Finite Group Databasebeta

← #14909477

Subgroups — #14909477

Order 2816.

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

normal subgroups only

This group has 504 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#13079203C212yesmaximal
2#13070869C211yesmaximal, characteristic, complemented
3#13070845C212yesmaximal, complemented
4#13070725C214yesmaximal
5#13070486C214yesmaximal, complemented
6C4×#66862C211yesmaximal, characteristic
7C11×#2254C211yesmaximal, characteristic, complemented
8#10623259—22no—
9C11×#500C2212yes—
10#10622706—22no—
11C2×Dic88C2214yes—
12C2×#66862C2212yes—
13#10622500—22no—
14#10622500C2214yes—
15#10622486—22no—
16#10622486C2214yes—
17#10622312C2212yes—
18C4×C8×D11C2211yescharacteristic
19C11×#367C2214yes—
20C4×C11×C16C2211yescharacteristic
21#10622140C2212yes—
22#10622130C2218yes—
23C4×C11⋊C16C2211yescharacteristic
24C11×C4⋊Q8—22no—
25#66999—42no—
26Q8×Dic11—42no—
27C2×Dic44—22no—
28C2×Dic44C2314yes—
29C2×C8×D11D411yescharacteristic
30C2×C8×D11C2311yescharacteristic
31#66950—24no—
32#66945—42no—
33#66943—42no—
34#66940—24no—
35C42×D11D411yescharacteristic
36#66922—22no—
37C2×C11×C16C2312yes—
38C11×#107—22no—
39C11×#107C2314yes—
40C4×C8×C11C2311yescharacteristic
41C8×Dic11D411yescharacteristic
42C8×Dic11C2311yescharacteristic
43C2×C11⋊C16C2312yes—
44#66874—24no—
45#66874—24no—
46C4×C11⋊C8D411yescharacteristic
47Dic88—28no—
48#66862—24no—
49#33749—111nomaximal, Sylow
50C2×Q8×C11—42no—
51C2×C4×D11D812yes—
52C2×C4×D11C2×D411yescharacteristic
53C2×Dic22—24no—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11C2411yescharacteristic
56C11×C4⋊C4—24no—
57C11×C4⋊C4—42no—
58C42×C11C2×D411yescharacteristic
59(C2×D11)⋊C4—44no—
60C4⋊Dic11—44no—
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63Dic11⋊C4—44no—
64C4×Dic11—44no—
65C4×Dic11D812yes—
66C4×Dic11C2×D411yescharacteristic
67C2×C11⋊C8C2×D411yescharacteristic
68C2×C11⋊C8C2×D411yescharacteristic
69Dic44—28no—
70Dic44—44no—
71C8×D11—22no—
72C8×D11—22no—
73C11×C16#4114yes—
74C11⋊C16—22no—
75#3170—112no—
76#2254D1111yescharacteristic, complemented
77#2247—111no—
78#2241—112no—
79#2219—114no—
80#2176—114no—
81C4×M32—111no—
82C22×D11C2×D811yescharacteristic
83Q8×C11—84no—
84C2×C4×C11—44no—
85C2×C4×C11C2×D812yes—
86C2×C4×C11C22×D411yescharacteristic
87C2×Dic11—44no—
88C2×Dic11C2×D812yes—
89C2×Dic11C2×D811yescharacteristic
90C4×D11—21no—
91C4×D11—21no—
92C4×D11—24no—
93Dic22—44no—
94Dic22—44no—
95C8×C11#13512yes—
96C8×C11C2×#4112yes—
97C11⋊C8—21no—
98C11⋊C8—21no—
99#533—222no—
100C2×Q32—114no—
101C2×M32—112no—
102#500C2×D1112yes—
103#494—112no—
104#487—222no—
105#467—114no—
106#467—222no—
107C4×Q16—114no—
108C4×Q16—222no—
109C2×C4×C8—111no—
110#367C2×D1114yes—
111#358—118no—
112#346—112no—
113C4×C16—111no—
114C4×C16C2×D1111yescharacteristic
115C22×C11C22×D811yescharacteristic
116C2×D11—22no—
117C2×D11—21no—
118C4×C11—84no—
119C4×C11#51014yes—
120C4×C11#53211yescharacteristic
121C4×C11C2×#13511yescharacteristic
122Dic11—22no—
123Dic11—21no—
124Dic11—84no—
125C2×Q16—114no—
126C2×Q16—222no—
127C22×C8—111no—
128C22×C8—111no—
129C4⋊Q8—22no—
130C4⋊Q8—222no—
131#125—442no—
132C22⋊Q8—224no—
133C22⋊Q8—442no—
134C4×Q8—224no—
135C4×Q8—442no—
136#117—442no—
137C2×C42—111no—
138Q32—228no—
139M32—224no—
140C2×C16—112no—
141C2×C16C22×D1112yes—
142#107—22no—
143#107C22×D1114yes—
144#103—224no—
145#103—224no—
146C4×C8—111no—
147C4×C8—111no—
148C4×C8—111no—
149C4×C8C22×D1111yescharacteristic
150C2×C11#316911yescharacteristic
151C2×C11C2×#51012yes—
152D11—41no—
153C2×Q8—42no—
154C2×Q8—224no—
155C22×C4—112no—
156C22×C4—111no—
157Q16—228no—
158Q16—444no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8—222no—
162C2×C8—222no—
163C2×C8D4×D1111yescharacteristic
164C2×C8C23×D1111yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—444no—
168C4⋊C4—444no—
169C4⋊C4—442no—
170C4⋊C4—442no—
171C22⋊C4—444no—
172C42—112no—
173C42—111no—
174C42—444no—
175C42D4×D1111yescharacteristic
176C16—222no—
177C16#434314yes—
178C11#3374911yescharacteristic, complemented, Sylow
179C23—111no—
180Q8—84no—
181Q8—444no—
182Q8—444no—
183C2×C4—44no—
184C2×C4—112no—
185C2×C4—111no—
186C2×C4—221no—
187C2×C4—224no—
188C2×C4—221no—
189C2×C4—444no—
190C2×C4D8×D1112yes—
191C2×C4C2×D4×D1111yescharacteristic
192C8—221no—
193C8—221no—
194C8#6697212yes—
195C8C2×#434312yes—
196C22—222no—
197C22—221no—
198C22C2×D8×D1111yescharacteristic
199C4—84no—
200C4—222no—
201C4—221no—
202C4—884no—
203C4#1062252814yes—
204C4#1062325611yescharacteristic
205C4C2×#6697211yescharacteristic
206C2—441no—
207C2#1307919611yescharacteristic
208C2C2×#1062252812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2254C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2254D11
hypocenterC11#33749
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
2. #13070869C2semidirect
3. #13070845C2semidirect
5. #13070486C2semidirect
7. C11×#2254C2semidirect
76. #2254D11semidirect
178. C11#33749semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130708692
#130708452
#130707252
#130704862
C4×#668622
C11×#22542
#3374911