Finite Group Databasebeta

← #14680782

Subgroups — #14680782

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622601C213yesmaximal, complemented
3C2×#10622282C213yesmaximal, complemented
4#13066858C213yesmaximal, complemented
5#13066856C213yesmaximal, complemented
6#95×Dic11C211yesmaximal, characteristic, complemented
7C11×#1444C211yesmaximal, characteristic, complemented
8C23×D44C2213yes—
9C22×C11×C4⋊C4C2213yes—
10C22×(C2×D11)⋊C4C2213yes—
11C22×(C2×D11)⋊C4C2213yes—
12C22×(C2×D11)⋊C4C2213yes—
13C22×(C2×D11)⋊C4C2216yes—
14C22×Dic11⋊C4C2211yescharacteristic
15C22×C4×Dic11C2213yes—
16C2×C11×#95C2213yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20#10622601—212no—
21#10622284C418yescomplemented
22#10622282—212no—
23C24×D11C2313yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×C4×C11C2313yes—
27C23×Dic11C2311yescharacteristic
28C23×Dic11C2313yes—
29C23×Dic11C2311yescharacteristic
30C22×D44—26no—
31C22×D44—26no—
32C22×D44—46no—
33C22×D44—46no—
34C22×D44C2×C4112yes—
35C2×C11×C4⋊C4—26no—
36C2×C11×C4⋊C4—46no—
37C2×(C2×D11)⋊C4—26no—
38C2×(C2×D11)⋊C4—26no—
39C2×(C2×D11)⋊C4—26no—
40C2×(C2×D11)⋊C4—26no—
41C2×(C2×D11)⋊C4—212no—
42C2×(C2×D11)⋊C4—212no—
43C2×(C2×D11)⋊C4—46no—
44C2×(C2×D11)⋊C4—46no—
45C2×(C2×D11)⋊C4—46no—
46C2×(C2×D11)⋊C4C2×C4112yes—
47C2×Dic11⋊C4—26no—
48C2×C4×Dic11—46no—
49C2×C4×Dic11D4112yescomplemented
50C11×#95—26no—
51C11×#95C2×C414yes—
52C11⋊#95—26no—
53C11⋊#95—26no—
54#14321—111nomaximal, Sylow
55C24×C11C2411yescharacteristic
56C23×D11—23no—
57C23×D11—26no—
58C23×D11—23no—
59C23×D11—26no—
60C23×D11—23no—
61C23×D11—26no—
62C23×D11—26no—
63C23×D11—23no—
64C23×D11—23no—
65C23×D11—23no—
66C23×D11C22×C416yes—
67C22×C4×C11—26no—
68C22×C4×C11—26no—
69C22×C4×C11—23no—
70C22×C4×C11—23no—
71C22×C4×C11—26no—
72C22×C4×C11—23no—
73C22×C4×C11—23no—
74C22×C4×C11—26no—
75C22×C4×C11—23no—
76C22×C4×C11—21no—
77C22×C4×C11C22×C416yes—
78C22×C4×C11C2×D416yes—
79C22×C4×C11#4116yes—
80C22×Dic11—23no—
81C22×Dic11—26no—
82C22×Dic11—23no—
83C22×Dic11—23no—
84C22×Dic11—26no—
85C22×Dic11—23no—
86C22×Dic11—23no—
87C22×Dic11—21no—
88C22×Dic11C22×C412yes—
89C22×Dic11C2×D416yes—
90C22×Dic11C2×D416yes—
91C2×D44—224no—
92C2×D44—424no—
93C2×D44—412no—
94C2×D44—412no—
95C2×D44—424no—
96C11×C4⋊C4—412no—
97(C2×D11)⋊C4—224no—
98(C2×D11)⋊C4—412no—
99(C2×D11)⋊C4—424no—
100(C2×D11)⋊C4—412no—
101Dic11⋊C4—44no—
102C4×Dic11—412no—
103C2×#392—111no—
104C2×#390—113no—
105C2×#388—113no—
106#1444D1111yescharacteristic, complemented
107#1439—113no—
108#1438—113no—
109C4×#95—111no—
110C23×C11C23×C411yescharacteristic
111C23×C11C22×D413yes—
112C23×C11C2×#4113yes—
113C23×C11H(5,𝔽2)13yes—
114C23×C11H(5,𝔽2)13yes—
115C23×C11H(5,𝔽2)11yescharacteristic
116C23×C112−1+411yescharacteristic
117C22×D11—26no—
118C22×D11—212no—
119C22×D11—26no—
120C22×D11—212no—
121C22×D11—26no—
122C22×D11—43no—
123C22×D11—43no—
124C22×D11—46no—
125C22×D11—43no—
126C22×D11—46no—
127C22×D11—46no—
128C22×D11—46no—
129C22×D11—43no—
130C22×D11—43no—
131C22×D11—43no—
132C22×D11—46no—
133C22×D11—46no—
134C22×D11—46no—
135C22×D11—46no—
136C22×D11—43no—
137C22×D11—46no—
138C22×D11—43no—
139C22×D11—46no—
140C2×C4×C11—212no—
141C2×C4×C11—26no—
142C2×C4×C11—26no—
143C2×C4×C11—212no—
144C2×C4×C11—41no—
145C2×C4×C11—43no—
146C2×C4×C11—43no—
147C2×C4×C11—46no—
148C2×C4×C11—46no—
149C2×C4×C11—43no—
150C2×C4×C11—43no—
151C2×C4×C11—43no—
152C2×C4×C11C4×D4112yes—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—26no—
156C2×Dic11—26no—
157C2×Dic11—26no—
158C2×Dic11—26no—
159C2×Dic11—41no—
160C2×Dic11—43no—
161C2×Dic11—46no—
162C2×Dic11—46no—
163C2×Dic11#12714yes—
164D44—448no—
165C23×D4—113no—
166C22×C4⋊C4—111no—
167C22×C4⋊C4C2×D1113yes—
168C22×C22⋊C4—113no—
169C22×C22⋊C4—113no—
170C22×C22⋊C4—113no—
171C22×C22⋊C4—116no—
172C22×C42—113no—
173#392—118no—
174#390—2212no—
175#388—2212no—
176C2×#95—113no—
177C2×#95—113no—
178C2×#95C2×D1113yes—
179C2×#95C2×D1111yescharacteristic
180C22×C11C2×C4×D413yes—
181C22×C11#51813yes—
182C22×C11#52011yescharacteristic
183C22×C11C2×#12711yescharacteristic
184C22×C11#53213yes—
185C22×C11#53413yes—
186C22×C11#53513yes—
187C22×C11#53513yes—
188C22×C11#53713yes—
189C22×C11#53816yes—
190C22×C11#54013yes—
191C22×C11#54213yes—
192C2×D11—46no—
193C2×D11—46no—
194C2×D11—412no—
195C2×D11—46no—
196C2×D11—412no—
197C2×D11—83no—
198C2×D11—83no—
199C2×D11—83no—
200C2×D11—86no—
201C2×D11—86no—
202C2×D11—83no—
203C4×C11—212no—
204C4×C11—81no—
205C4×C11—83no—
206Dic11—24no—
207Dic11—42no—
208Dic11—46no—
209C25—113no—
210C22×D4—1112no—
211C22×D4—226no—
212C22×D4—226no—
213C22×D4—446no—
214C22×D4—446no—
215C23×C4—111no—
216C23×C4—111no—
217C23×C4—113no—
218C23×C4C22×D1111yescharacteristic
219C23×C4C22×D1113yes—
220C23×C4C22×D1113yes—
221C2×C4⋊C4—26no—
222C2×C4⋊C4—46no—
223C2×C4⋊C4—226no—
224C2×C22⋊C4—1112no—
225C2×C22⋊C4—226no—
226C2×C22⋊C4—226no—
227C2×C22⋊C4—226no—
228C2×C22⋊C4—226no—
229C2×C22⋊C4—2212no—
230C2×C22⋊C4—2212no—
231C2×C22⋊C4—446no—
232C2×C22⋊C4—446no—
233C2×C22⋊C4—446no—
234C2×C42—1112no—
235C2×C42—446no—
236#95—26no—
237#95—226no—
238#95—226no—
239#95C4×D1114yes—
240C2×C11C4×#12711yescharacteristic
241C2×C11#232113yes—
242C2×C11#232413yes—
243C2×C11#265611yescharacteristic
244C2×C11#265711yescharacteristic
245C2×C11#266113yes—
246C2×C11#266213yes—
247D11—86no—
248C24—116no—
249C24—223no—
250C24—226no—
251C24—226no—
252C24—223no—
253C24—223no—
254C24—226no—
255C24—223no—
256C24—223no—
257C24—226no—
258C24—223no—
259C24C23×D1111yescharacteristic
260C2×D4—2224no—
261C2×D4—4424no—
262C2×D4—4412no—
263C2×D4—4424no—
264C2×D4—4412no—
265C22×C4—26no—
266C22×C4—26no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—26no—
270C22×C4—26no—
271C22×C4—23no—
272C22×C4—21no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—116no—
276C22×C4—112no—
277C22×C4—116no—
278C22×C4—221no—
279C22×C4—223no—
280C22×C4—223no—
281C22×C4—223no—
282C22×C4—226no—
283C22×C4—223no—
284C22×C4—226no—
285C22×C4—223no—
286C22×C4C2×C4×D1116yes—
287C22×C4D4×D1116yes—
288C22×C4#434316yes—
289C4⋊C4—412no—
290C4⋊C4—444no—
291C22⋊C4—2224no—
292C22⋊C4—4412no—
293C22⋊C4—4424no—
294C22⋊C4—4412no—
295C42—4412no—
296C11#1432111yescharacteristic, complemented, Sylow
297C23—226no—
298C23—2212no—
299C23—226no—
300C23—2212no—
301C23—226no—
302C23—443no—
303C23—443no—
304C23—446no—
305C23—446no—
306C23—443no—
307C23—446no—
308C23—443no—
309C23—446no—
310C23—443no—
311C23—443no—
312C23—446no—
313C23—446no—
314C23—446no—
315C23—446no—
316C23—443no—
317C23—446no—
318C23—443no—
319C23—446no—
320C23C22×C4×D1111yescharacteristic
321C23C2×D4×D1113yes—
322C23#6703713yes—
323C23C2×#434313yes—
324C23#6704011yescharacteristic
325C23#6704213yes—
326C23#6704211yescharacteristic
327D4—4448no—
328C2×C4—212no—
329C2×C4—26no—
330C2×C4—212no—
331C2×C4—26no—
332C2×C4—43no—
333C2×C4—41no—
334C2×C4—46no—
335C2×C4—43no—
336C2×C4—46no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—114no—
341C2×C4—226no—
342C2×C4—226no—
343C2×C4—226no—
344C2×C4—226no—
345C2×C4—226no—
346C2×C4—226no—
347C2×C4—441no—
348C2×C4—443no—
349C2×C4—446no—
350C2×C4—446no—
351C2×C4#66946112yes—
352C22—446no—
353C22—4412no—
354C22—446no—
355C22—446no—
356C22—4412no—
357C22—883no—
358C22—883no—
359C22—886no—
360C22—883no—
361C22—886no—
362C22—883no—
363C22C2×#6694613yes—
364C22#1062307613yes—
365C22#1062310511yescharacteristic
366C22#1062312313yes—
367C22#1062313813yes—
368C22#1062316013yes—
369C22#1062317516yes—
370C22#1062318413yes—
371C22#1062322913yes—
372C22D11×#12711yescharacteristic
373C22#1062325613yes—
374C22#1062326413yes—
375C4—212no—
376C4—81no—
377C4—83no—
378C4—224no—
379C4—446no—
380C4—442no—
381C2—886no—
382C2#1307117811yescharacteristic
383C2#1307127313yes—
384C2#1307130713yes—
385C2#1307471911yescharacteristic
386C2#1307472111yescharacteristic
387C2#1307474913yes—
388C2#1307476013yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1444D11
hypocenterC11#14321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622282C2semidirect
4. #13066858C2semidirect
5. #13066856C2semidirect
6. #95×Dic11C2semidirect
7. C11×#1444C2semidirect
21. #10622284C4semidirect
49. C2×C4×Dic11D4semidirect
106. #1444D11semidirect
296. C11#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106226012
C2×#106222822
#130668582
#130668562
#95×Dic112
C11×#14442
#1432111