Finite Group Databasebeta

← #14654340

Subgroups — #14654340

Order 2816.

772 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10622348C212yesmaximal, complemented
2#13074718C211yesmaximal, characteristic
3C2×#10622108C212yesmaximal, complemented
4#13066885C211yesmaximal, characteristic, complemented
5C11×#1280C211yesmaximal, characteristic, complemented
6C2×#66983—22no—
7C2×#66983C2212yes—
8C22×C4⋊Dic11C2211yescharacteristic
9C2×C11×C22⋊C8C2212yes—
10C2×C11×#95C2211yescharacteristic
11C2×C11⋊#95—22no—
12C2×C11⋊#95C2211yescharacteristic
13C2×#66885—22no—
14C2×#66881—22no—
15#10622348—24no—
16#10622348—24no—
17#10622290—22no—
18#10622284—22no—
19#10622108—24no—
20C23×C4×C11D412yes—
21C23×C4×C11C2311yescharacteristic
22C22×C22⋊D11—22no—
23C23×Dic11—21no—
24C23×Dic11—21no—
25C22×D44—22no—
26C22×D44D412yes—
27C22×C8×C11—22no—
28#66983—22no—
29#66983—22no—
30#66983—22no—
31#66983—22no—
32#66983—44no—
33#66983—44no—
34C2×(C2×D11)⋊C4—24no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D412yes—
41C2×C4⋊Dic11D412yescomplemented
42C11×C22⋊C8—22no—
43C11×C22⋊C8D414yescomplemented
44C11×#95—22no—
45C11⋊#95—22no—
46C11⋊#95—44no—
47#66885—28no—
48#66881—28no—
49#9968—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C23×D11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—42no—
55C22×C4×C11—42no—
56C22×C4×C11—42no—
57C22×C4×C11SD1614yes—
58C22×C4×C11C2×D412yes—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D412yes—
61C22×C4×C11#4111yescharacteristic
62C2×C22⋊D11—42no—
63C2×C22⋊D11—42no—
64C2×C22⋊D11—44no—
65C2×C22⋊D11—44no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11—22no—
69C22×Dic11—42no—
70C22×Dic11—41no—
71C22×Dic11—42no—
72C22×Dic11—42no—
73C22×Dic11—41no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—42no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—44no—
80C2×D44—44no—
81C2×D44—82no—
82C2×D44—82no—
83C2×C8×C11—24no—
84C2×C8×C11—44no—
85(C2×D11)⋊C4—48no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88C4⋊Dic11—22no—
89C4⋊Dic11—24no—
90C4⋊Dic11—22no—
91C4⋊Dic11—44no—
92C4⋊Dic11—42no—
93C2×#481—112no—
94#2656—111no—
95C2×#327—112no—
96#1445—111no—
97#1280D1111yescharacteristic, complemented
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—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—44no—
119C2×C4×C11—82no—
120C2×C4×C11#12012yes—
121C2×C4×C11#12112yes—
122C22⋊D11—84no—
123C22⋊D11—82no—
124C22⋊D11—82no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127C2×Dic11—44no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—44no—
131C2×Dic11—82no—
132C2×Dic11—81no—
133C2×Dic11—82no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137D44—44no—
138D44—82no—
139D44—88no—
140C8×C11—44no—
141C2×#121—112no—
142C2×#121—222no—
143C22×C4⋊C4—111no—
144#481—224no—
145#481—224no—
146C2×#106—222no—
147C2×#102—222no—
148C2×C22⋊C8C2×D1112yes—
149#399—222no—
150#392—222no—
151C2×#95—111no—
152C2×#95—222no—
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—
179Dic11—82no—
180Dic11—82no—
181Dic11—82no—
182C22×D4—112no—
183C22×D4—222no—
184C22×D4—222no—
185C23×C4—221no—
186C23×C4—221no—
187C23×C4D4412yes—
188C23×C4C22×D1111yescharacteristic
189C22×C8—22no—
190#121—222no—
191#121—222no—
192#121—222no—
193#121—222no—
194#121—444no—
195#121—444no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—221no—
202C2×C22⋊C4—224no—
203C2×C22⋊C4—222no—
204#106—228no—
205#102—228no—
206C22⋊C8—22no—
207C22⋊C8D4414yescomplemented
208#95—22no—
209#95—222no—
210#95—444no—
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×D4411yescharacteristic
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—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4—222no—
240C22×C4—442no—
241C22×C4—442no—
242C22×C4—441no—
243C22×C4—442no—
244C22×C4—441no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—442no—
248C22×C4#431414yes—
249C22×C4C2×D4412yes—
250C22×C4D4×D1112yes—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434311yescharacteristic
253C2×C8—24no—
254C2×C8—44no—
255C4⋊C4—224no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—444no—
259C4⋊C4—442no—
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#6692711yescharacteristic
273C23#6693511yescharacteristic
274C23#6694811yescharacteristic
275C23C2×#431412yes—
276C23#6696112yes—
277D4—444no—
278D4—882no—
279D4—888no—
280D4—882no—
281D4—882no—
282D4—884no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—82no—
292C2×C4—442no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—444no—
298C2×C4—882no—
299C2×C4—881no—
300C2×C4—882no—
301C2×C4—881no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4#6693512yes—
305C2×C4#6694812yes—
306C8—44no—
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#1062228411yescharacteristic
321C22#1062230611yescharacteristic
322C22#1062232511yescharacteristic
323C22#1062234412yes—
324C22#1062235512yes—
325C22#1062236011yescharacteristic
326C22#1062236611yescharacteristic
327C22#1062246112yes—
328C4—22no—
329C4—22no—
330C4—44no—
331C4—882no—
332C4—882no—
333C4—882no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—1762no—
338C2#1306763812yes—
339C2#1306765512yes—
340C2#1306966011yescharacteristic
341C2#1306970611yescharacteristic
342C2#1306974811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radical#13074718C2
hypercenter#1280D11
hypocenterC11#9968
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
1. C2×#10622348C2semidirect
3. C2×#10622108C2semidirect
4. #13066885C2semidirect
5. C11×#1280C2semidirect
41. C2×C4⋊Dic11D4semidirect
43. C11×C22⋊C8D4semidirect
97. #1280D11semidirect
207. C22⋊C8D44semidirect
263. C11#9968semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
#130747182
C2×#106221082
#130668852
C11×#12802
#996811