Finite Group Databasebeta

← #14654339

Subgroups — #14654339

Order 2816.

772 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 119 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×#10622581C212yesmaximal, complemented
2#13074718C211yesmaximal, characteristic
3C2×#10622089C212yesmaximal, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#1445C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983—22no—
8C2×#66983C2212yes—
9C2×C11×#95—22no—
10C2×C11×#95C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12C2×C22⋊(C11⋊C8)C2212yes—
13#10622581—24no—
14#10622581—24no—
15C2×#66873—22no—
16C2×#66872—22no—
17#10622290—22no—
18#10622284—22no—
19#10622089—24no—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11D412yes—
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—22no—
25C22×D44—22no—
26C22×D44D412yes—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D412yescomplemented
31#66983—22no—
32#66983—22no—
33#66983—22no—
34#66983—22no—
35#66983—44no—
36#66983—44no—
37C2×(C2×D11)⋊C4—24no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11D412yes—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95—44no—
45C22⋊(C11⋊C8)—22no—
46C22⋊(C11⋊C8)D414yescomplemented
47#66873—28no—
48#66872—28no—
49#9968—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C23×D11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—41no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—42no—
67C22×C4×C11SD1614yes—
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D412yes—
71C22×C4×C11#4111yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11—44no—
75C2×C22⋊D11—44no—
76C22×Dic11—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—44no—
80C2×D44—44no—
81C2×D44—82no—
82C2×D44—82no—
83C11×C4⋊C4—24no—
84C11×C4⋊C4—42no—
85(C2×D11)⋊C4—48no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90C4⋊Dic11—44no—
91C2×C11⋊C8—24no—
92C2×C11⋊C8—44no—
93C2×#481—112no—
94#2656—111no—
95C2×#327—112no—
96#1445D1111yescharacteristic, complemented
97#1280—111no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—22no—
101C23×C11#12011yescharacteristic
102C23×C11#12111yescharacteristic
103C23×C11#12711yescharacteristic
104C23×C11C2×SD1612yes—
105C23×C11AGL(1,ℤ/8)12yes—
106C22×D11—42no—
107C22×D11—44no—
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—44no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11—44no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—42no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—81no—
126C2×C4×C11—82no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#12012yes—
131C2×C4×C11#12112yes—
132C22⋊D11—84no—
133C22⋊D11—82no—
134C22⋊D11—82no—
135C2×Dic11—42no—
136C2×Dic11—44no—
137D44—44no—
138D44—82no—
139D44—88no—
140C11⋊C8—44no—
141C2×#121—112no—
142C2×#121—222no—
143C22×C4⋊C4C2×D1111yescharacteristic
144#481—224no—
145#481—224no—
146C2×#106—222no—
147C2×#102—222no—
148C2×C22⋊C8—112no—
149#399—222no—
150#392—222no—
151C2×#95—22no—
152C2×#95C2×D1111yescharacteristic
153C2×#95C2×D1111yescharacteristic
154#327—224no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11#39211yescharacteristic
164C22×C11#45012yes—
165C22×C11#45311yescharacteristic
166C22×C11#45411yescharacteristic
167C22×C11#45812yes—
168C22×C11#46012yes—
169C22×C11#49211yescharacteristic
170C22×C11#49611yescharacteristic
171C2×D11—84no—
172C2×D11—84no—
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11—82no—
181Dic11—82no—
182C22×D4—112no—
183C22×D4—222no—
184C22×D4—222no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4C22⋊D1112yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8—222no—
190#121—222no—
191#121—222no—
192#121—222no—
193#121—222no—
194#121—444no—
195#121—444no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4D4412yescomplemented
202C2×C22⋊C4—224no—
203C2×C22⋊C4—222no—
204#106—228no—
205#102—228no—
206C22⋊C8—114no—
207C22⋊C8—222no—
208#95—22no—
209#95—22no—
210#95—44no—
211C2×C11—21no—
212C2×C11—22no—
213C2×C11—21no—
214C2×C11#161312yes—
215C2×C11#161612yes—
216C2×C11#200611yescharacteristic
217C2×C11#201411yescharacteristic
218C2×C11#202211yescharacteristic
219D11—162no—
220C24—222no—
221C24C2×C22⋊D1111yescharacteristic
222C2×D4—222no—
223C2×D4—222no—
224C2×D4—444no—
225C2×D4—444no—
226C2×D4—442no—
227C2×D4—442no—
228C2×D4—444no—
229C2×D4—444no—
230C2×D4—882no—
231C2×D4—882no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—222no—
248C22×C4#432514yes—
249C22×C4C2×D4411yescharacteristic
250C22×C4#433911yescharacteristic
251C22×C4D4×D1112yes—
252C22×C4D4×D1112yes—
253C2×C8—224no—
254C2×C8—444no—
255C4⋊C4—24no—
256C4⋊C4—42no—
257C4⋊C4—222no—
258C4⋊C4—222no—
259C4⋊C4—444no—
260C22⋊C4—448no—
261C22⋊C4—442no—
262C22⋊C4—442no—
263C11#996811yescharacteristic, complemented, Sylow
264C23—22no—
265C23—21no—
266C23—21no—
267C23—442no—
268C23—444no—
269C23—444no—
270C23—442no—
271C23—442no—
272C23#6698311yescharacteristic
273C23#6699011yescharacteristic
274C23#6699311yescharacteristic
275C23C2×#432512yes—
276C23#6700212yes—
277D4—444no—
278D4—882no—
279D4—888no—
280D4—884no—
281D4—882no—
282D4—882no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—442no—
303C2×C4—444no—
304C2×C4#6693512yes—
305C2×C4#6693712yes—
306C8—444no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—882no—
316C22—884no—
317C22—884no—
318C22—882no—
319C22—882no—
320C22#1062257311yescharacteristic
321C22#1062264012yes—
322C22#1062265912yes—
323C22#1062266612yes—
324C22#1062267111yescharacteristic
325C22#1062267511yescharacteristic
326C22#1062269011yescharacteristic
327C22#1062269811yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—82no—
333C4—882no—
334C2—21no—
335C2—22no—
336C2—21no—
337C2—1762no—
338C2#1306763512yes—
339C2#1306765212yes—
340C2#1306965711yescharacteristic
341C2#1306970311yescharacteristic
342C2#1306974711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1445C2
socleC23×C11#120
prime radical#13074718C2
hypercenter#1445D11
hypocenterC11#9968
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1445

Complements

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

NH ≅ G/Ntype
1. C2×#10622581C2semidirect
3. C2×#10622089C2semidirect
4. #13066459C2semidirect
5. C11×#1445C2semidirect
30. C2×C11×C4⋊C4D4semidirect
46. C22⋊(C11⋊C8)D4semidirect
96. #1445D11semidirect
201. C2×C4⋊C4D44semidirect
263. C11#9968semidirect

Maximal subgroups

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

subgroupindex
C2×#106225812
#130747182
C2×#106220892
#130664592
C11×#14452
#996811