Finite Group Databasebeta

← #14719983

Subgroups — #14719983

Order 2816.

1284 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077065C212yesmaximal, complemented
2#13066980C216yesmaximal, complemented
3#13066954C213yesmaximal, complemented
4#13066934C213yesmaximal, complemented
5C2×C11×#548C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C23×Q8×C11C411yescharacteristic
8C11×#548—22no—
9C11×#548—26no—
10C2×C11×#124C413yes—
11C2×C11×C22⋊Q8C2213yes—
12C2×C11×#121C413yes—
13C2×C4×Q8×C11C411yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×#67001—22no—
16#10622847—26no—
17#10622820C2216yes—
18C2×C22⋊(C11⋊C8)C2216yes—
19#10622166C2216yes—
20#10622166C2216yes—
21#10622163C2211yescharacteristic
22#10622163C2213yes—
23C2×C11×#41—44no—
24C2×C11×#41D412yes—
25C2×C11×#41D416yes—
26C22×Q8×C11—23no—
27C22×Q8×C11—21no—
28C22×Q8×C11—44no—
29C22×Q8×C11C2×C411yescharacteristic
30C22×Q8×C11C2×C413yes—
31C22×D4×C11C2×C413yes—
32C22×D4×C11C2×C413yes—
33C23×C4×C11C2×C413yes—
34C23×C4×C11C2313yes—
35C11×#124—26no—
36C11×#124—26no—
37C11×C22⋊Q8—26no—
38C11×C22⋊Q8—26no—
39C11×#121—26no—
40C11×#121—26no—
41C4×Q8×C11—23no—
42C4×Q8×C11—21no—
43C4×D4×C11—26no—
44C4×D4×C11—26no—
45C2×C11×C4⋊C4C2×C413yes—
46C2×C11×C4⋊C4C2313yes—
47C2×C11×C22⋊C4C2×C413yes—
48C2×C11×C22⋊C4C2×C416yes—
49C2×C11×C22⋊C4C2311yescharacteristic
50C2×C42×C11C2×C413yes—
51#67001—48no—
52C2×#4318—26no—
53C22×C11⋊C8—26no—
54C22⋊(C11⋊C8)—26no—
55C22⋊(C11⋊C8)—26no—
56C22⋊(C11⋊C8)C2312yes—
57C22⋊(C11⋊C8)C2316yes—
58#17414—111nomaximal, Sylow
59C24×C11C22×C413yes—
60C24×C11C22×C411yescharacteristic
61C11×#41—28no—
62C11×#41—412no—
63C2×Q8×C11—24no—
64C2×Q8×C11—23no—
65C2×Q8×C11—23no—
66C2×Q8×C11—46no—
67C2×Q8×C11—412no—
68C2×Q8×C11—44no—
69C2×Q8×C11C22⋊C413yes—
70C2×Q8×C11C22⋊C411yescharacteristic
71C2×D4×C11—26no—
72C2×D4×C11—26no—
73C2×D4×C11—46no—
74C2×D4×C11—43no—
75C2×D4×C11C22⋊C416yes—
76C2×D4×C11C22⋊C416yes—
77C22×C4×C11—23no—
78C22×C4×C11—23no—
79C22×C4×C11—46no—
80C22×C4×C11—46no—
81C22×C4×C11C22×C413yes—
82C22×C4×C11C22×C413yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C413yes—
85C22×C4×C11C2×D416yes—
86C22×C4×C11C2×D416yes—
87C22×C4×C11C2411yescharacteristic
88C11×C4⋊C4—23no—
89C11×C4⋊C4—23no—
90C11×C4⋊C4—26no—
91C11×C22⋊C4—26no—
92C11×C22⋊C4—212no—
93C11×C22⋊C4—22no—
94C42×C11—23no—
95C42×C11—23no—
96#4318—412no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—26no—
99C2×C11⋊C8—412no—
100C2×#548D1111yescharacteristic
101#2880—112no—
102#1472—116no—
103#1465—113no—
104#1459—113no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—23no—
108C23×C11—23no—
109C23×C11—43no—
110C23×C11—43no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11C2×C22⋊C416yes—
114C23×C11#13112yescomplemented
115C23×C11C23×C411yescharacteristic
116Q8×C11—26no—
117Q8×C11—46no—
118Q8×C11—46no—
119Q8×C11#9914yes—
120D4×C11—212no—
121D4×C11—46no—
122D4×C11—412no—
123C2×C4×C11—212no—
124C2×C4×C11—26no—
125C2×C4×C11—21no—
126C2×C4×C11—23no—
127C2×C4×C11—23no—
128C2×C4×C11—23no—
129C2×C4×C11—23no—
130C2×C4×C11—41no—
131C2×C4×C11—46no—
132C2×C4×C11—46no—
133C2×C4×C11—46no—
134C2×C4×C11—43no—
135C2×C4×C11—41no—
136C2×C4×C11C2×C22⋊C413yes—
137C2×C4×C11C2×C22⋊C413yes—
138C2×C4×C11C22×D412yes—
139C11⋊C8—42no—
140C11⋊C8—46no—
141C22×#41C2×D1111yescharacteristic
142C23×Q8Dic1111yescharacteristic
143C2×#131—222no—
144#548—22no—
145#548—26no—
146C2×#124Dic1113yes—
147C2×C22⋊Q8C2×D1113yes—
148C2×#121Dic1113yes—
149C2×C4×Q8Dic1111yescharacteristic
150C2×C4×D4C2×D1113yes—
151#408—226no—
152#407—116no—
153C2×C22⋊C8—116no—
154#324—116no—
155#324—116no—
156#323—111no—
157#323—113no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—22no—
161C22×C11—26no—
162C22×C11—26no—
163C22×C11—26no—
164C22×C11—42no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—83no—
169C22×C11—83no—
170C22×C11C22×C22⋊C411yescharacteristic
171C22×C11C2×#13111yescharacteristic
172C22×C11#56811yescharacteristic
173C4×C11—22no—
174C4×C11—23no—
175C4×C11—43no—
176C4×C11—43no—
177C4×C11—41no—
178C4×C11C2×#9916yes—
179C2×#41—44no—
180C2×#41C22⋊D1112yes—
181C2×#41C22⋊D1116yes—
182C22×Q8—23no—
183C22×Q8—21no—
184C22×Q8—44no—
185C22×Q8C2×Dic1111yescharacteristic
186C22×Q8C2×Dic1113yes—
187C22×D4C2×Dic1113yes—
188C22×D4C2×Dic1113yes—
189C23×C4C2×Dic1113yes—
190C23×C4C22×D1113yes—
191#131—448no—
192C2×M16—226no—
193C22×C8—226no—
194#124—26no—
195#124—26no—
196C22⋊Q8—26no—
197C22⋊Q8—26no—
198#121—26no—
199#121—26no—
200C4×Q8—23no—
201C4×Q8—21no—
202C4×D4—26no—
203C4×D4—26no—
204C2×C4⋊C4C2×Dic1113yes—
205C2×C4⋊C4C22×D1113yes—
206C2×C22⋊C4C2×Dic1113yes—
207C2×C22⋊C4C2×Dic1116yes—
208C2×C22⋊C4C22×D1111yescharacteristic
209C2×C42C2×Dic1113yes—
210C22⋊C8—112no—
211C22⋊C8—116no—
212C22⋊C8—226no—
213C22⋊C8—226no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11—46no—
217C2×C11—42no—
218C2×C11#288011yescharacteristic
219C2×C11C22×#9911yescharacteristic
220C2×C11#288911yescharacteristic
221C24C22×Dic1111yescharacteristic
222C24C22×Dic1113yes—
223#41—28no—
224#41—412no—
225C2×Q8—24no—
226C2×Q8—23no—
227C2×Q8—23no—
228C2×Q8—46no—
229C2×Q8—412no—
230C2×Q8—44no—
231C2×Q8C22⋊Dic1113yes—
232C2×Q8C22⋊Dic1111yescharacteristic
233C2×D4—26no—
234C2×D4—26no—
235C2×D4—46no—
236C2×D4—43no—
237C2×D4C22⋊Dic1116yes—
238C2×D4C22⋊Dic1116yes—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—46no—
242C22×C4—46no—
243C22×C4C22×Dic1113yes—
244C22×C4C22×Dic1113yes—
245C22×C4C22×Dic1111yescharacteristic
246C22×C4C22×Dic1113yes—
247C22×C4C2×C22⋊D1116yes—
248C22×C4C2×C22⋊D1116yes—
249C22×C4C23×D1111yescharacteristic
250M16—4412no—
251C2×C8—222no—
252C2×C8—226no—
253C2×C8—4412no—
254C4⋊C4—23no—
255C4⋊C4—23no—
256C4⋊C4—26no—
257C22⋊C4—26no—
258C22⋊C4—212no—
259C22⋊C4—22no—
260C42—23no—
261C42—23no—
262C11#1741411yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—23no—
266C23—23no—
267C23—43no—
268C23—43no—
269C23—41no—
270C23—41no—
271C23#6700112yescomplemented
272C23C2×C22⋊Dic1116yes—
273C23C23×Dic1111yescharacteristic
274Q8—26no—
275Q8—46no—
276Q8—46no—
277Q8#6689814yes—
278D4—212no—
279D4—46no—
280D4—412no—
281C2×C4—212no—
282C2×C4—26no—
283C2×C4—23no—
284C2×C4—23no—
285C2×C4—21no—
286C2×C4—23no—
287C2×C4—23no—
288C2×C4—41no—
289C2×C4—46no—
290C2×C4—46no—
291C2×C4—46no—
292C2×C4—43no—
293C2×C4—41no—
294C2×C4C2×C22⋊Dic1113yes—
295C2×C4C2×C22⋊Dic1113yes—
296C2×C4C22×C22⋊D1112yes—
297C8—442no—
298C8—446no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—26no—
303C22—26no—
304C22—26no—
305C22—42no—
306C22—42no—
307C22—41no—
308C22—41no—
309C22—83no—
310C22—83no—
311C22C2×#6700111yescharacteristic
312C22#1062335011yescharacteristic
313C22C22×C22⋊Dic1111yescharacteristic
314C4—22no—
315C4—23no—
316C4—43no—
317C4—43no—
318C4—41no—
319C4C2×#6689816yes—
320C2—21no—
321C2—21no—
322C2—46no—
323C2—42no—
324C2#1307706511yescharacteristic
325C2C22×#6689811yescharacteristic
326C2#1307709911yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#548C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#548D11
hypocenterC11#17414
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #13077065C2semidirect
2. #13066980C2semidirect
3. #13066954C2semidirect
4. #13066934C2semidirect
114. C23×C11#131semidirect
262. C11#17414semidirect
271. C23#67001semidirect

Maximal subgroups

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

subgroupindex
#130770652
#130669802
#130669542
#130669342
C2×C11×#5482
#1741411