Finite Group Databasebeta

← #14650543

Subgroups — #14650543

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#13078082C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic, complemented
3#13068627C211yesmaximal, characteristic, complemented
4#13067177C211yesmaximal, characteristic, complemented
5#13067014C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×#66961—21no—
9#10623008C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622746—21no—
15C2×#66885—21no—
16#10622549C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622457—22no—
19#10622456C412yescomplemented
20#10622454C412yescomplemented
21#10622447—22no—
22D11×C22⋊C8—22no—
23C8×D44—22no—
24#10622189—21no—
25#10622121—22no—
26#10622108—22no—
27C2×#4339—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×M16—21no—
31C22×C8×C11—21no—
32C2×C42×C11C2311yescharacteristic
33#66983—21no—
34#66983—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38#66961—42no—
39#66961—42no—
40C2×D88—22no—
41C2×#4314—22no—
42C2×C8×D11—24no—
43#66928—21no—
44#66927C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44C2×C412yes—
50C4×D44D412yes—
51#66922C2×C411yescharacteristic
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8C2×C412yes—
57C11×C22⋊C8D412yes—
58C4×C8×C11—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62#66885—22no—
63#66885—42no—
64(C2×D11)⋊C8—24no—
65#66880—22no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8D412yes—
68#9305—111nomaximal, Sylow
69C23×D11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C2×C22⋊D11—41no—
74C22×Dic11—21no—
75C22×Dic11—41no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44C22⋊C412yes—
87C2×D44D812yes—
88C2×D44SD1612yes—
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—41no—
92C2×C4×D11—82no—
93C2×Dic22—21no—
94C11×M16—41no—
95C11×M16—41no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11C22⋊C412yes—
115C2×C11⋊C8—22no—
116D88—44no—
117#4314—44no—
118C8×D11—84no—
119#3036—111no—
120#2972—111no—
121#1804—111no—
122#1517—111no—
123#1480—111no—
124#1301D1111yescharacteristic, complemented
125#1286—111no—
126C23×C11#12111yescharacteristic
127C22×D11—22no—
128C22×D11—22no—
129C22×D11—22no—
130C22×D11—41no—
131C22×D11—81no—
132C22×D11—81no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×C4×C11C2×D811yescharacteristic
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C22⋊D11—81no—
146C22⋊D11—81no—
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153D44—22no—
154D44—22no—
155D44—22no—
156D44—42no—
157D44—41no—
158D44—41no—
159D44—81no—
160D44#10214yes—
161C4×D11—44no—
162C4×D11—82no—
163C4×D11—81no—
164C4×D11—81no—
165Dic22—41no—
166Dic22—41no—
167C8×C11—42no—
168C8×C11—42no—
169C8×C11—81no—
170C11⋊C8—42no—
171C2×AGL(1,ℤ/8)—221no—
172#532—111no—
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#423C2×D1111yescharacteristic
182C2×C4⋊C8C2×D1111yescharacteristic
183#417—221no—
184C2×#102—221no—
185C2×C22⋊C8—222no—
186#382—111no—
187#340—221no—
188#327—222no—
189D4⋊C8—222no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11#38611yescharacteristic
193C22×C11#46511yescharacteristic
194C22×C11#46611yescharacteristic
195C2×D11—24no—
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11C2×#10211yescharacteristic
208C4×C11#41611yescharacteristic
209C4×C11#46511yescharacteristic
210C4×C11#46611yescharacteristic
211Dic11—42no—
212Dic11—81no—
213Dic11—161no—
214C2×#41—221no—
215C22×D4—111no—
216C23×C4—221no—
217AGL(1,ℤ/8)—442no—
218AGL(1,ℤ/8)—442no—
219C2×SD16—222no—
220C2×D8—222no—
221C2×M16—21no—
222C22×C8—21no—
223C22×C8—224no—
224C4⋊Q8—111no—
225#127—111no—
226#124—221no—
227#121—221no—
228#121—221no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234C4×D4—221no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—221no—
244C4⋊C8C4×D1112yes—
245#103—222no—
246#102—222no—
247#102—442no—
248C22⋊C8—224no—
249C22⋊C8—221no—
250C22⋊C8D4412yes—
251C4×C8—21no—
252C4×C8—112no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11#188111yescharacteristic
258C2×C11#189311yescharacteristic
259C2×C11#190411yescharacteristic
260D11—44no—
261D11—161no—
262C24—221no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—221no—
268C2×D4—112no—
269C2×D4—112no—
270C2×D4—112no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—441no—
278C22×C4—221no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4—882no—
284C22×C4C2×D4411yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4#434311yescharacteristic
287SD16—444no—
288D8—444no—
289M16—41no—
290M16—41no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—222no—
297C2×C8—884no—
298C4⋊C4—112no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C42C2×C4×D1111yescharacteristic
309C42#433911yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C11#930511yescharacteristic, complemented, Sylow
313C23—222no—
314C23—222no—
315C23—222no—
316C23—441no—
317C23—881no—
318C23—881no—
319C23#6694811yescharacteristic
320Q8—441no—
321Q8—441no—
322D4—114no—
323D4—222no—
324D4—222no—
325D4—222no—
326D4—442no—
327D4—441no—
328D4—441no—
329D4—881no—
330D4—881no—
331D4—881no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—222no—
335C2×C4—444no—
336C2×C4—441no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4C4×D4411yescharacteristic
345C2×C4C22⋊C4×D1111yescharacteristic
346C2×C4#6693511yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6694611yescharacteristic
349C2×C4#6694711yescharacteristic
350C2×C4D8×D1111yescharacteristic
351C2×C4SD16×D1111yescharacteristic
352C2×C4#6696911yescharacteristic
353C2×C4#6697211yescharacteristic
354C8—42no—
355C8—42no—
356C8—81no—
357C8—442no—
358C22—21no—
359C22—21no—
360C22—224no—
361C22—442no—
362C22—442no—
363C22—882no—
364C22—882no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22#1062227811yescharacteristic
369C22#1062247711yescharacteristic
370C22#1062249611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—442no—
376C4—881no—
377C4—1761no—
378C4D11×#10211yescharacteristic
379C4#1062238811yescharacteristic
380C4#1062241711yescharacteristic
381C4#1062242011yescharacteristic
382C2—21no—
383C2—21no—
384C2—444no—
385C2—1761no—
386C2#1306897911yescharacteristic
387C2#1306904311yescharacteristic
388C2#1306910211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#386
prime radical#13078082C2
cosocleC2×C42×C11C23
hypercenter#1301D11
hypocenterC11#9305
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #13077639C2semidirect
3. #13068627C2semidirect
4. #13067177C2semidirect
5. #13067014C2semidirect
6. #13066476C2semidirect
7. C11×#1301C2semidirect
19. #10622456C4semidirect
20. #10622454C4semidirect
124. #1301D11semidirect
312. C11#9305semidirect

Maximal subgroups

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

subgroupindex
#130780822
#130776392
#130686272
#130671772
#130670142
#130664762
C11×#13012
#930511