Finite Group Databasebeta

← #14722225

Subgroups — #14722225

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 330 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#13067288C213yesmaximal, complemented
5#13067265C213yesmaximal, complemented
6C2×#10622185C213yesmaximal, complemented
7C11×#3499C211yesmaximal, characteristic
8C2×C11×2−1+4—21no—
9D4×Q8×C11—21no—
10D4×Q8×C11C412yes—
11C11×#547—23no—
12C11×#547C416yes—
13C11×#536—23no—
14C11×#532C2213yes—
15C2×C11×C4⋊Q8C2213yes—
16C4×C11×#41C2211yescharacteristic
17C2×#67001—21no—
18Q8×C11⋊C8—21no—
19D4×C11⋊C8—23no—
20#10622612—23no—
21#10622538C2213yes—
22#10622537C2213yes—
23C2×C4⋊(C11⋊C8)C2213yes—
24C2×C4⋊(C11⋊C8)C2213yes—
25#10622185C2213yes—
26#10622185C2213yes—
27#10622185C2216yes—
28#10622182C2211yescharacteristic
29#10622182C2213yes—
30C11×2−1+4—44no—
31C11×2−1+4—44no—
32C2×C11×#41—26no—
33C2×C11×#41—23no—
34C2×C11×#41D411yescharacteristic
35C22×Q8×C11—22no—
36C22×Q8×C11—23no—
37C11×C4⋊Q8—23no—
38C11×C4⋊Q8—23no—
39C11×C4⋊Q8C2×C416yes—
40C11×C4⋊Q8C2313yes—
41C11×#127C2311yescharacteristic
42C11×#124—23no—
43C11×#123—212no—
44C11×C22⋊Q8—26no—
45C11×C22⋊Q8—26no—
46C11×#121—23no—
47C11×#121C2×C416yes—
48C4×Q8×C11C2×C411yescharacteristic
49C4×Q8×C11D411yescharacteristic
50C4×D4×C11—23no—
51C4×D4×C11C2×C416yes—
52C4×D4×C11C2×C413yes—
53C4×D4×C11D413yes—
54C11×#117D413yes—
55C2×C11×C4⋊C4—23no—
56C2×C11×C4⋊C4C2×C416yes—
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#17721—111nomaximal, Sylow
72C11×#41—424no—
73C11×#41—46no—
74C11×#41—46no—
75C11×#41D814yes—
76C11×#41SD1614yes—
77C2×Q8×C11—26no—
78C2×Q8×C11—23no—
79C2×Q8×C11—48no—
80C2×Q8×C11—46no—
81C2×Q8×C11—46no—
82C2×Q8×C11C22⋊C411yescharacteristic
83C2×D4×C11—26no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11C22⋊C413yes—
87C2×D4×C11C22×C412yes—
88C22×C4×C11—26no—
89C22×C4×C11—26no—
90C22×C4×C11C22×C413yes—
91C22×C4×C11C2×D413yes—
92C22×C4×C11C2×D413yes—
93C11×C4⋊C4—26no—
94C11×C4⋊C4—26no—
95C11×C4⋊C4—23no—
96C11×C4⋊C4C22⋊C413yes—
97C11×C4⋊C4C22⋊C413yes—
98C11×C4⋊C4C22×C416yes—
99C11×C22⋊C4—26no—
100C11×C22⋊C4—26no—
101C11×C22⋊C4C22⋊C416yes—
102C42×C11C22×C413yes—
103C42×C11C2×D413yes—
104C42×C11C2×D413yes—
105C42×C11C2411yescharacteristic
106#4318—46no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—23no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—23no—
111C2×C11⋊C8—46no—
112C2×C11⋊C8—83no—
113#3499D1111yescharacteristic
114#2988—111no—
115#2906—111no—
116#1547—113no—
117#1546—113no—
118#1540—113no—
119C2×#332—113no—
120C23×C11—22no—
121C23×C11C2×C22⋊C413yes—
122Q8×C11—43no—
123Q8×C11—43no—
124Q8×C11—412no—
125Q8×C11#10214yes—
126D4×C11—42no—
127D4×C11—412no—
128D4×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—41no—
132D4×C11#102112yes—
133C2×C4×C11—23no—
134C2×C4×C11—23no—
135C2×C4×C11—26no—
136C2×C4×C11—43no—
137C2×C4×C11—412no—
138C2×C4×C11—412no—
139C2×C4×C11C2×C22⋊C413yes—
140C2×C4×C11C2×C22⋊C413yes—
141C2×C4×C11C2×C22⋊C413yes—
142C2×C4×C11C2×D816yes—
143C2×C4×C11C2×SD1616yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C11⋊C8—41no—
148C11⋊C8—43no—
149C11⋊C8—43no—
150C11⋊C8—41no—
151C2×2−1+4—21no—
152C2×#131—221no—
153D4×Q8—21no—
154D4×Q8Dic1112yes—
155#547—23no—
156#547Dic1116yes—
157#536—23no—
158#532C2×D1113yes—
159C2×C4⋊Q8C2×D1113yes—
160C4×#41C2×D1111yescharacteristic
161C8×Q8—221no—
162C8×D4—223no—
163#431—113no—
164#424—223no—
165#423—113no—
166C2×C4⋊C8—113no—
167C2×C4⋊C8—113no—
168#332—113no—
169#332—116no—
170#332—113no—
171#331—111no—
172#331—113no—
173C22×C11—23no—
174C22×C11—23no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11—42no—
178C22×C11C2×#10216yes—
179C22×C11C22×C22⋊C411yescharacteristic
180C4×C11—21no—
181C4×C11—23no—
182C4×C11—23no—
183C4×C11—46no—
184C4×C11C2×#10216yes—
185C4×C11C22×D811yescharacteristic
186C4×C11C22×SD1611yescharacteristic
187C4×C11#57711yescharacteristic
188C4×C11#57811yescharacteristic
1892−1+4—44no—
1902−1+4—44no—
191C2×#41—26no—
192C2×#41—23no—
193C2×#41C22⋊D1111yescharacteristic
194C22×Q8—22no—
195C22×Q8—23no—
196#131—444no—
197C2×M16—223no—
198C22×C8—223no—
199C22×C8—223no—
200C4⋊Q8—23no—
201C4⋊Q8—23no—
202C4⋊Q8C2×Dic1116yes—
203C4⋊Q8C22×D1113yes—
204#127C22×D1111yescharacteristic
205#124—23no—
206#123—212no—
207C22⋊Q8—26no—
208C22⋊Q8—26no—
209#121—23no—
210#121C2×Dic1116yes—
211C4×Q8C2×Dic1111yescharacteristic
212C4×Q8C22⋊D1111yescharacteristic
213C4×D4—23no—
214C4×D4C2×Dic1116yes—
215C4×D4C2×Dic1113yes—
216C4×D4C22⋊D1113yes—
217#117C22⋊D1113yes—
218C2×C4⋊C4—23no—
219C2×C4⋊C4C2×Dic1116yes—
220C2×C42C22×D1113yes—
221C4⋊C8—111no—
222C4⋊C8—113no—
223C4⋊C8—113no—
224C4⋊C8—111no—
225C4⋊C8—223no—
226C4⋊C8—223no—
227C4⋊C8—223no—
228C22⋊C8—223no—
229C4×C8—223no—
230C2×C11—26no—
231C2×C11—82no—
232C2×C11#288911yescharacteristic
233C2×C11C22×#10211yescharacteristic
234C2×C11#289811yescharacteristic
235#41—424no—
236#41—46no—
237#41—46no—
238#41#432314yes—
239#41#432414yes—
240C2×Q8—26no—
241C2×Q8—23no—
242C2×Q8—48no—
243C2×Q8—46no—
244C2×Q8—46no—
245C2×Q8C22⋊Dic1111yescharacteristic
246C2×D4—26no—
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊Dic1113yes—
250C2×D4C22×Dic1112yes—
251C22×C4—26no—
252C22×C4—26no—
253C22×C4C22×Dic1113yes—
254C22×C4C2×C22⋊D1113yes—
255C22×C4C2×C22⋊D1113yes—
256M16—446no—
257C2×C8—221no—
258C2×C8—223no—
259C2×C8—221no—
260C2×C8—223no—
261C2×C8—446no—
262C2×C8—883no—
263C4⋊C4—26no—
264C4⋊C4—26no—
265C4⋊C4—23no—
266C4⋊C4C22⋊Dic1113yes—
267C4⋊C4C22⋊Dic1113yes—
268C4⋊C4C22×Dic1116yes—
269C22⋊C4—26no—
270C22⋊C4—26no—
271C22⋊C4C22⋊Dic1116yes—
272C42C22×Dic1113yes—
273C42C2×C22⋊D1113yes—
274C42C2×C22⋊D1113yes—
275C42C23×D1111yescharacteristic
276C11#1772111yescharacteristic, complemented, Sylow
277C23—22no—
278C23C2×C22⋊Dic1113yes—
279Q8—43no—
280Q8—43no—
281Q8—412no—
282Q8#6689614yes—
283D4—42no—
284D4—412no—
285D4—41no—
286D4—41no—
287D4—41no—
288D4—41no—
289D4#66896112yes—
290C2×C4—23no—
291C2×C4—23no—
292C2×C4—26no—
293C2×C4—43no—
294C2×C4—412no—
295C2×C4—412no—
296C2×C4C2×#432316yes—
297C2×C4C2×#432416yes—
298C2×C4C2×C22⋊Dic1113yes—
299C2×C4C2×C22⋊Dic1113yes—
300C2×C4C2×C22⋊Dic1113yes—
301C2×C4C23×Dic1111yescharacteristic
302C2×C4C22×C22⋊D1111yescharacteristic
303C2×C4C22×C22⋊D1111yescharacteristic
304C8—441no—
305C8—443no—
306C8—443no—
307C8—441no—
308C22—23no—
309C22—23no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22C2×#6689616yes—
314C22C22×C22⋊Dic1111yescharacteristic
315C4—21no—
316C4—23no—
317C4—23no—
318C4—46no—
319C4C2×#6689616yes—
320C4C22×#432311yescharacteristic
321C4C22×#432411yescharacteristic
322C4#1062336811yescharacteristic
323C4#1062336911yescharacteristic
324C2—26no—
325C2—82no—
326C2#1307709911yescharacteristic
327C2C22×#6689611yescharacteristic
328C2#1307714911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3499C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3499D11
hypocenterC11#17721
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13077727C2semidirect
2. #13077184C2semidirect
3. #13067293C2semidirect
4. #13067288C2semidirect
5. #13067265C2semidirect
6. C2×#10622185C2semidirect
276. C11#17721semidirect

Maximal subgroups

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

subgroupindex
#130777272
#130771842
#130672932
#130672882
#130672652
C2×#106221852
C11×#34992
#1772111