Finite Group Databasebeta

← #14960216

Subgroups — #14960216

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076881C211yesmaximal, characteristic, complemented
2#13076731C216yesmaximal, complemented
3#13076709C213yesmaximal, complemented
4#13076703C212yesmaximal, complemented
5#13076614C213yesmaximal, complemented
6#13071919C212yesmaximal, complemented
7#13071896C211yesmaximal, characteristic, complemented
8#13071878C213yesmaximal, complemented
9#13071857C216yesmaximal, complemented
10#13071117C213yesmaximal, complemented
11C11×#2834C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×#66946C2216yes—
14C2×#66946C2213yescomplemented
15C2×#66945C2213yescomplemented
16C2×#66935C2213yes—
17C2×(C22⋊D11)⋊C4C2213yes—
18C11×#401C2212yescomplemented
19C11×#399C2211yescharacteristic
20C11×#398C2216yescomplemented
21C11×#397C2213yes—
22C11×#385C2213yes—
23#10622826C2213yes—
24#10622607C2216yes—
25#10622607C2216yescomplemented
26#10622606C2216yescomplemented
27#10622605C2213yescomplemented
28#10622604C2216yes—
29#10622602C2216yes—
30#10622593C2213yescomplemented
31#10622573C2213yes—
32#10622572C2216yes—
33#10622568C2213yes—
34#10622562C2213yes—
35C22⋊C4×Dic11C2213yes—
36#10622289C2212yes—
37#10622288C2216yes—
38#10622288C2216yescomplemented
39#10622285C2216yes—
40#10622285C2216yescomplemented
41#10622284C2216yes—
42#10622284C2211yescharacteristic, complemented
43#10622279C2216yes—
44#10622279C2213yescomplemented
45#10622278C2216yes—
46#10622272C2213yescomplemented
47#10622271C2216yescomplemented
48#10622262C2216yescomplemented
49#10622261C2211yescharacteristic, complemented
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11C2313yes—
53C23×Dic11C2311yescharacteristic
54C22×D44C2316yes—
55C22×D44C2313yes—
56C22×C4×D11—46no—
57C22×C4×D11C2313yes—
58C22×C4×D11C2312yes—
59C22×C4×D11C2312yes—
60C2×C11×C4⋊C4C2313yes—
61C2×C11×C4⋊C4C2316yes—
62C2×C11×C4⋊C4C2313yes—
63C2×C11×C22⋊C4C2313yes—
64C2×C11×C22⋊C4C2313yes—
65C2×C22⋊Dic11C2313yes—
66C2×(C2×D11)⋊C4C2316yes—
67C2×(C2×D11)⋊C4C2313yes—
68C2×(C2×D11)⋊C4C2316yes—
69C2×(C2×D11)⋊C4C2316yes—
70C2×(C2×D11)⋊C4C2316yes—
71C2×(C2×D11)⋊C4C2316yes—
72C2×(C2×D11)⋊C4C2316yes—
73C2×(C2×D11)⋊C4C2316yes—
74C2×C4⋊Dic11C2313yes—
75C2×Dic11⋊C4C2313yes—
76C2×Dic11⋊C4C2316yes—
77C2×Dic11⋊C4C2316yes—
78C2×C4×Dic11C2313yes—
79C2×C4×Dic11C2316yes—
80#66946—412no—
81#66946—46no—
82#66945—46no—
83#66935—212no—
84(C22⋊D11)⋊C4—46no—
85C11×#95C2311yescharacteristic
86C11×#95C2316yes—
87C11×#95C2316yes—
88C11×#95C2313yes—
89C11⋊#95C2313yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93C11⋊#95C2313yes—
94#36676—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—43no—
97C23×D11—43no—
98C23×D11#4114yes—
99C23×D11C2413yes—
100C23×D11C2412yes—
101C22×C4×C11—43no—
102C22×C4×C11C2412yes—
103C22×C4×C11C2416yes—
104C22×C4×C11C2413yes—
105C22×C4×C11C2413yes—
106C2×C22⋊D11—26no—
107C2×C22⋊D11—43no—
108C2×C22⋊D11—43no—
109C22×Dic11—26no—
110C22×Dic11C2413yes—
111C22×Dic11C2411yescharacteristic
112C22×Dic11C2416yes—
113C22×Dic11C2411yescharacteristic
114C2×D44—212no—
115C2×D44—43no—
116C2×D44—46no—
117C2×D44—46no—
118C2×D44—46no—
119C2×C4×D11—26no—
120C2×C4×D11—212no—
121C2×C4×D11—212no—
122C2×C4×D11—46no—
123C2×C4×D11—416no—
124C11×C4⋊C4—43no—
125C11×C4⋊C4—43no—
126C11×C4⋊C4—46no—
127C11×C22⋊C4—26no—
128C11×C22⋊C4—43no—
129C22⋊Dic11—43no—
130(C2×D11)⋊C4—212no—
131(C2×D11)⋊C4—43no—
132(C2×D11)⋊C4—46no—
133(C2×D11)⋊C4—46no—
134(C2×D11)⋊C4—46no—
135(C2×D11)⋊C4—46no—
136(C2×D11)⋊C4—46no—
137(C2×D11)⋊C4—46no—
138C4⋊Dic11—43no—
139Dic11⋊C4—43no—
140Dic11⋊C4—46no—
141Dic11⋊C4—46no—
142C4×Dic11—26no—
143C4×Dic11—212no—
144#2842—111no—
145#2834D1111yescharacteristic, complemented
146#2827—116no—
147#2826—113no—
148#2825—112no—
149#2812—113no—
150#2401—112no—
151#2397—111no—
152#2395—113no—
153#2392—116no—
154C4×#120—113no—
155C23×C11—23no—
156C23×C11—23no—
157C23×C11C2×#4112yes—
158C23×C11C2511yescharacteristic
159C22×D11—26no—
160C22×D11—26no—
161C22×D11—23no—
162C22×D11—23no—
163C22×D11—26no—
164C22×D11—26no—
165C22×D11—23no—
166C22×D11—412no—
167C22×D11—44no—
168C22×D11—412no—
169C22×D11C2×#4114yes—
170C2×C4×C11—26no—
171C2×C4×C11—23no—
172C2×C4×C11—26no—
173C2×C4×C11—23no—
174C2×C4×C11—26no—
175C2×C4×C11—26no—
176C2×C4×C11—26no—
177C2×C4×C11—26no—
178C2×C4×C11—44no—
179C22⋊D11—412no—
180C2×Dic11—23no—
181C2×Dic11—23no—
182C2×Dic11—26no—
183C2×Dic11—23no—
184C2×Dic11—26no—
185C2×Dic11—23no—
186C2×Dic11—26no—
187C2×Dic11—44no—
188C2×Dic11H(5,𝔽2)16yes—
189D44—424no—
190D44—412no—
191C4×D11—48no—
192C4×D11—412no—
193C4×D11—48no—
194C24×C4—111no—
195C2×#120—113no—
196C2×C4×D4—116no—
197C2×C4×D4—113no—
198C2×C4×D4—113no—
199C2×#117—113no—
200#401C2×D1112yescomplemented
201#400—116no—
202#400—113no—
203#399—113no—
204#399—113no—
205#399C2×D1111yescharacteristic
206#398—113no—
207#398C2×D1116yescomplemented
208#397—116no—
209#397—116no—
210#397—116no—
211#397C2×D1113yes—
212#396—116no—
213#396—116no—
214#396—112no—
215#394—116no—
216#394—116no—
217#394—116no—
218#394—116no—
219#392—113no—
220#392—111no—
221#392—116no—
222#386—113no—
223#386—116no—
224#385—116no—
225#385C2×D1113yes—
226#379—113no—
227C4×C4⋊C4—116no—
228C4×C22⋊C4—113no—
229C4×C22⋊C4—116no—
230C4×C22⋊C4—113no—
231#376—111no—
232C22×C11—26no—
233C22×C11—41no—
234C22×C11—43no—
235C22×C11C22×#4111yescharacteristic
236C22×C11C2×H(5,𝔽2)13yes—
237C22×C11#58513yes—
238C2×D11—212no—
239C2×D11—416no—
240C2×D11—42no—
241C2×D11—46no—
242C2×D11—46no—
243C2×D11—43no—
244C2×D11—43no—
245C2×D11—43no—
246C2×D11—46no—
247C4×C11—46no—
248C4×C11—42no—
249C4×C11—43no—
250C4×C11—43no—
251Dic11—43no—
252Dic11—41no—
253Dic11—46no—
254Dic11#56014yes—
255C25—111no—
256C22×D4—113no—
257C22×D4—116no—
258C22×D4—113no—
259C23×C4—111no—
260C23×C4—113no—
261C23×C4—112no—
262C23×C4—112no—
263C23×C4—446no—
264C23×C4C22×D1111yescharacteristic
265#120—2212no—
266C4×D4—446no—
267C4×D4—4412no—
268C4×D4—446no—
269#117—446no—
270C2×C4⋊C4—113no—
271C2×C4⋊C4—113no—
272C2×C4⋊C4—116no—
273C2×C4⋊C4—116no—
274C2×C4⋊C4C22×D1113yes—
275C2×C4⋊C4C22×D1116yes—
276C2×C4⋊C4C22×D1113yes—
277C2×C22⋊C4—116no—
278C2×C22⋊C4—113no—
279C2×C22⋊C4—116no—
280C2×C22⋊C4—116no—
281C2×C22⋊C4—113no—
282C2×C22⋊C4—116no—
283C2×C22⋊C4—116no—
284C2×C22⋊C4—116no—
285C2×C22⋊C4—116no—
286C2×C22⋊C4C22×D1113yes—
287C2×C22⋊C4C22×D1113yes—
288C2×C42—116no—
289C2×C42—113no—
290#95—113no—
291#95—116no—
292#95—116no—
293#95—113no—
294#95—116no—
295#95C22×D1111yescharacteristic
296#95C22×D1116yes—
297#95C22×D1113yes—
298#95C22×D1116yes—
299C2×C11—42no—
300C2×C11#345913yes—
301C2×C11C2×#56011yescharacteristic
302C2×C11#352913yes—
303D11—44no—
304D11—83no—
305C24—112no—
306C24—114no—
307C24—113no—
308C24—443no—
309C24—443no—
310C24C23×D1111yescharacteristic
311C2×D4—2212no—
312C2×D4—226no—
313C2×D4—443no—
314C2×D4—446no—
315C2×D4—446no—
316C2×D4—446no—
317C2×D4—443no—
318C2×D4—443no—
319C22×C4—43no—
320C22×C4—111no—
321C22×C4—113no—
322C22×C4—111no—
323C22×C4—116no—
324C22×C4—226no—
325C22×C4—2212no—
326C22×C4—2212no—
327C22×C4—226no—
328C22×C4—446no—
329C22×C4—4416no—
330C22×C4C23×D1112yes—
331C22×C4C23×D1116yes—
332C22×C4C23×D1113yes—
333C22×C4C23×D1113yes—
334C4⋊C4—43no—
335C4⋊C4—43no—
336C4⋊C4—46no—
337C4⋊C4—443no—
338C4⋊C4—443no—
339C4⋊C4—446no—
340C4⋊C4—446no—
341C22⋊C4—26no—
342C22⋊C4—43no—
343C22⋊C4—2212no—
344C22⋊C4—446no—
345C22⋊C4—443no—
346C22⋊C4—446no—
347C22⋊C4—446no—
348C22⋊C4—446no—
349C22⋊C4—446no—
350C22⋊C4—446no—
351C22⋊C4—443no—
352C42—2212no—
353C42—226no—
354C11#3667611yescharacteristic, complemented, Sylow
355C23—23no—
356C23—23no—
357C23—114no—
358C23—226no—
359C23—226no—
360C23—223no—
361C23—223no—
362C23—226no—
363C23—226no—
364C23—223no—
365C23—4412no—
366C23—444no—
367C23—4412no—
368C23#41×D1112yes—
369C23C24×D1111yescharacteristic
370D4—4424no—
371D4—4412no—
372D4—4412no—
373C2×C4—26no—
374C2×C4—23no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—26no—
378C2×C4—26no—
379C2×C4—26no—
380C2×C4—26no—
381C2×C4—44no—
382C2×C4—116no—
383C2×C4—223no—
384C2×C4—226no—
385C2×C4—223no—
386C2×C4—223no—
387C2×C4—226no—
388C2×C4—226no—
389C2×C4—223no—
390C2×C4—448no—
391C2×C4—4412no—
392C2×C4—448no—
393C2×C4—444no—
394C22—26no—
395C22—41no—
396C22—43no—
397C22—2212no—
398C22—4416no—
399C22—442no—
400C22—446no—
401C22—443no—
402C22—446no—
403C22—443no—
404C22—446no—
405C22—443no—
406C22C2×#41×D1111yescharacteristic
407C22D11×H(5,𝔽2)13yes—
408C22#1062345713yes—
409C4—42no—
410C4—43no—
411C4—43no—
412C4—46no—
413C4—114no—
414C4—441no—
415C4—446no—
416C4—443no—
417C2—42no—
418C2—444no—
419C2—883no—
420C2#1308202413yes—
421C2D11×#56011yescharacteristic
422C2#1308275713yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2834C2
hypercenter#2834D11
hypocenterC11#36676
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2834

Complements

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

NH ≅ G/Ntype
1. #13076881C2semidirect
2. #13076731C2semidirect
3. #13076709C2semidirect
4. #13076703C2semidirect
5. #13076614C2semidirect
6. #13071919C2semidirect
7. #13071896C2semidirect
8. #13071878C2semidirect
9. #13071857C2semidirect
10. #13071117C2semidirect
11. C11×#2834C2semidirect
14. C2×#66946C22semidirect
15. C2×#66945C22semidirect
18. C11×#401C22semidirect
20. C11×#398C22semidirect
25. #10622607C22semidirect
26. #10622606C22semidirect
27. #10622605C22semidirect
30. #10622593C22semidirect
38. #10622288C22semidirect
40. #10622285C22semidirect
42. #10622284C22semidirect
44. #10622279C22semidirect
46. #10622272C22semidirect
47. #10622271C22semidirect
48. #10622262C22semidirect
49. #10622261C22semidirect
145. #2834D11semidirect
200. #401C2×D11semidirect
207. #398C2×D11semidirect
354. C11#36676semidirect

Maximal subgroups

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

subgroupindex
#130768812
#130767312
#130767092
#130767032
#130766142
#130719192
#130718962
#130718782
#130718572
#130711172
C11×#28342
#3667611