Finite Group Databasebeta

← #14910132

Subgroups — #14910132

Order 2816.

572 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 151 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#13079195C212yesmaximal, complemented
2#13070764C214yesmaximal, complemented
3#13070719C214yesmaximal, complemented
4#13070652C214yesmaximal, complemented
5C11×#2150C211yesmaximal, characteristic, complemented
6#10623008—22no—
7C2×C11×M32C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622728—22no—
10#10622728C2214yes—
11C2×D176C2214yes—
12#10622308C2212yes—
13#10622307—22no—
14C4×D88—22no—
15C4×D88C2214yes—
16#10622295C2212yes—
17C11×C4⋊C16C2214yes—
18#10622147C2218yes—
19#10622143C2214yes—
20C2×#4339—42no—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66983—24no—
25#66983—42no—
26C2×D88—22no—
27C2×D88C2314yes—
28#66928—42no—
29#66927—22no—
30C4×D44—24no—
31C4×D44—42no—
32#66922—22no—
33C11×M32—42no—
34C2×C11×C16C2314yes—
35C4×C8×C11D412yes—
36C4×C8×C11C2312yes—
37#66885—24no—
38#66885—24no—
39#66882—22no—
40#66882C2314yes—
41D176—44no—
42#33819—111nomaximal, Sylow
43C22×C4×C11D812yes—
44C22×C4×C11C2×D411yescharacteristic
45C2×C22⋊D11—44no—
46#4339—88no—
47C2×D44—24no—
48C2×D44—42no—
49C2×D44—42no—
50C2×C4×D11—44no—
51C2×Dic22—42no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D412yes—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11C2411yescharacteristic
58C42×C11D811yescharacteristic
59C42×C11D811yescharacteristic
60C42×C11C2×D412yes—
61(C2×D11)⋊C4—44no—
62(C2×D11)⋊C4—44no—
63C4⋊Dic11—24no—
64C4⋊Dic11—42no—
65D88—24no—
66D88—24no—
67D88—44no—
68C11×C16—24no—
69#3169—112no—
70#2226—114no—
71#2218—114no—
72#2206—114no—
73#2150D1111yescharacteristic, complemented
74C23×C11C2×D811yescharacteristic
75C22×D11—44no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—24no—
79C2×C4×C11C2×D811yescharacteristic
80C2×C4×C11C2×D812yes—
81C2×C4×C11C2×D812yes—
82C2×C4×C11C22×D411yescharacteristic
83C22⋊D11—88no—
84C2×Dic11—44no—
85D44—44no—
86D44—44no—
87D44—84no—
88D44—84no—
89C4×D11—88no—
90Dic22—84no—
91C8×C11—21no—
92C8×C11—22no—
93C8×C11H(5,𝔽2)11yescharacteristic
94C8×C112−1+411yescharacteristic
95#532—222no—
96C2×D16—114no—
97C2×M32C2×D1112yes—
98#500—112no—
99#493—112no—
100#486—222no—
101#466—114no—
102#466—222no—
103C4×D8—114no—
104C4×D8—222no—
105C2×C4×C8C2×D1111yescharacteristic
106#367—114no—
107C4⋊C16C2×D1114yes—
108#357—118no—
109C22×C11—22no—
110C22×C11—21no—
111C22×C11C22×D811yescharacteristic
112C2×D11—84no—
113C2×D11—84no—
114C2×D11—84no—
115C4×C11—22no—
116C4×C11—21no—
117C4×C11#50914yes—
118C4×C11#53711yescharacteristic
119C4×C11#57511yescharacteristic
120Dic11—84no—
121C2×#41—442no—
122C2×D8—114no—
123C2×D8—222no—
124C22×C8D4411yescharacteristic
125C22×C8C22×D1111yescharacteristic
126C4⋊Q8—222no—
127#127—222no—
128#124—442no—
129#121—224no—
130#121—442no—
131C4×D4—224no—
132C4×D4—442no—
133C2×C42D4411yescharacteristic
134D16—444no—
135M32—42no—
136C2×C16C22×D1114yes—
137#107—114no—
138#107—222no—
139#102—224no—
140#102—224no—
141C4×C8D4412yes—
142C4×C8C22×D1112yes—
143C2×C11—41no—
144C2×C11#324511yescharacteristic
145C2×C11C2×#50912yes—
146D11—164no—
147#41—888no—
148C2×Q8—442no—
149C2×D4—224no—
150C2×D4—444no—
151C2×D4—442no—
152C2×D4—442no—
153C22×C4—444no—
154C22×C4D8812yes—
155C22×C4C2×D4411yescharacteristic
156D8—224no—
157D8—224no—
158D8—444no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—41no—
162C2×C8C2×D4412yes—
163C2×C8C2×D4411yescharacteristic
164C2×C8C23×D1111yescharacteristic
165C4⋊C4—224no—
166C4⋊C4—442no—
167C22⋊C4—444no—
168C22⋊C4—444no—
169C42D8811yescharacteristic
170C42D8811yescharacteristic
171C42C2×D4412yes—
172C16—24no—
173C11#3381911yescharacteristic, complemented, Sylow
174C23—444no—
175C23C2×D8811yescharacteristic
176Q8—884no—
177D4—444no—
178D4—444no—
179D4—884no—
180D4—888no—
181D4—884no—
182C2×C4—21no—
183C2×C4—24no—
184C2×C4—21no—
185C2×C4—444no—
186C2×C4—888no—
187C2×C4C2×D8811yescharacteristic
188C2×C4C2×D8812yes—
189C2×C4C2×D8812yes—
190C2×C4C22×D4411yescharacteristic
191C8—22no—
192C8—21no—
193C8#6703711yescharacteristic
194C8#6704011yescharacteristic
195C22—21no—
196C22—22no—
197C22—884no—
198C22—884no—
199C22—884no—
200C22C22×D8811yescharacteristic
201C4—21no—
202C4—22no—
203C4—884no—
204C4#1062252114yes—
205C4#1062304111yescharacteristic
206C4#1062327911yescharacteristic
207C2—41no—
208C2—1764no—
209C2#1307992611yescharacteristic
210C2C2×#1062252112yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2150C2
socleC22×C11C22×D8
hypercenter#2150D11
hypocenterC11#33819
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2150

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13070764C2semidirect
3. #13070719C2semidirect
4. #13070652C2semidirect
5. C11×#2150C2semidirect
73. #2150D11semidirect
173. C11#33819semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130707642
#130707192
#130706522
C11×#21502
#3381911