Finite Group Databasebeta

← #14647166

Subgroups — #14647166

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 334 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—44no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C412yes—
36C2×C4⋊Dic11C2×C412yes—
37C2×C4×Dic11—22no—
38C22×C11⋊C8—22no—
39C11×#95—24no—
40C11×#95—24no—
41C11×#95—42no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—24no—
45#8717—111nomaximal, Sylow
46C24×C11C2×D411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—24no—
52C22×C4×C11—41no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11SD1612yes—
66C22×C4×C11Q1612yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4114yes—
70C22×Dic11—22no—
71C22×Dic11—22no—
72C42×C11—22no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—22no—
76C22⋊Dic11—44no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—42no—
82C4⋊Dic11—42no—
83C4×Dic11—44no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87#2285—111no—
88#1817—111no—
89#1434D1111yescharacteristic
90#1294—114no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11C2×C22⋊C411yescharacteristic
96C23×C11#12312yes—
97C23×C11C2×SD1611yescharacteristic
98C23×C11C2×Q1611yescharacteristic
99C23×C11AGL(1,ℤ/8)12yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
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—24no—
111C2×C4×C11—24no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—82no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11—82no—
124C2×C4×C11#10312yes—
125C2×C4×C11#10312yes—
126C2×C4×C11#10412yes—
127C2×C4×C11#11712yes—
128C2×C4×C11#12312yes—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C11⋊C8—82no—
136C2×#117—221no—
137C22×C42C2×D1111yescharacteristic
138C2×C22⋊C8—112no—
139#384—111no—
140#384—111no—
141#382—221no—
142#380—112no—
143#380—221no—
144C4×C4⋊C4—112no—
145C4×C4⋊C4—221no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95C2×D1112yes—
149#336—221no—
150#336—221no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11#38111yescharacteristic
160C22×C11#41011yescharacteristic
161C22×C11#41011yescharacteristic
162C22×C11C2×#10311yescharacteristic
163C22×C11#41811yescharacteristic
164C22×C11C2×#10411yescharacteristic
165C22×C11#42111yescharacteristic
166C22×C11#48112yes—
167C22×C11#48412yes—
168C4×C11—22no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—84no—
175Dic11—82no—
176Dic11—82no—
177C23×C4—22no—
178C23×C4C22⋊D1111yescharacteristic
179C23×C4C22⋊D1111yescharacteristic
180C23×C4C22×D1111yescharacteristic
181C22×C8—222no—
182#117—444no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C22⋊C4—222no—
190C2×C42—24no—
191C2×C42—222no—
192C2×C42C4×D1111yescharacteristic
193C2×C42C4×D1111yescharacteristic
194C2×C42D4411yescharacteristic
195C2×C42D4411yescharacteristic
196C22⋊C8—224no—
197#95—24no—
198#95—24no—
199#95—42no—
200#95—222no—
201#95—222no—
202C2×C11—22no—
203C2×C11—22no—
204C2×C11#150311yescharacteristic
205C2×C11#150511yescharacteristic
206C2×C11#151411yescharacteristic
207C2×C11#151811yescharacteristic
208C2×C11#182011yescharacteristic
209C2×C11#182411yescharacteristic
210C2×C11#182611yescharacteristic
211C24C2×C22⋊D1111yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—222no—
227C22×C4—222no—
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4#432412yes—
233C22×C4#432612yes—
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4C2×D4411yescharacteristic
236C22×C4#434114yes—
237C2×C8—442no—
238C2×C8—442no—
239C2×C8—442no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C22⋊C4—444no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—444no—
252C11#871711yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23C2×(C2×D11)⋊C411yescharacteristic
258C23C2×#432411yescharacteristic
259C23#6698812yes—
260C23C2×#432611yescharacteristic
261C23#6700212yes—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4#6686912yes—
293C2×C4#6687412yes—
294C2×C4#6687412yes—
295C2×C4#6693012yes—
296C2×C4#6693912yes—
297C8—882no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—21no—
304C22—21no—
305C22—22no—
306C22C2×#6686911yescharacteristic
307C22#1062255611yescharacteristic
308C22C2×#6687411yescharacteristic
309C22#1062261411yescharacteristic
310C22#1062261811yescharacteristic
311C22#1062261911yescharacteristic
312C22#1062261911yescharacteristic
313C22#1062264712yes—
314C22#1062265712yes—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—84no—
322C4—882no—
323C4—882no—
324C2—22no—
325C2—22no—
326C2#1306711411yescharacteristic
327C2#1306712311yescharacteristic
328C2#1306716211yescharacteristic
329C2#1306717911yescharacteristic
330C2#1306869111yescharacteristic
331C2#1306870411yescharacteristic
332C2#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#8717
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
252. C11#8717semidirect

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
#871711