Finite Group Databasebeta

← #14722218

Subgroups — #14722218

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#13077727C211yesmaximal, characteristic, complemented
2#13077184C211yesmaximal, characteristic, complemented
3#13067293C213yesmaximal, complemented
4#13067284C213yesmaximal, complemented
5#13067265C213yesmaximal, complemented
6C2×#10622182C213yesmaximal, complemented
7C11×#3498C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#550—21no—
10C11×#550C412yes—
11D42×C11—23no—
12D42×C11C416yes—
13C11×#535—23no—
14C11×#532C2213yes—
15C2×C11×#127C2213yes—
16C4×C11×#41C2211yescharacteristic
17C2×#67001—21no—
18Q8×C11⋊C8—21no—
19D4×C11⋊C8—23no—
20#10622612—23no—
21#10622538C2213yescomplemented
22#10622537C2213yescomplemented
23C2×C4⋊(C11⋊C8)C2213yescomplemented
24C2×C4⋊(C11⋊C8)C2213yescomplemented
25#10622185C2211yescharacteristic, complemented
26#10622185C2213yescomplemented
27#10622182C2213yescomplemented
28#10622182C2213yescomplemented
29#10622182C2216yescomplemented
30C11×H(5,𝔽2)—44no—
31C11×H(5,𝔽2)—44no—
32C2×C11×#41—22no—
33C2×C11×#41—23no—
34C2×C11×#41D411yescharacteristic
35C22×D4×C11—26no—
36C22×D4×C11—23no—
37C22×D4×C11—23no—
38C22×D4×C11C2×C416yes—
39C11×C4⋊Q8C2311yescharacteristic
40C11×#127—23no—
41C11×#127—23no—
42C11×#127C2×C416yes—
43C11×#127C2313yes—
44C11×#124—23no—
45C11×#121—23no—
46C11×#121—26no—
47C11×#121—26no—
48C11×#121C2×C416yes—
49C11×#120—212no—
50C4×Q8×C11C2×C411yescharacteristic
51C4×Q8×C11D411yescharacteristic
52C4×D4×C11—23no—
53C4×D4×C11C2×C416yes—
54C4×D4×C11C2×C413yes—
55C4×D4×C11D413yes—
56C11×#117D413yes—
57C2×C42×C11C2313yes—
58#67001—44no—
59C2×#4318—23no—
60C22×C11⋊C8—23no—
61C22×C11⋊C8—23no—
62C22⋊(C11⋊C8)—23no—
63C4⋊(C11⋊C8)—23no—
64C4⋊(C11⋊C8)—23no—
65C4⋊(C11⋊C8)—23no—
66C4⋊(C11⋊C8)C2311yescharacteristic
67C4⋊(C11⋊C8)C2313yes—
68C4⋊(C11⋊C8)C2313yes—
69C4⋊(C11⋊C8)C2311yescharacteristic
70C4×C11⋊C8—23no—
71#17720—111nomaximal, Sylow
72C24×C11—26no—
73C11×#41—48no—
74C11×#41—46no—
75C11×#41—46no—
76C11×#41D814yes—
77C11×#41SD1614yes—
78C2×Q8×C11—21no—
79C2×Q8×C11C22⋊C411yescharacteristic
80C2×D4×C11—26no—
81C2×D4×C11—26no—
82C2×D4×C11—26no—
83C2×D4×C11—26no—
84C2×D4×C11—23no—
85C2×D4×C11—23no—
86C2×D4×C11—424no—
87C2×D4×C11—46no—
88C2×D4×C11—46no—
89C2×D4×C11—83no—
90C2×D4×C11—83no—
91C2×D4×C11—86no—
92C2×D4×C11C22⋊C413yes—
93C2×D4×C11C22×C416yes—
94C22×C4×C11—26no—
95C22×C4×C11C22×C413yes—
96C22×C4×C11C2×D413yes—
97C22×C4×C11C2×D413yes—
98C11×C4⋊C4—21no—
99C11×C4⋊C4C22⋊C413yes—
100C11×C4⋊C4C22⋊C413yes—
101C11×C4⋊C4C22×C412yes—
102C11×C22⋊C4—26no—
103C11×C22⋊C4—26no—
104C11×C22⋊C4C22⋊C416yes—
105C42×C11C22×C413yes—
106C42×C11C2×D413yes—
107C42×C11C2×D413yes—
108C42×C11C2411yescharacteristic
109#4318—46no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—23no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—23no—
114C2×C11⋊C8—46no—
115C2×C11⋊C8—83no—
116#3498D1111yescharacteristic
117#2988—111no—
118#2906—111no—
119#1547—113no—
120#1545—113no—
121#1540—113no—
122C2×#331—113no—
123C23×C11—26no—
124C23×C11—412no—
125C23×C11—86no—
126C23×C11—86no—
127C23×C11C2×C22⋊C413yes—
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11#10214yes—
131D4×C11—46no—
132D4×C11—412no—
133D4×C11—43no—
134D4×C11—43no—
135D4×C11—43no—
136D4×C11—43no—
137D4×C11—412no—
138D4×C11—86no—
139D4×C11—86no—
140D4×C11#102112yes—
141C2×C4×C11—23no—
142C2×C4×C11—23no—
143C2×C4×C11—22no—
144C2×C4×C11—43no—
145C2×C4×C11—412no—
146C2×C4×C11C2×C22⋊C413yes—
147C2×C4×C11C2×C22⋊C413yes—
148C2×C4×C11C2×C22⋊C413yes—
149C2×C4×C11C2×D816yes—
150C2×C4×C11C2×SD1616yes—
151C2×C4×C11C23×C411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C11⋊C8—41no—
155C11⋊C8—43no—
156C11⋊C8—43no—
157C11⋊C8—41no—
158C2×H(5,𝔽2)—21no—
159C2×#131—221no—
160#550—21no—
161#550Dic1112yes—
162D42—23no—
163D42Dic1116yes—
164#535—23no—
165#532C2×D1113yes—
166C2×#127C2×D1113yes—
167C4×#41C2×D1111yescharacteristic
168C8×Q8—221no—
169C8×D4—223no—
170#431—113no—
171#424—223no—
172#423—113no—
173C2×C4⋊C8—113no—
174C2×C4⋊C8—113no—
175#332—111no—
176#332—113no—
177#331—113no—
178#331—116no—
179#331—113no—
180C22×C11—23no—
181C22×C11—23no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11—46no—
185C22×C11—1612no—
186C22×C11C2×#10216yes—
187C22×C11C22×C22⋊C411yescharacteristic
188C4×C11—21no—
189C4×C11—23no—
190C4×C11—23no—
191C4×C11—42no—
192C4×C11C2×#10216yes—
193C4×C11C22×D811yescharacteristic
194C4×C11C22×SD1611yescharacteristic
195C4×C11#57611yescharacteristic
196C4×C11#57711yescharacteristic
197H(5,𝔽2)—44no—
198H(5,𝔽2)—44no—
199C2×#41—22no—
200C2×#41—23no—
201C2×#41C22⋊D1111yescharacteristic
202C22×D4—26no—
203C22×D4—23no—
204C22×D4—23no—
205C22×D4C2×Dic1116yes—
206#131—444no—
207C2×M16—223no—
208C22×C8—223no—
209C22×C8—223no—
210C4⋊Q8C22×D1111yescharacteristic
211#127—23no—
212#127—23no—
213#127C2×Dic1116yes—
214#127C22×D1113yes—
215#124—23no—
216#121—23no—
217#121—26no—
218#121—26no—
219#121C2×Dic1116yes—
220#120—212no—
221C4×Q8C2×Dic1111yescharacteristic
222C4×Q8C22⋊D1111yescharacteristic
223C4×D4—23no—
224C4×D4C2×Dic1116yes—
225C4×D4C2×Dic1113yes—
226C4×D4C22⋊D1113yes—
227#117C22⋊D1113yes—
228C2×C42C22×D1113yes—
229C4⋊C8—111no—
230C4⋊C8—113no—
231C4⋊C8—113no—
232C4⋊C8—111no—
233C4⋊C8—223no—
234C4⋊C8—223no—
235C4⋊C8—223no—
236C22⋊C8—223no—
237C4×C8—223no—
238C2×C11—26no—
239C2×C11—86no—
240C2×C11#288811yescharacteristic
241C2×C11C22×#10211yescharacteristic
242C2×C11#289711yescharacteristic
243C24—26no—
244#41—48no—
245#41—46no—
246#41—46no—
247#41#432314yes—
248#41#432414yes—
249C2×Q8—21no—
250C2×Q8C22⋊Dic1111yescharacteristic
251C2×D4—26no—
252C2×D4—26no—
253C2×D4—26no—
254C2×D4—26no—
255C2×D4—23no—
256C2×D4—23no—
257C2×D4—424no—
258C2×D4—46no—
259C2×D4—46no—
260C2×D4—83no—
261C2×D4—83no—
262C2×D4—86no—
263C2×D4C22⋊Dic1113yes—
264C2×D4C22×Dic1116yes—
265C22×C4—26no—
266C22×C4C22×Dic1113yes—
267C22×C4C2×C22⋊D1113yes—
268C22×C4C2×C22⋊D1113yes—
269M16—446no—
270C2×C8—221no—
271C2×C8—223no—
272C2×C8—221no—
273C2×C8—223no—
274C2×C8—446no—
275C2×C8—883no—
276C4⋊C4—21no—
277C4⋊C4C22⋊Dic1113yes—
278C4⋊C4C22⋊Dic1113yes—
279C4⋊C4C22×Dic1112yes—
280C22⋊C4—26no—
281C22⋊C4—26no—
282C22⋊C4C22⋊Dic1116yes—
283C42C22×Dic1113yes—
284C42C2×C22⋊D1113yes—
285C42C2×C22⋊D1113yes—
286C42C23×D1111yescharacteristic
287C11#1772011yescharacteristic, complemented, Sylow
288C23—26no—
289C23—412no—
290C23—86no—
291C23—86no—
292C23C2×C22⋊Dic1113yes—
293Q8—41no—
294Q8—41no—
295Q8#6689614yes—
296D4—46no—
297D4—412no—
298D4—43no—
299D4—43no—
300D4—412no—
301D4—43no—
302D4—43no—
303D4—86no—
304D4—86no—
305D4#66896112yes—
306C2×C4—23no—
307C2×C4—23no—
308C2×C4—22no—
309C2×C4—43no—
310C2×C4—412no—
311C2×C4C2×#432316yes—
312C2×C4C2×#432416yes—
313C2×C4C2×C22⋊Dic1113yes—
314C2×C4C2×C22⋊Dic1113yes—
315C2×C4C2×C22⋊Dic1113yes—
316C2×C4C23×Dic1111yescharacteristic
317C2×C4C22×C22⋊D1111yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—441no—
320C8—443no—
321C8—443no—
322C8—441no—
323C22—23no—
324C22—23no—
325C22—46no—
326C22—46no—
327C22—46no—
328C22—1612no—
329C22C2×#6689616yes—
330C22C22×C22⋊Dic1111yescharacteristic
331C4—21no—
332C4—23no—
333C4—23no—
334C4—42no—
335C4C2×#6689616yes—
336C4C22×#432311yescharacteristic
337C4C22×#432411yescharacteristic
338C4#1062336611yescharacteristic
339C4#1062336711yescharacteristic
340C2—26no—
341C2—86no—
342C2#1307709511yescharacteristic
343C2C22×#6689611yescharacteristic
344C2#1307714211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3498C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3498D11
hypocenterC11#17720
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #13077727C2semidirect
2. #13077184C2semidirect
3. #13067293C2semidirect
4. #13067284C2semidirect
5. #13067265C2semidirect
6. C2×#10622182C2semidirect
21. #10622538C22semidirect
22. #10622537C22semidirect
23. C2×C4⋊(C11⋊C8)C22semidirect
24. C2×C4⋊(C11⋊C8)C22semidirect
25. #10622185C22semidirect
26. #10622185C22semidirect
27. #10622182C22semidirect
28. #10622182C22semidirect
29. #10622182C22semidirect
287. C11#17720semidirect

Maximal subgroups

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

subgroupindex
#130777272
#130771842
#130672932
#130672842
#130672652
C2×#106221822
C11×#34982
#1772011