Finite Group Databasebeta

← #27171660

Subgroups — #27171660

Order 12928.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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#20265944C211yesmaximal, characteristic, complemented
2#20265182C212yesmaximal, complemented
3#20265151C211yesmaximal, characteristic, complemented
4#20264933C212yesmaximal, complemented
5#535×C101C211yesmaximal, characteristic
6#15692262—24no—
7C2×#13108058—22no—
8C2×#13108058C2212yes—
9#15692214C2212yes—
10#15692176—24no—
11#15692170—22no—
12C2×#41×C101C2211yescharacteristic
13C22×D4×C101C2211yescharacteristic
14#127×C101C412yescomplemented
15#124×C101C412yescomplemented
16#121×C101—22no—
17#120×C101—22no—
18#117×C101C2211yescharacteristic
19#13108058—24no—
20#13108058—22no—
21#13108058—22no—
22C2×#11717579—24no—
23C2×#11717579D414yescomplemented
24C4⋊Dic101—22no—
25C22⋊Dic101—22no—
26C4×Dic101—22no—
27C24×C101—21no—
28#41×C101—22no—
29#41×C101—22no—
30C2×Q8×C101C2×C411yescharacteristic
31C2×D4×C101—24no—
32C2×D4×C101—22no—
33C2×D4×C101—21no—
34C2×D4×C101—22no—
35C2×D4×C101C2×C412yes—
36C2×D4×C101C2×C411yescharacteristic
37C2×D4×C101D412yes—
38C22×C4×C101D412yes—
39C22×C4×C101C2311yescharacteristic
40C4⋊C4×C101—21no—
41C22⋊C4×C101—21no—
42C22⋊C4×C101—24no—
43C42×C101C2×C412yes—
44C23×C101—22no—
45C23×C101—42no—
46C23×C101—82no—
47C23×C101C22⋊C412yes—
48C23×C101C2×D411yescharacteristic
49Q8×C101—22no—
50D4×C101—24no—
51D4×C101—22no—
52D4×C101—24no—
53D4×C101—41no—
54D4×C101—41no—
55D4×C101—84no—
56C2×C4×C101—22no—
57C2×C4×C101—22no—
58C2×C4×C101—22no—
59C2×C4×C101C22⋊C412yes—
60C2×C4×C101C22×C411yescharacteristic
61C2×C4×C101C2×D412yes—
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101#4112yes—
64C2×Dic101—42no—
65#11717579—24no—
66C22×C101—22no—
67C22×C101—41no—
68C22×C101—42no—
69C22×C101—44no—
70C22×C101—42no—
71C22×C101—84no—
72C22×C101C2×C22⋊C411yescharacteristic
73C22×C101#12112yes—
74C4×C101—22no—
75C4×C101—42no—
76C4×C101C4×D412yes—
77C4×C101#12011yescharacteristic
78C4×C101#12311yescharacteristic
79Dic101—82no—
80C2×C101—22no—
81C2×C101—21no—
82C2×C101—42no—
83C2×C101—82no—
84C2×C101#38611yescharacteristic
85#1910—1011nomaximal, Sylow
86C101#191011yescharacteristic, complemented, Sylow
87#568—1011no—
88#535D10111yescharacteristic
89#418—1012no—
90#410—1011no—
91H(3,ℤ/4)—1012no—
92C2×#41C2×D10111yescharacteristic
93C22×D4C2×D10111yescharacteristic
94#131—2024no—
95C2×M16—1012no—
96C2×M16—2022no—
97#127Dic10112yescomplemented
98#124Dic10112yescomplemented
99#121—22no—
100#120—22no—
101#117—1012no—
102#117C2×D10111yescharacteristic
103#102—2024no—
104#99—2022no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic10111yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic10112yes—
114C2×D4C2×Dic10111yescharacteristic
115C2×D4C22⋊D10112yes—
116C22×C4C22⋊D10112yes—
117C22×C4C22×D10111yescharacteristic
118M16—2024no—
119M16—2022no—
120M16—2022no—
121C2×C8—1014no—
122C2×C8—2024no—
123C4⋊C4—21no—
124C4⋊C4—2022no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—2022no—
128C42—2022no—
129C42C2×Dic10112yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic10112yes—
134C23C2×C22⋊D10111yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—4042no—
146C2×C4C22⋊Dic10112yes—
147C2×C4C22×Dic10111yescharacteristic
148C2×C4D4×D10112yes—
149C2×C4C2×C22⋊D10111yescharacteristic
150C2×C4#1310807312yes—
151C8—2024no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic10111yescharacteristic
159C22#1569222712yes—
160C4—22no—
161C4—42no—
162C4—8082no—
163C4D4×Dic10112yes—
164C4#1569222311yescharacteristic
165C4#1569223611yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2026505711yescharacteristic
subgroupG/H
centerC2#20265057
commutatorC2×C4×C101C22×C4
FrattiniC22×C4C22×D101
Fitting, prime radical#535×C101C2
socleC2×C101#386
cosocleC22×C4×C101C23
hypercenter#535D101
hypocenterC101#1910
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20265944C2semidirect
2. #20265182C2semidirect
3. #20265151C2semidirect
4. #20264933C2semidirect
14. #127×C101C4semidirect
15. #124×C101C4semidirect
23. C2×#11717579D4semidirect
86. C101#1910semidirect
97. #127Dic101semidirect
98. #124Dic101semidirect

Maximal subgroups

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

subgroupindex
#202659442
#202651822
#202651512
#202649332
#535×C1012
#1910101