Finite Group Databasebeta

← #14960202

Subgroups — #14960202

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#13076807C211yesmaximal, characteristic, complemented
3#13076805C212yesmaximal, complemented
4#13076698C213yesmaximal, complemented
5#13076692C216yesmaximal, complemented
6#13076610C213yesmaximal, complemented
7#13071903C216yesmaximal, complemented
8#13071900C213yesmaximal, complemented
9#13071829C212yesmaximal, complemented
10C4×#66990C213yesmaximal, complemented
11C11×#2388C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×#66990C2213yes—
16C2×C4×C22⋊D11C2216yes—
17C2×C4×Dic22C2213yescomplemented
18C11×#395C2211yescharacteristic, complemented
19C11×#394C2213yescomplemented
20C11×#393C2211yescharacteristic
21C11×#392C2213yes—
22C4×C11×C22⋊C4C2213yescomplemented
23#10622844C2212yes—
24#10622842C2212yescomplemented
25#10622836C2216yes—
26#10622835C2216yes—
27#10622835C2216yescomplemented
28#10622833C2213yes—
29C4×C22⋊Dic11C2213yes—
30C4×C22⋊Dic11C2216yescomplemented
31#10622602C2216yes—
32#10622595C2216yescomplemented
33#10622574C2216yes—
34#10622572C2216yes—
35#10622569C2216yes—
36#10622568C2213yes—
37#10622566C2213yes—
38#10622566C2213yescomplemented
39#10622565C2216yescomplemented
40#10622560C2213yes—
41#10622560C2213yescomplemented
42#10622560C2216yescomplemented
43#10622559C2213yes—
44C4×(C2×D11)⋊C4C2216yes—
45#10622545C2213yescomplemented
46#10622288C2216yes—
47#10622286C2216yes—
48#10622273C2216yescomplemented
49#10622271C2216yescomplemented
50C24×D11C2311yescharacteristic
51C2×C11×#41—46no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11C2313yes—
54C22×D4×C11C2313yes—
55C23×C4×C11C2313yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11C2316yes—
58C23×Dic11C2311yescharacteristic
59C22×C4×D11—46no—
60C22×C4×D11C2312yes—
61C22×C4×D11C2312yes—
62C22×Dic22C2313yes—
63C4×D4×C11—46no—
64C2×C11×C4⋊C4C2313yes—
65C2×C11×C22⋊C4C2313yes—
66C2×C11×C22⋊C4C2316yes—
67C2×C11×C22⋊C4C2313yes—
68C2×C42×C11C2313yes—
69C2×C22⋊Dic11C2313yes—
70C2×C22⋊Dic11C2316yes—
71C2×C22⋊Dic11C2313yes—
72C2×C22⋊Dic11C2316yes—
73C2×C22⋊Dic11C2316yes—
74#66990—212no—
75C4×C22⋊D11—412no—
76C2×(C2×D11)⋊C4C2316yes—
77C2×(C2×D11)⋊C4C2316yes—
78C2×(C2×D11)⋊C4C2316yes—
79C2×C4⋊Dic11C2313yes—
80C2×Dic11⋊C4C2316yes—
81C2×Dic11⋊C4C2316yes—
82C2×C4×Dic11C2316yes—
83C4×Dic22—46no—
84C11×#95C2313yes—
85C11×#95C2313yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2313yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2313yes—
93C11⋊#95C2316yes—
94#36675—111nomaximal, Sylow
95C24×C11C2413yes—
96C24×C11C2411yescharacteristic
97C23×D11—43no—
98C23×D11—43no—
99C23×D11#4114yescomplemented
100C23×D11C2412yes—
101C11×#41—416no—
102C2×Q8×C11—43no—
103C2×D4×C11—26no—
104C2×D4×C11—43no—
105C2×D4×C11—43no—
106C2×D4×C11—46no—
107C2×D4×C11—43no—
108C22×C4×C11—212no—
109C22×C4×C11—26no—
110C22×C4×C11—26no—
111C22×C4×C11C2411yescharacteristic
112C22×C4×C11C2413yes—
113C22×C4×C11C2413yes—
114C22×C4×C11C2413yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—212no—
117C2×C22⋊D11—46no—
118C2×C22⋊D11—46no—
119C22×Dic11—43no—
120C22×Dic11C2416yes—
121C22×Dic11C2416yes—
122C22×Dic11C2412yes—
123C2×C4×D11—212no—
124C2×C4×D11—46no—
125C2×C4×D11—416no—
126C2×Dic22—43no—
127C2×Dic22—46no—
128C11×C4⋊C4—43no—
129C11×C22⋊C4—46no—
130C11×C22⋊C4—43no—
131C11×C22⋊C4—43no—
132C42×C11—26no—
133C22⋊Dic11—26no—
134C22⋊Dic11—46no—
135C22⋊Dic11—43no—
136C22⋊Dic11—46no—
137C22⋊Dic11—46no—
138(C2×D11)⋊C4—212no—
139(C2×D11)⋊C4—46no—
140(C2×D11)⋊C4—46no—
141C4⋊Dic11—43no—
142Dic11⋊C4—46no—
143Dic11⋊C4—46no—
144C4×Dic11—212no—
145#2840—111no—
146#2835—112no—
147#2835—111no—
148#2824—116no—
149#2824—113no—
150#2812—113no—
151#2398—116no—
152#2398—113no—
153#2388—112no—
154#2388D1111yescharacteristic, complemented
155C4×#120—113no—
156C23×C11—23no—
157C23×C11—23no—
158C23×C11—23no—
159C23×C11—26no—
160C23×C11—23no—
161C23×C11—23no—
162C23×C11—26no—
163C23×C11C2×#4112yes—
164C23×C11C2511yescharacteristic
165C22×D11—26no—
166C22×D11—26no—
167C22×D11—412no—
168C22×D11—44no—
169C22×D11—412no—
170C22×D11C2×#4114yes—
171Q8×C11—44no—
172D4×C11—412no—
173D4×C11—412no—
174C2×C4×C11—23no—
175C2×C4×C11—23no—
176C2×C4×C11—26no—
177C2×C4×C11—23no—
178C2×C4×C11—23no—
179C2×C4×C11—23no—
180C2×C4×C11—26no—
181C2×C4×C11—23no—
182C2×C4×C11—44no—
183C2×C4×C11—412no—
184C2×C4×C11H(5,𝔽2)16yes—
185C22⋊D11—424no—
186C2×Dic11—26no—
187C2×Dic11—26no—
188C2×Dic11—26no—
189C2×Dic11—26no—
190C2×Dic11—26no—
191C2×Dic11—26no—
192C2×Dic11—26no—
193C2×Dic11—44no—
194C4×D11—48no—
195C4×D11—48no—
196Dic22—412no—
197C22×#41C2×D1111yescharacteristic, complemented
198C24×C4—111no—
199C2×#120—113no—
200C2×C4×Q8—113no—
201C2×C4×D4—116no—
202C2×C4×D4C2×D1113yes—
203#400—116no—
204#400—116no—
205#400—116no—
206#397—116no—
207#397—113no—
208#397—113no—
209#397—116no—
210#395—112no—
211#395C2×D1111yescharacteristic, complemented
212#394—116no—
213#394—116no—
214#394—116no—
215#394—116no—
216#394C2×D1113yescomplemented
217#393—112no—
218#393—116no—
219#393—113no—
220#393—113no—
221#393—116no—
222#393C2×D1111yescharacteristic
223#392—116no—
224#392C2×D1113yes—
225#386—113no—
226#386—116no—
227#385—116no—
228#385—113no—
229#379—113no—
230C4×C22⋊C4—116no—
231C4×C22⋊C4—113no—
232C4×C22⋊C4—116no—
233C4×C22⋊C4C2×D1113yescomplemented
234#376—113no—
235C22×C11—26no—
236C22×C11—41no—
237C22×C11—43no—
238C22×C11—43no—
239C22×C11—46no—
240C22×C11—43no—
241C22×C11—46no—
242C22×C11—43no—
243C22×C11C22×#4111yescharacteristic
244C22×C11C2×H(5,𝔽2)13yes—
245C22×C11#58513yes—
246C2×D11—212no—
247C2×D11—416no—
248C2×D11—42no—
249C2×D11—46no—
250C4×C11—43no—
251C4×C11—43no—
252C4×C11—41no—
253C4×C11—43no—
254C4×C11H(3,𝔽4)14yes—
255Dic11—46no—
256Dic11—42no—
257Dic11—46no—
258C25—111no—
259C2×#41—46no—
260C22×Q8—113no—
261C22×Q8C22×D1111yescharacteristic
262C22×D4—116no—
263C22×D4C22×D1113yes—
264C22×D4C22×D1113yes—
265C23×C4—111no—
266C23×C4—112no—
267C23×C4—112no—
268C23×C4—446no—
269C23×C4C22×D1113yes—
270C23×C4C22×D1111yescharacteristic
271#120—2212no—
272C4×Q8—446no—
273C4×D4—46no—
274C4×D4—4412no—
275C2×C4⋊C4—116no—
276C2×C4⋊C4—116no—
277C2×C4⋊C4—113no—
278C2×C4⋊C4C22×D1113yes—
279C2×C22⋊C4—113no—
280C2×C22⋊C4—116no—
281C2×C22⋊C4—116no—
282C2×C22⋊C4—113no—
283C2×C22⋊C4—116no—
284C2×C22⋊C4—116no—
285C2×C22⋊C4—116no—
286C2×C22⋊C4—116no—
287C2×C22⋊C4C22×D1113yes—
288C2×C22⋊C4C22×D1113yes—
289C2×C22⋊C4C22×D1116yes—
290C2×C42—116no—
291C2×C42C22×D1113yes—
292#95—113no—
293#95—116no—
294#95—113no—
295#95—116no—
296#95—116no—
297#95—116no—
298#95—116no—
299#95—116no—
300#95C22×D1113yes—
301#95C22×D1113yes—
302C2×C11—42no—
303C2×C11—83no—
304C2×C11#345913yes—
305C2×C11C2×H(3,𝔽4)11yescharacteristic
306C2×C11#352913yes—
307D11—44no—
308C24—112no—
309C24—114no—
310C24—443no—
311C24—443no—
312C24C23×D1113yes—
313C24C23×D1111yescharacteristic
314#41—416no—
315C2×Q8—43no—
316C2×Q8—443no—
317C2×Q8—446no—
318C2×D4—26no—
319C2×D4—43no—
320C2×D4—43no—
321C2×D4—46no—
322C2×D4—43no—
323C2×D4—2212no—
324C2×D4—446no—
325C2×D4—446no—
326C22×C4—26no—
327C22×C4—26no—
328C22×C4—212no—
329C22×C4—116no—
330C22×C4—116no—
331C22×C4—112no—
332C22×C4—2212no—
333C22×C4—446no—
334C22×C4—4416no—
335C22×C4—443no—
336C22×C4C23×D1111yescharacteristic
337C22×C4C23×D1113yes—
338C22×C4C23×D1113yes—
339C22×C4C23×D1113yes—
340C22×C4C23×D1111yescharacteristic
341C4⋊C4—43no—
342C4⋊C4—446no—
343C4⋊C4—446no—
344C4⋊C4—443no—
345C22⋊C4—43no—
346C22⋊C4—43no—
347C22⋊C4—46no—
348C22⋊C4—2212no—
349C22⋊C4—226no—
350C22⋊C4—446no—
351C22⋊C4—446no—
352C22⋊C4—446no—
353C22⋊C4—446no—
354C22⋊C4—446no—
355C22⋊C4—443no—
356C42—26no—
357C42—2212no—
358C11#3667511yescharacteristic, complemented, Sylow
359C23—23no—
360C23—23no—
361C23—23no—
362C23—26no—
363C23—23no—
364C23—26no—
365C23—23no—
366C23—114no—
367C23—226no—
368C23—226no—
369C23—4412no—
370C23—444no—
371C23—4412no—
372C23#41×D1112yes—
373C23C24×D1111yescharacteristic
374Q8—44no—
375Q8—4412no—
376D4—412no—
377D4—412no—
378D4—4424no—
379C2×C4—23no—
380C2×C4—23no—
381C2×C4—23no—
382C2×C4—23no—
383C2×C4—26no—
384C2×C4—23no—
385C2×C4—23no—
386C2×C4—26no—
387C2×C4—44no—
388C2×C4—412no—
389C2×C4—226no—
390C2×C4—226no—
391C2×C4—226no—
392C2×C4—226no—
393C2×C4—226no—
394C2×C4—226no—
395C2×C4—226no—
396C2×C4—448no—
397C2×C4—444no—
398C2×C4—448no—
399C2×C4#6703716yes—
400C22—26no—
401C22—41no—
402C22—43no—
403C22—43no—
404C22—43no—
405C22—46no—
406C22—43no—
407C22—46no—
408C22—2212no—
409C22—4416no—
410C22—442no—
411C22—446no—
412C22C2×#6703713yes—
413C22C2×#41×D1111yescharacteristic
414C22#1062345313yes—
415C4—41no—
416C4—43no—
417C4—43no—
418C4—43no—
419C4—442no—
420C4—446no—
421C4—446no—
422C4#1062312514yes—
423C2—42no—
424C2—83no—
425C2—444no—
426C2#1308202313yes—
427C2C2×#1062312511yescharacteristic
428C2#1308275213yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2388C2
hypercenter#2388D11
hypocenterC11#36675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. #13076868C2semidirect
2. #13076807C2semidirect
3. #13076805C2semidirect
4. #13076698C2semidirect
5. #13076692C2semidirect
6. #13076610C2semidirect
7. #13071903C2semidirect
8. #13071900C2semidirect
9. #13071829C2semidirect
10. C4×#66990C2semidirect
11. C11×#2388C2semidirect
12. C22×C11×#41C22semidirect
17. C2×C4×Dic22C22semidirect
18. C11×#395C22semidirect
19. C11×#394C22semidirect
22. C4×C11×C22⋊C4C22semidirect
24. #10622842C22semidirect
27. #10622835C22semidirect
30. C4×C22⋊Dic11C22semidirect
32. #10622595C22semidirect
38. #10622566C22semidirect
39. #10622565C22semidirect
41. #10622560C22semidirect
42. #10622560C22semidirect
45. #10622545C22semidirect
48. #10622273C22semidirect
49. #10622271C22semidirect
99. C23×D11#41semidirect
154. #2388D11semidirect
197. C22×#41C2×D11semidirect
211. #395C2×D11semidirect
216. #394C2×D11semidirect
233. C4×C22⋊C4C2×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
#130768072
#130768052
#130766982
#130766922
#130766102
#130719032
#130719002
#130718292
C4×#669902
C11×#23882
#3667511