Finite Group Databasebeta

← #14680546

Subgroups — #14680546

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622844C211yesmaximal, characteristic
3C2×#10622282C213yesmaximal
4#13066880C213yesmaximal, complemented
5#13066862C213yesmaximal
6#13066841C213yesmaximal, complemented
7C11×#1446C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C2×Q8×Dic11—212no—
10C22×(C2×D11)⋊C4C2211yescharacteristic
11C22×(C2×D11)⋊C4C2213yes—
12C22×(C2×D11)⋊C4C2213yes—
13C22×C4⋊Dic11C2213yes—
14C22×Dic11⋊C4C2213yes—
15C22×C4×Dic11C2213yes—
16C2×C11×#95C2213yes—
17C2×C11×#95C2213yes—
18#10622844C418yescomplemented
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2216yes—
21C2×C11⋊#95C2213yes—
22#10622282—212no—
23C24×D11C2311yescharacteristic
24C22×Q8×C11—26no—
25C22×Q8×C11—26no—
26C22×Q8×C11C2×C414yes—
27C23×C4×C11C2311yescharacteristic
28C23×C4×C11C2313yes—
29C23×C4×C11C2313yes—
30C23×Dic11C2313yes—
31C23×Dic11C2313yes—
32C23×Dic11C2311yescharacteristic
33Q8×Dic11—232no—
34C2×(C2×D11)⋊C4—26no—
35C2×(C2×D11)⋊C4—26no—
36C2×(C2×D11)⋊C4—26no—
37C2×(C2×D11)⋊C4—26no—
38C2×(C2×D11)⋊C4—46no—
39C2×(C2×D11)⋊C4C2×C4112yes—
40C2×C4⋊Dic11—26no—
41C2×C4⋊Dic11—212no—
42C2×Dic11⋊C4—26no—
43C2×Dic11⋊C4—46no—
44C2×C4×Dic11—212no—
45C2×C4×Dic11D4112yes—
46C11×#95—26no—
47C11×#95—26no—
48C11⋊#95—26no—
49C11⋊#95—46no—
50C11⋊#95C2×C4112yes—
51#14301—111nomaximal, Sylow
52C24×C11C2411yescharacteristic
53C23×D11—23no—
54C23×D11—23no—
55C23×D11—23no—
56C23×D11—21no—
57C23×D11—21no—
58C23×D11—23no—
59C23×D11C22×C412yes—
60C2×Q8×C11—28no—
61C2×Q8×C11—224no—
62C2×Q8×C11—224no—
63C22×C4×C11—26no—
64C22×C4×C11—26no—
65C22×C4×C11—23no—
66C22×C4×C11—23no—
67C22×C4×C11—26no—
68C22×C4×C11—26no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—23no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C416yes—
74C22×C4×C11C2×D416yes—
75C22×C4×C11#4116yes—
76C22×Dic11—23no—
77C22×Dic11—26no—
78C22×Dic11—23no—
79C22×Dic11—23no—
80C22×Dic11—26no—
81C22×Dic11—26no—
82C22×Dic11—23no—
83C22×Dic11—21no—
84C22×Dic11—23no—
85C22×Dic11—26no—
86C22×Dic11C22×C416yes—
87C22×Dic11C2×D416yes—
88C22×Dic11C2×D416yes—
89(C2×D11)⋊C4—224no—
90(C2×D11)⋊C4—412no—
91(C2×D11)⋊C4—44no—
92C4⋊Dic11—224no—
93Dic11⋊C4—412no—
94C4×Dic11—224no—
95C22×C4×Q8—111no—
96C2×#393—111no—
97C2×#388—113no—
98#1446D1111yescharacteristic, complemented
99#1444—113no—
100#1439—113no—
101#1434—113no—
102C23×C11C23×C411yescharacteristic
103C23×C11C22×D413yes—
104C23×C11C2×#4113yes—
105C23×C11H(5,𝔽2)13yes—
106C23×C112−1+411yescharacteristic
107C23×C112−1+413yes—
108C23×C112−1+411yescharacteristic
109C22×D11—26no—
110C22×D11—22no—
111C22×D11—26no—
112C22×D11—41no—
113C22×D11—43no—
114C22×D11—43no—
115C22×D11—43no—
116C22×D11—43no—
117C22×D11—43no—
118C22×D11—43no—
119C22×D11—46no—
120C22×D11—43no—
121Q8×C11—232no—
122C2×C4×C11—212no—
123C2×C4×C11—26no—
124C2×C4×C11—26no—
125C2×C4×C11—212no—
126C2×C4×C11—41no—
127C2×C4×C11—43no—
128C2×C4×C11—43no—
129C2×C4×C11—43no—
130C2×C4×C11—43no—
131C2×C4×C11—43no—
132C2×C4×C11—46no—
133C2×C4×C11—46no—
134C2×C4×C11C4×D4112yes—
135C2×Dic11—26no—
136C2×Dic11—26no—
137C2×Dic11—26no—
138C2×Dic11—212no—
139C2×Dic11—26no—
140C2×Dic11—26no—
141C2×Dic11—26no—
142C2×Dic11—43no—
143C2×Dic11—46no—
144C2×Dic11—43no—
145C2×Dic11—46no—
146C2×Dic11—46no—
147C2×Dic11#12014yes—
148C23×Q8C2×D1111yescharacteristic
149C2×C4×Q8—2212no—
150C22×C4⋊C4—113no—
151C22×C4⋊C4—113no—
152C22×C22⋊C4—113no—
153C22×C22⋊C4—111no—
154C22×C22⋊C4—113no—
155C22×C42—113no—
156#393—118no—
157#388—2212no—
158C2×#95—113no—
159C2×#95—113no—
160C2×#95—116no—
161C2×#95C2×D1113yes—
162C2×#95C2×D1113yes—
163C22×C11C2×C4×D413yes—
164C22×C11#51911yescharacteristic
165C22×C11#52013yes—
166C22×C11C2×#12011yescharacteristic
167C22×C11#52513yes—
168C22×C11#53513yes—
169C22×C11#53613yes—
170C22×C11#53613yes—
171C22×C11#53713yes—
172C22×C11#54113yes—
173C22×C11#54216yes—
174C22×C11#54213yes—
175C2×D11—46no—
176C2×D11—46no—
177C2×D11—42no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—83no—
181C2×D11—83no—
182C4×C11—212no—
183C4×C11—81no—
184C4×C11—83no—
185Dic11—24no—
186Dic11—46no—
187Dic11—46no—
188C25—111no—
189C22×Q8—26no—
190C22×Q8—26no—
191C22×Q8C4×D1114yes—
192C23×C4—111no—
193C23×C4—113no—
194C23×C4—113no—
195C23×C4C22×D1111yescharacteristic
196C23×C4C22×D1113yes—
197C23×C4C22×D1113yes—
198C4×Q8—2232no—
199C2×C4⋊C4—2212no—
200C2×C4⋊C4—226no—
201C2×C4⋊C4—226no—
202C2×C4⋊C4—446no—
203C2×C22⋊C4—1112no—
204C2×C22⋊C4—226no—
205C2×C22⋊C4—226no—
206C2×C22⋊C4—226no—
207C2×C22⋊C4—226no—
208C2×C22⋊C4—446no—
209C2×C42—1112no—
210C2×C42—2212no—
211#95—26no—
212#95—26no—
213#95—1112no—
214#95—226no—
215#95—446no—
216C2×C11C4×#12011yescharacteristic
217C2×C11#232313yes—
218C2×C11#232613yes—
219C2×C11#261411yescharacteristic
220C2×C11#261511yescharacteristic
221C2×C11#263213yes—
222C2×C11#263713yes—
223D11—82no—
224C24—112no—
225C24—223no—
226C24—223no—
227C24—221no—
228C24—223no—
229C24—223no—
230C24—221no—
231C24C23×D1111yescharacteristic
232C2×Q8—28no—
233C2×Q8—224no—
234C2×Q8—224no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—21no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—116no—
246C22×C4—116no—
247C22×C4—116no—
248C22×C4—223no—
249C22×C4—221no—
250C22×C4—223no—
251C22×C4—226no—
252C22×C4—223no—
253C22×C4—226no—
254C22×C4—223no—
255C22×C4—223no—
256C22×C4—226no—
257C22×C4—226no—
258C22×C4C2×C4×D1116yes—
259C22×C4D4×D1116yes—
260C22×C4#434116yes—
261C4⋊C4—2224no—
262C4⋊C4—4412no—
263C22⋊C4—2224no—
264C22⋊C4—444no—
265C22⋊C4—4412no—
266C42—2224no—
267C11#1430111yescharacteristic, complemented, Sylow
268C23—226no—
269C23—222no—
270C23—226no—
271C23—443no—
272C23—443no—
273C23—443no—
274C23—441no—
275C23—443no—
276C23—443no—
277C23—446no—
278C23—443no—
279C23—443no—
280C23C22×C4×D1111yescharacteristic
281C23C2×D4×D1113yes—
282C23C2×#434113yes—
283C23#6704013yes—
284C23#6704011yescharacteristic
285C23#6704213yes—
286C23#6704311yescharacteristic
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—212no—
291C2×C4—26no—
292C2×C4—43no—
293C2×C4—41no—
294C2×C4—43no—
295C2×C4—43no—
296C2×C4—46no—
297C2×C4—43no—
298C2×C4—43no—
299C2×C4—46no—
300C2×C4—114no—
301C2×C4—226no—
302C2×C4—226no—
303C2×C4—226no—
304C2×C4—2212no—
305C2×C4—226no—
306C2×C4—226no—
307C2×C4—226no—
308C2×C4—443no—
309C2×C4—446no—
310C2×C4—446no—
311C2×C4—443no—
312C2×C4—446no—
313C2×C4(C22⋊D11)⋊C4112yes—
314C22—442no—
315C22—446no—
316C22—446no—
317C22—883no—
318C22—883no—
319C22—881no—
320C22—881no—
321C22C2×(C22⋊D11)⋊C413yes—
322C22#1062310311yescharacteristic
323C22#1062310513yes—
324C22#1062311713yes—
325C22D11×#12011yescharacteristic
326C22#1062315913yes—
327C22#1062316013yes—
328C22#1062317416yes—
329C22#1062320513yes—
330C22#1062321313yes—
331C22#1062325513yes—
332C22#1062326213yes—
333C4—212no—
334C4—83no—
335C4—81no—
336C4—224no—
337C4—446no—
338C4—446no—
339C2—882no—
340C2#1307111511yescharacteristic
341C2#1307130113yes—
342C2#1307133013yes—
343C2#1307433611yescharacteristic
344C2#1307434311yescharacteristic
345C2#1307447513yes—
346C2#1307452313yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1446D11
hypocenterC11#14301
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic11C2semidirect
4. #13066880C2semidirect
6. #13066841C2semidirect
7. C11×#1446C2semidirect
18. #10622844C4semidirect
98. #1446D11semidirect
267. C11#14301semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228442
C2×#106222822
#130668802
#130668622
#130668412
C11×#14462
#1430111