Finite Group Databasebeta

← #14647162

Subgroups — #14647162

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066495C214yesmaximal
4C11×#1434C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66979—21no—
7C2×C11×#95—21no—
8C2×C11×#95—21no—
9C2×C11×#95C2212yes—
10#10622825—21no—
11#10622825C2212yes—
12C2×C22⋊(C11⋊C8)C2212yes—
13#10622549—21no—
14#10622548C411yescharacteristic, complemented
15#10622548C411yescharacteristic, complemented
16C4×C4⋊Dic11—21no—
17C4×C4⋊Dic11C412yescomplemented
18#10622162—21no—
19#10622162—21no—
20C23×C4×C11—22no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C2×C42×C11—24no—
25C2×C42×C11C2×C411yescharacteristic
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
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×#95—24no—
41C11×#95—24no—
42C11×#95—42no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C22⋊(C11⋊C8)—24no—
46#8716—111nomaximal, Sylow
47C24×C11C2×D411yescharacteristic
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—24no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11D812yes—
67C22×C4×C11SD1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4114yes—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—22no—
76C42×C11—22no—
77C22⋊Dic11—42no—
78C22⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84C4⋊Dic11—42no—
85C4×Dic11—44no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—42no—
89#2285—111no—
90#1817—111no—
91#1434D1111yescharacteristic
92#1294—114no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11C2×C22⋊C411yescharacteristic
98C23×C11#12312yes—
99C23×C11C2×D811yescharacteristic
100C23×C11C2×SD1611yescharacteristic
101C23×C11#13712yes—
102C2×C4×C11—21no—
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—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11—82no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11#10212yes—
127C2×C4×C11#10212yes—
128C2×C4×C11#10412yes—
129C2×C4×C11#11712yes—
130C2×C4×C11#12312yes—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C11⋊C8—82no—
138C2×#117—221no—
139C22×C42C2×D1111yescharacteristic
140C2×C22⋊C8—112no—
141#384—111no—
142#384—111no—
143#382—221no—
144#380—112no—
145#380—221no—
146C4×C4⋊C4—112no—
147C4×C4⋊C4—221no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95C2×D1112yes—
151#336—221no—
152#336—221no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38111yescharacteristic
162C22×C11#41011yescharacteristic
163C22×C11#41011yescharacteristic
164C22×C11C2×#10211yescharacteristic
165C22×C11#41911yescharacteristic
166C22×C11C2×#10411yescharacteristic
167C22×C11#42111yescharacteristic
168C22×C11#48012yes—
169C22×C11#48312yes—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—22no—
175C4×C11—41no—
176C4×C11—84no—
177Dic11—82no—
178Dic11—82no—
179C23×C4—22no—
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22⋊D1111yescharacteristic
182C23×C4C22×D1111yescharacteristic
183C22×C8—222no—
184#117—442no—
185#117—442no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C22⋊C4—222no—
193C2×C42—24no—
194C2×C42—222no—
195C2×C42C4×D1111yescharacteristic
196C2×C42C4×D1111yescharacteristic
197C2×C42D4411yescharacteristic
198C2×C42D4411yescharacteristic
199C22⋊C8—224no—
200#95—24no—
201#95—24no—
202#95—42no—
203#95—222no—
204#95—222no—
205C2×C11—22no—
206C2×C11—22no—
207C2×C11#150211yescharacteristic
208C2×C11#150611yescharacteristic
209C2×C11#151511yescharacteristic
210C2×C11#151711yescharacteristic
211C2×C11#182011yescharacteristic
212C2×C11#182311yescharacteristic
213C2×C11#182611yescharacteristic
214C24C2×C22⋊D1111yescharacteristic
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—24no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—222no—
230C22×C4—222no—
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4#432312yes—
236C22×C4#432512yes—
237C22×C4C2×C4×D1111yescharacteristic
238C22×C4C2×D4411yescharacteristic
239C22×C4#434114yes—
240C2×C8—442no—
241C2×C8—442no—
242C2×C8—442no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—442no—
247C4⋊C4—442no—
248C4⋊C4—442no—
249C22⋊C4—442no—
250C22⋊C4—442no—
251C42—22no—
252C42—22no—
253C42—22no—
254C42—22no—
255C42—444no—
256C11#871611yescharacteristic, complemented, Sylow
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23C2×(C2×D11)⋊C411yescharacteristic
262C23C2×#432311yescharacteristic
263C23#6698812yes—
264C23C2×#432511yescharacteristic
265C23#6700412yes—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4#6686912yes—
297C2×C4#6687312yes—
298C2×C4#6687312yes—
299C2×C4#6693012yes—
300C2×C4#6693912yes—
301C8—882no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22C2×#6686911yescharacteristic
311C22#1062255611yescharacteristic
312C22C2×#6687311yescharacteristic
313C22#1062261711yescharacteristic
314C22#1062261811yescharacteristic
315C22#1062261911yescharacteristic
316C22#1062261911yescharacteristic
317C22#1062264612yes—
318C22#1062265612yes—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—41no—
325C4—84no—
326C4—882no—
327C4—882no—
328C2—22no—
329C2—22no—
330C2#1306711011yescharacteristic
331C2#1306712711yescharacteristic
332C2#1306716611yescharacteristic
333C2#1306717511yescharacteristic
334C2#1306869111yescharacteristic
335C2#1306870011yescharacteristic
336C2#1306871611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8716
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
14. #10622548C4semidirect
15. #10622548C4semidirect
17. C4×C4⋊Dic11C4semidirect
256. C11#8716semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130686842
#130664952
C11×#14342
#871611