dic11—82no—
165Dic11—82no—
166C23×C4C4×D1111yescharacteristic
167C23×C4D4411yescharacteristic
168C23×C4C22⋊D1111yescharacteristic
169C22×C8—22no—
170C22×C8—222no—
171#117—442no—
172#117—442no—
173C2×C4⋊C4—112no—
174C2×C4⋊C4—112no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—221no—
177C2×C4⋊C4—221no—
178C2×C4⋊C4—221no—
179C2×C22⋊C4—222no—
180C2×C42—24no—
181C2×C42—222no—
182C2×C42C4×D1111yescharacteristic
183C2×C42D4411yescharacteristic
184C2×C42C22⋊D1111yescharacteristic
185C2×C42C22×D1111yescharacteristic
186C4⋊C8—24no—
187C22⋊C8—42no—
188C22⋊C8—224no—
189C4×C8—224no—
190#95—222no—
191#95—222no—
192C2×C11—42no—
193C2×C11#148011yescharacteristic
194C2×C11#148511yescharacteristic
195C2×C11#149211yescharacteristic
196C2×C11#149711yescharacteristic
197C2×C11#181811yescharacteristic
198C2×C11#182311yescharacteristic
199C2×C11#182611yescharacteristic
200C24(C2×D11)⋊C411yescharacteristic
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4#432312yes—
215C22×C4#432512yes—
216C22×C4C2×C4×D1111yescharacteristic
217C22×C4C2×D4411yescharacteristic
218C22×C4C2×C22⋊D1111yescharacteristic
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—224no—
223C2×C8—442no—
224C2×C8—442no—
225C4⋊C4—224no—
226C4⋊C4—224no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C22⋊C4—444no—
232C42—22no—
233C42—22no—
234C42—22no—
235C42—442no—
236C42—442no—
237C42#434114yes—
238C11#870911yescharacteristic, complemented, Sylow
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23#6687312yes—
246C23C2×(C2×D11)⋊C411yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4#6687312yes—
267C2×C4#6688912yes—
268C2×C4#6693012yes—
269C2×C4#6693912yes—
270C2×C4#6695412yes—
271C2×C4#6696012yes—
272C2×C4C2×#432311yescharacteristic
273C2×C4#6698812yes—
274C2×C4C2×#432511yescharacteristic
275C2×C4#6700412yes—
276C8—82no—
277C8—444no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22#1062255611yescharacteristic
286C22C2×#6687311yescharacteristic
287C22#1062261711yescharacteristic
288C22#1062272311yescharacteristic
289C22#1062274211yescharacteristic
290C22C2×#6688911yescharacteristic
291C22#1062275211yescharacteristic
292C4—22no—
293C4—22no—
294C4—22no—
295C4—41no—
296C4—882no—
297C4—882no—
298C4#1062233314yes—
299C4#1062264612yes—
300C4#1062265612yes—
301C2—42no—
302C2#1306701411yescharacteristic
303C2#1306703611yescharacteristic
304C2#1306706611yescharacteristic
305C2#1306708811yescharacteristic
306C2#1306868511yescharacteristic
307C2#1306870011yescharacteristic
308C2#1306871311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13066455C2semidirect
238. C11#8709semidirect

Maximal subgroups

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

subgroupindex
#130710232
C4×C22⋊(C11⋊C8)2
#130664552
C11×#17972
#870911