Finite Group Databasebeta

← #14653949

Subgroups — #14653949

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076926C211yesmaximal, characteristic
2C4×C11⋊#95C211yesmaximal, characteristic
3#13066496C212yesmaximal
4#13066496C212yesmaximal
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C22×C4×Dic11—21no—
8C2×#66923C411yescharacteristic, complemented
9C2×C11×C4⋊C8—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622825C2211yescharacteristic
12#10622825C2211yescharacteristic
13#10622823—21no—
14#10622823—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17#10622549C411yescharacteristic, complemented
18#10622546—21no—
19#10622546—21no—
20#10622541C411yescharacteristic, complemented
21#10622541C411yescharacteristic, complemented
22C11×#336—21no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—22no—
27C22×C8×C11—22no—
28C2×C42×C11—42no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—24no—
44C2×C4×Dic11—42no—
45C2×C4×Dic11—42no—
46#66923—42no—
47C11×C4⋊C8—42no—
48C11×C22⋊C8—24no—
49C11⋊#95—24no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—22no—
57C11⋊#95Q814yes—
58#9910—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q812yes—
76C22×C4×C11#4112yes—
77C22×Dic11—24no—
78C22×Dic11—24no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—24no—
84C22×Dic11—42no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C2×C8×C11—42no—
89C2×C8×C11—42no—
90C2×C8×C11—42no—
91C42×C11—22no—
92C42×C11—22no—
93C42×C11—41no—
94C42×C11—41no—
95C22⋊Dic11—42no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—42no—
106C4×Dic11—48no—
107#2851—111no—
108#1797D1111yescharacteristic
109C4×#95—111no—
110#1294—112no—
111#1294—112no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11C2×C22⋊C411yescharacteristic
117C23×C11C22⋊Q812yes—
118C23×C11#13512yes—
119C23×C11AGL(1,ℤ/8)11yescharacteristic
120C23×C11#13711yescharacteristic
121C2×C4×C11—24no—
122C2×C4×C11—24no—
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—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—44no—
139C2×C4×C11#9912yes—
140C2×C4×C11#10412yes—
141C2×C4×C11#10412yes—
142C2×C4×C11C4×Q812yes—
143C2×C4×C11#12411yescharacteristic
144C2×C4×C11C4⋊Q811yescharacteristic
145C2×Dic11—28no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—44no—
150C2×Dic11—44no—
151C2×Dic11—44no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C8×C11—82no—
165C2×#125—111no—
166C22×C42—221no—
167C22×C42C2×D1111yescharacteristic
168C2×C4⋊C8—21no—
169C2×C22⋊C8C2×D1112yes—
170#389—111no—
171#389—111no—
172#387—221no—
173#387—221no—
174#385—221no—
175#385—221no—
176#382—111no—
177#380—111no—
178#380—111no—
179C2×#95—112no—
180C2×#95—221no—
181#336—21no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#39111yescharacteristic
191C22×C11C2×#9911yescharacteristic
192C22×C11#41011yescharacteristic
193C22×C11#41611yescharacteristic
194C22×C11#41711yescharacteristic
195C22×C11C2×#10411yescharacteristic
196C22×C11C2×#10411yescharacteristic
197C22×C11#47812yes—
198C22×C11#47912yes—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—41no—
206Dic11—48no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210Dic11—81no—
211C23×C4—222no—
212C23×C4D4411yescharacteristic
213C23×C4D4411yescharacteristic
214C23×C4C22×D1111yescharacteristic
215C22×C8—22no—
216#125—442no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C42—42no—
228C2×C42—224no—
229C2×C42—442no—
230C2×C42—442no—
231C2×C42C4×D1111yescharacteristic
232C2×C42C4×D1111yescharacteristic
233C2×C42C22⋊D1111yescharacteristic
234C2×C42C22⋊D1111yescharacteristic
235C4⋊C8—42no—
236C22⋊C8—24no—
237#95—114no—
238#95—224no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—222no—
244#95—221no—
245#95—221no—
246C2×C11—22no—
247C2×C11—22no—
248C2×C11#150011yescharacteristic
249C2×C11#150111yescharacteristic
250C2×C11#150411yescharacteristic
251C2×C11#150911yescharacteristic
252C2×C11#198911yescharacteristic
253C2×C11#199411yescharacteristic
254C2×C11#199611yescharacteristic
255C24C2×D4411yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—224no—
266C22×C4—224no—
267C22×C4—224no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—442no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4—442no—
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4(C2×D11)⋊C411yescharacteristic
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4#434112yes—
282C22×C4Q8×D1112yes—
283C22×C4C2×C22⋊D1111yescharacteristic
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—442no—
292C4⋊C4—442no—
293C4⋊C4—442no—
294C4⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C42—22no—
299C42—22no—
300C42—41no—
301C42—41no—
302C42—448no—
303C11#991011yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#6695012yes—
309C23#6695712yes—
310C23#6696111yescharacteristic
311C23#6696211yescharacteristic
312C23C2×(C2×D11)⋊C411yescharacteristic
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—228no—
332C2×C4—444no—
333C2×C4—444no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4—444no—
337C2×C4—444no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4#6687012yes—
351C2×C4#6688912yes—
352C2×C4#6688912yes—
353C2×C4#6694012yes—
354C2×C4#6698911yescharacteristic
355C2×C4#6699711yescharacteristic
356C8—82no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22#1062244212yes—
366C22#1062246012yes—
367C22C2×#6687011yescharacteristic
368C22#1062258711yescharacteristic
369C22#1062261911yescharacteristic
370C22#1062272611yescharacteristic
371C22#1062274611yescharacteristic
372C22C2×#6688911yescharacteristic
373C22C2×#6688911yescharacteristic
374C4—21no—
375C4—22no—
376C4—21no—
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—448no—
382C4—881no—
383C4—881no—
384C4—881no—
385C4—881no—
386C2—22no—
387C2—22no—
388C2#1306710311yescharacteristic
389C2#1306710811yescharacteristic
390C2#1306712111yescharacteristic
391C2#1306714211yescharacteristic
392C2#1306957111yescharacteristic
393C2#1306959211yescharacteristic
394C2#1306960011yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9910
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
8. C2×#66923C4semidirect
17. #10622549C4semidirect
20. #10622541C4semidirect
21. #10622541C4semidirect
303. C11#9910semidirect

Maximal subgroups

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

subgroupindex
#130769262
C4×C11⋊#952
#130664962
C11×#17972
#991011