Finite Group Databasebeta

← #14960207

Subgroups — #14960207

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076868C211yesmaximal, characteristic, complemented
2#13076805C212yesmaximal, complemented
3#13076697C216yesmaximal, complemented
4#13076696C213yesmaximal, complemented
5#13076614C213yesmaximal, complemented
6#13071905C216yesmaximal, complemented
7#13071901C213yesmaximal, complemented
8#13071834C212yesmaximal, complemented
9#13071833C211yesmaximal, characteristic, complemented
10#13071117C213yesmaximal, complemented
11C11×#2835C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C2×#66946C2216yes—
15C2×#66940C2213yescomplemented
16C2×#66935C2213yes—
17C2×(C22⋊D11)⋊C4C2213yes—
18C11×#400C2216yescomplemented
19C11×#397C2213yes—
20C11×#395C2212yescomplemented
21C11×#393C2211yescharacteristic
22C11×#385C2213yes—
23#10622844C2212yes—
24#10622842C2211yescharacteristic, complemented
25#10622826C2213yes—
26#10622606C2213yescomplemented
27#10622604C2216yes—
28#10622604C2216yescomplemented
29#10622602C2216yes—
30#10622595C2216yescomplemented
31#10622573C2213yes—
32#10622572C2216yes—
33#10622568C2213yes—
34#10622560C2213yes—
35C22⋊C4×Dic11C2213yes—
36#10622288C2216yes—
37#10622288C2216yescomplemented
38#10622286C2216yes—
39#10622286C2213yescomplemented
40#10622286C2216yescomplemented
41#10622285C2216yes—
42#10622285C2213yescomplemented
43#10622284C2216yes—
44#10622279C2216yes—
45#10622279C2216yescomplemented
46#10622279C2213yescomplemented
47#10622278C2216yes—
48#10622271C2216yescomplemented
49#10622261C2213yescomplemented
50C24×D11C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11C2313yes—
54C23×Dic11C2311yescharacteristic
55C2×#4343—46no—
56C22×D44C2316yes—
57C22×D44C2313yes—
58C22×C4×D11—46no—
59C22×C4×D11C2313yes—
60C22×C4×D11C2312yes—
61C22×C4×D11C2312yes—
62C22×Dic22C2313yes—
63C2×C11×C4⋊C4C2313yes—
64C2×C11×C4⋊C4C2316yes—
65C2×C11×C22⋊C4C2313yes—
66C2×C11×C22⋊C4C2313yes—
67C2×C22⋊Dic11C2313yes—
68C2×(C2×D11)⋊C4C2316yes—
69C2×(C2×D11)⋊C4C2313yes—
70C2×(C2×D11)⋊C4C2316yes—
71C2×(C2×D11)⋊C4C2316yes—
72C2×(C2×D11)⋊C4C2316yes—
73C2×(C2×D11)⋊C4C2316yes—
74C2×(C2×D11)⋊C4C2316yes—
75C2×(C2×D11)⋊C4C2316yes—
76C2×Dic11⋊C4C2313yes—
77C2×Dic11⋊C4C2316yes—
78C2×C4×Dic11C2313yes—
79C2×C4×Dic11C2316yes—
80#66946—412no—
81#66940—46no—
82#66935—212no—
83(C22⋊D11)⋊C4—46no—
84C11×#95C2313yes—
85C11×#95C2316yes—
86C11×#95C2316yes—
87C11×#95C2313yes—
88C11⋊#95C2316yes—
89C11⋊#95C2313yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93C11⋊#95C2313yes—
94#36675—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—43no—
97C23×D11—43no—
98C23×D11#4114yescomplemented
99C23×D11C2413yes—
100C23×D11C2412yes—
101C2×Q8×C11—43no—
102C22×C4×C11—43no—
103C22×C4×C11C2413yes—
104C22×C4×C11C2412yes—
105C22×C4×C11C2416yes—
106C22×C4×C11C2413yes—
107C2×C22⋊D11—26no—
108C2×C22⋊D11—43no—
109C2×C22⋊D11—43no—
110C22×Dic11—26no—
111C22×Dic11C2413yes—
112C22×Dic11C2416yes—
113C22×Dic11C2411yescharacteristic
114C22×Dic11C2411yescharacteristic
115#4343—416no—
116C2×D44—212no—
117C2×D44—46no—
118C2×D44—46no—
119C2×D44—43no—
120C2×D44—46no—
121C2×C4×D11—26no—
122C2×C4×D11—212no—
123C2×C4×D11—212no—
124C2×C4×D11—46no—
125C2×C4×D11—416no—
126C2×Dic22—43no—
127C2×Dic22—46no—
128C11×C4⋊C4—43no—
129C11×C4⋊C4—46no—
130C11×C22⋊C4—26no—
131C11×C22⋊C4—43no—
132C22⋊Dic11—43no—
133(C2×D11)⋊C4—212no—
134(C2×D11)⋊C4—43no—
135(C2×D11)⋊C4—46no—
136(C2×D11)⋊C4—46no—
137(C2×D11)⋊C4—46no—
138(C2×D11)⋊C4—46no—
139(C2×D11)⋊C4—46no—
140(C2×D11)⋊C4—46no—
141Dic11⋊C4—43no—
142Dic11⋊C4—46no—
143C4×Dic11—26no—
144C4×Dic11—212no—
145#2840—111no—
146#2835—112no—
147#2835D1111yescharacteristic, complemented
148#2824—116no—
149#2824—113no—
150#2812—113no—
151#2398—116no—
152#2398—113no—
153#2388—112no—
154#2388—111no—
155C4×#120—113no—
156C23×C11—23no—
157C23×C11—23no—
158C23×C11C2×#4112yes—
159C23×C11C2511yescharacteristic
160C22×D11—26no—
161C22×D11—26no—
162C22×D11—23no—
163C22×D11—26no—
164C22×D11—23no—
165C22×D11—26no—
166C22×D11—23no—
167C22×D11—412no—
168C22×D11—44no—
169C22×D11—412no—
170C22×D11C2×#4114yes—
171Q8×C11—44no—
172C2×C4×C11—26no—
173C2×C4×C11—26no—
174C2×C4×C11—23no—
175C2×C4×C11—23no—
176C2×C4×C11—26no—
177C2×C4×C11—26no—
178C2×C4×C11—26no—
179C2×C4×C11—26no—
180C2×C4×C11—44no—
181C22⋊D11—412no—
182C2×Dic11—23no—
183C2×Dic11—23no—
184C2×Dic11—26no—
185C2×Dic11—23no—
186C2×Dic11—26no—
187C2×Dic11—23no—
188C2×Dic11—26no—
189C2×Dic11—44no—
190C2×Dic11H(5,𝔽2)16yes—
191D44—424no—
192D44—412no—
193C4×D11—48no—
194C4×D11—48no—
195C4×D11—412no—
196Dic22—412no—
197C22×#41—111no—
198C24×C4—111no—
199C2×#120—113no—
200C2×C4×Q8—113no—
201C2×C4×D4—116no—
202C2×C4×D4—113no—
203#400—116no—
204#400—116no—
205#400C2×D1116yescomplemented
206#397—113no—
207#397—116no—
208#397—116no—
209#397C2×D1113yes—
210#395—111no—
211#395C2×D1112yescomplemented
212#394—116no—
213#394—116no—
214#394—116no—
215#394—113no—
216#394—116no—
217#393—112no—
218#393—113no—
219#393—116no—
220#393—113no—
221#393—116no—
222#393C2×D1111yescharacteristic
223#392—113no—
224#392—116no—
225#386—113no—
226#386—116no—
227#385—116no—
228#385C2×D1113yes—
229#379—113no—
230C4×C22⋊C4—113no—
231C4×C22⋊C4—116no—
232C4×C22⋊C4—113no—
233C4×C22⋊C4—116no—
234#376—113no—
235C22×C11—26no—
236C22×C11—41no—
237C22×C11—43no—
238C22×C11C22×#4111yescharacteristic
239C22×C11C2×H(5,𝔽2)13yes—
240C22×C11#58513yes—
241C2×D11—212no—
242C2×D11—416no—
243C2×D11—42no—
244C2×D11—46no—
245C2×D11—46no—
246C2×D11—43no—
247C2×D11—43no—
248C2×D11—46no—
249C2×D11—43no—
250C4×C11—46no—
251C4×C11—42no—
252C4×C11—43no—
253C4×C11—43no—
254Dic11—43no—
255Dic11—41no—
256Dic11—46no—
257Dic11H(3,𝔽4)14yes—
258C25—111no—
259C2×#41—446no—
260C22×Q8—113no—
261C22×Q8C22×D1111yescharacteristic
262C22×D4—113no—
263C22×D4—116no—
264C22×D4—113no—
265C23×C4—111no—
266C23×C4—112no—
267C23×C4—113no—
268C23×C4—112no—
269C23×C4—446no—
270C23×C4C22×D1111yescharacteristic
271#120—2212no—
272C4×Q8—446no—
273C4×D4—446no—
274C4×D4—4412no—
275C2×C4⋊C4—113no—
276C2×C4⋊C4—116no—
277C2×C4⋊C4C22×D1116yes—
278C2×C4⋊C4C22×D1113yes—
279C2×C22⋊C4—116no—
280C2×C22⋊C4—113no—
281C2×C22⋊C4—116no—
282C2×C22⋊C4—116no—
283C2×C22⋊C4—113no—
284C2×C22⋊C4—116no—
285C2×C22⋊C4—116no—
286C2×C22⋊C4—116no—
287C2×C22⋊C4—116no—
288C2×C22⋊C4C22×D1113yes—
289C2×C22⋊C4C22×D1113yes—
290C2×C42—116no—
291C2×C42—113no—
292#95—113no—
293#95—116no—
294#95—116no—
295#95—116no—
296#95—113no—
297#95—116no—
298#95C22×D1113yes—
299#95C22×D1116yes—
300#95C22×D1116yes—
301#95C22×D1113yes—
302C2×C11—42no—
303C2×C11#345913yes—
304C2×C11C2×H(3,𝔽4)11yescharacteristic
305C2×C11#352913yes—
306D11—44no—
307D11—83no—
308C24—112no—
309C24—114no—
310C24—113no—
311C24—443no—
312C24—443no—
313C24C23×D1111yescharacteristic
314#41—4416no—
315C2×Q8—43no—
316C2×Q8—443no—
317C2×Q8—446no—
318C2×D4—2212no—
319C2×D4—226no—
320C2×D4—446no—
321C2×D4—443no—
322C2×D4—446no—
323C2×D4—446no—
324C2×D4—443no—
325C2×D4—443no—
326C22×C4—43no—
327C22×C4—111no—
328C22×C4—116no—
329C22×C4—113no—
330C22×C4—111no—
331C22×C4—2212no—
332C22×C4—226no—
333C22×C4—2212no—
334C22×C4—226no—
335C22×C4—446no—
336C22×C4—4416no—
337C22×C4C23×D1112yes—
338C22×C4C23×D1113yes—
339C22×C4C23×D1116yes—
340C22×C4C23×D1113yes—
341C4⋊C4—46no—
342C4⋊C4—43no—
343C4⋊C4—443no—
344C4⋊C4—446no—
345C22⋊C4—26no—
346C22⋊C4—43no—
347C22⋊C4—2212no—
348C22⋊C4—443no—
349C22⋊C4—446no—
350C22⋊C4—446no—
351C22⋊C4—446no—
352C22⋊C4—446no—
353C22⋊C4—446no—
354C22⋊C4—446no—
355C22⋊C4—443no—
356C42—226no—
357C42—2212no—
358C11#3667511yescharacteristic, complemented, Sylow
359C23—23no—
360C23—23no—
361C23—114no—
362C23—226no—
363C23—226no—
364C23—223no—
365C23—226no—
366C23—223no—
367C23—226no—
368C23—223no—
369C23—4412no—
370C23—444no—
371C23—4412no—
372C23#41×D1112yes—
373C23C24×D1111yescharacteristic
374Q8—44no—
375Q8—4412no—
376D4—4424no—
377D4—4412no—
378D4—4412no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—26no—
382C2×C4—23no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—44no—
388C2×C4—116no—
389C2×C4—223no—
390C2×C4—226no—
391C2×C4—223no—
392C2×C4—223no—
393C2×C4—223no—
394C2×C4—226no—
395C2×C4—226no—
396C2×C4—448no—
397C2×C4—4412no—
398C2×C4—448no—
399C2×C4—444no—
400C22—26no—
401C22—41no—
402C22—43no—
403C22—2212no—
404C22—4416no—
405C22—442no—
406C22—446no—
407C22—443no—
408C22—446no—
409C22—443no—
410C22—446no—
411C22—443no—
412C22C2×#41×D1111yescharacteristic
413C22D11×H(5,𝔽2)13yes—
414C22#1062345713yes—
415C4—42no—
416C4—43no—
417C4—43no—
418C4—46no—
419C4—114no—
420C4—441no—
421C4—446no—
422C4—443no—
423C2—42no—
424C2—444no—
425C2—883no—
426C2#1308202413yes—
427C2D11×H(3,𝔽4)11yescharacteristic
428C2#1308275713yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2835C2
hypercenter#2835D11
hypocenterC11#36675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2835

Complements

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

NH ≅ G/Ntype
1. #13076868C2semidirect
2. #13076805C2semidirect
3. #13076697C2semidirect
4. #13076696C2semidirect
5. #13076614C2semidirect
6. #13071905C2semidirect
7. #13071901C2semidirect
8. #13071834C2semidirect
9. #13071833C2semidirect
10. #13071117C2semidirect
11. C11×#2835C2semidirect
12. C22×#4343C22semidirect
15. C2×#66940C22semidirect
18. C11×#400C22semidirect
20. C11×#395C22semidirect
24. #10622842C22semidirect
26. #10622606C22semidirect
28. #10622604C22semidirect
30. #10622595C22semidirect
37. #10622288C22semidirect
39. #10622286C22semidirect
40. #10622286C22semidirect
42. #10622285C22semidirect
45. #10622279C22semidirect
46. #10622279C22semidirect
48. #10622271C22semidirect
49. #10622261C22semidirect
98. C23×D11#41semidirect
147. #2835D11semidirect
205. #400C2×D11semidirect
211. #395C2×D11semidirect
358. C11#36675semidirect

Maximal subgroups

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

subgroupindex
#130768682
#130768052
#130766972
#130766962
#130766142
#130719052
#130719012
#130718342
#130718332
#130711172
C11×#28352
#3667511