Finite Group Databasebeta

← #14651024

Subgroups — #14651024

Order 2816.

368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079832C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic
3#13067317C211yesmaximal, characteristic
4#13067253C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066485C211yesmaximal, characteristic
7C11×#1287C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622539C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622464—21no—
16#10622463—21no—
17#10622441—22no—
18#10622336—22no—
19#10622333—22no—
20#10622316C412yes—
21#10622315C412yes—
22#10622292—21no—
23C8×Dic22—21no—
24#10622124—21no—
25#10622120—21no—
26#10622103—22no—
27#10622094—21no—
28#10622094—21no—
29C2×C42×C11C2311yescharacteristic
30#66979—21no—
31#66979D412yes—
32#66977—21no—
33#66977—21no—
34#66977—21no—
35#66977—21no—
36C22×C11⋊C8—21no—
37#66923—21no—
38#66923C2×C412yes—
39#66922C2×C411yescharacteristic
40#66922C2×C411yescharacteristic
41#66922D411yescharacteristic
42#66922D411yescharacteristic
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97C2×C412yes—
55C4×C8×C11D411yescharacteristic
56C4×C8×C11D411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66882—22no—
59#66881—22no—
60#66880—22no—
61#66880—22no—
62#66879—22no—
63Dic11⋊C8—22no—
64Dic11⋊C8—22no—
65C8×Dic11—22no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#66867D412yes—
70#9374—111nomaximal, Sylow
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×C8×C11—22no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—41no—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C22⋊Dic11—22no—
87C22⋊Dic11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C22⋊C412yes—
95C4⋊Dic11C22⋊C412yes—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C4×Dic11—22no—
101C4×Dic11—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—81no—
105#3237—111no—
106#2985—111no—
107#1552—111no—
108#1537—111no—
109#1481—111no—
110#1290—111no—
111#1287D1111yescharacteristic
112C23×C11#12311yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×Dic11—22no—
124C2×Dic11—22no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127Dic22—41no—
128Dic22—41no—
129Dic22—42no—
130Dic22—42no—
131Dic22—81no—
132C8×C11—42no—
133C8×C11—41no—
134C8×C11—41no—
135C8×C11—81no—
136C11⋊C8—42no—
137C11⋊C8—81no—
138#533—111no—
139#533—111no—
140#501—112no—
141#491—112no—
142#485—222no—
143#477—221no—
144#475—221no—
145#446—222no—
146#446—221no—
147C8×Q8—221no—
148#433—222no—
149#432—111no—
150#432C2×D1111yescharacteristic
151#432C2×D1111yescharacteristic
152#431C2×D1111yescharacteristic
153C2×C4⋊C8—111no—
154#332—221no—
155#332—221no—
156#330—222no—
157Q8⋊C8—221no—
158Q8⋊C8—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#38611yescharacteristic
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11#47111yescharacteristic
169C4×C11#47311yescharacteristic
170Dic11—42no—
171Dic11—42no—
172Dic11—81no—
173Dic11—81no—
174C22×C8—221no—
175C4⋊Q8—111no—
176C4⋊Q8—111no—
177C4⋊Q8—111no—
178C4⋊Q8—111no—
179#125—112no—
180#125—221no—
181C22⋊Q8—221no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185C4×Q8—221no—
186C4×Q8—221no—
187C4×Q8—221no—
188C4×Q8—221no—
189#117—112no—
190#117—221no—
191C2×C42C22×D1111yescharacteristic
192#107—222no—
193#106—222no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—222no—
198C4⋊C8—222no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201C4⋊C8—221no—
202#103—222no—
203#103—222no—
204C22⋊C8—21no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207C22⋊C8—221no—
208#97—21no—
209#97—112no—
210#97—222no—
211#97C4×D1112yes—
212C4×C8—222no—
213C4×C8D4411yescharacteristic
214C4×C8D4411yescharacteristic
215C2×C11—41no—
216C2×C11#188111yescharacteristic
217C2×C11#190811yescharacteristic
218C2×C11#191211yescharacteristic
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8—221no—
222C2×Q8—221no—
223C22×C4#433911yescharacteristic
224C22×C4D4×D1111yescharacteristic
225C22×C4#434311yescharacteristic
226C2×C8—22no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—41no—
230C2×C8—222no—
231C2×C8—441no—
232C2×C8—881no—
233C4⋊C4—112no—
234C4⋊C4—112no—
235C4⋊C4—222no—
236C4⋊C4—221no—
237C4⋊C4—222no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C22⋊C4—222no—
246C22⋊C4—441no—
247C42—222no—
248C42—441no—
249C42C2×C4×D1111yescharacteristic
250C42C2×D4411yescharacteristic
251C42D4×D1111yescharacteristic
252C42D4×D1111yescharacteristic
253C11#937411yescharacteristic, complemented, Sylow
254C23#6694711yescharacteristic
255Q8—442no—
256Q8—442no—
257Q8—441no—
258Q8—441no—
259Q8—881no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4C4×D4411yescharacteristic
269C2×C4C22⋊C4×D1111yescharacteristic
270C2×C4#6693511yescharacteristic
271C2×C4#6693711yescharacteristic
272C2×C4#6694611yescharacteristic
273C2×C4#6694811yescharacteristic
274C8—41no—
275C8—41no—
276C8—42no—
277C8—81no—
278C8—442no—
279C8—881no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#1062227811yescharacteristic
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—442no—
290C4—442no—
291C4—881no—
292C4—881no—
293C4#1062250911yescharacteristic
294C4#1062251111yescharacteristic
295C2—41no—
296C2#1306897711yescharacteristic
297C2#1306913011yescharacteristic
298C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1287C2
socleC22×C11#386
prime radicalC23×C11#123
cosocleC2×C42×C11C23
hypercenter#1287D11
hypocenterC11#9374
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
253. C11#9374semidirect

Maximal subgroups

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

subgroupindex
#130798322
#130777102
#130673172
#130672532
#130670202
#130664852
C11×#12872
#937411