Finite Group Databasebeta

← #14658755

Subgroups — #14658755

Order 2816.

372 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 101 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#13069414C211yesmaximal, characteristic
2#13068791C211yesmaximal, characteristic, complemented
3#13067387C212yesmaximal, complemented
4#13067042C212yesmaximal
5C11×#1275C211yesmaximal, characteristic, complemented
6C2×C4×D44C2211yescharacteristic
7C11×#431C2212yes—
8C2×C11×#97C2211yescharacteristic
9C2×(C2×D11)⋊C8—22no—
10C2×#66883—22no—
11#10622537C2212yes—
12C2×C4⋊(C11⋊C8)C2211yescharacteristic
13#10622097—24no—
14#10622095—24no—
15C22×D44Q811yescharacteristic
16C22×C4×D11—21no—
17C22×C8×C11D412yes—
18C2×C42×C11C2311yescharacteristic
19C2×(C2×D11)⋊C4—21no—
20C2×C4⋊Dic11Q811yescharacteristic
21C2×#4318—22no—
22C22×C11⋊C8—21no—
23C4×D44—22no—
24C4×D44—22no—
25C11×C4⋊C8—22no—
26C11×C22⋊C8—22no—
27C11×#97—22no—
28C4×C8×C11D414yes—
29(C2×D11)⋊C8—44no—
30#66883—44no—
31C4⋊(C11⋊C8)—22no—
32C4⋊(C11⋊C8)—22no—
33C4⋊(C11⋊C8)—22no—
34#10661—111nomaximal, Sylow
35C23×D11—21no—
36C22×C4×C11C2×D411yescharacteristic
37C22×C4×C11C2×Q811yescharacteristic
38C22×C4×C11#4111yescharacteristic
39C22×Dic11—21no—
40C2×D44—22no—
41C2×D44—42no—
42C2×C4×D11—41no—
43C2×C4×D11—41no—
44C2×C4×D11—42no—
45C2×C4×D11—42no—
46C2×C8×C11—22no—
47C2×C8×C11—24no—
48C2×C8×C11—22no—
49C2×C8×C11SD1614yes—
50C42×C11C2×D412yes—
51C42×C11#4112yes—
52(C2×D11)⋊C4—42no—
53C4⋊Dic11—22no—
54#4318—44no—
55C2×C11⋊C8—41no—
56C2×C11⋊C8—42no—
57C2×C11⋊C8—42no—
58#1955—111no—
59#1849—111no—
60#1570—112no—
61#1486—112no—
62#1275D1111yescharacteristic, complemented
63C23×C11C22⋊Q811yescharacteristic
64C22×D11—22no—
65C22×D11—41no—
66C22×D11—42no—
67C22×D11—41no—
68C22×D11—42no—
69C2×C4×C11—41no—
70C2×C4×C11—41no—
71C2×C4×C11C22⋊Q812yes—
72C2×C4×C11#12312yes—
73C2×C4×C11#12311yescharacteristic
74C2×C4×C11#12711yescharacteristic
75C2×C4×C11C2×SD1612yes—
76C2×C4×C11AGL(1,ℤ/8)12yes—
77C2×Dic11—41no—
78C2×Dic11—42no—
79D44—24no—
80D44—42no—
81C4×D11—82no—
82C4×D11—81no—
83C4×D11—81no—
84C8×C11—24no—
85C8×C11—44no—
86C11⋊C8—81no—
87C11⋊C8—82no—
88C2×C4×D4—111no—
89#431C2×D1112yes—
90C2×#108—222no—
91#423—112no—
92C2×C4⋊C8—111no—
93C2×C22⋊C8—222no—
94C2×#97C2×D1111yescharacteristic
95#334—224no—
96D4⋊C8—224no—
97C22×C11—21no—
98C22×C11—21no—
99C22×C11#39911yescharacteristic
100C22×C11#47612yes—
101C2×D11—44no—
102C2×D11—42no—
103C2×D11—82no—
104C2×D11—81no—
105C2×D11—81no—
106C4×C11—22no—
107C4×C11—22no—
108C4×C11#48112yes—
109C4×C11#49211yescharacteristic
110C4×C11#49611yescharacteristic
111Dic11—81no—
112C22×D4—111no—
113C23×C4—221no—
114C2×M16—222no—
115C22×C8—221no—
116C22×C8D4412yes—
117C4×D4—222no—
118C4×D4—222no—
119C2×C4⋊C4—111no—
120C2×C22⋊C4—221no—
121C2×C42C22×D1111yescharacteristic
122#108—444no—
123C4⋊C8—22no—
124C4⋊C8—222no—
125C4⋊C8—222no—
126C4⋊C8—222no—
127C22⋊C8—22no—
128C22⋊C8—444no—
129#97—22no—
130C4×C8D4414yes—
131C2×C11—22no—
132C2×C11#209111yescharacteristic
133C2×C11#209411yescharacteristic
134C2×C11#209811yescharacteristic
135D11—82no—
136C24—221no—
137C2×D4—222no—
138C2×D4—442no—
139C22×C4—221no—
140C22×C4—441no—
141C22×C4—441no—
142C22×C4—442no—
143C22×C4—442no—
144C22×C4C2×D4411yescharacteristic
145C22×C4#434111yescharacteristic
146C22×C4Q8×D1111yescharacteristic
147M16—444no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—24no—
151C2×C8—441no—
152C2×C8—442no—
153C2×C8—442no—
154C2×C8#431414yes—
155C4⋊C4—222no—
156C22⋊C4—442no—
157C42C2×D4412yes—
158C42#434112yes—
159C11#1066111yescharacteristic, complemented, Sylow
160C23—222no—
161C23—441no—
162C23—442no—
163C23—441no—
164C23—442no—
165C23#6695011yescharacteristic
166D4—224no—
167D4—442no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—441no—
171C2×C4—442no—
172C2×C4—881no—
173C2×C4—881no—
174C2×C4—882no—
175C2×C4#6692711yescharacteristic
176C2×C4#6693912yes—
177C2×C4#6693911yescharacteristic
178C2×C4#6695012yes—
179C2×C4C2×#431412yes—
180C2×C4#6696112yes—
181C8—24no—
182C8—44no—
183C8—881no—
184C8—882no—
185C22—21no—
186C22—21no—
187C22—444no—
188C22—442no—
189C22—882no—
190C22—881no—
191C22—881no—
192C22#1062229011yescharacteristic
193C22#1062245512yes—
194C4—22no—
195C4—22no—
196C4—881no—
197C4#1062230611yescharacteristic
198C4#1062232511yescharacteristic
199C4#1062234812yes—
200C2—22no—
201C2—882no—
202C2#1307013311yescharacteristic
203C2#1307014811yescharacteristic
204C2#1307017011yescharacteristic
subgroupG/H
centerC2×C4#66927
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1275C2
socleC22×C11#399
prime radicalC22×D44Q8
hypercenter#1275D11
hypocenterC11#10661
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
2. #13068791C2semidirect
3. #13067387C2semidirect
5. C11×#1275C2semidirect
62. #1275D11semidirect
159. C11#10661semidirect

Maximal subgroups

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

subgroupindex
#130694142
#130687912
#130673872
#130670422
C11×#12752
#1066111