Finite Group Databasebeta

← #14909470

Subgroups — #14909470

Order 2816.

592 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 147 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#13079196C212yesmaximal, complemented
2#13070866C211yesmaximal, characteristic, complemented
3#13070841C212yesmaximal, complemented
4#13070720C214yesmaximal, complemented
5#13070491C214yesmaximal, complemented
6C4×#66862C211yesmaximal, characteristic, complemented
7C11×#2254C211yesmaximal, characteristic, complemented
8#10623256—22no—
9C11×#500C2212yes—
10#10622701—22no—
11C2×D176C2214yes—
12C2×#66862C2212yes—
13#10622496—22no—
14#10622496C2214yes—
15#10622485—22no—
16#10622485C2214yes—
17#10622308C2212yes—
18C4×C8×D11C2211yescharacteristic
19C11×#367C2214yes—
20C4×C11×C16C2211yescharacteristic
21#10622140C2212yes—
22#10622129C2218yes—
23C4×C11⋊C16C2211yescharacteristic
24C2×#4343—42no—
25C11×C4⋊Q8—22no—
26#67000—42no—
27C2×D88—22no—
28C2×D88C2314yes—
29C2×C8×D11D411yescharacteristic
30C2×C8×D11C2311yescharacteristic
31#66948—24no—
32#66948—42no—
33#66946—24no—
34#66946—42no—
35#66927—22no—
36C42×D11D411yescharacteristic
37C2×C11×C16C2312yes—
38C11×#107—22no—
39C11×#107C2314yes—
40C4×C8×C11C2311yescharacteristic
41C8×Dic11D411yescharacteristic
42C8×Dic11C2311yescharacteristic
43C2×C11⋊C16C2312yes—
44#66873—24no—
45#66873—24no—
46C4×C11⋊C8D411yescharacteristic
47D176—28no—
48#66862—24no—
49#33748—111nomaximal, Sylow
50C2×Q8×C11—42no—
51#4343—88no—
52C2×D44—24no—
53C2×D44—44no—
54C2×D44—42no—
55C2×D44—42no—
56C2×C4×D11—44no—
57C2×C4×D11D812yes—
58C2×C4×D11C2×D411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11C2411yescharacteristic
61C11×C4⋊C4—24no—
62C11×C4⋊C4—42no—
63C42×C11C2×D411yescharacteristic
64(C2×D11)⋊C4—44no—
65(C2×D11)⋊C4—44no—
66C4×Dic11D812yes—
67C4×Dic11C2×D411yescharacteristic
68C2×C11⋊C8C2×D411yescharacteristic
69C2×C11⋊C8C2×D411yescharacteristic
70D88—28no—
71D88—44no—
72C8×D11—22no—
73C8×D11—22no—
74C11×C16#4114yescomplemented
75C11⋊C16—22no—
76#3169—112no—
77#2254D1111yescharacteristic, complemented
78#2246—111no—
79#2240—112no—
80#2218—114no—
81#2177—114no—
82C4×M32—111no—
83C22×D11—44no—
84C22×D11C2×D811yescharacteristic
85Q8×C11—84no—
86C2×C4×C11—44no—
87C2×C4×C11C2×D812yes—
88C2×C4×C11C22×D411yescharacteristic
89C2×Dic11C2×D811yescharacteristic
90C2×Dic11C2×D812yes—
91D44—44no—
92D44—44no—
93D44—88no—
94D44—84no—
95D44—84no—
96C4×D11—21no—
97C4×D11—21no—
98C4×D11—24no—
99C4×D11—88no—
100C8×C11#13512yes—
101C8×C11C2×#4112yes—
102C11⋊C8—21no—
103C11⋊C8—21no—
104#532—222no—
105C2×D16—114no—
106C2×M32—112no—
107#500C2×D1112yes—
108#493—112no—
109#486—222no—
110#466—114no—
111#466—222no—
112C4×D8—114no—
113C4×D8—222no—
114C2×C4×C8—111no—
115#367C2×D1114yes—
116#357—118no—
117#346—112no—
118C4×C16—111no—
119C4×C16C2×D1111yescharacteristic
120C22×C11C22×D811yescharacteristic
121C2×D11—22no—
122C2×D11—21no—
123C2×D11—84no—
124C2×D11—84no—
125C2×D11—84no—
126C4×C11—84no—
127C4×C11#50914yes—
128C4×C11#53211yescharacteristic
129C4×C11C2×#13511yescharacteristic
130Dic11—22no—
131Dic11—21no—
132C2×#41—442no—
133C2×D8—114no—
134C2×D8—222no—
135C22×C8—111no—
136C22×C8—111no—
137C4⋊Q8—22no—
138#127—222no—
139#124—442no—
140#121—224no—
141#121—442no—
142C4×D4—224no—
143C4×D4—442no—
144C2×C42—111no—
145D16—228no—
146M32—224no—
147C2×C16—112no—
148C2×C16C22×D1112yes—
149#107—22no—
150#107C22×D1114yes—
151#102—224no—
152#102—224no—
153C4×C8—111no—
154C4×C8—111no—
155C4×C8—111no—
156C4×C8C22×D1111yescharacteristic
157C2×C11#316911yescharacteristic
158C2×C11C2×#50912yes—
159D11—41no—
160D11—164no—
161#41—888no—
162C2×Q8—42no—
163C2×D4—224no—
164C2×D4—444no—
165C2×D4—442no—
166C2×D4—442no—
167C22×C4—112no—
168C22×C4—111no—
169C22×C4—444no—
170D8—228no—
171D8—444no—
172C2×C8—111no—
173C2×C8—111no—
174C2×C8—222no—
175C2×C8—222no—
176C2×C8D4×D1111yescharacteristic
177C2×C8C23×D1111yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—42no—
180C22⋊C4—444no—
181C22⋊C4—444no—
182C42—112no—
183C42—111no—
184C42D4×D1111yescharacteristic
185C16—222no—
186C16#434314yescomplemented
187C11#3374811yescharacteristic, complemented, Sylow
188C23—111no—
189C23—444no—
190Q8—84no—
191D4—444no—
192D4—444no—
193D4—888no—
194D4—884no—
195D4—884no—
196C2×C4—44no—
197C2×C4—111no—
198C2×C4—112no—
199C2×C4—221no—
200C2×C4—224no—
201C2×C4—221no—
202C2×C4—888no—
203C2×C4D8×D1112yes—
204C2×C4C2×D4×D1111yescharacteristic
205C8—221no—
206C8—221no—
207C8#6697212yes—
208C8C2×#434312yes—
209C22—222no—
210C22—221no—
211C22—884no—
212C22—884no—
213C22—884no—
214C22C2×D8×D1111yescharacteristic
215C4—84no—
216C4—222no—
217C4—221no—
218C4#1062252714yes—
219C4#1062325611yescharacteristic
220C4C2×#6697211yescharacteristic
221C2—441no—
222C2—1764no—
223C2#1307919611yescharacteristic
224C2C2×#1062252712yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2254C2
socleC22×C11C22×D8
hypercenter#2254D11
hypocenterC11#33748
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2254

Complements

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

NH ≅ G/Ntype
1. #13079196C2semidirect
2. #13070866C2semidirect
3. #13070841C2semidirect
4. #13070720C2semidirect
5. #13070491C2semidirect
6. C4×#66862C2semidirect
7. C11×#2254C2semidirect
74. C11×C16#41semidirect
77. #2254D11semidirect
186. C16#4343semidirect
187. C11#33748semidirect

Maximal subgroups

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

subgroupindex
#130791962
#130708662
#130708412
#130707202
#130704912
C4×#668622
C11×#22542
#3374811