Finite Group Databasebeta

← #27179451

Subgroups — #27179451

Order 12928.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×C4×Dic101C211yesmaximal, characteristic, complemented
2#20265065C214yesmaximal, complemented
3#20265058C214yesmaximal, complemented
4#20265057C212yesmaximal
5#20265049C212yesmaximal, complemented
6#20265040C211yesmaximal, characteristic, complemented
7C2×#123×C101C211yesmaximal, characteristic
8C23×Dic101C2212yes—
9C2×#13108053C2214yes—
10C2×C22⋊Dic101C2212yes—
11C2×C22⋊Dic101C2214yes—
12C2×C4×Dic101—24no—
13C2×C4×Dic101C2214yes—
14#15692162C2214yes—
15#15692162C2214yes—
16#15692162C2214yes—
17C22×D4×C101C2211yescharacteristic
18C23×C4×C101C2211yescharacteristic
19#123×C101—24no—
20C2×C4⋊C4×C101C2212yes—
21C2×C22⋊C4×C101C2211yescharacteristic
22C2×C22⋊C4×C101C2212yes—
23C22×Dic101—24no—
24C22×Dic101—28no—
25C22×Dic101C2314yes—
26C22×Dic101C2314yes—
27#13108053—28no—
28C22⋊Dic101—24no—
29C22⋊Dic101—28no—
30C4×Dic101—28no—
31C24×C101C2311yescharacteristic
32C24×C101C2311yescharacteristic
33C2×D4×C101—22no—
34C2×D4×C101—24no—
35C22×C4×C101—24no—
36C22×C4×C101D414yes—
37C22×C4×C101C2312yes—
38C22×C4×C101C2311yescharacteristic
39C22×C4×C101C2312yes—
40C4⋊C4×C101—24no—
41C22⋊C4×C101—22no—
42C22⋊C4×C101—24no—
43C23×C101—24no—
44C23×C101—21no—
45C23×C101—22no—
46C23×C101—24no—
47C23×C101C2×D412yes—
48C23×C101#4114yes—
49C23×C101C2411yescharacteristic
50D4×C101—44no—
51C2×C4×C101—28no—
52C2×C4×C101—24no—
53C2×C4×C101—22no—
54C2×C4×C101—21no—
55C2×C4×C101—22no—
56C2×C4×C101—24no—
57C2×C4×C101C2×D414yes—
58C2×Dic101—216no—
59C2×Dic101—24no—
60C2×Dic101—24no—
61C2×Dic101—24no—
62C2×Dic101—24no—
63C2×Dic101—24no—
64C2×Dic101#4118yes—
65C22×C101—24no—
66C22×C101—28no—
67C22×C101—41no—
68C22×C101—42no—
69C22×C101—44no—
70C22×C101#12314yes—
71C22×C101C22×D411yescharacteristic
72C22×C101C2×#4114yes—
73C22×C101C2×#4112yes—
74C4×C101—24no—
75C4×C101—41no—
76C4×C101—42no—
77Dic101—28no—
78Dic101—44no—
79C2×C101—24no—
80C2×C101—81no—
81C2×C101C2×#12311yescharacteristic
82C2×C101#52512yes—
83C2×C101#52914yes—
84#2853—1011nomaximal, Sylow
85C101#285311yescharacteristic, complemented, Sylow
86C2×#123D10111yescharacteristic
87C22×C42—1011no—
88#388—1014no—
89#387—1014no—
90#386—1012no—
91#385—1012no—
92#381—1011no—
93C22×D4C2×D10111yescharacteristic
94C23×C4—1012no—
95C23×C4C2×D10111yescharacteristic
96#123—24no—
97C2×C4⋊C4—1014no—
98C2×C4⋊C4C2×D10112yes—
99C2×C22⋊C4—1012no—
100C2×C22⋊C4—1014no—
101C2×C22⋊C4C2×D10111yescharacteristic
102C2×C22⋊C4C2×D10112yes—
103C2×C42—1014no—
104C2×C42—2024no—
105#95—1014no—
106#95—1014no—
107#95—1014no—
108C24C22×D10111yescharacteristic
109C24C22×D10111yescharacteristic
110C2×D4—22no—
111C2×D4—24no—
112C22×C4—24no—
113C22×C4—1014no—
114C22×C4—1014no—
115C22×C4—2028no—
116C22×C4—2024no—
117C22×C4C22⋊D10114yes—
118C22×C4C22×D10111yescharacteristic
119C22×C4C22×D10112yes—
120C22×C4C22×D10112yes—
121C4⋊C4—24no—
122C4⋊C4—2028no—
123C22⋊C4—22no—
124C22⋊C4—24no—
125C22⋊C4—2028no—
126C22⋊C4—2024no—
127C42—2028no—
128C23—24no—
129C23—21no—
130C23—24no—
131C23—22no—
132C23C2×C22⋊D10112yes—
133C23#1310807314yes—
134C23C23×D10111yescharacteristic
135D4—44no—
136C2×C4—24no—
137C2×C4—28no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—1018no—
143C2×C4—2024no—
144C2×C4—2024no—
145C2×C4—2024no—
146C2×C4—20216no—
147C2×C4—2024no—
148C2×C4—2024no—
149C2×C4C2×C22⋊D10114yes—
150C22—24no—
151C22—28no—
152C22—41no—
153C22—42no—
154C22—44no—
155C22#1569223614yes—
156C22C22×C22⋊D10111yescharacteristic
157C22#41×D10114yes—
158C22C2×#1310807312yes—
159C4—24no—
160C4—41no—
161C4—42no—
162C4—4044no—
163C4—2028no—
164C2—24no—
165C2—81no—
166C2C2×#1569223611yescharacteristic
167C2#2026568412yes—
168C2#2026570414yes—
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
FittingC2×#123×C101C2
prime radicalC22×D4×C101C22
hypercenterC2×#123D101
hypocenterC101#2853
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic101C2semidirect
2. #20265065C2semidirect
3. #20265058C2semidirect
5. #20265049C2semidirect
6. #20265040C2semidirect
85. C101#2853semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1012
#202650652
#202650582
#202650572
#202650492
#202650402
C2×#123×C1012
#2853101