Finite Group Databasebeta

← #14649379

Subgroups — #14649379

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66867C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3C2×#10622181C212yesmaximal, complemented
4#13066497C212yesmaximal, complemented
5C11×#2851C211yesmaximal, characteristic
6C2×C11×#125C2211yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C23×C11⋊C8—21no—
9C11×#389C411yescharacteristic
10C11×#389C411yescharacteristic
11C11×#387—21no—
12C11×#387—21no—
13C11×#385—21no—
14C11×#385—21no—
15C11×#382C2211yescharacteristic
16C11×#380C411yescharacteristic
17C11×#380C411yescharacteristic
18C2×C22⋊(C11⋊C8)—21no—
19C2×#66867—21no—
20C2×#66867—24no—
21C2×#66867C2212yes—
22C2×#66867C2212yes—
23#10622181—24no—
24#10622162—21no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C11×#125—22no—
29C11×#125—22no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—22no—
41C2×C42×C11—22no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C22×C11⋊C8—24no—
47C22×C11⋊C8—24no—
48C22×C11⋊C8—24no—
49C22×C11⋊C8—22no—
50C22×C11⋊C8—22no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C22⋊(C11⋊C8)—24no—
58#66867—24no—
59#66867—22no—
60#66867—22no—
61#66867—22no—
62#66867D414yes—
63#9121—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C42×C11—22no—
97C42×C11—21no—
98C42×C11—22no—
99C42×C11—21no—
100C42×C11C2×D412yes—
101C42×C11#4112yes—
102C2×C11⋊C8—216no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—24no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—42no—
108C2×C11⋊C8—42no—
109C22×#97—111no—
110#2851D1111yescharacteristic
111#1749—111no—
112C2×#330—112no—
113#1295—112no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11#10112yes—
119C23×C11#10412yes—
120C23×C11#10412yes—
121C23×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11—24no—
123C2×C4×C11—24no—
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—21no—
137C2×C4×C11—21no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11#10412yes—
153C2×C4×C11C4×D412yes—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12112yes—
156C2×C4×C11#12311yescharacteristic
157C11⋊C8—28no—
158C11⋊C8—44no—
159C23×C8—221no—
160C2×#125C2×D1111yescharacteristic
161C22×C42C2×D1111yescharacteristic
162C2×C22⋊C8—221no—
163C2×#97—112no—
164C2×#97—112no—
165C2×#97—224no—
166C2×#97—221no—
167#389Dic1111yescharacteristic
168#389Dic1111yescharacteristic
169#387—21no—
170#387—21no—
171#385—21no—
172#385—21no—
173#382C2×D1111yescharacteristic
174#380Dic1111yescharacteristic
175#380Dic1111yescharacteristic
176#336—221no—
177#330—224no—
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11#33014yescomplemented
185C22×C11#38611yescharacteristic
186C22×C11C2×#10111yescharacteristic
187C22×C11#41311yescharacteristic
188C22×C11C2×#10411yescharacteristic
189C22×C11C2×#10411yescharacteristic
190C22×C11C2×#10411yescharacteristic
191C22×C11#42111yescharacteristic
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—22no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C23×C4C2×Dic1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C23×C4C22⋊D1111yescharacteristic
206C22×C8—224no—
207C22×C8—224no—
208C22×C8—224no—
209C22×C8—222no—
210C22×C8—222no—
211#125—22no—
212#125—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×Dic1111yescharacteristic
218C2×C4⋊C4C2×Dic1111yescharacteristic
219C2×C4⋊C4C2×Dic1111yescharacteristic
220C2×C4⋊C4C2×Dic1111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C2×Dic1111yescharacteristic
226C2×C42C22⋊D1111yescharacteristic
227C2×C42C22⋊D1111yescharacteristic
228C2×C42C22×D1111yescharacteristic
229C22⋊C8—224no—
230#97—114no—
231#97—224no—
232#97—222no—
233#97—222no—
234#97—222no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×C11—24no—
242C2×C11C2×#33011yescharacteristic
243C2×C11#152411yescharacteristic
244C2×C11#153111yescharacteristic
245C2×C11#153211yescharacteristic
246C2×C11#187111yescharacteristic
247C2×C11#189611yescharacteristic
248C2×C11#190111yescharacteristic
249C24C22⋊Dic1111yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C22⋊Dic1111yescharacteristic
265C22×C4C22⋊Dic1111yescharacteristic
266C22×C4C22⋊Dic1111yescharacteristic
267C22×C4C22×Dic1111yescharacteristic
268C22×C4C2×C22⋊D1111yescharacteristic
269C22×C4C2×C22⋊D1111yescharacteristic
270C2×C8—2216no—
271C2×C8—224no—
272C2×C8—224no—
273C2×C8—224no—
274C2×C8—224no—
275C2×C8—442no—
276C2×C8—442no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—22no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42D4×D1112yes—
293C42#434112yes—
294C11#912111yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#6690012yes—
300C23#6690112yes—
301C23#6690112yes—
302C23C2×C22⋊Dic1111yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4#6690112yes—
334C2×C4D4×Dic1112yes—
335C2×C4#6698811yescharacteristic
336C2×C4#6699011yescharacteristic
337C2×C4#6699212yes—
338C8—228no—
339C8—444no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22#1062218114yescomplemented
347C22#1062283311yescharacteristic
348C22C2×#6690011yescharacteristic
349C22C2×#6690111yescharacteristic
350C22C2×#6690111yescharacteristic
351C22C2×#6690111yescharacteristic
352C22#1062284911yescharacteristic
353C22#1062285011yescharacteristic
354C4—21no—
355C4—22no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C2—24no—
366C2C2×#1062218111yescharacteristic
367C2#1306720411yescharacteristic
368C2#1306723111yescharacteristic
369C2#1306723611yescharacteristic
370C2#1306891911yescharacteristic
371C2#1306906011yescharacteristic
372C2#1306908511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2851C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2851D11
hypocenterC11#9121
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#10622181C2semidirect
4. #13066497C2semidirect
184. C22×C11#330semidirect
294. C11#9121semidirect
346. C22#10622181semidirect

Maximal subgroups

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

subgroupindex
C22×#668672
#130683782
C2×#106221812
#130664972
C11×#28512
#912111