Finite Group Databasebeta

← #1458×C281 #49090983

Subgroups — #1458×C281 #49090983

Order 35968.

264 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 120 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×#117×C281C211yesmaximal, characteristic
2#431×C281C212yesmaximal, complemented
3#324×C281C212yesmaximal, complemented
4#323×C281C212yesmaximal
5C23×C4×C281C411yescharacteristic
6#117×C281—22no—
7#117×C281—22no—
8C2×C4⋊C4×C281C411yescharacteristic
9C2×C4⋊C4×C281C2211yescharacteristic
10C2×C22⋊C4×C281C411yescharacteristic
11C2×C22⋊C4×C281C2211yescharacteristic
12C2×C42×C281C411yescharacteristic
13C2×C42×C281C2211yescharacteristic
14C4⋊C8×C281—22no—
15C22⋊C8×C281C2214yes—
16C4×C8×C281—22no—
17C24×C281C2×C411yescharacteristic
18C22×C4×C281—21no—
19C22×C4×C281—21no—
20C22×C4×C281—22no—
21C22×C4×C281C814yescomplemented
22C22×C4×C281C2×C411yescharacteristic
23C22×C4×C281C2×C411yescharacteristic
24C22×C4×C281C2×C411yescharacteristic
25C22×C4×C281C2×C411yescharacteristic
26C22×C4×C281C2×C411yescharacteristic
27C22×C4×C281C2311yescharacteristic
28C2×C8×C281—24no—
29C4⋊C4×C281—22no—
30C4⋊C4×C281—22no—
31C22⋊C4×C281—22no—
32C22⋊C4×C281—22no—
33C42×C281—21no—
34C42×C281—21no—
35C42×C281D412yes—
36C42×C281D412yes—
37C23×C281—21no—
38C23×C281—21no—
39C23×C281—41no—
40C23×C281—41no—
41C23×C281C2×C812yes—
42C23×C281C22×C411yescharacteristic
43C2×C4×C281—21no—
44C2×C4×C281—21no—
45C2×C4×C281—24no—
46C2×C4×C281—24no—
47C2×C4×C281—21no—
48C2×C4×C281—21no—
49C2×C4×C281—41no—
50C2×C4×C281—41no—
51C2×C4×C281—41no—
52C2×C4×C281—41no—
53C2×C4×C281C22⋊C412yes—
54C2×C4×C281C22⋊C411yescharacteristic
55C2×C4×C281C22⋊C411yescharacteristic
56C2×C4×C281C2×C812yes—
57C2×C4×C281C2×C812yes—
58C2×C4×C281M1612yes—
59C2×C4×C281C2×D412yes—
60C8×C281—44no—
61C22×C281—21no—
62C22×C281—21no—
63C22×C281—22no—
64C22×C281—42no—
65C22×C281—42no—
66C22×C281—41no—
67C22×C281—41no—
68C22×C281C2×C22⋊C411yescharacteristic
69C22×C281C22×C811yescharacteristic
70C22×C281C2×M1611yescharacteristic
71C4×C281—22no—
72C4×C281—22no—
73C4×C281—22no—
74C4×C281—41no—
75C4×C281—41no—
76C4×C281C22⋊C812yes—
77C4×C281C22⋊C812yes—
78C2×C281—21no—
79C2×C281—21no—
80C2×C281—42no—
81C2×C281C2×C22⋊C811yescharacteristic
82C2×C281#41011yescharacteristic
83C2×C281#41311yescharacteristic
84C281#145811yescharacteristic, direct product factor, Sylow
85#1458C28111yesmaximal, characteristic, direct product factor, Sylow
86C2×#117C2×C28111yescharacteristic
87#431C2×C28112yescomplemented
88#324C2×C28112yescomplemented
89#323C2×C28112yes—
90C23×C4C4×C28111yescharacteristic
91#117—22no—
92#117—22no—
93C2×C4⋊C4C4×C28111yescharacteristic
94C2×C4⋊C4C22×C28111yescharacteristic
95C2×C22⋊C4C4×C28111yescharacteristic
96C2×C22⋊C4C22×C28111yescharacteristic
97C2×C42C4×C28111yescharacteristic
98C2×C42C22×C28111yescharacteristic
99C4⋊C8—22no—
100C22⋊C8C22×C28114yes—
101C4×C8—22no—
102C24C2×C4×C28111yescharacteristic
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—22no—
106C22×C4C8×C28114yescomplemented
107C22×C4C2×C4×C28111yescharacteristic
108C22×C4C2×C4×C28111yescharacteristic
109C22×C4C2×C4×C28111yescharacteristic
110C22×C4C2×C4×C28111yescharacteristic
111C22×C4C2×C4×C28111yescharacteristic
112C22×C4C23×C28111yescharacteristic
113C2×C8—24no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42—21no—
119C42—21no—
120C42D4×C28112yes—
121C42D4×C28112yes—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23C2×C8×C28112yes—
127C23C22×C4×C28111yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—24no—
131C2×C4—24no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4C22⋊C4×C28112yes—
139C2×C4C22⋊C4×C28111yescharacteristic
140C2×C4C22⋊C4×C28111yescharacteristic
141C2×C4C2×C8×C28112yes—
142C2×C4C2×C8×C28112yes—
143C2×C4M16×C28112yes—
144C2×C4C2×D4×C28112yes—
145C8—44no—
146C22—21no—
147C22—21no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22C2×C22⋊C4×C28111yescharacteristic
154C22C22×C8×C28111yescharacteristic
155C22C2×M16×C28111yescharacteristic
156C4—22no—
157C4—22no—
158C4—22no—
159C4—41no—
160C4—41no—
161C4C22⋊C8×C28112yes—
162C4C22⋊C8×C28112yes—
163C2—21no—
164C2—21no—
165C2—42no—
166C2C2×C22⋊C8×C28111yescharacteristic
167C2#410×C28111yescharacteristic
168C2#413×C28111yescharacteristic
subgroupG/H
centerC2×C4×C281C22⋊C4
commutatorC22C22×C8×C281
Frattini, cosocleC22×C4C23×C281
socleC22×C281C2×C22⋊C4
prime radicalC24×C281C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C281 ◁ C2×C42×C281 ◁ G

Complements

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

NH ≅ G/Ntype
2. #431×C281C2semidirect
3. #324×C281C2semidirect
21. C22×C4×C281C8semidirect
84. C281#1458direct (N × H)
85. #1458C281direct (N × H)
87. #431C2×C281semidirect
88. #324C2×C281semidirect
106. C22×C4C8×C281semidirect

Maximal subgroups

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

subgroupindex
C2×#117×C2812
#431×C2812
#324×C2812
#323×C2812
#1458281