Finite Group Databasebeta

← #14680781

Subgroups — #14680781

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×#10622834C213yesmaximal, complemented
2C2×#10622564C213yesmaximal, complemented
3#13066881C211yesmaximal, characteristic, complemented
4#13066861C213yesmaximal, complemented
5#13066857C213yesmaximal, complemented
6#95×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#392C211yesmaximal, characteristic
8C23×D4×C11C2213yes—
9C22×C11×C22⋊C4C2213yes—
10C22×C22⋊Dic11C2213yes—
11C22×C22⋊Dic11C2213yes—
12C22×C22⋊Dic11C2216yes—
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2213yes—
15C22×C4×Dic11C2213yes—
16C11×#392C418yescomplemented
17C2×C11×#95C2211yescharacteristic
18#10622834—212no—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C2×C11⋊#95C2213yes—
22#10622564—212no—
23C25×C11C2313yes—
24C22×D4×C11—26no—
25C22×D4×C11—26no—
26C22×D4×C11—46no—
27C22×D4×C11—46no—
28C22×D4×C11C2×C4112yes—
29C23×C4×C11C2311yescharacteristic
30C23×C4×C11C2313yes—
31C23×Dic11C2313yes—
32C23×Dic11C2311yescharacteristic
33C23×Dic11C2313yes—
34C23×Dic11C2311yescharacteristic
35C2×C11×C22⋊C4—26no—
36C2×C11×C22⋊C4—26no—
37C2×C11×C22⋊C4C2×C4112yes—
38C2×C22⋊Dic11—26no—
39C2×C22⋊Dic11—26no—
40C2×C22⋊Dic11—212no—
41C2×C22⋊Dic11—212no—
42C2×C22⋊Dic11—46no—
43C2×C22⋊Dic11—46no—
44C2×C22⋊Dic11—46no—
45C2×C4⋊Dic11—26no—
46C2×C4⋊Dic11—26no—
47C2×C4⋊Dic11—46no—
48C2×C4×Dic11—46no—
49C2×C4×Dic11D4112yescomplemented
50C11×#95C2×C414yes—
51C11⋊#95—26no—
52C11⋊#95—26no—
53C11⋊#95—26no—
54#14321—111nomaximal, Sylow
55C24×C11—23no—
56C24×C11—26no—
57C24×C11—23no—
58C24×C11—26no—
59C24×C11—23no—
60C24×C11—26no—
61C24×C11—26no—
62C24×C11—23no—
63C24×C11—23no—
64C24×C11—23no—
65C24×C11C22×C416yes—
66C24×C11C2411yescharacteristic
67C2×D4×C11—224no—
68C2×D4×C11—424no—
69C2×D4×C11—412no—
70C2×D4×C11—412no—
71C2×D4×C11—424no—
72C22×C4×C11—26no—
73C22×C4×C11—26no—
74C22×C4×C11—23no—
75C22×C4×C11—23no—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C416yes—
78C22×C4×C11C2×D416yes—
79C22×C4×C11#4116yes—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—26no—
83C22×Dic11—26no—
84C22×Dic11—23no—
85C22×Dic11—26no—
86C22×Dic11—23no—
87C22×Dic11—23no—
88C22×Dic11—23no—
89C22×Dic11—26no—
90C22×Dic11—23no—
91C22×Dic11—23no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11C2×D416yes—
95C22×Dic11C2×D416yes—
96C11×C22⋊C4—224no—
97C22⋊Dic11—412no—
98C22⋊Dic11—424no—
99C22⋊Dic11—412no—
100C4⋊Dic11—412no—
101C4⋊Dic11—44no—
102C4×Dic11—412no—
103C2×#392D1111yescharacteristic
104C2×#390—113no—
105C2×#388—113no—
106#1444—111no—
107#1439—113no—
108#1438—113no—
109C4×#95—111no—
110C23×C11—26no—
111C23×C11—212no—
112C23×C11—26no—
113C23×C11—212no—
114C23×C11—26no—
115C23×C11—43no—
116C23×C11—43no—
117C23×C11—46no—
118C23×C11—43no—
119C23×C11—46no—
120C23×C11—46no—
121C23×C11—46no—
122C23×C11—43no—
123C23×C11—43no—
124C23×C11—43no—
125C23×C11—46no—
126C23×C11—46no—
127C23×C11—46no—
128C23×C11—46no—
129C23×C11—43no—
130C23×C11—46no—
131C23×C11—43no—
132C23×C11—46no—
133C23×C11C23×C411yescharacteristic
134C23×C11C22×D413yes—
135C23×C11C2×#4113yes—
136C23×C11H(5,𝔽2)13yes—
137C23×C11H(5,𝔽2)13yes—
138C23×C11H(5,𝔽2)11yescharacteristic
139C23×C112−1+411yescharacteristic
140D4×C11—448no—
141C2×C4×C11—212no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—212no—
145C2×C4×C11—26no—
146C2×C4×C11—41no—
147C2×C4×C11—43no—
148C2×C4×C11C4×D4112yes—
149C2×Dic11—26no—
150C2×Dic11—26no—
151C2×Dic11—26no—
152C2×Dic11—26no—
153C2×Dic11—26no—
154C2×Dic11—46no—
155C2×Dic11—46no—
156C2×Dic11—41no—
157C2×Dic11—43no—
158C2×Dic11—43no—
159C2×Dic11—46no—
160C2×Dic11—46no—
161C2×Dic11—43no—
162C2×Dic11—43no—
163C2×Dic11—43no—
164C2×Dic11#12714yes—
165C23×D4C2×D1113yes—
166C22×C4⋊C4—111no—
167C22×C4⋊C4—113no—
168C22×C22⋊C4—113no—
169C22×C22⋊C4—113no—
170C22×C22⋊C4—116no—
171C22×C22⋊C4C2×D1113yes—
172C22×C42—113no—
173#392Dic1118yescomplemented
174#390—2212no—
175#388—2212no—
176C2×#95—113no—
177C2×#95—113no—
178C2×#95—113no—
179C2×#95C2×D1111yescharacteristic
180C22×C11—46no—
181C22×C11—412no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11—412no—
185C22×C11—83no—
186C22×C11—83no—
187C22×C11—83no—
188C22×C11—86no—
189C22×C11—86no—
190C22×C11—83no—
191C22×C11C2×C4×D413yes—
192C22×C11#51813yes—
193C22×C11#52011yescharacteristic
194C22×C11C2×#12711yescharacteristic
195C22×C11#53213yes—
196C22×C11#53413yes—
197C22×C11#53513yes—
198C22×C11#53513yes—
199C22×C11#53713yes—
200C22×C11#53816yes—
201C22×C11#54013yes—
202C22×C11#54213yes—
203C4×C11—212no—
204C4×C11—42no—
205Dic11—24no—
206Dic11—46no—
207Dic11—81no—
208Dic11—83no—
209C25C22×D1113yes—
210C22×D4—26no—
211C22×D4—26no—
212C22×D4—46no—
213C22×D4—46no—
214C22×D4C2×Dic11112yes—
215C23×C4—111no—
216C23×C4—113no—
217C23×C4—113no—
218C23×C4—111no—
219C23×C4C22×D1111yescharacteristic
220C23×C4C22×D1113yes—
221C2×C4⋊C4—226no—
222C2×C4⋊C4—226no—
223C2×C4⋊C4—446no—
224C2×C22⋊C4—26no—
225C2×C22⋊C4—26no—
226C2×C22⋊C4—226no—
227C2×C22⋊C4—226no—
228C2×C22⋊C4—2212no—
229C2×C22⋊C4—2212no—
230C2×C22⋊C4—446no—
231C2×C22⋊C4—446no—
232C2×C22⋊C4—446no—
233C2×C22⋊C4C2×Dic11112yes—
234C2×C42—1112no—
235C2×C42—446no—
236#95—226no—
237#95—226no—
238#95—226no—
239#95C2×Dic1114yes—
240C2×C11—86no—
241C2×C11C4×#12711yescharacteristic
242C2×C11#232113yes—
243C2×C11#232413yes—
244C2×C11#265611yescharacteristic
245C2×C11#265711yescharacteristic
246C2×C11#266113yes—
247C2×C11#266213yes—
248C24—23no—
249C24—26no—
250C24—23no—
251C24—26no—
252C24—26no—
253C24—26no—
254C24—23no—
255C24—23no—
256C24—23no—
257C24—23no—
258C24C22×Dic1116yes—
259C24C23×D1111yescharacteristic
260C2×D4—224no—
261C2×D4—424no—
262C2×D4—412no—
263C2×D4—412no—
264C2×D4—424no—
265C22×C4—26no—
266C22×C4—26no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—116no—
270C22×C4—116no—
271C22×C4—223no—
272C22×C4—221no—
273C22×C4—226no—
274C22×C4—226no—
275C22×C4—223no—
276C22×C4—223no—
277C22×C4—223no—
278C22×C4—223no—
279C22×C4—226no—
280C22×C4—223no—
281C22×C4—226no—
282C22×C4—223no—
283C22×C4—223no—
284C22×C4—221no—
285C22×C4D4×D1116yes—
286C22×C4#434116yes—
287C22×C4C22×Dic1112yes—
288C22×C4C22×Dic1116yes—
289C4⋊C4—4412no—
290C4⋊C4—444no—
291C22⋊C4—224no—
292C22⋊C4—4412no—
293C22⋊C4—4412no—
294C22⋊C4—4424no—
295C42—4412no—
296C11#1432111yescharacteristic, complemented, Sylow
297C23—26no—
298C23—212no—
299C23—26no—
300C23—212no—
301C23—26no—
302C23—43no—
303C23—43no—
304C23—46no—
305C23—43no—
306C23—46no—
307C23—46no—
308C23—43no—
309C23—46no—
310C23—46no—
311C23—46no—
312C23—43no—
313C23—46no—
314C23—46no—
315C23—43no—
316C23—43no—
317C23—46no—
318C23—43no—
319C23—46no—
320C23C2×D4×D1113yes—
321C23C2×#434113yes—
322C23#6703713yes—
323C23#6703713yes—
324C23#6704211yescharacteristic
325C23#6704311yescharacteristic
326C23C23×Dic1111yescharacteristic
327D4—448no—
328C2×C4—212no—
329C2×C4—26no—
330C2×C4—26no—
331C2×C4—212no—
332C2×C4—26no—
333C2×C4—41no—
334C2×C4—43no—
335C2×C4—114no—
336C2×C4—226no—
337C2×C4—226no—
338C2×C4—226no—
339C2×C4—226no—
340C2×C4—226no—
341C2×C4—446no—
342C2×C4—446no—
343C2×C4—443no—
344C2×C4—441no—
345C2×C4—443no—
346C2×C4—446no—
347C2×C4—443no—
348C2×C4—446no—
349C2×C4—443no—
350C2×C4—443no—
351C2×C4D4×Dic11112yes—
352C22—46no—
353C22—412no—
354C22—46no—
355C22—46no—
356C22—412no—
357C22—83no—
358C22—83no—
359C22—83no—
360C22—86no—
361C22—86no—
362C22—83no—
363C22#1062312013yes—
364C22#1062312313yes—
365C22#1062312416yes—
366C22#1062313413yes—
367C22#1062313813yes—
368C22#1062313913yes—
369C22#1062315013yes—
370C22D11×#12711yescharacteristic
371C22#1062324713yes—
372C22C2×D4×Dic1113yes—
373C22#1062332913yes—
374C22#1062335811yescharacteristic
375C4—212no—
376C4—42no—
377C4—224no—
378C4—446no—
379C4—881no—
380C4—883no—
381C2—86no—
382C2#127×Dic1111yescharacteristic
383C2#1307127713yes—
384C2#1307131113yes—
385C2#1307471711yescharacteristic
386C2#1307472111yescharacteristic
387C2#1307474713yes—
388C2#1307475813yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC2×C11×#392C2
socle, cosocleC24×C11C24
hypercenterC2×#392D11
hypocenterC11#14321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622564C2semidirect
3. #13066881C2semidirect
4. #13066861C2semidirect
5. #13066857C2semidirect
6. #95×Dic11C2semidirect
16. C11×#392C4semidirect
49. C2×C4×Dic11D4semidirect
173. #392Dic11semidirect
296. C11#14321semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225642
#130668812
#130668612
#130668572
#95×Dic112
C2×C11×#3922
#1432111