Finite Group Databasebeta

← #14767617

Subgroups — #14767617

Order 2816.

1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.

normal subgroups only

This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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
1C2×#10622308C211yesmaximal, characteristic
2#13071341C212yesmaximal, complemented
3#13069440C212yesmaximal, complemented
4#13068963C218yesmaximal, complemented
5#13068747C211yesmaximal, characteristic, complemented
6C11×#1746C211yesmaximal, characteristic, complemented
7C22×D88C2214yes—
8C2×#66927C2212yes—
9C2×C4×D44C2214yes—
10C2×C11×#97C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#376C2211yescharacteristic
13C2×#66885C2218yes—
14#10622552C2214yes—
15#10622549C2212yes—
16#10622308C418yescomplemented
17#10622278—28no—
18C11×#336C2214yes—
19#10622189C2214yes—
20C22×D44—24no—
21C22×D44C2314yes—
22C22×C4×D11—24no—
23C22×C8×C11C2312yes—
24C22×C8×C11C2312yes—
25C2×C42×C11C2312yes—
26C2×C42×C11C2311yescharacteristic
27C2×(C2×D11)⋊C4—24no—
28C2×(C2×D11)⋊C4—28no—
29C2×C4⋊Dic11C2314yes—
30C2×D88—48no—
31C2×D88C2×C4116yescomplemented
32#66927—24no—
33#66927C2×C418yescomplemented
34C4×D44—48no—
35C11×#97—22no—
36C4×C8×C11C2×C414yescomplemented
37C11×#95D414yes—
38C11⋊#95—24no—
39#66885—48no—
40#22276—111nomaximal, Sylow
41C23×D11—24no—
42C22×C4×C11C2×D414yes—
43C22×C4×C11C2×D412yes—
44C22×C4×C11C2411yescharacteristic
45C22×Dic11—24no—
46C2×D44—216no—
47C2×D44—24no—
48C2×D44—28no—
49C2×D44—28no—
50C2×D44—88no—
51C2×D44C22×C418yes—
52C2×C4×D11—48no—
53C2×C4×D11—88no—
54C2×C8×C11—22no—
55C2×C8×C11—24no—
56C2×C8×C11—24no—
57C2×C8×C11C22×C414yes—
58C42×C11—24no—
59C42×C11C22×C412yes—
60C42×C11#4112yes—
61(C2×D11)⋊C4—48no—
62(C2×D11)⋊C4—88no—
63C4⋊Dic11—28no—
64D88—416no—
65C2×#493—111no—
66#2328—112no—
67#1961—112no—
68#1879—118no—
69#1835—111no—
70#1746D1111yescharacteristic, complemented
71C23×C11C22×D411yescharacteristic
72C22×D11—28no—
73C22×D11—44no—
74C22×D11—44no—
75C22×D11—48no—
76C22×D11—48no—
77C2×C4×C11—24no—
78C2×C4×C11—24no—
79C2×C4×C11—28no—
80C2×C4×C11C4×D414yes—
81C2×C4×C11C23×C411yescharacteristic
82C2×C4×C11C2×#4111yescharacteristic
83C2×C4×C11H(5,𝔽2)14yes—
84C2×Dic11—44no—
85C2×Dic11—48no—
86D44—216no—
87D44—48no—
88D44—816no—
89C4×D11—816no—
90C8×C11—24no—
91C8×C11—42no—
92C22×D8—114no—
93C2×#127—112no—
94C2×C4×D4—114no—
95#493—118no—
96C2×#102—118no—
97C2×#97C2×D1111yescharacteristic
98C2×C4×C8C2×D1111yescharacteristic
99#390—114no—
100#386—228no—
101#382—112no—
102#376C2×D1111yescharacteristic
103#340—114no—
104#336C2×D1114yes—
105C22×C11C2×C4×D411yescharacteristic
106C22×C11#53512yes—
107C22×C11#57614yes—
108C2×D11—48no—
109C2×D11—416no—
110C2×D11—84no—
111C2×D11—88no—
112C2×D11—84no—
113C4×C11—24no—
114C4×C11—44no—
115C4×C11#51812yes—
116C4×C11#54012yes—
117Dic11—84no—
118C22×D4—114no—
119C22×D4—224no—
120C23×C4—224no—
121C2×D8—1116no—
122C2×D8—448no—
123C22×C8C22×D1112yes—
124C22×C8C22×D1112yes—
125#127—118no—
126#127—224no—
127C4×D4—448no—
128C2×C4⋊C4—114no—
129C2×C22⋊C4—224no—
130C2×C22⋊C4—228no—
131C2×C42C22×D1112yes—
132C2×C42C22×D1111yescharacteristic
133#102—448no—
134#97—22no—
135C4×C8C4×D1114yescomplemented
136#95—224no—
137#95D4414yes—
138C2×C11#232811yescharacteristic
139C2×C11#294812yes—
140C2×C11#322014yes—
141D11—88no—
142C24—224no—
143C2×D4—118no—
144C2×D4—2216no—
145C2×D4—224no—
146C2×D4—228no—
147C2×D4—228no—
148C2×D4—888no—
149C22×C4—224no—
150C22×C4—448no—
151C22×C4—888no—
152C22×C4C2×D4414yes—
153C22×C4C2×D4412yes—
154C22×C4C23×D1111yescharacteristic
155D8—4416no—
156C2×C8—24no—
157C2×C8—22no—
158C2×C8—24no—
159C2×C8C2×C4×D1114yes—
160C4⋊C4—228no—
161C22⋊C4—448no—
162C22⋊C4—888no—
163C42—24no—
164C42C2×C4×D1112yes—
165C42#433912yes—
166C11#2227611yescharacteristic, complemented, Sylow
167C23—228no—
168C23—448no—
169C23—448no—
170C23—444no—
171C23—444no—
172C23C22×D4411yescharacteristic
173D4—2216no—
174D4—448no—
175D4—8816no—
176C2×C4—24no—
177C2×C4—28no—
178C2×C4—24no—
179C2×C4—448no—
180C2×C4—444no—
181C2×C4—8816no—
182C2×C4C4×D4414yes—
183C2×C4C22×C4×D1111yescharacteristic
184C2×C4C2×#433911yescharacteristic
185C2×C4#6704214yes—
186C8—24no—
187C8—42no—
188C22—4416no—
189C22—448no—
190C22—884no—
191C22—884no—
192C22—888no—
193C22C2×C4×D4411yescharacteristic
194C22#1062305612yes—
195C22#1062328314yes—
196C4—24no—
197C4—44no—
198C4—884no—
199C4#1062305212yes—
200C4#1062306612yes—
201C2—888no—
202C2#1307134111yescharacteristic
203C2#1307746912yes—
204C2#1307966814yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC23×C11C22×D4
prime radicalC2×#10622308C2
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22276
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #13071341C2semidirect
3. #13069440C2semidirect
4. #13068963C2semidirect
5. #13068747C2semidirect
6. C11×#1746C2semidirect
16. #10622308C4semidirect
31. C2×D88C2×C4semidirect
33. #66927C2×C4semidirect
36. C4×C8×C11C2×C4semidirect
70. #1746D11semidirect
135. C4×C8C4×D11semidirect
166. C11#22276semidirect

Maximal subgroups

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

subgroupindex
C2×#106223082
#130713412
#130694402
#130689632
#130687472
C11×#17462
#2227611