Finite Group Databasebeta

← #14642228

Subgroups — #14642228

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076955C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic
3#13066441C212yesmaximal, complemented
4#13066440C212yesmaximal, complemented
5C2×C11×#336C211yesmaximal, characteristic
6C23×C8×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977C411yescharacteristic
9C22×#4318—21no—
10#10622825C411yescharacteristic
11#10622824—21no—
12#10622823—21no—
13#10622546—21no—
14#10622546—21no—
15#10622542C411yescharacteristic
16#10622542C2211yescharacteristic
17#10622541C411yescharacteristic
18#10622541C2211yescharacteristic
19C11×#336—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C22×C8×C11—24no—
28C22×C8×C11—22no—
29C22×C8×C11—42no—
30C22×C8×C11—42no—
31C2×C42×C11—42no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—42no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×#4318—24no—
46C2×#4318—42no—
47C2×#4318—42no—
48C22×C11⋊C8—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#7681—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11SD1612yes—
71C22×C4×C11Q1612yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×Dic22—22no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×C8×C11—24no—
83C2×C8×C11—48no—
84C2×C8×C11—42no—
85C2×C8×C11—42no—
86C42×C11—41no—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11—41no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C4⋊Dic11—22no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99#4318—48no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—42no—
102C2×C11⋊C8—42no—
103#2855—111no—
104#1728—111no—
105C2×#336D1111yescharacteristic
106#1272—112no—
107#1271—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#9912yes—
113C23×C11#10312yes—
114C23×C11#10412yes—
115C23×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—24no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—44no—
134C2×C4×C11#10312yes—
135C2×C4×C11#10412yes—
136C2×C4×C11#13112yes—
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11C2×Q1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153Dic22—82no—
154C8×C11—44no—
155C11⋊C8—44no—
156C22×M16—221no—
157C23×C8—21no—
158C2×C22⋊Q8—111no—
159C22×C42C2×D1111yescharacteristic
160#391—111no—
161#391—111no—
162#389—111no—
163#389—111no—
164#387—221no—
165#387—221no—
166#385—221no—
167#381—221no—
168#380—111no—
169#336—21no—
170#336—112no—
171#336—221no—
172#336C2×D1112yes—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11#32814yes—
180C22×C11#40811yescharacteristic
181C22×C11C2×#9911yescharacteristic
182C22×C11#41311yescharacteristic
183C22×C11C2×#10311yescharacteristic
184C22×C11#41711yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—22no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—41no—
195Dic11—81no—
196Dic11—81no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—111no—
200C23×C4C4×D1111yescharacteristic
201C23×C4D4411yescharacteristic
202C23×C4C22⋊D1111yescharacteristic
203C2×M16—224no—
204C2×M16—442no—
205C2×M16—442no—
206C22×C8—24no—
207C22×C8—22no—
208C22×C8—42no—
209C22×C8—42no—
210C22×C8—222no—
211C22⋊Q8—442no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C42—42no—
221C2×C42C4×D1111yescharacteristic
222C2×C42D4411yescharacteristic
223C2×C42C22⋊D1111yescharacteristic
224C2×C42C22×D1111yescharacteristic
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11—24no—
233C2×C11#146811yescharacteristic
234C2×C11#148311yescharacteristic
235C2×C11#149311yescharacteristic
236C2×C11C2×#32811yescharacteristic
237C2×C11#150411yescharacteristic
238C2×C11#152411yescharacteristic
239C2×C11#155011yescharacteristic
240C24(C2×D11)⋊C411yescharacteristic
241C2×Q8—222no—
242C2×Q8—441no—
243C2×Q8—441no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4#431412yes—
258C22×C4Dic4412yes—
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4(C2×D11)⋊C411yescharacteristic
261C22×C4(C2×D11)⋊C411yescharacteristic
262C22×C4C2×C4×D1111yescharacteristic
263C22×C4C2×D4411yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—448no—
266C2×C8—24no—
267C2×C8—48no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—224no—
271C2×C8—442no—
272C2×C8—442no—
273C4⋊C4—222no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—41no—
286C11#768111yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#6687012yes—
292C23#6688012yes—
293C23#6688912yes—
294C23C2×(C2×D11)⋊C411yescharacteristic
295Q8—882no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4#6686912yes—
327C2×C4#6688012yes—
328C2×C4#6695412yes—
329C2×C4C2×#431411yescharacteristic
330C2×C4C2×Dic4411yescharacteristic
331C2×C4#6698511yescharacteristic
332C2×C4#6699511yescharacteristic
333C8—44no—
334C8—444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22#1062210514yes—
342C22C2×#6686911yescharacteristic
343C22C2×#6687011yescharacteristic
344C22#1062257911yescharacteristic
345C22C2×#6688011yescharacteristic
346C22#1062272311yescharacteristic
347C22#1062274511yescharacteristic
348C22C2×#6688911yescharacteristic
349C4—21no—
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—22no—
356C4—41no—
357C4—881no—
358C4—881no—
359C4—881no—
360C4—881no—
361C2—24no—
362C2#1306696211yescharacteristic
363C2#1306702711yescharacteristic
364C2#1306707211yescharacteristic
365C2C2×#1062210511yescharacteristic
366C2#1306711811yescharacteristic
367C2#1306720211yescharacteristic
368C2#1306730411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#336C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#336D11
hypocenterC11#7681
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #13066441C2semidirect
4. #13066440C2semidirect
286. C11#7681semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130683102
#130664412
#130664402
C2×C11×#3362
#768111