Finite Group Databasebeta

← #14960218

Subgroups — #14960218

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#13076802C211yesmaximal, characteristic, complemented
3#13076717C216yesmaximal, complemented
4#13076715C213yesmaximal, complemented
5#13076705C212yesmaximal, complemented
6#13076610C213yesmaximal, complemented
7#13071914C212yesmaximal, complemented
8#13071875C213yesmaximal, complemented
9#13071858C216yesmaximal, complemented
10C4×#66990C213yesmaximal, complemented
11C11×#2397C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C4×D4×C11C2213yes—
14C2×C4×D4×C11C2213yescomplemented
15C2×#66990C2213yes—
16C2×C4×C22⋊D11C2216yes—
17C2×#66979C2213yescomplemented
18C11×#399C2211yescharacteristic
19C11×#399C2213yescomplemented
20C11×#392C2213yes—
21C11×#392C2211yescharacteristic, complemented
22C11×#376C2211yescharacteristic, complemented
23#10622836C2216yes—
24#10622835C2216yes—
25#10622835C2216yescomplemented
26#10622833C2213yes—
27C4×C22⋊Dic11C2213yes—
28C4×C22⋊Dic11C2213yescomplemented
29#10622607C2216yes—
30#10622602C2216yes—
31#10622599C2213yescomplemented
32#10622597C2216yescomplemented
33#10622596C2213yescomplemented
34#10622574C2216yes—
35#10622572C2216yes—
36#10622569C2216yes—
37#10622568C2213yes—
38#10622566C2213yes—
39#10622565C2216yescomplemented
40#10622565C2216yescomplemented
41#10622562C2213yes—
42#10622561C2216yescomplemented
43#10622559C2213yes—
44C4×(C2×D11)⋊C4C2216yes—
45C4×Dic11⋊C4C2216yescomplemented
46#10622289C2212yes—
47#10622288C2216yes—
48C11⋊#401C2212yescomplemented
49#10622271C2216yescomplemented
50C24×D11C2311yescharacteristic
51C22×D4×C11C2313yes—
52C22×D4×C11C2313yes—
53C23×C4×C11C2313yes—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11C2316yes—
56C23×Dic11C2311yescharacteristic
57C22×C4×D11—46no—
58C22×C4×D11C2312yes—
59C22×C4×D11C2312yes—
60C4×D4×C11—46no—
61C4×D4×C11—46no—
62C2×C11×C4⋊C4C2313yes—
63C2×C11×C4⋊C4C2313yes—
64C2×C11×C22⋊C4C2313yes—
65C2×C11×C22⋊C4C2316yes—
66C2×C11×C22⋊C4C2313yes—
67C2×C42×C11C2313yes—
68C2×C22⋊Dic11C2313yes—
69C2×C22⋊Dic11C2316yes—
70C2×C22⋊Dic11C2316yes—
71C2×C22⋊Dic11C2316yes—
72C2×C22⋊Dic11C2313yes—
73#66990—212no—
74C4×C22⋊D11—412no—
75C2×(C2×D11)⋊C4C2316yes—
76C2×(C2×D11)⋊C4C2316yes—
77C2×(C2×D11)⋊C4C2316yes—
78#66979—46no—
79C2×C4⋊Dic11C2313yes—
80C2×C4⋊Dic11C2313yes—
81C2×Dic11⋊C4C2316yes—
82C2×Dic11⋊C4C2316yes—
83C2×Dic11⋊C4C2316yes—
84C2×C4×Dic11C2316yes—
85C11×#95C2313yes—
86C11×#95C2311yescharacteristic
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2313yes—
92C11⋊#95C2316yes—
93C11⋊#95C2313yes—
94#36676—111nomaximal, Sylow
95C24×C11C2413yes—
96C24×C11C2411yescharacteristic
97C23×D11—43no—
98C23×D11—43no—
99C23×D11#4114yes—
100C23×D11C2412yes—
101C2×D4×C11—26no—
102C2×D4×C11—43no—
103C2×D4×C11—43no—
104C2×D4×C11—43no—
105C2×D4×C11—46no—
106C22×C4×C11—26no—
107C22×C4×C11—212no—
108C22×C4×C11—26no—
109C22×C4×C11C2411yescharacteristic
110C22×C4×C11C2413yes—
111C22×C4×C11C2413yes—
112C22×C4×C11C2413yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—212no—
115C2×C22⋊D11—46no—
116C2×C22⋊D11—46no—
117C22×Dic11—43no—
118C22×Dic11C2416yes—
119C22×Dic11C2412yes—
120C22×Dic11C2416yes—
121C2×C4×D11—212no—
122C2×C4×D11—46no—
123C2×C4×D11—416no—
124C11×C4⋊C4—43no—
125C11×C4⋊C4—43no—
126C11×C22⋊C4—46no—
127C11×C22⋊C4—43no—
128C11×C22⋊C4—43no—
129C42×C11—26no—
130C22⋊Dic11—26no—
131C22⋊Dic11—46no—
132C22⋊Dic11—46no—
133C22⋊Dic11—43no—
134C22⋊Dic11—46no—
135(C2×D11)⋊C4—212no—
136(C2×D11)⋊C4—46no—
137(C2×D11)⋊C4—46no—
138C4⋊Dic11—43no—
139C4⋊Dic11—43no—
140Dic11⋊C4—46no—
141Dic11⋊C4—46no—
142Dic11⋊C4—46no—
143C4×Dic11—212no—
144#2842—111no—
145#2834—111no—
146#2827—116no—
147#2826—113no—
148#2825—112no—
149#2812—113no—
150#2401—112no—
151#2397D1111yescharacteristic, complemented
152#2395—113no—
153#2392—116no—
154C4×#120—113no—
155C23×C11—23no—
156C23×C11—23no—
157C23×C11—23no—
158C23×C11—23no—
159C23×C11—26no—
160C23×C11—26no—
161C23×C11—23no—
162C23×C11C2×#4112yes—
163C23×C11C2511yescharacteristic
164C22×D11—26no—
165C22×D11—26no—
166C22×D11—412no—
167C22×D11—44no—
168C22×D11—412no—
169C22×D11C2×#4114yes—
170D4×C11—412no—
171D4×C11—412no—
172C2×C4×C11—23no—
173C2×C4×C11—26no—
174C2×C4×C11—23no—
175C2×C4×C11—23no—
176C2×C4×C11—23no—
177C2×C4×C11—23no—
178C2×C4×C11—23no—
179C2×C4×C11—26no—
180C2×C4×C11—44no—
181C2×C4×C11—412no—
182C2×C4×C11H(5,𝔽2)16yes—
183C22⋊D11—424no—
184C2×Dic11—26no—
185C2×Dic11—26no—
186C2×Dic11—26no—
187C2×Dic11—26no—
188C2×Dic11—26no—
189C2×Dic11—26no—
190C2×Dic11—26no—
191C2×Dic11—44no—
192C4×D11—48no—
193C4×D11—48no—
194C24×C4—111no—
195C2×#120—113no—
196C2×C4×D4—116no—
197C2×C4×D4C2×D1113yes—
198C2×C4×D4C2×D1113yescomplemented
199C2×#117—113no—
200#401—112no—
201#400—113no—
202#400—116no—
203#399—113no—
204#399C2×D1111yescharacteristic
205#399C2×D1113yescomplemented
206#398—113no—
207#398—116no—
208#397—116no—
209#397—116no—
210#397—113no—
211#397—116no—
212#396—116no—
213#396—116no—
214#396—112no—
215#394—116no—
216#394—116no—
217#394—116no—
218#394—116no—
219#392—116no—
220#392C2×D1113yes—
221#392C2×D1111yescharacteristic, complemented
222#386—113no—
223#386—116no—
224#385—116no—
225#385—113no—
226#379—113no—
227C4×C4⋊C4—116no—
228C4×C22⋊C4—113no—
229C4×C22⋊C4—113no—
230C4×C22⋊C4—116no—
231#376C2×D1111yescharacteristic, complemented
232C22×C11—26no—
233C22×C11—41no—
234C22×C11—43no—
235C22×C11—43no—
236C22×C11—46no—
237C22×C11—43no—
238C22×C11—46no—
239C22×C11—43no—
240C22×C11C22×#4111yescharacteristic
241C22×C11C2×H(5,𝔽2)13yes—
242C22×C11#58513yes—
243C2×D11—212no—
244C2×D11—416no—
245C2×D11—42no—
246C2×D11—46no—
247C4×C11—43no—
248C4×C11—43no—
249C4×C11—41no—
250C4×C11—43no—
251C4×C11#56014yes—
252Dic11—46no—
253Dic11—42no—
254Dic11—46no—
255C25—111no—
256C22×D4—116no—
257C22×D4C22×D1113yes—
258C22×D4C22×D1113yes—
259C23×C4—111no—
260C23×C4—112no—
261C23×C4—112no—
262C23×C4—446no—
263C23×C4C22×D1113yes—
264C23×C4C22×D1111yescharacteristic
265#120—2212no—
266C4×D4—46no—
267C4×D4—46no—
268C4×D4—4412no—
269#117—446no—
270C2×C4⋊C4—113no—
271C2×C4⋊C4—113no—
272C2×C4⋊C4—116no—
273C2×C4⋊C4—116no—
274C2×C4⋊C4—116no—
275C2×C4⋊C4C22×D1113yes—
276C2×C4⋊C4C22×D1113yes—
277C2×C22⋊C4—113no—
278C2×C22⋊C4—116no—
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⋊C4C22×D1113yes—
286C2×C22⋊C4C22×D1113yes—
287C2×C22⋊C4C22×D1116yes—
288C2×C42—116no—
289C2×C42C22×D1113yes—
290#95—116no—
291#95—116no—
292#95—116no—
293#95—113no—
294#95—113no—
295#95—116no—
296#95—116no—
297#95C22×D1113yes—
298#95C22×D1111yescharacteristic
299C2×C11—42no—
300C2×C11—83no—
301C2×C11#345913yes—
302C2×C11C2×#56011yescharacteristic
303C2×C11#352913yes—
304D11—44no—
305C24—112no—
306C24—114no—
307C24—443no—
308C24—443no—
309C24C23×D1113yes—
310C24C23×D1111yescharacteristic
311C2×D4—26no—
312C2×D4—43no—
313C2×D4—43no—
314C2×D4—46no—
315C2×D4—43no—
316C2×D4—2212no—
317C2×D4—446no—
318C2×D4—446no—
319C22×C4—26no—
320C22×C4—212no—
321C22×C4—26no—
322C22×C4—116no—
323C22×C4—112no—
324C22×C4—116no—
325C22×C4—2212no—
326C22×C4—446no—
327C22×C4—4416no—
328C22×C4—443no—
329C22×C4C23×D1111yescharacteristic
330C22×C4C23×D1113yes—
331C22×C4C23×D1113yes—
332C22×C4C23×D1113yes—
333C22×C4C23×D1111yescharacteristic
334C4⋊C4—43no—
335C4⋊C4—43no—
336C4⋊C4—443no—
337C4⋊C4—443no—
338C4⋊C4—446no—
339C4⋊C4—446no—
340C4⋊C4—446no—
341C22⋊C4—46no—
342C22⋊C4—43no—
343C22⋊C4—43no—
344C22⋊C4—2212no—
345C22⋊C4—226no—
346C22⋊C4—446no—
347C22⋊C4—446no—
348C22⋊C4—446no—
349C22⋊C4—446no—
350C22⋊C4—443no—
351C22⋊C4—446no—
352C42—26no—
353C42—2212no—
354C11#3667611yescharacteristic, complemented, Sylow
355C23—23no—
356C23—23no—
357C23—23no—
358C23—26no—
359C23—23no—
360C23—26no—
361C23—23no—
362C23—114no—
363C23—226no—
364C23—226no—
365C23—4412no—
366C23—444no—
367C23—4412no—
368C23#41×D1112yes—
369C23C24×D1111yescharacteristic
370D4—412no—
371D4—412no—
372D4—4424no—
373C2×C4—23no—
374C2×C4—23no—
375C2×C4—26no—
376C2×C4—23no—
377C2×C4—23no—
378C2×C4—23no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—412no—
382C2×C4—44no—
383C2×C4—226no—
384C2×C4—226no—
385C2×C4—226no—
386C2×C4—226no—
387C2×C4—226no—
388C2×C4—226no—
389C2×C4—226no—
390C2×C4—448no—
391C2×C4—444no—
392C2×C4—448no—
393C2×C4#6703716yes—
394C22—26no—
395C22—41no—
396C22—43no—
397C22—43no—
398C22—46no—
399C22—43no—
400C22—43no—
401C22—46no—
402C22—2212no—
403C22—4416no—
404C22—442no—
405C22—446no—
406C22C2×#6703713yes—
407C22C2×#41×D1111yescharacteristic
408C22#1062345313yes—
409C4—41no—
410C4—43no—
411C4—43no—
412C4—43no—
413C4—442no—
414C4—446no—
415C4—446no—
416C4#1062325114yes—
417C2—42no—
418C2—83no—
419C2—444no—
420C2#1308202313yes—
421C2C2×#1062325111yescharacteristic
422C2#1308275413yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2397C2
hypercenter#2397D11
hypocenterC11#36676
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13076881C2semidirect
2. #13076802C2semidirect
3. #13076717C2semidirect
4. #13076715C2semidirect
5. #13076705C2semidirect
6. #13076610C2semidirect
7. #13071914C2semidirect
8. #13071875C2semidirect
9. #13071858C2semidirect
10. C4×#66990C2semidirect
11. C11×#2397C2semidirect
14. C2×C4×D4×C11C22semidirect
17. C2×#66979C22semidirect
19. C11×#399C22semidirect
21. C11×#392C22semidirect
22. C11×#376C22semidirect
25. #10622835C22semidirect
28. C4×C22⋊Dic11C22semidirect
31. #10622599C22semidirect
32. #10622597C22semidirect
33. #10622596C22semidirect
39. #10622565C22semidirect
40. #10622565C22semidirect
42. #10622561C22semidirect
45. C4×Dic11⋊C4C22semidirect
48. C11⋊#401C22semidirect
49. #10622271C22semidirect
151. #2397D11semidirect
198. C2×C4×D4C2×D11semidirect
205. #399C2×D11semidirect
221. #392C2×D11semidirect
231. #376C2×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
#130768022
#130767172
#130767152
#130767052
#130766102
#130719142
#130718752
#130718582
C4×#669902
C11×#23972
#3667611