Finite Group Databasebeta

← #14720023

Subgroups — #14720023

Order 2816.

1342 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077065C212yesmaximal, complemented
2#13066976C216yesmaximal, complemented
3#13066954C213yesmaximal, complemented
4#13066934C213yesmaximal, complemented
5C2×C11×#550C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic
7C22×C11×#41C2211yescharacteristic
8C11×#550—22no—
9C11×#550—26no—
10C2×C11×#127C413yes—
11C2×C11×#121C413yes—
12C2×C11×#121C2213yes—
13C2×C4×Q8×C11C411yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×#67001—22no—
16#10622847—26no—
17#10622820C2216yes—
18C2×C22⋊(C11⋊C8)C2216yes—
19#10622166C2211yescharacteristic
20#10622166C2213yes—
21#10622163C2216yes—
22#10622163C2216yes—
23C2×C11×#41—23no—
24C2×C11×#41—21no—
25C2×C11×#41—44no—
26C2×C11×#41—44no—
27C2×C11×#41D412yes—
28C2×C11×#41D416yes—
29C22×Q8×C11C2×C411yescharacteristic
30C22×D4×C11C2×C413yes—
31C22×D4×C11C2×C413yes—
32C22×D4×C11C2×C416yes—
33C22×D4×C11C2×C413yes—
34C23×C4×C11C2×C413yes—
35C23×C4×C11C2313yes—
36C11×#127—26no—
37C11×#127—26no—
38C11×#121—26no—
39C11×#121—26no—
40C11×#121—26no—
41C11×#121—26no—
42C4×Q8×C11—23no—
43C4×Q8×C11—21no—
44C4×D4×C11—26no—
45C4×D4×C11—26no—
46C2×C11×C4⋊C4C2×C413yes—
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C22⋊C4C2×C413yes—
49C2×C11×C22⋊C4C2313yes—
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#17419—111nomaximal, Sylow
59C24×C11C22×C413yes—
60C24×C11C22×C413yes—
61C11×#41—28no—
62C11×#41—412no—
63C11×#41—412no—
64C11×#41—44no—
65C2×Q8×C11—24no—
66C2×Q8×C11C22⋊C413yes—
67C2×Q8×C11C22⋊C411yescharacteristic
68C2×D4×C11—26no—
69C2×D4×C11—212no—
70C2×D4×C11—23no—
71C2×D4×C11—23no—
72C2×D4×C11—26no—
73C2×D4×C11—46no—
74C2×D4×C11—43no—
75C2×D4×C11—46no—
76C2×D4×C11—86no—
77C2×D4×C11C22⋊C416yes—
78C2×D4×C11C22⋊C416yes—
79C22×C4×C11—23no—
80C22×C4×C11—23no—
81C22×C4×C11—46no—
82C22×C4×C11—46no—
83C22×C4×C11C22×C413yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C413yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D416yes—
88C22×C4×C11C2×D416yes—
89C22×C4×C11C2411yescharacteristic
90C11×C4⋊C4—23no—
91C11×C4⋊C4—23no—
92C11×C4⋊C4—22no—
93C11×C22⋊C4—26no—
94C11×C22⋊C4—26no—
95C42×C11—23no—
96C42×C11—23no—
97#4318—412no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—26no—
100C2×C11⋊C8—412no—
101C2×#550D1111yescharacteristic
102#2880—112no—
103#1471—116no—
104#1465—113no—
105#1459—113no—
106C23×C11—23no—
107C23×C11—23no—
108C23×C11—23no—
109C23×C11—23no—
110C23×C11—23no—
111C23×C11—43no—
112C23×C11—43no—
113C23×C11—43no—
114C23×C11—43no—
115C23×C11C2×C22⋊C416yes—
116C23×C11C23×C411yescharacteristic
117Q8×C11—26no—
118Q8×C11#9914yes—
119D4×C11—212no—
120D4×C11—46no—
121D4×C11—412no—
122D4×C11—46no—
123D4×C11—46no—
124D4×C11—812no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—212no—
128C2×C4×C11—26no—
129C2×C4×C11—23no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—46no—
133C2×C4×C11—46no—
134C2×C4×C11—46no—
135C2×C4×C11—41no—
136C2×C4×C11—43no—
137C2×C4×C11C2×C22⋊C413yes—
138C2×C4×C11C2×C22⋊C413yes—
139C2×C4×C11#13112yescomplemented
140C2×C4×C11C22×D412yes—
141C11⋊C8—42no—
142C11⋊C8—46no—
143C22×#41Dic1111yescharacteristic
144C22×#41C2×D1111yescharacteristic
145C2×#131—222no—
146#550—22no—
147#550—26no—
148C2×#127Dic1113yes—
149C2×#121Dic1113yes—
150C2×#121C2×D1113yes—
151C2×C4×Q8Dic1111yescharacteristic
152C2×C4×D4C2×D1113yes—
153#408—226no—
154#407—116no—
155C2×C22⋊C8—116no—
156#324—111no—
157#324—113no—
158#323—116no—
159#323—116no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—26no—
163C22×C11—26no—
164C22×C11—26no—
165C22×C11—43no—
166C22×C11—43no—
167C22×C11—43no—
168C22×C11—83no—
169C22×C11—83no—
170C22×C11—83no—
171C22×C11—83no—
172C22×C11C22×C22⋊C411yescharacteristic
173C22×C11C2×#13111yescharacteristic
174C22×C11#56811yescharacteristic
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—23no—
178C4×C11—41no—
179C4×C11—43no—
180C4×C11C2×#9916yes—
181C2×#41—23no—
182C2×#41—21no—
183C2×#41—44no—
184C2×#41—44no—
185C2×#41C22⋊D1112yes—
186C2×#41C22⋊D1116yes—
187C22×Q8C2×Dic1111yescharacteristic
188C22×D4C2×Dic1113yes—
189C22×D4C2×Dic1113yes—
190C22×D4C2×Dic1116yes—
191C22×D4C2×Dic1113yes—
192C23×C4C2×Dic1113yes—
193C23×C4C22×D1113yes—
194#131—448no—
195C2×M16—226no—
196C22×C8—226no—
197#127—26no—
198#127—26no—
199#121—26no—
200#121—26no—
201#121—26no—
202#121—26no—
203C4×Q8—23no—
204C4×Q8—21no—
205C4×D4—26no—
206C4×D4—26no—
207C2×C4⋊C4C2×Dic1113yes—
208C2×C4⋊C4C22×D1111yescharacteristic
209C2×C22⋊C4C2×Dic1113yes—
210C2×C22⋊C4C22×D1113yes—
211C2×C42C2×Dic1113yes—
212C22⋊C8—112no—
213C22⋊C8—116no—
214C22⋊C8—226no—
215C22⋊C8—226no—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11—46no—
219C2×C11—83no—
220C2×C11#288011yescharacteristic
221C2×C11C22×#9911yescharacteristic
222C2×C11#288811yescharacteristic
223C24C22×Dic1113yes—
224C24C22×Dic1113yes—
225#41—28no—
226#41—412no—
227#41—412no—
228#41—44no—
229C2×Q8—24no—
230C2×Q8C22⋊Dic1113yes—
231C2×Q8C22⋊Dic1111yescharacteristic
232C2×D4—26no—
233C2×D4—212no—
234C2×D4—26no—
235C2×D4—23no—
236C2×D4—23no—
237C2×D4—46no—
238C2×D4—43no—
239C2×D4—46no—
240C2×D4—86no—
241C2×D4C22⋊Dic1116yes—
242C2×D4C22⋊Dic1116yes—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—46no—
246C22×C4—46no—
247C22×C4C22×Dic1111yescharacteristic
248C22×C4C22×Dic1113yes—
249C22×C4C22×Dic1113yes—
250C22×C4C22×Dic1111yescharacteristic
251C22×C4C2×C22⋊D1116yes—
252C22×C4C2×C22⋊D1116yes—
253C22×C4C23×D1111yescharacteristic
254M16—4412no—
255C2×C8—222no—
256C2×C8—226no—
257C2×C8—4412no—
258C4⋊C4—23no—
259C4⋊C4—23no—
260C4⋊C4—22no—
261C22⋊C4—26no—
262C22⋊C4—26no—
263C42—23no—
264C42—23no—
265C11#1741911yescharacteristic, complemented, Sylow
266C23—23no—
267C23—23no—
268C23—23no—
269C23—23no—
270C23—23no—
271C23—43no—
272C23—43no—
273C23—43no—
274C23—43no—
275C23C2×C22⋊Dic1116yes—
276C23C23×Dic1111yescharacteristic
277Q8—26no—
278Q8#6689814yes—
279D4—212no—
280D4—46no—
281D4—412no—
282D4—46no—
283D4—46no—
284D4—812no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—212no—
288C2×C4—26no—
289C2×C4—23no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—46no—
293C2×C4—46no—
294C2×C4—46no—
295C2×C4—41no—
296C2×C4—43no—
297C2×C4#6700112yescomplemented
298C2×C4C2×C22⋊Dic1113yes—
299C2×C4C2×C22⋊Dic1113yes—
300C2×C4C22×C22⋊D1112yes—
301C8—442no—
302C8—446no—
303C22—21no—
304C22—21no—
305C22—26no—
306C22—26no—
307C22—26no—
308C22—43no—
309C22—43no—
310C22—43no—
311C22—83no—
312C22—83no—
313C22—83no—
314C22—83no—
315C22C2×#6700111yescharacteristic
316C22#1062335011yescharacteristic
317C22C22×C22⋊Dic1111yescharacteristic
318C4—22no—
319C4—22no—
320C4—23no—
321C4—41no—
322C4—43no—
323C4C2×#6689816yes—
324C2—21no—
325C2—21no—
326C2—46no—
327C2—83no—
328C2#1307706511yescharacteristic
329C2C22×#6689811yescharacteristic
330C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#17419
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13077065C2semidirect
2. #13066976C2semidirect
3. #13066954C2semidirect
4. #13066934C2semidirect
139. C2×C4×C11#131semidirect
265. C11#17419semidirect
297. C2×C4#67001semidirect

Maximal subgroups

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

subgroupindex
#130770652
#130669762
#130669542
#130669342
C2×C11×#5502
#1741911