Finite Group Databasebeta

← #49093565

Subgroups — #49093565

Order 35968.

476 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22582786C213yesmaximal
2C2×#22582786C213yesmaximal
3C2×#95×C281C211yesmaximal, characteristic
4C23×Dic281C2213yes—
5C23×Dic281C2211yescharacteristic
6#22582786—26no—
7#22582786—26no—
8C23×C4×C281C2213yes—
9#95×C281C414yescomplemented
10C22×Dic281—23no—
11C22×Dic281—23no—
12C22×Dic281—23no—
13C22×Dic281—23no—
14C22×Dic281—23no—
15C22×Dic281—23no—
16C22×Dic281—23no—
17C22×Dic281—23no—
18C22×Dic281D416yes—
19C22×Dic281Q812yes—
20C24×C281C2311yescharacteristic
21C22×C4×C281—23no—
22C22×C4×C281—23no—
23C22×C4×C281—23no—
24C22×C4×C281—23no—
25C22×C4×C281—23no—
26C22×C4×C281—23no—
27C22×C4×C281C2×C416yes—
28C2×Dic281—26no—
29C2×Dic281—26no—
30C2×Dic281—26no—
31C2×Dic281—26no—
32C2×Dic281—43no—
33C2×Dic281—43no—
34C2×Dic281—43no—
35C2×Dic281—41no—
36C2×Dic281—43no—
37C2×Dic281—43no—
38C23×C281C22×C411yescharacteristic
39C23×C281C2×D413yes—
40C23×C281C2×Q811yescharacteristic
41C23×C281#4113yes—
42C23×C281#4113yes—
43C23×C281#4113yes—
44C23×C281#4111yescharacteristic
45C2×C4×C281—26no—
46C2×C4×C281—26no—
47C2×C4×C281—26no—
48C2×C4×C281—43no—
49C2×C4×C281—43no—
50C2×C4×C281—43no—
51C2×C4×C281—43no—
52C22×C281#11713yes—
53C22×C281C4×D413yes—
54C22×C281C4×Q811yescharacteristic
55C22×C281#12113yes—
56C22×C281C22⋊Q813yes—
57C22×C281#12313yes—
58C22×C281#12313yes—
59C22×C281#12413yes—
60C22×C281#12513yes—
61C22×C281#12613yes—
62C22×C281#12611yescharacteristic
63C22×C281#12613yes—
64C22×C281#12613yes—
65C4×C281—46no—
66Dic281—42no—
67Dic281—46no—
68C2×C281#38311yescharacteristic
69C2×C281#38713yes—
70C2×C281#38813yes—
71C2×C281#39611yescharacteristic
72C2×C281#39713yes—
73C2×C281#40013yes—
74C2×C281#40111yescharacteristic
75C281#144311yescharacteristic, complemented, Sylow
76#1443—2811nomaximal, Sylow
77C2×#95—2813no—
78C2×#95—2813no—
79C2×#95D28111yescharacteristic
80C23×C4—2813no—
81C23×C4—2811no—
82C23×C4C2×D28113yes—
83#95—5626no—
84#95—5626no—
85#95Dic28114yescomplemented
86C24C22×D28111yescharacteristic
87C22×C4—23no—
88C22×C4—23no—
89C22×C4—23no—
90C22×C4—23no—
91C22×C4—23no—
92C22×C4—23no—
93C22×C4—2816no—
94C22×C4—2812no—
95C22×C4—5623no—
96C22×C4—5623no—
97C22×C4—5623no—
98C22×C4—5623no—
99C22×C4—5623no—
100C22×C4—5623no—
101C22×C4—5623no—
102C22×C4—5623no—
103C22×C4C2×Dic28116yes—
104C23C22×Dic28111yescharacteristic
105C23D4×D28113yes—
106C23Q8×D28111yescharacteristic
107C23#1798513713yes—
108C23#1798513813yes—
109C23#1798513813yes—
110C23#1798513911yescharacteristic
111C2×C4—26no—
112C2×C4—26no—
113C2×C4—26no—
114C2×C4—43no—
115C2×C4—43no—
116C2×C4—43no—
117C2×C4—43no—
118C2×C4—5626no—
119C2×C4—5626no—
120C2×C4—5626no—
121C2×C4—5626no—
122C2×C4—11243no—
123C2×C4—11243no—
124C2×C4—11243no—
125C2×C4—11241no—
126C2×C4—11243no—
127C2×C4—11243no—
128C22#2258283813yes—
129C22D4×Dic28113yes—
130C22Q8×Dic28111yescharacteristic
131C22#2258285213yes—
132C22#2258285713yes—
133C22#2258286113yes—
134C22#2258286413yes—
135C22#2258286513yes—
136C22#2258286913yes—
137C22#2258287213yes—
138C22#2258287311yescharacteristic
139C22#2258287313yes—
140C22#2258287413yes—
141C4—46no—
142C4—11242no—
143C4—11246no—
144C2#3182333111yescharacteristic
145C2#3182334913yes—
146C2#3182335613yes—
147C2#3182338711yescharacteristic
148C2#3182339213yes—
149C2#3182340413yes—
150C2C281⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D281
commutatorC23×C281C22×C4
FittingC2×#95×C281C2
socle, prime radical, cosocleC24×C281C23
hypercenterC2×#95D281
hypocenterC281#1443
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
9. #95×C281C4semidirect
75. C281#1443semidirect
85. #95Dic281semidirect

Maximal subgroups

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

subgroupindex
C2×#225827862
C2×#95×C2812
#1443281