Finite Group Databasebeta

← #14649516

Subgroups — #14649516

Order 2816.

756 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#13076947C211yesmaximal, characteristic
2C2×#10622545C211yesmaximal, characteristic, complemented
3C2×#10622108C212yesmaximal
4#13066496C212yesmaximal, complemented
5C11×#1817C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C22×C4×Dic11—21no—
10C2×C11×C22⋊C8C2212yes—
11#10622826—21no—
12#10622825C2211yescharacteristic
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622553—22no—
16#10622552C412yescomplemented
17#10622545—24no—
18#10622541C412yescomplemented
19C11×#336—22no—
20#10622108—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C23×Dic11—22no—
26C22×D44C2×C411yescharacteristic
27C22×C8×C11—22no—
28C2×C42×C11—22no—
29C2×C42×C11—22no—
30C2×C42×C11C2×C412yes—
31C2×C42×C11D412yes—
32C2×C22⋊Dic11—21no—
33#66983—22no—
34#66983—22no—
35#66982—44no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C412yes—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—24no—
43C2×C4×Dic11—28no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—22no—
46C11⋊#95—24no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C11⋊#95D414yes—
51#9149—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C23×D11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—24no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D412yes—
67C22×C4×C11#4112yes—
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—42no—
71C2×C22⋊D11—42no—
72C22×Dic11—28no—
73C22×Dic11—21no—
74C22×Dic11—22no—
75C22×Dic11—24no—
76C22×Dic11—44no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C2×D44—22no—
80C2×D44—42no—
81C2×C8×C11—44no—
82C2×C8×C11—42no—
83C42×C11—24no—
84C42×C11—24no—
85C22⋊Dic11—42no—
86(C2×D11)⋊C4—44no—
87(C2×D11)⋊C4—44no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90C4⋊Dic11—42no—
91Dic11⋊C4—44no—
92C4×Dic11—216no—
93#2854—111no—
94C2×#376—111no—
95#1817D1111yescharacteristic, complemented
96C2×#327—112no—
97#1294—112no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11C2×C22⋊C411yescharacteristic
101C23×C11#12011yescharacteristic
102C23×C11#12311yescharacteristic
103C23×C11#13512yes—
104C23×C11AGL(1,ℤ/8)12yes—
105C22×D11—41no—
106C22×D11—42no—
107C22×D11—41no—
108C22×D11—41no—
109C22×D11—42no—
110C2×C4×C11—24no—
111C2×C4×C11—24no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11#10414yes—
124C2×C4×C11C4×D412yes—
125C2×C4×C11#12112yes—
126C22⋊D11—82no—
127C22⋊D11—82no—
128C2×Dic11—28no—
129C2×Dic11—44no—
130C2×Dic11—48no—
131C2×Dic11—48no—
132C2×Dic11—44no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139D44—82no—
140C8×C11—82no—
141C2×#123—221no—
142C2×#121—111no—
143C22×C42—221no—
144C22×C42C2×D1111yescharacteristic
145C2×C22⋊C8C2×D1112yes—
146#390—112no—
147#389—112no—
148#388—222no—
149#386—221no—
150#380—111no—
151#376—224no—
152C2×#95—112no—
153C2×#95—221no—
154#336—22no—
155#327—224no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—24no—
161C22×C11—24no—
162C22×C11#38611yescharacteristic
163C22×C11#41012yes—
164C22×C11#41611yescharacteristic
165C22×C11#41811yescharacteristic
166C22×C11C2×#10412yes—
167C22×C11#44912yes—
168C22×C11#48212yes—
169C2×D11—81no—
170C2×D11—81no—
171C2×D11—81no—
172C2×D11—82no—
173C2×D11—82no—
174C4×C11—24no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—42no—
178Dic11—48no—
179Dic11—81no—
180Dic11—82no—
181C22×D4—111no—
182C22×D4—221no—
183C23×C4—222no—
184C23×C4D4411yescharacteristic
185C23×C4D4411yescharacteristic
186C23×C4C22×D1111yescharacteristic
187C22×C8—22no—
188#123—444no—
189#121—222no—
190#121—222no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—222no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—222no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—221no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—224no—
201C2×C42—228no—
202C2×C42C4×D1112yes—
203C2×C42C22⋊D1112yes—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#95—114no—
207#95—224no—
208#95—222no—
209#95—222no—
210#95—221no—
211C2×C11—22no—
212C2×C11—22no—
213C2×C11#150012yes—
214C2×C11#150512yes—
215C2×C11#187511yescharacteristic
216C2×C11#189611yescharacteristic
217C2×C11#189911yescharacteristic
218D11—161no—
219C24—221no—
220C24C2×D4411yescharacteristic
221C2×D4—222no—
222C2×D4—442no—
223C2×D4—441no—
224C2×D4—441no—
225C2×D4—442no—
226C2×D4—442no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—42no—
235C22×C4—228no—
236C22×C4—224no—
237C22×C4—222no—
238C22×C4—221no—
239C22×C4—444no—
240C22×C4—442no—
241C22×C4—442no—
242C22×C4(C2×D11)⋊C412yes—
243C22×C4(C2×D11)⋊C412yes—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4D4×D1112yes—
246C22×C4#434112yes—
247C22×C4C2×C22⋊D1111yescharacteristic
248C2×C8—44no—
249C2×C8—42no—
250C4⋊C4—222no—
251C4⋊C4—442no—
252C4⋊C4—444no—
253C22⋊C4—444no—
254C22⋊C4—442no—
255C22⋊C4—444no—
256C22⋊C4—442no—
257C42—24no—
258C42—24no—
259C42—2216no—
260C11#914911yescharacteristic, complemented, Sylow
261C23—22no—
262C23—22no—
263C23—441no—
264C23—441no—
265C23—442no—
266C23—441no—
267C23—442no—
268C23#6693511yescharacteristic
269C23#6693911yescharacteristic
270C23#6695712yes—
271C23#6696112yes—
272C23C2×(C2×D11)⋊C411yescharacteristic
273D4—882no—
274D4—882no—
275D4—882no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—228no—
290C2×C4—444no—
291C2×C4—448no—
292C2×C4—448no—
293C2×C4—444no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—441no—
297C2×C4—442no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4#6688914yes—
301C2×C4(C22⋊D11)⋊C412yes—
302C2×C4#6699212yes—
303C8—82no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—24no—
310C22—881no—
311C22—881no—
312C22—882no—
313C22—882no—
314C22—881no—
315C22#1062234712yes—
316C22#1062235012yes—
317C22#1062257111yescharacteristic
318C22#1062261912yes—
319C22#1062272611yescharacteristic
320C22#1062274411yescharacteristic
321C22C2×#6688912yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—448no—
327C4—882no—
328C4—881no—
329C2—22no—
330C2—22no—
331C2—1761no—
332C2#1306710312yes—
333C2#1306712512yes—
334C2#1306893611yescharacteristic
335C2#1306905711yescharacteristic
336C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1817C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1817D11
hypocenterC11#9149
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#10622545C2semidirect
4. #13066496C2semidirect
5. C11×#1817C2semidirect
16. #10622552C4semidirect
18. #10622541C4semidirect
95. #1817D11semidirect
260. C11#9149semidirect

Maximal subgroups

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

subgroupindex
#130769472
C2×#106225452
C2×#106221082
#130664962
C11×#18172
#914911