Finite Group Databasebeta

← #14656072

Subgroups — #14656072

Order 2816.

828 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622456C212yesmaximal, complemented
2#13073532C211yesmaximal, characteristic, complemented
3#13069421C211yesmaximal, characteristic, complemented
4C2×#10622121C212yesmaximal, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C22×D88—22no—
7C2×#66948—22no—
8C2×#66927C2211yescharacteristic
9C2×C4×D44C2212yes—
10C2×C11×C4⋊C8C2212yes—
11C11×#384C2211yescharacteristic
12C2×#66885—22no—
13#10622604—22no—
14#10622600—22no—
15C2×#66873—22no—
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622456—24no—
18#10622456—24no—
19#10622121—24no—
20C22×D44—22no—
21C22×D44—21no—
22C22×D44—22no—
23C22×D44D412yes—
24C22×C4×D11—22no—
25C22×C8×C11—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4D412yes—
28C2×C42×C11C2311yescharacteristic
29C2×(C2×D11)⋊C4—24no—
30C2×(C2×D11)⋊C4—22no—
31C2×C4⋊Dic11D412yes—
32C22×C11⋊C8—21no—
33C2×D88—28no—
34C2×D88—44no—
35C2×D88—44no—
36#66948—44no—
37#66948—44no—
38#66927—22no—
39#66927—21no—
40#66927D412yescomplemented
41C4×D44—22no—
42C4×D44—22no—
43C4×D44—22no—
44C4×D44—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8D414yescomplemented
47C11⋊#95—22no—
48#66885—28no—
49#66873—44no—
50C4×C11⋊C8—22no—
51#10228—111nomaximal, Sylow
52C23×D11—22no—
53C23×D11—41no—
54C22×C4×C11—22no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D412yes—
57C22×Dic11—22no—
58C2×D44—22no—
59C2×D44—24no—
60C2×D44—22no—
61C2×D44—22no—
62C2×D44—22no—
63C2×D44—22no—
64C2×D44—22no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—48no—
68C2×D44—42no—
69C2×D44—41no—
70C2×D44—42no—
71C2×D44—42no—
72C2×D44—42no—
73C2×D44—42no—
74C2×D44—82no—
75C2×D44D814yescomplemented
76C2×C4×D11—42no—
77C2×C4×D11—42no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C4×D11—42no—
82C2×C8×C11—24no—
83C2×C8×C11—42no—
84C2×C8×C11—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D412yes—
90C42×C11#4111yescharacteristic
91(C2×D11)⋊C4—48no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99D88—416no—
100C2×#459—112no—
101#2537—111no—
102#1957—111no—
103C2×D4⋊C8—112no—
104#1296D1111yescharacteristic, complemented
105C23×C11#12011yescharacteristic
106C22×D11—24no—
107C22×D11—42no—
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—42no—
111C22×D11—42no—
112C22×D11—42no—
113C22×D11—42no—
114C22×D11—82no—
115C22×D11—82no—
116C22×D11—81no—
117C22×D11—81no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—44no—
121C2×C4×C11—42no—
122C2×C4×C11#12012yes—
123C2×C4×C11#12111yescharacteristic
124C2×C4×C11#12112yes—
125C2×C4×C11#12711yescharacteristic
126C2×C4×C11C2×D812yes—
127C2×C4×C11#13512yes—
128C2×C4×C11AGL(1,ℤ/8)12yes—
129C2×C4×C11AGL(1,ℤ/8)12yes—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133D44—24no—
134D44—24no—
135D44—44no—
136D44—44no—
137D44—42no—
138D44—44no—
139D44—42no—
140D44—82no—
141D44—88no—
142D44—82no—
143D44—82no—
144C4×D11—82no—
145C4×D11—82no—
146C4×D11—82no—
147C4×D11—82no—
148C8×C11—44no—
149C11⋊C8—42no—
150C22×D8—222no—
151C2×#127—111no—
152C2×#121—222no—
153C2×C4×D4—112no—
154#459—224no—
155#459—224no—
156C2×C4⋊C8C2×D1112yes—
157C2×#102—222no—
158C2×#102—222no—
159C2×C4×C8—111no—
160#394—222no—
161#384C2×D1111yescharacteristic
162#380—222no—
163D4⋊C8—224no—
164C22×C11#39211yescharacteristic
165C22×C11#44712yes—
166C22×C11#44912yes—
167C22×C11#45311yescharacteristic
168C22×C11#45411yescharacteristic
169C2×D11—44no—
170C2×D11—44no—
171C2×D11—44no—
172C2×D11—82no—
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C2×D11—84no—
177C2×D11—82no—
178C2×D11—161no—
179C2×D11—161no—
180C2×D11—162no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11#44712yes—
185C4×C11#44912yes—
186C4×C11#46612yes—
187C4×C11#46912yes—
188Dic11—82no—
189C22×D4—112no—
190C22×D4—222no—
191C22×D4—221no—
192C22×D4—222no—
193C23×C4—222no—
194C2×D8—228no—
195C2×D8—444no—
196C2×D8—444no—
197C22×C8—22no—
198C22×C8—221no—
199#127—112no—
200#127—222no—
201#127—221no—
202#121—444no—
203#121—444no—
204C4×D4—222no—
205C4×D4—222no—
206C4×D4—222no—
207C4×D4—222no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4D4412yes—
211C2×C22⋊C4—224no—
212C2×C22⋊C4—222no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—22no—
215C4⋊C8D4414yescomplemented
216#102—228no—
217#102—444no—
218C4×C8—222no—
219#95—222no—
220C2×C11#161911yescharacteristic
221C2×C11#162411yescharacteristic
222C2×C11#162512yes—
223C2×C11#199912yes—
224C2×C11#200611yescharacteristic
225D11—84no—
226D11—162no—
227C24—222no—
228C24—441no—
229C2×D4—114no—
230C2×D4—222no—
231C2×D4—224no—
232C2×D4—222no—
233C2×D4—222no—
234C2×D4—222no—
235C2×D4—222no—
236C2×D4—222no—
237C2×D4—442no—
238C2×D4—442no—
239C2×D4—448no—
240C2×D4—441no—
241C2×D4—442no—
242C2×D4—442no—
243C2×D4—442no—
244C2×D4—442no—
245C2×D4—442no—
246C2×D4—882no—
247C22×C4—22no—
248C22×C4—222no—
249C22×C4—442no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4—442no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4C2×D4411yescharacteristic
256C22×C4D4×D1112yes—
257D8—4416no—
258C2×C8—24no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—222no—
262C2×C8—441no—
263C2×C8—441no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C22⋊C4—448no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C42C2×D4412yes—
273C42D4×D1111yescharacteristic
274C42#434311yescharacteristic
275C11#1022811yescharacteristic, complemented, Sylow
276C23—224no—
277C23—442no—
278C23—442no—
279C23—442no—
280C23—442no—
281C23—442no—
282C23—442no—
283C23—442no—
284C23—881no—
285C23—881no—
286C23—882no—
287C23—882no—
288C23#6693511yescharacteristic
289D4—224no—
290D4—224no—
291D4—444no—
292D4—442no—
293D4—444no—
294D4—442no—
295D4—444no—
296D4—882no—
297D4—888no—
298D4—882no—
299D4—882no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—882no—
308C2×C4—882no—
309C2×C4—882no—
310C2×C4—882no—
311C2×C4#6692711yescharacteristic
312C2×C4#6693512yes—
313C2×C4#6694811yescharacteristic
314C2×C4#6694812yes—
315C2×C4D8×D1112yes—
316C2×C4#6696712yes—
317C2×C4#6696712yes—
318C2×C4#6697212yes—
319C8—44no—
320C8—442no—
321C22—444no—
322C22—444no—
323C22—444no—
324C22—882no—
325C22—882no—
326C22—882no—
327C22—882no—
328C22—884no—
329C22—882no—
330C22—1761no—
331C22—1761no—
332C22—1762no—
333C22#1062228411yescharacteristic
334C22#1062236011yescharacteristic
335C22#1062236611yescharacteristic
336C22#1062238612yes—
337C22#1062242412yes—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—882no—
342C4#1062238612yes—
343C4#1062242412yes—
344C4#1062247812yes—
345C4#1062249612yes—
346C2—884no—
347C2—1762no—
348C2#1306767111yescharacteristic
349C2#1306770011yescharacteristic
350C2#1306770612yes—
351C2#1306961512yes—
352C2#1306966011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#120
hypercenter#1296D11
hypocenterC11#10228
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#10622456C2semidirect
2. #13073532C2semidirect
3. #13069421C2semidirect
4. C2×#10622121C2semidirect
5. C11×#1296C2semidirect
40. #66927D4semidirect
46. C11×C4⋊C8D4semidirect
75. C2×D44D8semidirect
104. #1296D11semidirect
215. C4⋊C8D44semidirect
275. C11#10228semidirect

Maximal subgroups

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

subgroupindex
C2×#106224562
#130735322
#130694212
C2×#106221212
C11×#12962
#1022811