Finite Group Databasebeta

← #14650751

Subgroups — #14650751

Order 2816.

400 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079808C211yesmaximal, characteristic
2#13077686C211yesmaximal, characteristic
3#13067322C211yesmaximal, characteristic
4#13067242C211yesmaximal, characteristic, complemented
5#13066973C211yesmaximal, characteristic, complemented
6#13066479C211yesmaximal, characteristic, complemented
7C11×#1308C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#432C2211yescharacteristic
13#10622539C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622460—22no—
16#10622449—22no—
17#10622349C412yes—
18#10622348C412yes—
19#10622340—22no—
20#10622326—21no—
21#10622319—22no—
22#10622315—21no—
23#10622124—21no—
24#10622123—21no—
25#10622107—22no—
26#10622103—22no—
27C2×#4339—21no—
28C2×C42×C11C2311yescharacteristic
29#66983—21no—
30#66983C2×C412yes—
31C2×C4⋊Dic11C2×C411yescharacteristic
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×Dic11⋊C4—21no—
35C2×#4313—22no—
36C2×C8×D11—22no—
37#66928—21no—
38#66927D411yescharacteristic
39C4×D44—21no—
40C4×D44D412yes—
41#66923—21no—
42#66923—21no—
43#66923—21no—
44#66923—21no—
45#66922D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8C2×C412yes—
51C11×C22⋊C8D412yes—
52C11×#97—21no—
53C11×#97—21no—
54C11×#97—21no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57#66885—22no—
58#66885—22no—
59(C2×D11)⋊C8—24no—
60#66882—22no—
61#66881—22no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867D412yes—
65C4×C11⋊C8—21no—
66#9335—111nomaximal, Sylow
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C22⋊D11—22no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73#4339—81no—
74#4339—81no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C22⋊C412yes—
78C2×C4×D11—22no—
79C2×Dic22—21no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C22⋊C412yes—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101#4313—82no—
102C8×D11—82no—
103#3234—111no—
104#2980—111no—
105#1553—111no—
106#1534—111no—
107#1470—111no—
108#1308D1111yescharacteristic, complemented
109#1287—111no—
110C23×C11C4×D411yescharacteristic
111C22×D11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12311yescharacteristic
121C22⋊D11—82no—
122C2×Dic11—22no—
123C2×Dic11—42no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—81no—
127D44—42no—
128D44—81no—
129D44—81no—
130C4×D11—42no—
131C4×D11—42no—
132Dic22—81no—
133C8×C11—42no—
134C8×C11—42no—
135C8×C11—81no—
136C11⋊C8—42no—
137C11⋊C8—81no—
138#532—111no—
139C2×#125—111no—
140#501—221no—
141#490—221no—
142#481—112no—
143#480—112no—
144#478—222no—
145#435—222no—
146#435—222no—
147#432—111no—
148#432C2×D1111yescharacteristic
149#432C2×D1111yescharacteristic
150#432C2×D1111yescharacteristic
151#431—111no—
152#408—222no—
153#332—221no—
154#331—221no—
155#330—222no—
156#324—222no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11#38611yescharacteristic
161C2×D11—42no—
162C2×D11—42no—
163C2×D11—42no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170Dic11—42no—
171Dic11—81no—
172Dic11—81no—
173C2×#41—221no—
174C2×M16—222no—
175C22×C8—222no—
176C4⋊Q8—111no—
177#127—111no—
178#125—221no—
179#125—221no—
180#125—221no—
181#125—221no—
182#124—221no—
183#121—112no—
184#121—221no—
185C4×D4—112no—
186C4×D4—221no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C42C22×D1111yescharacteristic
192#107—222no—
193#106—222no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199#102—222no—
200#102—222no—
201C22⋊C8—21no—
202C22⋊C8—224no—
203C22⋊C8—221no—
204C22⋊C8—221no—
205C22⋊C8C4×D1112yes—
206C22⋊C8D4412yes—
207#97—21no—
208#97—21no—
209#97—21no—
210#97—112no—
211C4×C8—221no—
212C2×C11—41no—
213C2×C11#188111yescharacteristic
214C2×C11#190411yescharacteristic
215C2×C11#191511yescharacteristic
216D11—82no—
217#41—881no—
218#41—881no—
219C2×Q8—221no—
220C2×D4—112no—
221C2×D4—222no—
222C2×D4—221no—
223C2×D4—221no—
224C22×C4—222no—
225C22×C4—221no—
226C22×C4—221no—
227C22×C4C2×C4×D1111yescharacteristic
228C22×C4C2×D4411yescharacteristic
229C22×C4#433911yescharacteristic
230M16—882no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—41no—
234C2×C8—222no—
235C2×C8—441no—
236C2×C8—882no—
237C4⋊C4—112no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—441no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C22⋊C4—222no—
248C22⋊C4—222no—
249C42D4×D1111yescharacteristic
250C42D4×D1111yescharacteristic
251C42D4×D1111yescharacteristic
252C42#434311yescharacteristic
253C11#933511yescharacteristic, complemented, Sylow
254C23—222no—
255C23C4×D4411yescharacteristic
256Q8—881no—
257D4—442no—
258D4—881no—
259D4—881no—
260D4—882no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—222no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4—441no—
269C2×C4—441no—
270C2×C4—881no—
271C2×C4C22⋊C4×D1111yescharacteristic
272C2×C4#6693511yescharacteristic
273C2×C4#6693711yescharacteristic
274C2×C4#6694611yescharacteristic
275C2×C4#6694711yescharacteristic
276C2×C4#6694811yescharacteristic
277C8—42no—
278C8—42no—
279C8—81no—
280C8—442no—
281C8—881no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—442no—
286C22—442no—
287C22—442no—
288C22#1062227811yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—442no—
296C4—881no—
297C4—881no—
298C2—41no—
299C2—882no—
300C2#1306897711yescharacteristic
301C2#1306910211yescharacteristic
302C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1308C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1308D11
hypocenterC11#9335
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1308

Complements

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

NH ≅ G/Ntype
4. #13067242C2semidirect
5. #13066973C2semidirect
6. #13066479C2semidirect
7. C11×#1308C2semidirect
108. #1308D11semidirect
253. C11#9335semidirect

Maximal subgroups

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

subgroupindex
#130798082
#130776862
#130673222
#130672422
#130669732
#130664792
C11×#13082
#933511