Finite Group Databasebeta

← #14960201

Subgroups — #14960201

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076869C211yesmaximal, characteristic, complemented
2#13076806C213yesmaximal, complemented
3#13076699C216yesmaximal, complemented
4#13076698C213yesmaximal, complemented
5#13076611C212yesmaximal, complemented
6#13071904C216yesmaximal, complemented
7#13071901C213yesmaximal, complemented
8#13071828C213yesmaximal, complemented
9#120×Dic11C212yesmaximal, complemented
10#13071115C211yesmaximal, characteristic, complemented
11C11×#2812C211yesmaximal, characteristic, complemented
12C24×Dic11C2211yescharacteristic
13C22×#4341C2211yescharacteristic, complemented
14C2×C11×#120C2212yes—
15C2×#67006C2211yescharacteristic
16C2×D4×Dic11C2216yes—
17C2×#66940C2213yescomplemented
18C2×(C22⋊D11)⋊C4C2213yes—
19C11×#397C2213yes—
20C11×#394C2216yes—
21C11×#392C2213yes—
22C11×#379C2211yescharacteristic
23#10622860C2212yes—
24#10622836C2216yes—
25#10622835C2216yes—
26#10622835C2213yescomplemented
27#10622833C2216yes—
28#10622606C2213yescomplemented
29#10622599C2216yescomplemented
30#10622574C2216yescomplemented
31#10622572C2216yes—
32#10622571C2213yes—
33#10622565C2216yes—
34#10622565C2216yescomplemented
35#10622563C2216yes—
36#10622560C2213yes—
37#10622560C2216yes—
38#10622560C2213yes—
39#10622560C2216yescomplemented
40#10622559C2213yes—
41C22⋊C4×Dic11C2213yes—
42C22⋊C4×Dic11C2216yes—
43C22⋊C4×Dic11C2216yescomplemented
44#10622286C2213yescomplemented
45#10622279C2213yescomplemented
46#10622272C2216yescomplemented
47#10622271C2216yescomplemented
48#10622269C2213yescomplemented
49#10622261C2213yescomplemented
50C25×C11C2311yescharacteristic
51C22×D4×C11C2316yes—
52C22×D4×C11C2311yescharacteristic
53C22×C22⋊D11C2313yes—
54C22×C22⋊D11C2312yes—
55C23×Dic11—46no—
56C23×Dic11C2313yes—
57C23×Dic11C2312yes—
58C23×Dic11C2313yes—
59C2×#4341—46no—
60C22×C4×D11C2311yescharacteristic
61C22×Dic22C2313yes—
62C22×Dic22C2311yescharacteristic
63C11×#120—28no—
64C2×C11×C4⋊C4C2313yes—
65C2×C11×C22⋊C4C2316yes—
66C2×C11×C22⋊C4C2313yes—
67C2×C11×C22⋊C4C2313yes—
68C2×C11×C22⋊C4C2316yes—
69#67006—24no—
70C2×C22⋊Dic11C2313yes—
71C2×C22⋊Dic11C2316yes—
72C2×C22⋊Dic11C2316yes—
73C2×C22⋊Dic11C2316yes—
74C2×C22⋊Dic11C2316yes—
75D4×Dic11—412no—
76C2×(C2×D11)⋊C4C2313yes—
77C2×(C2×D11)⋊C4C2316yes—
78C2×C4⋊Dic11C2316yes—
79C2×Dic11⋊C4C2313yes—
80C2×Dic11⋊C4C2316yes—
81C2×C4×Dic11C2313yes—
82C2×C4×Dic11C2316yes—
83#66940—46no—
84(C22⋊D11)⋊C4—46no—
85C11×#95C2313yes—
86C11×#95C2313yes—
87C11⋊#95C2316yes—
88C11⋊#95C2313yes—
89C11⋊#95C2316yes—
90C11⋊#95C2313yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93C11⋊#95C2316yes—
94C11⋊#95C2316yes—
95#36675—111nomaximal, Sylow
96C24×C11—43no—
97C24×C11—43no—
98C24×C11#4114yescomplemented
99C24×C11C2412yes—
100C24×C11C2413yes—
101C23×D11C2411yescharacteristic
102C2×D4×C11—212no—
103C2×D4×C11—46no—
104C2×D4×C11—43no—
105C2×D4×C11—46no—
106C22×C4×C11C2413yes—
107C22×C4×C11C2416yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—26no—
110C2×C22⋊D11—43no—
111C2×C22⋊D11—46no—
112C2×C22⋊D11—43no—
113C22×Dic11—26no—
114C22×Dic11—212no—
115C22×Dic11—212no—
116C22×Dic11—46no—
117C22×Dic11—43no—
118C22×Dic11—416no—
119C22×Dic11C2413yes—
120C22×Dic11C2416yes—
121C22×Dic11C2413yes—
122C22×Dic11C2412yes—
123C22×Dic11C2411yescharacteristic
124#4341—416no—
125C2×C4×D11—26no—
126C2×Dic22—43no—
127C2×Dic22—46no—
128C2×Dic22—43no—
129C11×C4⋊C4—43no—
130C11×C22⋊C4—212no—
131C11×C22⋊C4—43no—
132C11×C22⋊C4—46no—
133C11×C22⋊C4—43no—
134C22⋊Dic11—26no—
135C22⋊Dic11—46no—
136C22⋊Dic11—46no—
137C22⋊Dic11—46no—
138C22⋊Dic11—46no—
139(C2×D11)⋊C4—43no—
140(C2×D11)⋊C4—46no—
141C4⋊Dic11—46no—
142Dic11⋊C4—43no—
143Dic11⋊C4—46no—
144C4×Dic11—26no—
145C4×Dic11—212no—
146#2840—111no—
147#2835—113no—
148#2824—116no—
149#2824—113no—
150#2812—112no—
151#2812D1111yescharacteristic, complemented
152#2398—113no—
153#2398—116no—
154#2388—113no—
155C4×#120—111no—
156C4×#120—112no—
157C23×C11—26no—
158C23×C11—23no—
159C23×C11—26no—
160C23×C11—23no—
161C23×C11—22no—
162C23×C11—26no—
163C23×C11—26no—
164C23×C11—412no—
165C23×C11—44no—
166C23×C11—412no—
167C23×C11C2×#4116yes—
168C23×C11C2511yescharacteristic
169C22×D11—21no—
170C22×D11—23no—
171C22×D11—23no—
172D4×C11—424no—
173D4×C11—44no—
174C2×C4×C11—26no—
175C2×C4×C11—26no—
176C2×C4×C11—23no—
177C2×C4×C11—23no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C22⋊D11—412no—
181C22⋊D11—48no—
182C2×Dic11—23no—
183C2×Dic11—23no—
184C2×Dic11—26no—
185C2×Dic11—23no—
186C2×Dic11—26no—
187C2×Dic11—26no—
188C2×Dic11—26no—
189C2×Dic11—26no—
190C2×Dic11—23no—
191C2×Dic11—412no—
192C2×Dic11—48no—
193C2×Dic11—412no—
194C2×Dic11H(5,𝔽2)16yes—
195C4×D11—44no—
196Dic22—412no—
197Dic22—44no—
198C22×#41—111no—
199C24×C4—111no—
200C2×#120—111no—
201C2×#120C2×D1112yes—
202C2×C4×Q8—113no—
203C2×C4×D4—116no—
204C2×C4×D4—113no—
205#400—116no—
206#400—116no—
207#400—116no—
208#397—113no—
209#397—116no—
210#397—116no—
211#397C2×D1113yes—
212#395—113no—
213#394—113no—
214#394—116no—
215#394—116no—
216#394—116no—
217#394C2×D1116yes—
218#393—116no—
219#393—116no—
220#393—113no—
221#393—113no—
222#393—113no—
223#392—116no—
224#392C2×D1113yes—
225#386—116no—
226#386—113no—
227#385—113no—
228#385—116no—
229#379—112no—
230#379C2×D1111yescharacteristic
231C4×C22⋊C4—116no—
232C4×C22⋊C4—113no—
233C4×C22⋊C4—116no—
234C4×C22⋊C4—113no—
235#376—113no—
236C22×C11—212no—
237C22×C11—26no—
238C22×C11—416no—
239C22×C11—43no—
240C22×C11—46no—
241C22×C11—43no—
242C22×C11—46no—
243C22×C11—42no—
244C22×C11—46no—
245C22×C11C22×#4111yescharacteristic
246C22×C11C2×H(5,𝔽2)13yes—
247C22×C11#58513yes—
248C2×D11—43no—
249C2×D11—41no—
250C2×D11—43no—
251C4×C11—46no—
252C4×C11—41no—
253C4×C11—43no—
254Dic11—43no—
255Dic11—42no—
256Dic11—43no—
257Dic11—46no—
258Dic11H(3,𝔽4)14yes—
259C25C22×D1111yescharacteristic
260C2×#41—446no—
261C22×Q8—113no—
262C22×Q8—111no—
263C22×D4—113no—
264C22×D4—112no—
265C22×D4C22×D1116yes—
266C22×D4C22×D1111yescharacteristic
267C23×C4—113no—
268C23×C4—112no—
269C23×C4—113no—
270C23×C4—111no—
271C23×C4—446no—
272#120—28no—
273#120—224no—
274C4×Q8—446no—
275C4×D4—446no—
276C4×D4—4412no—
277C2×C4⋊C4—113no—
278C2×C4⋊C4—116no—
279C2×C4⋊C4—116no—
280C2×C4⋊C4C22×D1113yes—
281C2×C22⋊C4—113no—
282C2×C22⋊C4—116no—
283C2×C22⋊C4—116no—
284C2×C22⋊C4—116no—
285C2×C22⋊C4—116no—
286C2×C22⋊C4—113no—
287C2×C22⋊C4—116no—
288C2×C22⋊C4C22×D1116yes—
289C2×C22⋊C4C22×D1113yes—
290C2×C22⋊C4C22×D1113yes—
291C2×C22⋊C4C22×D1116yes—
292C2×C42—116no—
293C2×C42—113no—
294#95—113no—
295#95—116no—
296#95—116no—
297#95—116no—
298#95—116no—
299#95—116no—
300#95—113no—
301#95—116no—
302#95C22×D1113yes—
303#95C22×D1113yes—
304C2×C11—46no—
305C2×C11—82no—
306C2×C11#345913yes—
307C2×C11C2×H(3,𝔽4)11yescharacteristic
308C2×C11#352913yes—
309D11—81no—
310C24—43no—
311C24—43no—
312C24—111no—
313C24#434114yescomplemented
314C24C23×D1112yes—
315C24C23×D1113yes—
316#41—4416no—
317C2×Q8—443no—
318C2×Q8—443no—
319C2×Q8—446no—
320C2×D4—212no—
321C2×D4—46no—
322C2×D4—43no—
323C2×D4—46no—
324C2×D4—226no—
325C2×D4—443no—
326C2×D4—446no—
327C2×D4—443no—
328C22×C4—111no—
329C22×C4—116no—
330C22×C4—113no—
331C22×C4—113no—
332C22×C4—112no—
333C22×C4—226no—
334C22×C4—226no—
335C22×C4—2212no—
336C22×C4—2212no—
337C22×C4—443no—
338C22×C4—446no—
339C22×C4—4416no—
340C22×C4C23×D1113yes—
341C22×C4C23×D1116yes—
342C22×C4C23×D1111yescharacteristic
343C4⋊C4—43no—
344C4⋊C4—443no—
345C4⋊C4—446no—
346C4⋊C4—446no—
347C22⋊C4—212no—
348C22⋊C4—43no—
349C22⋊C4—43no—
350C22⋊C4—46no—
351C22⋊C4—226no—
352C22⋊C4—443no—
353C22⋊C4—446no—
354C22⋊C4—446no—
355C22⋊C4—446no—
356C22⋊C4—446no—
357C22⋊C4—446no—
358C42—226no—
359C42—2212no—
360C11#3667511yescharacteristic, complemented, Sylow
361C23—23no—
362C23—26no—
363C23—23no—
364C23—26no—
365C23—22no—
366C23—26no—
367C23—26no—
368C23—412no—
369C23—44no—
370C23—412no—
371C23—221no—
372C23—223no—
373C23—223no—
374C23C2×#434116yes—
375C23C24×D1111yescharacteristic
376Q8—444no—
377Q8—4412no—
378D4—424no—
379D4—44no—
380D4—4412no—
381D4—448no—
382C2×C4—26no—
383C2×C4—23no—
384C2×C4—26no—
385C2×C4—23no—
386C2×C4—26no—
387C2×C4—26no—
388C2×C4—116no—
389C2×C4—223no—
390C2×C4—226no—
391C2×C4—223no—
392C2×C4—223no—
393C2×C4—226no—
394C2×C4—226no—
395C2×C4—223no—
396C2×C4—226no—
397C2×C4—226no—
398C2×C4—444no—
399C2×C4—4412no—
400C2×C4—448no—
401C2×C4—4412no—
402C22—212no—
403C22—26no—
404C22—416no—
405C22—43no—
406C22—43no—
407C22—46no—
408C22—42no—
409C22—46no—
410C22—46no—
411C22—441no—
412C22—443no—
413C22—443no—
414C22C22×#434111yescharacteristic
415C22D11×H(5,𝔽2)13yes—
416C22#1062345513yes—
417C4—41no—
418C4—43no—
419C4—46no—
420C4—114no—
421C4—443no—
422C4—442no—
423C4—446no—
424C4—443no—
425C2—46no—
426C2—82no—
427C2—881no—
428C2#1308202213yes—
429C2D11×H(3,𝔽4)11yescharacteristic
430C2#1308275113yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2812C2
hypercenter#2812D11
hypocenterC11#36675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2812

Complements

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

NH ≅ G/Ntype
1. #13076869C2semidirect
2. #13076806C2semidirect
3. #13076699C2semidirect
4. #13076698C2semidirect
5. #13076611C2semidirect
6. #13071904C2semidirect
7. #13071901C2semidirect
8. #13071828C2semidirect
9. #120×Dic11C2semidirect
10. #13071115C2semidirect
11. C11×#2812C2semidirect
13. C22×#4341C22semidirect
17. C2×#66940C22semidirect
26. #10622835C22semidirect
28. #10622606C22semidirect
29. #10622599C22semidirect
30. #10622574C22semidirect
34. #10622565C22semidirect
39. #10622560C22semidirect
43. C22⋊C4×Dic11C22semidirect
44. #10622286C22semidirect
45. #10622279C22semidirect
46. #10622272C22semidirect
47. #10622271C22semidirect
48. #10622269C22semidirect
49. #10622261C22semidirect
98. C24×C11#41semidirect
151. #2812D11semidirect
313. C24#4341semidirect
360. C11#36675semidirect

Maximal subgroups

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

subgroupindex
#130768692
#130768062
#130766992
#130766982
#130766112
#130719042
#130719012
#130718282
#120×Dic112
#130711152
C11×#28122
#3667511