Finite Group Databasebeta

← #14645921

Subgroups — #14645921

Order 2816.

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

normal subgroups only

This group has 746 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
1#13082419C211yesmaximal, characteristic
2#13069415C211yesmaximal, characteristic
3#13067317C212yesmaximal, complemented
4#13067232C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7#10623329C412yes—
8C2×#66977—22no—
9#10623074—22no—
10#10623070—24no—
11D4×Dic22—22no—
12#10623031C412yes—
13#10623014—22no—
14#10623001C2212yes—
15C11×#432C2212yes—
16C2×C22⋊(C11⋊C8)—22no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19C11×#323—22no—
20#10622124—22no—
21#10622120—22no—
22#10622103—24no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D412yes—
25C22×Dic22—22no—
26C4×D4×C11—22no—
27C4×D4×C11—22no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4D412yes—
30C2×C42×C11C2311yescharacteristic
31C2×C22⋊Dic11—24no—
32D4×Dic11—24no—
33D4×Dic11—24no—
34#66979C2×C414yes—
35C2×C4⋊Dic11—22no—
36#66977—24no—
37#66977—24no—
38#66977—24no—
39#66977—22no—
40#66977—22no—
41C2×Dic11⋊C4—24no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66943—24no—
45#66941—24no—
46#66931—28no—
47#66931—28no—
48#66923D414yes—
49#66922D412yes—
50#66922D412yes—
51C4×Dic22—22no—
52C4×Dic22—22no—
53C11×C4⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×#97—22no—
56C22⋊(C11⋊C8)—44no—
57C4⋊(C11⋊C8)—22no—
58#66867—22no—
59#8457—111nomaximal, Sylow
60C24×C11C22⋊C412yes—
61C2×D4×C11—24no—
62C2×D4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—24no—
72C22×Dic11—24no—
73C2×Dic22—24no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—82no—
77C2×Dic22—82no—
78C2×C8×C11—42no—
79C11×C4⋊C4—22no—
80C11×C22⋊C4—24no—
81C42×C11C2×D412yes—
82C42×C11C2×D412yes—
83C22⋊Dic11—28no—
84C22⋊Dic11—24no—
85C4⋊Dic11—24no—
86C4⋊Dic11—22no—
87C4⋊Dic11—22no—
88C4⋊Dic11C22⋊C414yes—
89C4⋊Dic11C22⋊C414yes—
90Dic11⋊C4—28no—
91Dic11⋊C4—24no—
92Dic11⋊C4—24no—
93C4×Dic11—24no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99#3501—111no—
100#1955—111no—
101#1552—112no—
102#1531—112no—
103#1466D1111yescharacteristic
104C23×C11—22no—
105C23×C11—22no—
106C23×C11—42no—
107C23×C11—42no—
108C23×C11#10114yes—
109C23×C11C2×C22⋊C411yescharacteristic
110D4×C11—28no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—82no—
120C2×C4×C11C2×C22⋊C412yes—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12012yes—
124C2×Dic11—24no—
125C2×Dic11—24no—
126C2×Dic11—84no—
127C2×Dic11—84no—
128Dic22—42no—
129Dic22—42no—
130Dic22—82no—
131Dic22—84no—
132C8×C11—82no—
133C11⋊C8—42no—
134C11⋊C8—81no—
135#554—224no—
136#554—222no—
137D4×Q8—222no—
138#544—112no—
139#543—222no—
140#533—112no—
141C2×C22⋊Q8—222no—
142#518—112no—
143C2×C4×D4C2×D1111yescharacteristic
144#432C2×D1112yes—
145C2×C4⋊C8—111no—
146C2×C22⋊C8—222no—
147C2×#97—111no—
148#332—222no—
149#332—222no—
150#330—224no—
151#323—22no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—24no—
155C22×C11—44no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—82no—
159C22×C11#37911yescharacteristic
160C22×C11C2×#10112yes—
161C4×C11—21no—
162C4×C11—22no—
163C4×C11—22no—
164C4×C11—42no—
165C4×C11#45311yescharacteristic
166C4×C11#45511yescharacteristic
167Dic11—44no—
168Dic11—44no—
169C22×Q8—222no—
170C22×D4C4×D1111yescharacteristic
171C23×C4D4412yes—
172C22×C8—221no—
173C22×C8—221no—
174C4⋊Q8—112no—
175C4⋊Q8—112no—
176C4⋊Q8—224no—
177#125—114no—
178#125—224no—
179C22⋊Q8—228no—
180C22⋊Q8—228no—
181C22⋊Q8—224no—
182C22⋊Q8—224no—
183C22⋊Q8—224no—
184C22⋊Q8—222no—
185C22⋊Q8—222no—
186C4×Q8—222no—
187C4×Q8—222no—
188C4×D4—22no—
189C4×D4—22no—
190C4×D4—224no—
191C4×D4—224no—
192#117—114no—
193C2×C4⋊C4—224no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4C4×D1111yescharacteristic
196C2×C22⋊C4—224no—
197C2×C22⋊C4C22⋊D1112yes—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—22no—
200C4⋊C8—222no—
201C22⋊C8—22no—
202C22⋊C8—444no—
203#97—22no—
204#97—222no—
205C2×C11—22no—
206C2×C11—44no—
207C2×C11#178411yescharacteristic
208C2×C11#179211yescharacteristic
209C2×C11#179411yescharacteristic
210C24(C2×D11)⋊C412yes—
211C2×Q8—224no—
212C2×Q8—222no—
213C2×Q8—222no—
214C2×Q8—882no—
215C2×Q8—882no—
216C2×D4—24no—
217C2×D4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—224no—
223C22×C4—224no—
224C22×C4(C2×D11)⋊C412yes—
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—42no—
229C2×C8—222no—
230C2×C8—441no—
231C2×C8—441no—
232C2×C8—442no—
233C2×C8—441no—
234C4⋊C4—22no—
235C4⋊C4—114no—
236C4⋊C4—114no—
237C4⋊C4—224no—
238C4⋊C4—228no—
239C4⋊C4—224no—
240C4⋊C4—222no—
241C4⋊C4—224no—
242C4⋊C4—222no—
243C22⋊C4—24no—
244C22⋊C4—228no—
245C22⋊C4—224no—
246C42—224no—
247C42D4×D1112yes—
248C42D4×D1112yes—
249C11#845711yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23#6688814yes—
255C23C2×(C2×D11)⋊C411yescharacteristic
256Q8—442no—
257Q8—442no—
258Q8—882no—
259Q8—884no—
260D4—28no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—82no—
270C2×C4—224no—
271C2×C4—224no—
272C2×C4—884no—
273C2×C4—884no—
274C2×C4C22⋊C4×D1112yes—
275C2×C4#6693511yescharacteristic
276C2×C4#6693511yescharacteristic
277C2×C4#6699012yes—
278C8—82no—
279C8—442no—
280C8—881no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—44no—
285C22—42no—
286C22—42no—
287C22—82no—
288C22#1062256811yescharacteristic
289C22C2×#6688812yes—
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—444no—
295C4—444no—
296C4#1062235911yescharacteristic
297C4#1062236011yescharacteristic
298C2—22no—
299C2—44no—
300C2#1306853911yescharacteristic
301C2#1306857211yescharacteristic
302C2#1306858211yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1466C2
socleC22×C11#379
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1466D11
hypocenterC11#8457
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13067317C2semidirect
4. #13067232C2semidirect
249. C11#8457semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130694152
#130673172
#130672322
C11×#14662
#845711