Finite Group Databasebeta

← #14681031

Subgroups — #14681031

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622280C213yesmaximal
2C2×#10622600C213yesmaximal
3C2×D11×#95C211yesmaximal, characteristic
4#13066881C211yesmaximal, characteristic, complemented
5#13066880C213yesmaximal, complemented
6#13066879C213yesmaximal, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C23×C4×D11C2213yes—
9C22×C11×C4⋊C4C2213yes—
10C22×(C2×D11)⋊C4C2213yes—
11C22×(C2×D11)⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2213yes—
13C22×Dic11⋊C4C2213yes—
14C22×Dic11⋊C4C2213yes—
15C2×C11×#95C2213yes—
16C2×C11×#95C2211yescharacteristic
17C2×C11⋊#95C2216yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20#10622600—212no—
21#10622280—212no—
22D11×#95C418yescomplemented
23C24×D11C2311yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×C4×C11C2313yes—
27C23×Dic11C2311yescharacteristic
28C23×Dic11C2313yes—
29C23×Dic11C2313yes—
30C22×C4×D11—46no—
31C22×C4×D11—46no—
32C22×C4×D11C2×C4112yes—
33C22×C4×D11D4112yes—
34C22×C4×D11Q8112yes—
35C2×C11×C4⋊C4—26no—
36C2×C11×C4⋊C4—46no—
37C2×(C2×D11)⋊C4—26no—
38C2×(C2×D11)⋊C4—26no—
39C2×(C2×D11)⋊C4—212no—
40C2×C4⋊Dic11—26no—
41C2×C4⋊Dic11—46no—
42C2×Dic11⋊C4—26no—
43C2×Dic11⋊C4—26no—
44C2×Dic11⋊C4—46no—
45C2×Dic11⋊C4—46no—
46C11×#95—26no—
47C11×#95C2×C414yes—
48C11⋊#95—26no—
49C11⋊#95—212no—
50C11⋊#95C2×C4112yes—
51#14353—111nomaximal, Sylow
52C24×C11C2411yescharacteristic
53C23×D11—23no—
54C23×D11—23no—
55C23×D11—21no—
56C23×D11—21no—
57C23×D11C22×C412yes—
58C23×D11C2×D416yes—
59C23×D11C2×Q816yes—
60C22×C4×C11—26no—
61C22×C4×C11—26no—
62C22×C4×C11—26no—
63C22×C4×C11—23no—
64C22×C4×C11—23no—
65C22×C4×C11—23no—
66C22×C4×C11—26no—
67C22×C4×C11—23no—
68C22×C4×C11—21no—
69C22×C4×C11—23no—
70C22×C4×C11C22×C416yes—
71C22×C4×C11C2×D416yes—
72C22×C4×C11C2×Q816yes—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—26no—
76C22×Dic11—26no—
77C22×Dic11—26no—
78C22×Dic11—23no—
79C22×Dic11—26no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—21no—
83C22×Dic11C22×C416yes—
84C22×Dic11C2×D416yes—
85C22×Dic11C2×Q816yes—
86C2×C4×D11—424no—
87C2×C4×D11—412no—
88C2×C4×D11—412no—
89C2×C4×D11—424no—
90C2×C4×D11C4⋊C4148yescomplemented
91C11×C4⋊C4—412no—
92(C2×D11)⋊C4—44no—
93(C2×D11)⋊C4—412no—
94C4⋊Dic11—412no—
95Dic11⋊C4—412no—
96Dic11⋊C4—412no—
97C2×#380—113no—
98C2×#380—113no—
99C22×#95—111no—
100#1444—113no—
101#1444—111no—
102#1444—113no—
103#1444D1111yescharacteristic, complemented
104C23×C11C23×C411yescharacteristic
105C23×C11C22×D413yes—
106C23×C11C22×Q813yes—
107C23×C11H(5,𝔽2)13yes—
108C23×C11H(5,𝔽2)13yes—
109C23×C112−1+411yescharacteristic
110C23×C112−1+411yescharacteristic
111C22×D11—26no—
112C22×D11—22no—
113C22×D11—26no—
114C22×D11—26no—
115C22×D11—26no—
116C22×D11—26no—
117C22×D11—212no—
118C22×D11—26no—
119C22×D11—26no—
120C22×D11C2×C4⋊C4112yes—
121C22×D11#12714yes—
122C22×D11C4⋊Q8112yes—
123C2×C4×C11—212no—
124C2×C4×C11—26no—
125C2×C4×C11—26no—
126C2×C4×C11—212no—
127C2×C4×C11—43no—
128C2×C4×C11—41no—
129C2×C4×C11—43no—
130C2×C4×C11—43no—
131C2×C4×C11—46no—
132C2×C4×C11—46no—
133C2×C4×C11—43no—
134C2×C4×C11—43no—
135C2×C4×C11C2×C4⋊C4112yes—
136C2×Dic11—212no—
137C2×Dic11—26no—
138C2×Dic11—26no—
139C2×Dic11—212no—
140C2×Dic11—41no—
141C2×Dic11—43no—
142C2×Dic11—43no—
143C2×Dic11—43no—
144C2×Dic11—46no—
145C2×Dic11—43no—
146C2×Dic11—43no—
147C2×Dic11—46no—
148C2×Dic11C2×C4⋊C4112yes—
149C4×D11—448no—
150C24×C4—113no—
151C22×C4⋊C4—113no—
152C22×C4⋊C4—113no—
153C22×C4⋊C4—113no—
154C22×C4⋊C4C2×D1113yes—
155C22×C22⋊C4—111no—
156C22×C22⋊C4—113no—
157#380—2212no—
158#380—2212no—
159C2×#95—113no—
160C2×#95—118no—
161C2×#95—116no—
162C2×#95—113no—
163C2×#95C2×D1113yes—
164C2×#95C2×D1111yescharacteristic
165C22×C11C22×C4⋊C413yes—
166C22×C11#51813yes—
167C22×C11#51911yescharacteristic
168C22×C11C2×#12711yescharacteristic
169C22×C11C2×C4⋊Q813yes—
170C22×C11#53413yes—
171C22×C11#53413yes—
172C22×C11#53713yes—
173C22×C11#53713yes—
174C22×C11#54316yes—
175C22×C11#54413yes—
176C22×C11#54413yes—
177C2×D11—212no—
178C2×D11—212no—
179C2×D11—24no—
180C2×D11—24no—
181C2×D11—212no—
182C2×D11—212no—
183C2×D11#38418yes—
184C4×C11—212no—
185C4×C11—83no—
186C4×C11—81no—
187Dic11—212no—
188Dic11—81no—
189Dic11—83no—
190C25—111no—
191C23×C4—113no—
192C23×C4—1112no—
193C23×C4—1112no—
194C23×C4—1112no—
195C23×C4—111no—
196C23×C4—113no—
197C23×C4—446no—
198C23×C4—446no—
199C23×C4C22×D1111yescharacteristic
200C23×C4C22×D1113yes—
201C23×C4C22×D1113yes—
202C2×C4⋊C4—26no—
203C2×C4⋊C4—46no—
204C2×C4⋊C4—226no—
205C2×C4⋊C4—226no—
206C2×C4⋊C4—226no—
207C2×C4⋊C4—446no—
208C2×C4⋊C4—446no—
209C2×C4⋊C4—446no—
210C2×C22⋊C4—226no—
211C2×C22⋊C4—226no—
212C2×C22⋊C4—2212no—
213#95—26no—
214#95—1112no—
215#95—2212no—
216#95—226no—
217#95C4×D1114yes—
218C2×C11C2×#38411yescharacteristic
219C2×C11#231513yes—
220C2×C11#231613yes—
221C2×C11#265611yescharacteristic
222C2×C11#265611yescharacteristic
223C2×C11#265913yes—
224C2×C11#265913yes—
225D11—28no—
226C24—112no—
227C24—116no—
228C24—116no—
229C24—223no—
230C24—221no—
231C24—223no—
232C24—221no—
233C24C23×D1111yescharacteristic
234C22×C4—26no—
235C22×C4—26no—
236C22×C4—23no—
237C22×C4—23no—
238C22×C4—26no—
239C22×C4—23no—
240C22×C4—26no—
241C22×C4—21no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—116no—
245C22×C4—116no—
246C22×C4—116no—
247C22×C4—1148no—
248C22×C4—226no—
249C22×C4—226no—
250C22×C4—223no—
251C22×C4—226no—
252C22×C4—223no—
253C22×C4—223no—
254C22×C4—223no—
255C22×C4—226no—
256C22×C4—223no—
257C22×C4—221no—
258C22×C4—4424no—
259C22×C4—4412no—
260C22×C4—4424no—
261C22×C4—4412no—
262C22×C4C2×C4×D1116yes—
263C22×C4D4×D1116yes—
264C22×C4Q8×D1116yes—
265C4⋊C4—412no—
266C4⋊C4—4412no—
267C4⋊C4—4412no—
268C4⋊C4—4412no—
269C22⋊C4—4412no—
270C22⋊C4—444no—
271C11#1435311yescharacteristic, complemented, Sylow
272C23—114no—
273C23—1112no—
274C23—1112no—
275C23—226no—
276C23—226no—
277C23—222no—
278C23—226no—
279C23—226no—
280C23—226no—
281C23—2212no—
282C23—226no—
283C23—226no—
284C23C22×C4×D1111yescharacteristic
285C23C2×D4×D1113yes—
286C23#6703713yes—
287C23C2×Q8×D1113yes—
288C23#6704011yescharacteristic
289C23#6704213yes—
290C23#6704311yescharacteristic
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—26no—
295C2×C4—43no—
296C2×C4—41no—
297C2×C4—46no—
298C2×C4—43no—
299C2×C4—43no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—1112no—
304C2×C4—2212no—
305C2×C4—226no—
306C2×C4—2212no—
307C2×C4—226no—
308C2×C4—4448no—
309C2×C4—441no—
310C2×C4—443no—
311C2×C4—443no—
312C2×C4—443no—
313C2×C4—446no—
314C2×C4—443no—
315C2×C4—446no—
316C2×C4—443no—
317C2×C4C4⋊C4×D11112yes—
318C22—118no—
319C22—224no—
320C22—224no—
321C22—2212no—
322C22—2212no—
323C22—2212no—
324C22—2212no—
325C22C2×C4⋊C4×D1113yes—
326C22#1062307613yes—
327C22#1062310311yescharacteristic
328C22#1062312013yes—
329C22#1062313913yes—
330C22#1062316013yes—
331C22#1062316516yes—
332C22#1062318413yes—
333C22#1062322013yes—
334C22D11×#12711yescharacteristic
335C22D11×C4⋊Q813yes—
336C22#1062326013yes—
337C4—212no—
338C4—83no—
339C4—81no—
340C4—2212no—
341C4—881no—
342C4—883no—
343C2—228no—
344C2D11×#38411yescharacteristic
345C2#1307122713yes—
346C2#1307123113yes—
347C2#1307471711yescharacteristic
348C2#1307471911yescharacteristic
349C2#1307472913yes—
350C2#1307473113yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11#14353
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #13066881C2semidirect
5. #13066880C2semidirect
6. #13066879C2semidirect
7. C11×#1444C2semidirect
22. D11×#95C4semidirect
90. C2×C4×D11C4⋊C4semidirect
103. #1444D11semidirect
271. C11#14353semidirect

Maximal subgroups

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

subgroupindex
C2×#106222802
C2×#106226002
C2×D11×#952
#130668812
#130668802
#130668792
C11×#14442
#1435311