Finite Group Databasebeta

← #14959861

Subgroups — #14959861

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076999C213yesmaximal, complemented
2#13076998C211yesmaximal, characteristic, complemented
3#13076980C213yesmaximal, complemented
4#13076930C216yesmaximal, complemented
5#13076928C212yesmaximal, complemented
6#13071170C216yesmaximal, complemented
7#126×Dic11C212yesmaximal, complemented
8#13071103C213yesmaximal
9#13071097C213yesmaximal, complemented
10C43×D11C211yesmaximal, characteristic, complemented
11C11×#2860C211yesmaximal, characteristic, complemented
12C22×#4341C2211yescharacteristic
13C2×C11×#126C2212yes—
14C2×#66945C2213yes—
15C2×#66932C2216yes—
16C2×C42×D11C2211yescharacteristic
17C2×C42×D11C2213yes—
18C2×C42×D11C2213yes—
19C11×#390C2213yes—
20C11×#389C2213yes—
21C11×#388C2216yes—
22C43×C11C2211yescharacteristic
23#10622834C2213yes—
24#10622602C2216yes—
25#10622598C2213yes—
26#10622594C2216yes—
27#10622591C2216yes—
28C4⋊C4×Dic11C2216yes—
29#10622587C2213yes—
30#10622586C2213yes—
31#10622569C2216yes—
32#10622569C2216yes—
33#10622564C2216yes—
34#10622558C2216yes—
35#10622557C2216yes—
36C22⋊C4×Dic11C2216yes—
37C22⋊C4×Dic11C2216yes—
38#10622550C2212yes—
39#10622546C2216yes—
40C42×Dic11C2213yes—
41C42×Dic11C2211yescharacteristic
42C42×Dic11C2213yes—
43#10622542C2213yes—
44#10622541C2213yes—
45#10622281C2216yes—
46#10622267C2216yes—
47#10622264C2216yes—
48#10622262C2216yes—
49C22×D4×C11C2311yescharacteristic
50C22×C22⋊D11C2312yes—
51C23×Dic11C2312yes—
52C2×#4341—212no—
53C22×C4×D11C2313yes—
54C22×C4×D11C2313yes—
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2311yescharacteristic
57C11×#126—28no—
58C2×C11×C4⋊C4C2313yes—
59C2×C11×C4⋊C4C2316yes—
60C2×C11×C22⋊C4C2316yes—
61C2×C11×C22⋊C4C2316yes—
62C2×C42×C11C2313yes—
63C2×C42×C11C2313yes—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11C2316yes—
66C2×C22⋊Dic11C2316yes—
67C2×(C2×D11)⋊C4C2316yes—
68C2×C4⋊Dic11C2316yes—
69C2×C4⋊Dic11C2313yes—
70C2×Dic11⋊C4C2316yes—
71C2×Dic11⋊C4C2316yes—
72C2×C4×Dic11C2313yes—
73C2×C4×Dic11C2313yes—
74C2×C4×Dic11C2313yes—
75C2×C4×Dic11C2313yes—
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78C2×C4×Dic11C2316yes—
79C2×C4×Dic11C2313yes—
80#66945—212no—
81#66932—224no—
82C42×D11—212no—
83C42×D11—24no—
84C42×D11—212no—
85C11×#95C2316yes—
86C11⋊#95C2316yes—
87C11⋊#95C2316yes—
88C11⋊#95C2316yes—
89C11⋊#95C2316yes—
90C11⋊#95C2316yes—
91C11⋊#95C2316yes—
92C11⋊#95C2316yes—
93#36641—111nomaximal, Sylow
94C24×C11C2412yes—
95C23×D11C2411yescharacteristic
96C2×D4×C11—26no—
97C22×C4×C11C2416yes—
98C22×C4×C11C2413yes—
99C22×C4×C11C2413yes—
100C22×C4×C11C2411yescharacteristic
101C2×C22⋊D11—212no—
102C22×Dic11—212no—
103C22×Dic11C2412yes—
104C22×Dic11C2416yes—
105C22×Dic11C2413yes—
106C22×Dic11C2413yes—
107C22×Dic11C2411yescharacteristic
108#4341—416no—
109C2×C4×D11—26no—
110C2×C4×D11—26no—
111C2×C4×D11—26no—
112C2×C4×D11—26no—
113C2×C4×D11—26no—
114C2×C4×D11—26no—
115C2×C4×D11#41112yes—
116C2×Dic22—26no—
117C11×C4⋊C4—26no—
118C11×C4⋊C4—212no—
119C11×C22⋊C4—212no—
120C11×C22⋊C4—212no—
121C42×C11—26no—
122C42×C11—26no—
123C42×C11#4114yescomplemented
124C22⋊Dic11—212no—
125C22⋊Dic11—212no—
126(C2×D11)⋊C4—212no—
127C4⋊Dic11—212no—
128C4⋊Dic11—26no—
129Dic11⋊C4—212no—
130Dic11⋊C4—212no—
131C4×Dic11—26no—
132C4×Dic11—26no—
133C4×Dic11—26no—
134C4×Dic11—26no—
135C4×Dic11—212no—
136C4×Dic11—26no—
137C4×Dic11—26no—
138C4×Dic11#41112yescomplemented
139#2863—113no—
140#2863—111no—
141#2860—113no—
142#2860D1111yescharacteristic, complemented
143#2852—116no—
144#2852—112no—
145C4×#126—116no—
146C4×#126—112no—
147#2297—113no—
148#2296—113no—
149C2×C43—111no—
150C23×C11—26no—
151C23×C11—22no—
152C23×C11—26no—
153C23×C11C2511yescharacteristic
154C22×D11—21no—
155C22×D11—23no—
156C22×D11C2×#4116yes—
157D4×C11—44no—
158C2×C4×C11—23no—
159C2×C4×C11—23no—
160C2×C4×C11—23no—
161C2×C4×C11—23no—
162C2×C4×C11—26no—
163C2×C4×C11—26no—
164C2×C4×C11—26no—
165C2×C4×C11C2×#4116yes—
166C2×C4×C11C2×#4116yes—
167C2×C4×C11C2×#4116yes—
168C22⋊D11—48no—
169C2×Dic11—23no—
170C2×Dic11—23no—
171C2×Dic11—23no—
172C2×Dic11—23no—
173C2×Dic11—26no—
174C2×Dic11—26no—
175C2×Dic11—26no—
176C2×Dic11—26no—
177C2×Dic11—48no—
178C2×Dic11C2×#4116yes—
179C2×Dic11C2×#4116yes—
180C2×Dic11C2×#4116yes—
181C4×D11—224no—
182C4×D11—224no—
183C4×D11#126116yescomplemented
184Dic22—44no—
185C22×#41—111no—
186C2×#126—116no—
187C2×#126C2×D1112yes—
188C2×#117—113no—
189C22×C42—113no—
190C22×C42—111no—
191C22×C42—113no—
192#391—113no—
193#391—113no—
194#390—113no—
195#390C2×D1113yes—
196#389—113no—
197#389—113no—
198#389—113no—
199#389C2×D1113yes—
200#388—116no—
201#388—116no—
202#388—116no—
203#388C2×D1116yes—
204#387—116no—
205#387—116no—
206#387—116no—
207#387—116no—
208#386—116no—
209#386—116no—
210#385—116no—
211#385—116no—
212#383—112no—
213#383—116no—
214C4×C4⋊C4—116no—
215C4×C4⋊C4—116no—
216C4×C22⋊C4—116no—
217C4×C22⋊C4—116no—
218C43—113no—
219C43—111no—
220C43—113no—
221C43C2×D1111yescharacteristic
222C22×C11—42no—
223C22×C11—46no—
224C22×C11—46no—
225C22×C11C22×#4111yescharacteristic
226C22×C11C22×#4113yes—
227C22×C11C22×#4113yes—
228C2×D11—26no—
229C2×D11—26no—
230C2×D11C2×#12614yes—
231C4×C11—26no—
232C4×C11—26no—
233C4×C11—46no—
234C4×C11C2×#12614yes—
235Dic11—26no—
236Dic11—26no—
237Dic11—42no—
238Dic11—46no—
239Dic11C2×#12614yes—
240C2×#41—2212no—
241C22×Q8—111no—
242C22×D4—112no—
243C22×D4C22×D1111yescharacteristic
244C23×C4—111no—
245C23×C4—112no—
246C23×C4—113no—
247C23×C4—113no—
248#126—28no—
249#126—2224no—
250#117—2212no—
251C2×C4⋊C4—113no—
252C2×C4⋊C4—116no—
253C2×C4⋊C4—116no—
254C2×C4⋊C4—116no—
255C2×C4⋊C4C22×D1113yes—
256C2×C4⋊C4C22×D1116yes—
257C2×C22⋊C4—116no—
258C2×C22⋊C4—116no—
259C2×C22⋊C4—116no—
260C2×C22⋊C4C22×D1116yes—
261C2×C22⋊C4C22×D1116yes—
262C2×C42—113no—
263C2×C42—116no—
264C2×C42—113no—
265C2×C42—113no—
266C2×C42—113no—
267C2×C42—113no—
268C2×C42—113no—
269C2×C42—113no—
270C2×C42—2212no—
271C2×C42—2212no—
272C2×C42—224no—
273C2×C42C22×D1113yes—
274C2×C42C22×D1113yes—
275C2×C42C22×D1111yescharacteristic
276#95—116no—
277#95—116no—
278#95—116no—
279#95—116no—
280#95—116no—
281#95—116no—
282#95—116no—
283#95C22×D1116yes—
284C2×C11—82no—
285C2×C11C22×#12611yescharacteristic
286C2×C11#344413yes—
287C2×C11#344413yes—
288D11—24no—
289C24—111no—
290C24C23×D1112yes—
291#41—4416no—
292C2×Q8—226no—
293C2×D4—26no—
294C2×D4—2212no—
295C22×C4—111no—
296C22×C4—1112no—
297C22×C4—113no—
298C22×C4—113no—
299C22×C4—112no—
300C22×C4—116no—
301C22×C4—226no—
302C22×C4—226no—
303C22×C4—226no—
304C22×C4—226no—
305C22×C4—2212no—
306C22×C4—226no—
307C22×C4—226no—
308C22×C4C23×D1116yes—
309C22×C4C23×D1113yes—
310C22×C4C23×D1113yes—
311C22×C4C23×D1111yescharacteristic
312C4⋊C4—212no—
313C4⋊C4—26no—
314C4⋊C4—2212no—
315C4⋊C4—2212no—
316C4⋊C4—226no—
317C4⋊C4—2212no—
318C22⋊C4—212no—
319C22⋊C4—212no—
320C22⋊C4—2212no—
321C22⋊C4—2212no—
322C22⋊C4—2212no—
323C42—26no—
324C42—26no—
325C42—1112no—
326C42—226no—
327C42—226no—
328C42—226no—
329C42—226no—
330C42—2212no—
331C42—226no—
332C42—226no—
333C42#434114yescomplemented
334C11#3664111yescharacteristic, complemented, Sylow
335C23—22no—
336C23—26no—
337C23—26no—
338C23—116no—
339C23—221no—
340C23—223no—
341C23C24×D1111yescharacteristic
342Q8—444no—
343D4—44no—
344D4—448no—
345C2×C4—23no—
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—23no—
349C2×C4—26no—
350C2×C4—26no—
351C2×C4—26no—
352C2×C4—116no—
353C2×C4—1116no—
354C2×C4—116no—
355C2×C4—116no—
356C2×C4—2224no—
357C2×C4—2224no—
358C2×C4—223no—
359C2×C4—223no—
360C2×C4—223no—
361C2×C4—223no—
362C2×C4—226no—
363C2×C4—226no—
364C2×C4—226no—
365C2×C4—226no—
366C2×C4—448no—
367C2×C4C2×#434116yes—
368C2×C4#41×D1116yes—
369C2×C4#41×D1116yes—
370C22—42no—
371C22—46no—
372C22—46no—
373C22—114no—
374C22—226no—
375C22—226no—
376C22C22×#434111yescharacteristic
377C22C2×#41×D1113yes—
378C22C2×#41×D1113yes—
379C4—26no—
380C4—26no—
381C4—46no—
382C4—114no—
383C4—226no—
384C4—226no—
385C4—442no—
386C4—446no—
387C4D11×#12614yes—
388C2—82no—
389C2—224no—
390C2C2×D11×#12611yescharacteristic
391C2#1308191013yes—
392C2#1308191113yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2860C2
prime radicalC22×#4341C22
hypercenter#2860D11
hypocenterC11#36641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #13076999C2semidirect
2. #13076998C2semidirect
3. #13076980C2semidirect
4. #13076930C2semidirect
5. #13076928C2semidirect
6. #13071170C2semidirect
7. #126×Dic11C2semidirect
9. #13071097C2semidirect
10. C43×D11C2semidirect
11. C11×#2860C2semidirect
123. C42×C11#41semidirect
138. C4×Dic11#41semidirect
142. #2860D11semidirect
183. C4×D11#126semidirect
333. C42#4341semidirect
334. C11#36641semidirect

Maximal subgroups

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

subgroupindex
#130769992
#130769982
#130769802
#130769302
#130769282
#130711702
#126×Dic112
#130711032
#130710972
C43×D112
C11×#28602
#3664111