Finite Group Databasebeta

← #14722219

Subgroups — #14722219

Order 2816.

1308 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082394C211yesmaximal, characteristic
2#13077727C211yesmaximal, characteristic, complemented
3#13067294C213yesmaximal, complemented
4#13067285C213yesmaximal, complemented
5#13067266C213yesmaximal, complemented
6C2×#10622123C213yesmaximal, complemented
7C11×#2906C211yesmaximal, characteristic, complemented
8C2×#67042—21no—
9C2×C11×#131—21no—
10C4×C11×#41C2211yescharacteristic
11#10623108—21no—
12#10623108C412yes—
13D4×D44—23no—
14D4×D44C416yes—
15#10623056—23no—
16#10623008C2213yes—
17C2×#66927C2213yes—
18C11×#424—23no—
19C11×#423C2213yescomplemented
20C2×C11×C4⋊C8C2213yescomplemented
21Q8×C11⋊C8—21no—
22D4×C11⋊C8—23no—
23#10622538C2213yescomplemented
24C2×C4⋊(C11⋊C8)C2213yescomplemented
25#10622123C2213yescomplemented
26#10622123C2213yescomplemented
27#10622123C2216yescomplemented
28#10622120C2211yescharacteristic, complemented
29#10622120C2213yescomplemented
30C2×C11×#41D411yescharacteristic
31#67042—44no—
32#67042—44no—
33C2×#4343—22no—
34C2×D4×D11—26no—
35C2×#4339—23no—
36C22×D44—23no—
37C22×D44—23no—
38C22×D44C2×C416yes—
39C11×#131—44no—
40C2×C11×M16—23no—
41C22×C8×C11—23no—
42C4×Q8×C11C2×C411yescharacteristic
43C4×Q8×C11D411yescharacteristic
44C4×D4×C11C2×C413yes—
45C4×D4×C11D413yes—
46C11×#117D413yes—
47C2×C42×C11C2313yes—
48#66983—23no—
49#66983C2×C416yes—
50C22×C11⋊C8—23no—
51#66948—26no—
52#66948—26no—
53#66935—212no—
54#66928—23no—
55#66927—23no—
56#66927—23no—
57#66927C2×C416yes—
58#66927C2313yes—
59C4×D44—23no—
60C4×D44C2×C416yes—
61#66922C2311yescharacteristic
62C11×C4⋊C8—23no—
63C11×C4⋊C8—23no—
64C11×C4⋊C8C2311yescharacteristic
65C11×C4⋊C8C2313yes—
66C22⋊(C11⋊C8)—23no—
67C4⋊(C11⋊C8)—23no—
68C4⋊(C11⋊C8)C2313yes—
69C4⋊(C11⋊C8)C2311yescharacteristic
70C4×C11⋊C8—23no—
71#17720—111nomaximal, Sylow
72C23×D11—26no—
73C11×#41D814yes—
74C11×#41SD1614yes—
75C2×Q8×C11C22⋊C411yescharacteristic
76C2×D4×C11C22⋊C413yes—
77C22×C4×C11C22×C413yes—
78C22×C4×C11C2×D413yes—
79C22×C4×C11C2×D413yes—
80C2×C22⋊D11—26no—
81#4343—48no—
82D4×D11—424no—
83#4339—46no—
84#4339—46no—
85C2×D44—26no—
86C2×D44—26no—
87C2×D44—26no—
88C2×D44—23no—
89C2×D44—23no—
90C2×D44—46no—
91C2×D44—46no—
92C2×D44—83no—
93C2×D44—83no—
94C2×D44—86no—
95C2×D44C22×C416yes—
96C2×C4×D11—26no—
97C2×Dic22—21no—
98C11×M16—46no—
99C2×C8×C11—21no—
100C2×C8×C11—23no—
101C2×C8×C11—46no—
102C11×C4⋊C4C22⋊C413yes—
103C11×C4⋊C4C22⋊C413yes—
104C11×C22⋊C4C22⋊C416yes—
105C42×C11C22×C413yes—
106C42×C11C2×D413yes—
107C42×C11C2×D413yes—
108C42×C11C2411yescharacteristic
109(C2×D11)⋊C4—26no—
110(C2×D11)⋊C4—26no—
111C4⋊Dic11—21no—
112C4⋊Dic11C22×C412yes—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—23no—
115C2×C11⋊C8—83no—
116#3498—111no—
117#2988—111no—
118#2906D1111yescharacteristic, complemented
119#1547—113no—
120#1545—113no—
121#1540—113no—
122C2×#331—113no—
123C23×C11C2×C22⋊C413yes—
124C22×D11—26no—
125C22×D11—412no—
126C22×D11—86no—
127C22×D11—86no—
128Q8×C11#10214yes—
129D4×C11#102112yes—
130C2×C4×C11—23no—
131C2×C4×C11—23no—
132C2×C4×C11—43no—
133C2×C4×C11C2×C22⋊C413yes—
134C2×C4×C11C2×C22⋊C413yes—
135C2×C4×C11C2×C22⋊C413yes—
136C2×C4×C11C2×D816yes—
137C2×C4×C11C2×SD1616yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—412no—
142C2×Dic11—22no—
143D44—46no—
144D44—43no—
145D44—43no—
146D44—43no—
147D44—43no—
148D44—412no—
149D44—86no—
150D44—86no—
151C4×D11—412no—
152Dic22—41no—
153Dic22—41no—
154C8×C11—41no—
155C8×C11—43no—
156C11⋊C8—43no—
157C11⋊C8—41no—
158C2×H(5,𝔽2)—221no—
159C2×#131—21no—
160#550—112no—
161#550—221no—
162D42—116no—
163D42—223no—
164#535—223no—
165#532—113no—
166C2×#127—113no—
167C4×#41C2×D1111yescharacteristic
168C8×Q8—221no—
169C8×D4—223no—
170#431—113no—
171#424—23no—
172#423C2×D1113yescomplemented
173C2×C4⋊C8—113no—
174C2×C4⋊C8C2×D1113yescomplemented
175#332—111no—
176#332—113no—
177#331—113no—
178#331—116no—
179#331—113no—
180C22×C11—23no—
181C22×C11—23no—
182C22×C11C2×#10216yes—
183C22×C11C22×C22⋊C411yescharacteristic
184C2×D11—46no—
185C2×D11—46no—
186C2×D11—46no—
187C2×D11—1612no—
188C4×C11—21no—
189C4×C11—23no—
190C4×C11—23no—
191C4×C11C2×#10216yes—
192C4×C11C22×D811yescharacteristic
193C4×C11C22×SD1611yescharacteristic
194C4×C11#57611yescharacteristic
195C4×C11#57711yescharacteristic
196Dic11—42no—
197H(5,𝔽2)—444no—
198H(5,𝔽2)—444no—
199C2×#41—222no—
200C2×#41—223no—
201C2×#41C22⋊D1111yescharacteristic
202C22×D4—116no—
203C22×D4—226no—
204C22×D4—223no—
205C22×D4—223no—
206#131—44no—
207C2×M16—23no—
208C22×C8—23no—
209C22×C8—223no—
210C4⋊Q8—111no—
211#127—116no—
212#127—113no—
213#127—223no—
214#127—223no—
215#124—223no—
216#121—116no—
217#121—223no—
218#121—226no—
219#121—226no—
220#120—2212no—
221C4×Q8C4×D1111yescharacteristic
222C4×Q8D4411yescharacteristic
223C4×D4—116no—
224C4×D4—223no—
225C4×D4C4×D1113yes—
226C4×D4D4413yes—
227#117C22⋊D1113yes—
228C2×C42C22×D1113yes—
229C4⋊C8—23no—
230C4⋊C8—23no—
231C4⋊C8—113no—
232C4⋊C8—111no—
233C4⋊C8—223no—
234C4⋊C8C22×D1111yescharacteristic
235C4⋊C8C22×D1113yes—
236C22⋊C8—223no—
237C4×C8—223no—
238C2×C11—26no—
239C2×C11#288811yescharacteristic
240C2×C11C22×#10211yescharacteristic
241C2×C11#289711yescharacteristic
242D11—86no—
243C24—226no—
244#41—448no—
245#41—446no—
246#41—446no—
247#41#432314yes—
248#41#432514yes—
249C2×Q8—221no—
250C2×Q8(C2×D11)⋊C411yescharacteristic
251C2×D4—116no—
252C2×D4—226no—
253C2×D4—226no—
254C2×D4—226no—
255C2×D4—226no—
256C2×D4—223no—
257C2×D4—223no—
258C2×D4—4424no—
259C2×D4—446no—
260C2×D4—446no—
261C2×D4—883no—
262C2×D4—883no—
263C2×D4—886no—
264C2×D4(C2×D11)⋊C413yes—
265C22×C4—226no—
266C22×C4C2×C4×D1113yes—
267C22×C4C2×D4413yes—
268C22×C4C2×C22⋊D1113yes—
269M16—46no—
270C2×C8—21no—
271C2×C8—23no—
272C2×C8—46no—
273C2×C8—221no—
274C2×C8—223no—
275C2×C8—883no—
276C4⋊C4—112no—
277C4⋊C4—221no—
278C4⋊C4(C2×D11)⋊C413yes—
279C4⋊C4(C2×D11)⋊C413yes—
280C22⋊C4—226no—
281C22⋊C4—226no—
282C22⋊C4(C2×D11)⋊C416yes—
283C42C2×C4×D1113yes—
284C42C2×D4413yes—
285C42C2×C22⋊D1113yes—
286C42C23×D1111yescharacteristic
287C11#1772011yescharacteristic, complemented, Sylow
288C23—226no—
289C23—4412no—
290C23—886no—
291C23—886no—
292C23C2×(C2×D11)⋊C413yes—
293Q8—441no—
294Q8—441no—
295Q8#6687314yes—
296D4—446no—
297D4—4412no—
298D4—443no—
299D4—443no—
300D4—443no—
301D4—443no—
302D4—4412no—
303D4—886no—
304D4—886no—
305D4#66873112yes—
306C2×C4—23no—
307C2×C4—23no—
308C2×C4—43no—
309C2×C4—222no—
310C2×C4—4412no—
311C2×C4C2×(C2×D11)⋊C413yes—
312C2×C4C2×(C2×D11)⋊C413yes—
313C2×C4C2×(C2×D11)⋊C413yes—
314C2×C4C2×#432316yes—
315C2×C4C2×#432516yes—
316C2×C4C22×C4×D1111yescharacteristic
317C2×C4C22×D4411yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—41no—
320C8—43no—
321C8—441no—
322C8—443no—
323C22—23no—
324C22—23no—
325C22—446no—
326C22—446no—
327C22—446no—
328C22—17612no—
329C22C2×#6687316yes—
330C22C22×(C2×D11)⋊C411yescharacteristic
331C4—21no—
332C4—23no—
333C4—23no—
334C4—442no—
335C4C2×#6687316yes—
336C4#1062328211yescharacteristic
337C4#1062328311yescharacteristic
338C4C22×#432311yescharacteristic
339C4C22×#432511yescharacteristic
340C2—26no—
341C2—886no—
342C2#1307709411yescharacteristic
343C2C22×#6687311yescharacteristic
344C2#1307714311yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2906C2
socleC22×C11C22×C22⋊C4
prime radical#13082394C2
cosocleC42×C11C24
hypercenter#2906D11
hypocenterC11#17720
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077727C2semidirect
3. #13067294C2semidirect
4. #13067285C2semidirect
5. #13067266C2semidirect
6. C2×#10622123C2semidirect
7. C11×#2906C2semidirect
19. C11×#423C22semidirect
20. C2×C11×C4⋊C8C22semidirect
23. #10622538C22semidirect
24. C2×C4⋊(C11⋊C8)C22semidirect
25. #10622123C22semidirect
26. #10622123C22semidirect
27. #10622123C22semidirect
28. #10622120C22semidirect
29. #10622120C22semidirect
118. #2906D11semidirect
172. #423C2×D11semidirect
174. C2×C4⋊C8C2×D11semidirect
287. C11#17720semidirect

Maximal subgroups

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

subgroupindex
#130823942
#130777272
#130672942
#130672852
#130672662
C2×#106221232
C11×#29062
#1772011