Finite Group Databasebeta

← #14650708

Subgroups — #14650708

Order 2816.

530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078707C211yesmaximal, characteristic
2#13071259C211yesmaximal, characteristic, complemented
3#13069535C211yesmaximal, characteristic, complemented
4#13067125C211yesmaximal, characteristic, complemented
5#13066510C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1490C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622834—21no—
13#10622830—21no—
14#10622825—21no—
15#10622824—21no—
16C2×#66889—22no—
17#10622628C412yescomplemented
18#10622627—22no—
19#10622621C412yescomplemented
20#10622598—21no—
21#10622581—21no—
22#10622564—22no—
23C4×C4⋊Dic11C2211yescharacteristic
24#10622545C2211yescharacteristic
25#10622539C2211yescharacteristic
26C11×D4⋊C8—22no—
27#10622108—21no—
28#10622108—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×#4339—21no—
32C2×C11×M16—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11C2×C412yes—
36C4×D4×C11D412yes—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—22no—
42C2×#4323—22no—
43#66983—21no—
44#66983—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—22no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11D412yes—
49#66928—21no—
50#66927C2×C411yescharacteristic
51C4×D44—21no—
52C4×D44—21no—
53#66922C2×C411yescharacteristic
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59#66896—22no—
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66#66889—44no—
67#66873—22no—
68#66872—22no—
69C4⋊(C11⋊C8)C2×C412yes—
70#66867—21no—
71#9329—111nomaximal, Sylow
72C24×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—42no—
75C2×D4×C11C22⋊C412yes—
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×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—22no—
86C22×Dic11—21no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44—21no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4C22⋊C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—82no—
107C22⋊Dic11—82no—
108#4323—44no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4⋊Dic11—82no—
115C4×Dic11—42no—
116C4×Dic11—42no—
117C2×C11⋊C8—22no—
118#3109—111no—
119#2319—111no—
120#1980—111no—
121#1505—111no—
122#1490D1111yescharacteristic, complemented
123#1300—111no—
124#1285—111no—
125C23×C11—22no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C22×D11—41no—
132D4×C11—22no—
133D4×C11—22no—
134D4×C11—42no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C22⋊D11—81no—
150C22⋊D11—81no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161D44—42no—
162D44—42no—
163D44—81no—
164C4×D11—82no—
165Dic22—42no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169#532—111no—
170C2×C4×D4C2×D1111yescharacteristic
171#481—221no—
172#476—112no—
173#459—112no—
174#447—221no—
175#442—222no—
176#432—111no—
177#432C2×D1111yescharacteristic
178C2×#104—222no—
179C4×M16C2×D1111yescharacteristic
180#390—221no—
181#389—221no—
182#388—222no—
183#381—221no—
184#380—221no—
185C4×C4⋊C4—111no—
186#376—111no—
187#327—221no—
188#327—221no—
189D4⋊C8—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11#38611yescharacteristic
198C22×C11#45311yescharacteristic
199C22×C11#45411yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—42no—
209C4×C11#42112yes—
210Dic11—81no—
211Dic11—82no—
212Dic11—81no—
213Dic11—81no—
214C2×#41—221no—
215C22×D4D4411yescharacteristic
216C23×C4—21no—
217C2×D8—222no—
218C2×M16—21no—
219C4⋊Q8—111no—
220#127—111no—
221#124—221no—
222#121—221no—
223#121—221no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4C4×D1112yes—
229C4×D4C22⋊D1112yes—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—222no—
232C2×C4⋊C4D4411yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—222no—
235C2×C22⋊C4—222no—
236C2×C42—112no—
237C2×C42—221no—
238C2×C42C22×D1111yescharacteristic
239#106—222no—
240C4⋊C8—21no—
241C4⋊C8—112no—
242#104—444no—
243#102—222no—
244#102—222no—
245C22⋊C8—21no—
246C22⋊C8—221no—
247#97—21no—
248#97—21no—
249#97—221no—
250C4×C8—21no—
251#95—111no—
252#95—111no—
253#95—222no—
254#95—221no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—82no—
259C2×C11#188311yescharacteristic
260C2×C11#189711yescharacteristic
261C2×C11#190411yescharacteristic
262D11—161no—
263C24—21no—
264#41—442no—
265#41—442no—
266C2×Q8—221no—
267C2×D4—21no—
268C2×D4—42no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—441no—
273C2×D4(C2×D11)⋊C412yes—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—82no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—222no—
281C22×C4—441no—
282C22×C4C2×D4411yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285D8—444no—
286M16—22no—
287M16—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—222no—
291C4⋊C4—21no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—882no—
296C4⋊C4(C2×D11)⋊C412yes—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—882no—
302C22⋊C4—882no—
303C42—442no—
304C42—442no—
305C42C2×C4×D1111yescharacteristic
306C42#434111yescharacteristic
307C42#434111yescharacteristic
308C42C2×C22⋊D1111yescharacteristic
309C11#932911yescharacteristic, complemented, Sylow
310C23—22no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23—41no—
315C23—441no—
316C23#6693511yescharacteristic
317Q8—442no—
318D4—22no—
319D4—22no—
320D4—42no—
321D4—442no—
322D4—442no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—882no—
345C2×C4(C22⋊D11)⋊C411yescharacteristic
346C2×C4(C22⋊D11)⋊C411yescharacteristic
347C2×C4#6693911yescharacteristic
348C2×C4C2×(C2×D11)⋊C411yescharacteristic
349C2×C4#6699211yescharacteristic
350C2×C4#6699211yescharacteristic
351C8—42no—
352C8—81no—
353C8—442no—
354C22—21no—
355C22—21no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—82no—
360C22—82no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22#1062243511yescharacteristic
365C22#1062244011yescharacteristic
366C22#1062257111yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—42no—
373C4—881no—
374C4—882no—
375C4—881no—
376C4—881no—
377C4#1062275212yes—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—1761no—
382C2#1306899011yescharacteristic
383C2#1306906211yescharacteristic
384C2#1306910111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1490C2
socleC22×C11#386
prime radical#13078707C2
cosocleC2×C42×C11C23
hypercenter#1490D11
hypocenterC11#9329
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #13071259C2semidirect
3. #13069535C2semidirect
4. #13067125C2semidirect
5. #13066510C2semidirect
6. #13066471C2semidirect
7. C11×#1490C2semidirect
17. #10622628C4semidirect
19. #10622621C4semidirect
122. #1490D11semidirect
309. C11#9329semidirect

Maximal subgroups

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

subgroupindex
#130787072
#130712592
#130695352
#130671252
#130665102
#130664712
C11×#14902
#932911