Finite Group Databasebeta

← #14658263

Subgroups — #14658263

Order 2816.

426 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073652C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13069377C211yesmaximal, characteristic
4#13066499C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1834C211yesmaximal, characteristic
8C2×#66943—21no—
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622598—21no—
13#10622597—22no—
14#10622589—21no—
15#10622586—21no—
16C2×#66872—21no—
17C2×#66872—21no—
18C4×C4⋊Dic11C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—22no—
23#10622167—21no—
24#10622167—21no—
25C22×C8×C11—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D412yes—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66943—42no—
45#66943—42no—
46C4×C8×C11—21no—
47C4×C8×C11Q812yes—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51#66872—42no—
52#66872—42no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)Q812yes—
56C4⋊(C11⋊C8)Q812yes—
57#10582—111nomaximal, Sylow
58C22×C4×C11—22no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×C8×C11—22no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11C2×Q811yescharacteristic
81C42×C11C2×Q811yescharacteristic
82C42×C11C2×Q811yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—44no—
91C4⋊Dic11SD1612yes—
92C4⋊Dic11SD1612yes—
93Dic11⋊C4—44no—
94Dic11⋊C4—82no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2552—111no—
106#1948—111no—
107#1948—111no—
108#1834D1111yescharacteristic
109#1296—111no—
110#1279—111no—
111#1279—111no—
112C23×C11#12011yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C4⋊Q811yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C2×C4×C11C4⋊Q811yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×C4×C11#13511yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C8×C11—42no—
148C11⋊C8—42no—
149C11⋊C8—42no—
150C2×#125—221no—
151C2×#106—221no—
152C2×#106—221no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C2×C4×C8C2×D1111yescharacteristic
156#398—222no—
157#389—221no—
158#389—221no—
159#384—221no—
160#384C2×D1111yescharacteristic
161#384C2×D1111yescharacteristic
162C4×C4⋊C4—111no—
163C4×C4⋊C4—111no—
164#340—22no—
165#340—221no—
166#340—221no—
167C22×C11#39511yescharacteristic
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45011yescharacteristic
171C22×C11#45211yescharacteristic
172C22×C11#45411yescharacteristic
173C22×C11#45511yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11—161no—
178C4×C11#47511yescharacteristic
179C4×C11#47611yescharacteristic
180C4×C11#47811yescharacteristic
181C4×C11#47911yescharacteristic
182C4×C11#49811yescharacteristic
183C4×C11#49911yescharacteristic
184C4×C11#50111yescharacteristic
185C4×C11#50111yescharacteristic
186Dic11—42no—
187Dic11—42no—
188Dic11—81no—
189Dic11—81no—
190C22×C8—21no—
191C22×C8—221no—
192C22×C8—221no—
193#125—442no—
194#125—442no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—222no—
205C2×C4⋊C4—222no—
206C2×C4⋊C4—222no—
207C2×C4⋊C4C22⋊D1112yes—
208C2×C42—221no—
209C2×C42—221no—
210C2×C42C22×D1111yescharacteristic
211#106—442no—
212#106—442no—
213C4⋊C8—112no—
214C4⋊C8—112no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4×C8—21no—
218C4×C8Dic2212yes—
219#95—222no—
220#95—221no—
221#95—221no—
222C2×C11#162611yescharacteristic
223C2×C11#163511yescharacteristic
224C2×C11#164211yescharacteristic
225C2×C11#164311yescharacteristic
226C2×C11#205811yescharacteristic
227C2×C11#205911yescharacteristic
228C2×C11#206111yescharacteristic
229C22×C4—22no—
230C22×C4—41no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4D4×D1111yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—222no—
242C2×C8—222no—
243C2×C8—441no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—112no—
258C4⋊C4—112no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—444no—
266C4⋊C4—444no—
267C4⋊C4—882no—
268C42—441no—
269C42—441no—
270C42—441no—
271C42—441no—
272C42C2×Dic2211yescharacteristic
273C42#433911yescharacteristic
274C42Q8×D1111yescharacteristic
275C42Q8×D1111yescharacteristic
276C11#1058211yescharacteristic, complemented, Sylow
277C23#6699011yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4#6694111yescharacteristic
299C2×C4#6694111yescharacteristic
300C2×C4#6694911yescharacteristic
301C2×C4#6694911yescharacteristic
302C2×C4#6696411yescharacteristic
303C2×C4#6696511yescharacteristic
304C2×C4SD16×D1111yescharacteristic
305C2×C4SD16×D1111yescharacteristic
306C2×C4#6696711yescharacteristic
307C2×C4#6696811yescharacteristic
308C2×C4#6697111yescharacteristic
309C2×C4#6697211yescharacteristic
310C2×C4#6697711yescharacteristic
311C2×C4#6699711yescharacteristic
312C8—42no—
313C8—442no—
314C8—442no—
315C22#1062259211yescharacteristic
316C22#1062267411yescharacteristic
317C22#1062267511yescharacteristic
318C22#1062277111yescharacteristic
319C22#1062278211yescharacteristic
320C22#1062278311yescharacteristic
321C22#1062280011yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—161no—
326C4—442no—
327C4—442no—
328C4—881no—
329C4—881no—
330C4#1062246711yescharacteristic
331C4#1062246811yescharacteristic
332C4#1062246911yescharacteristic
333C4#1062248311yescharacteristic
334C4#1062248911yescharacteristic
335C4#1062249011yescharacteristic
336C4#1062249111yescharacteristic
337C4#1062250411yescharacteristic
338C2#1306770911yescharacteristic
339C2#1306776411yescharacteristic
340C2#1306781311yescharacteristic
341C2#1306782011yescharacteristic
342C2#1306994711yescharacteristic
343C2#1306995211yescharacteristic
344C2#1306996611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1834C2
socle, prime radicalC23×C11#120
hypercenter#1834D11
hypocenterC11#10582
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
276. C11#10582semidirect

Maximal subgroups

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

subgroupindex
#130736522
#130693772
#130664992
#130664562
C11×#18342
#1058211