Finite Group Databasebeta

← #14650542

Subgroups — #14650542

Order 2816.

542 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078080C211yesmaximal, characteristic
2#13068626C211yesmaximal, characteristic, complemented
3#13067177C211yesmaximal, characteristic, complemented
4#13067016C211yesmaximal, characteristic, complemented
5#13066512C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#2972C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66985—21no—
10#10623008C2211yescharacteristic
11C8×D4×C11—22no—
12C8×D4×C11—22no—
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C22⋊C8—22no—
16C2×#66896—21no—
17#10622632C412yescomplemented
18#10622629—22no—
19#10622628C412yescomplemented
20#10622579—21no—
21#10622549C2211yescharacteristic
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622167—21no—
25#10622108—22no—
26#10622097—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C2×#4339—21no—
30C22×C8×C11—24no—
31C4×D4×C11—21no—
32C4×D4×C11—21no—
33C4×D4×C11C2×C412yes—
34C4×D4×C11D412yes—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4324—22no—
39#66985—42no—
40#66985—42no—
41C2×#4323—22no—
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47#66928—21no—
48#66927C2×C411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922C2×C411yescharacteristic
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—24no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8D412yes—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66896—42no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62#66874—22no—
63#66873—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)C2×C412yes—
68#9305—111nomaximal, Sylow
69C24×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11C22⋊C412yes—
74C2×D4×C11D812yes—
75C2×D4×C11SD1612yes—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—82no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—41no—
85#4339—41no—
86#4339—41no—
87#4339—41no—
88#4339—41no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—84no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4C22⋊C412yes—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105#4324—44no—
106#4323—44no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—41no—
114#4318—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#3036—111no—
120#2972D1111yescharacteristic, complemented
121#1804—111no—
122#1517—111no—
123#1480—111no—
124#1301—111no—
125#1286—111no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11#12111yescharacteristic
132C22×D11—41no—
133D4×C11—22no—
134D4×C11—22no—
135D4×C11—22no—
136D4×C11#10214yes—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—44no—
141C2×C4×C11—82no—
142C2×C4×C11—81no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C22⋊D11—81no—
154C22⋊D11—81no—
155C2×Dic11—41no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159D44—42no—
160D44—41no—
161D44—41no—
162D44—81no—
163C4×D11—81no—
164C4×D11—81no—
165Dic22—41no—
166Dic22—41no—
167C8×C11—42no—
168C8×C11—42no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×AGL(1,ℤ/8)—221no—
172#532—111no—
173C2×C4×D4C2×D1111yescharacteristic
174#463—222no—
175#461—112no—
176#459—112no—
177C8×D4—22no—
178C8×D4—22no—
179#431C2×D1111yescharacteristic
180#431C2×D1111yescharacteristic
181#423—111no—
182C2×C4⋊C8—111no—
183#417—221no—
184C2×#102—221no—
185C2×C22⋊C8—22no—
186#382—111no—
187#340—221no—
188#327—222no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—24no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11#38611yescharacteristic
198C22×C11#46511yescharacteristic
199C22×C11#46611yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11C2×#10211yescharacteristic
209C4×C11#41611yescharacteristic
210C4×C11#46511yescharacteristic
211C4×C11#46611yescharacteristic
212Dic11—81no—
213Dic11—161no—
214C2×#41—221no—
215C22×D4D4411yescharacteristic
216C23×C4—21no—
217AGL(1,ℤ/8)—442no—
218AGL(1,ℤ/8)—442no—
219C2×SD16—222no—
220C2×D8—222no—
221C2×M16—221no—
222C22×C8—24no—
223C22×C8—221no—
224C4⋊Q8—111no—
225#127—111no—
226#124—221no—
227#121—221no—
228#121—221no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4C4×D1112yes—
234C4×D4C22⋊D1112yes—
235C2×C4⋊C4—221no—
236C2×C4⋊C4D4411yescharacteristic
237C2×C22⋊C4—21no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—112no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#103—222no—
246#102—222no—
247#102—442no—
248C22⋊C8—24no—
249C22⋊C8—21no—
250C22⋊C8C22⋊D1112yes—
251C4×C8—21no—
252C4×C8C22⋊D1112yes—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—44no—
258C2×C11#188111yescharacteristic
259C2×C11#189311yescharacteristic
260C2×C11#190411yescharacteristic
261D11—161no—
262C24—21no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—221no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—441no—
275C2×D4#431412yes—
276C2×D4D8812yes—
277C2×D4(C2×D11)⋊C412yes—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—82no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4C2×D4411yescharacteristic
285C22×C4#433911yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—444no—
288D8—444no—
289M16—441no—
290M16—441no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—84no—
294C2×C8—222no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—21no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4(C2×D11)⋊C412yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42C2×C4×D1111yescharacteristic
309C42#433911yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#930511yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—22no—
316C23—81no—
317C23—81no—
318C23—441no—
319C23#6698311yescharacteristic
320Q8—441no—
321Q8—441no—
322D4—22no—
323D4—22no—
324D4—22no—
325D4—442no—
326D4—441no—
327D4—441no—
328D4—881no—
329D4—881no—
330D4—881no—
331D4#6688514yes—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4C2×#431411yescharacteristic
345C2×C4C2×D8811yescharacteristic
346C2×C4#6695711yescharacteristic
347C2×C4#6695711yescharacteristic
348C2×C4C2×(C2×D11)⋊C411yescharacteristic
349C2×C4C4×C22⋊D1111yescharacteristic
350C2×C4C4×C22⋊D1111yescharacteristic
351C2×C4#6698211yescharacteristic
352C2×C4#6698311yescharacteristic
353C2×C4#6700611yescharacteristic
354C8—42no—
355C8—42no—
356C8—442no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—24no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22#1062272711yescharacteristic
369C22#1062272811yescharacteristic
370C22#1062282611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—881no—
377C4—1761no—
378C4C2×#6688511yescharacteristic
379C4#1062272611yescharacteristic
380C4#1062272711yescharacteristic
381C4#1062272811yescharacteristic
382C2—21no—
383C2—21no—
384C2—44no—
385C2—1761no—
386C2#1306897811yescharacteristic
387C2#1306904411yescharacteristic
388C2#1306910311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2972C2
socleC22×C11#386
prime radical#13078080C2
cosocleC2×C42×C11C23
hypercenter#2972D11
hypocenterC11#9305
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13068626C2semidirect
3. #13067177C2semidirect
4. #13067016C2semidirect
5. #13066512C2semidirect
6. #13066475C2semidirect
7. C11×#2972C2semidirect
17. #10622632C4semidirect
19. #10622628C4semidirect
120. #2972D11semidirect
312. C11#9305semidirect

Maximal subgroups

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

subgroupindex
#130780802
#130686262
#130671772
#130670162
#130665122
#130664752
C11×#29722
#930511