Finite Group Databasebeta

← #14650539

Subgroups — #14650539

Order 2816.

542 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 113 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#13078076C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic, complemented
3#13068623C211yesmaximal, characteristic, complemented
4#13067015C211yesmaximal, characteristic, complemented
5#13066512C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67002—21no—
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622845—21no—
14#10622696C412yescomplemented
15#10622685C412yescomplemented
16#10622670—22no—
17C2×#66873—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24C11×#327—22no—
25D4⋊(C11⋊C8)—22no—
26#10622167—21no—
27C2×C11×#41—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#127C2×C411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11C2311yescharacteristic
39#67002—42no—
40#67002—42no—
41C2×#4325—22no—
42C2×#4323—22no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C2×C8×D11—24no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44C2×C412yes—
51C4×D44D412yes—
52C11×C4⋊C8—21no—
53C11×C22⋊C8D412yes—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57#66899—22no—
58#66896—22no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—24no—
61#66873—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)C2×C412yes—
67C4×C11⋊C8D412yes—
68#9305—111nomaximal, Sylow
69C23×D11—21no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44C22⋊C412yes—
89C2×D44D812yes—
90C2×D44SD1612yes—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—82no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105#4325—44no—
106#4323—44no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11C22⋊C412yes—
111#4318—41no—
112#4318—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C8×D11—84no—
119#3036—111no—
120#2972—111no—
121#1804—111no—
122#1517D1111yescharacteristic, complemented
123#1480—111no—
124#1301—111no—
125#1286—111no—
126C23×C11—41no—
127C23×C11#12111yescharacteristic
128C22×D11—22no—
129C22×D11—22no—
130C22×D11—22no—
131C22×D11—81no—
132C22×D11—81no—
133Q8×C11—41no—
134Q8×C11—41no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×SD1611yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—81no—
161D44—22no—
162D44—22no—
163D44—22no—
164D44#10214yes—
165C4×D11—44no—
166C4×D11—82no—
167C8×C11—42no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170C11⋊C8—81no—
171C2×AGL(1,ℤ/8)—221no—
172#532C2×D1111yescharacteristic
173C2×C4×D4—111no—
174#463—222no—
175#461—112no—
176#459—112no—
177C8×D4—222no—
178C8×D4—222no—
179#431—111no—
180#431C2×D1111yescharacteristic
181#423—111no—
182C2×C4⋊C8—111no—
183#417—221no—
184C2×#102—221no—
185C2×C22⋊C8—222no—
186#382C2×D1111yescharacteristic
187#340—221no—
188#327—22no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11#38611yescharacteristic
196C22×C11#46511yescharacteristic
197C22×C11#46611yescharacteristic
198C2×D11—24no—
199C2×D11—42no—
200C2×D11—42no—
201C2×D11—82no—
202C2×D11—82no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—81no—
208C4×C11—161no—
209C4×C11C2×#10211yescharacteristic
210C4×C11#41611yescharacteristic
211C4×C11#46511yescharacteristic
212C4×C11#46611yescharacteristic
213Dic11—42no—
214C2×#41—21no—
215C22×D4—111no—
216C23×C4—221no—
217AGL(1,ℤ/8)—442no—
218AGL(1,ℤ/8)—442no—
219C2×SD16—222no—
220C2×D8—222no—
221C2×M16—221no—
222C22×C8—224no—
223C22×C8—221no—
224C4⋊Q8C4×D1111yescharacteristic
225#127C4×D1111yescharacteristic
226#124—21no—
227#121—21no—
228#121—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4—112no—
232C4×D4—112no—
233C4×D4—221no—
234C4×D4—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—112no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245#103—222no—
246#102—222no—
247#102—442no—
248C22⋊C8—224no—
249C22⋊C8—221no—
250C22⋊C8C22⋊D1112yes—
251C4×C8—21no—
252C4×C8—112no—
253#95—21no—
254#95—21no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—161no—
258C2×C11#188111yescharacteristic
259C2×C11#189311yescharacteristic
260C2×C11#190411yescharacteristic
261D11—44no—
262C24—221no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—112no—
273C2×D4—112no—
274C2×D4—112no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—221no—
281C22×C4—222no—
282C22×C4—222no—
283C22×C4—882no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—444no—
288D8—444no—
289M16—441no—
290M16—441no—
291C2×C8—22no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8—441no—
297C2×C8—884no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—112no—
303C4⋊C4—221no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C42C2×C4×D1111yescharacteristic
309C42#433911yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C11#930511yescharacteristic, complemented, Sylow
313C23—41no—
314C23—222no—
315C23—222no—
316C23—222no—
317C23—881no—
318C23—881no—
319C23#6699111yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—81no—
326D4—81no—
327D4—81no—
328D4—114no—
329D4—222no—
330D4—222no—
331D4—222no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—222no—
341C2×C4—444no—
342C2×C4—882no—
343C2×C4—881no—
344C2×C4C22⋊C4×D1111yescharacteristic
345C2×C4(C22⋊D11)⋊C411yescharacteristic
346C2×C4#6693611yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4D8×D1111yescharacteristic
349C2×C4#6696511yescharacteristic
350C2×C4SD16×D1111yescharacteristic
351C2×C4#6696911yescharacteristic
352C2×C4C4×C22⋊D1111yescharacteristic
353C2×C4#6699011yescharacteristic
354C8—42no—
355C8—442no—
356C8—442no—
357C8—881no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—224no—
364C22—442no—
365C22—442no—
366C22—882no—
367C22—882no—
368C22#1062256911yescharacteristic
369C22#1062277011yescharacteristic
370C22#1062278411yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—161no—
377C4—442no—
378C4D11×#10211yescharacteristic
379C4#1062238511yescharacteristic
380C4#1062238811yescharacteristic
381C4#1062239111yescharacteristic
382C2—21no—
383C2—21no—
384C2—161no—
385C2—444no—
386C2#1306897511yescharacteristic
387C2#1306904111yescharacteristic
388C2#1306910611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#386
prime radical#13078076C2
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9305
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13077639C2semidirect
3. #13068623C2semidirect
4. #13067015C2semidirect
5. #13066512C2semidirect
6. #13066474C2semidirect
7. C11×#1517C2semidirect
14. #10622696C4semidirect
15. #10622685C4semidirect
122. #1517D11semidirect
312. C11#9305semidirect

Maximal subgroups

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

subgroupindex
#130780762
#130776392
#130686232
#130670152
#130665122
#130664742
C11×#15172
#930511