Finite Group Databasebeta

← #49094521

Subgroups — #49094521

Order 35968.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#31824193C211yesmaximal, characteristic
2#31823745C211yesmaximal, characteristic
3#31823670C211yesmaximal, characteristic
4#31823212C211yesmaximal, characteristic
5#31823195C211yesmaximal, characteristic
6#31823195C211yesmaximal, characteristic
7#487×C281C211yesmaximal, characteristic
8C2×#17985128—21no—
9#22582878—21no—
10#22582878—21no—
11#22582877—22no—
12C4×Dic562C2211yescharacteristic
13C4×Dic562C2211yescharacteristic
14#22582844—21no—
15#22582844—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582802—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#103×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562—22no—
26C2×Dic562D411yescharacteristic
27C2×Dic562D411yescharacteristic
28#17985128—42no—
29C2×#14555886—21no—
30C2×#14555886—21no—
31C4⋊Dic281D411yescharacteristic
32C4⋊Dic281D411yescharacteristic
33#17985117—22no—
34#17985117—22no—
35#17985117—21no—
36#17985117—21no—
37C4×Dic281—22no—
38C4×Dic281—21no—
39C4×Dic281—21no—
40C2×Q8×C281—21no—
41C2×Q8×C281D412yes—
42C2×C8×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48Dic562—21no—
49Dic562—21no—
50Dic562—82no—
51Dic562SD1612yes—
52Dic562Q1612yescomplemented
53C2×Dic281—21no—
54C2×Dic281—21no—
55C2×Dic281—21no—
56C2×Dic281—21no—
57#14555886—41no—
58#14555886—41no—
59Q8×C281—42no—
60Q8×C281—41no—
61Q8×C281—41no—
62C2×C4×C281—22no—
63C2×C4×C281—41no—
64C2×C4×C281C2×D411yescharacteristic
65C2×C4×C281C2×D411yescharacteristic
66C2×C4×C281C2×D411yescharacteristic
67C8×C281—41no—
68C22×C281#12011yescharacteristic
69C4×C281—21no—
70C4×C281—42no—
71C4×C281—81no—
72C4×C281C2×SD1611yescharacteristic
73C4×C281C2×Q1611yescharacteristic
74C4×C281#13711yescharacteristic
75C4×C281#13711yescharacteristic
76Dic281—22no—
77Dic281—22no—
78Dic281—41no—
79Dic281—41no—
80C2×C281#44811yescharacteristic
81C2×C281#45111yescharacteristic
82C2×C281#45511yescharacteristic
83C281#164511yescharacteristic, complemented, Sylow
84#1645—2811nomaximal, Sylow
85Q82—2811no—
86#487D28111yescharacteristic
87#475—2811no—
88#462—2811no—
89#333—2811no—
90Q8⋊C8—2811no—
91Q8⋊C8—2811no—
92C2×Q16—5621no—
93C4⋊Q8—5621no—
94C4⋊Q8—5621no—
95C4⋊Q8—5622no—
96C4⋊Q8C2×D28111yescharacteristic
97C4⋊Q8C2×D28111yescharacteristic
98C4×Q8—2811no—
99C4×Q8—2811no—
100C4×Q8—5621no—
101C4×Q8—5621no—
102#106—5621no—
103C4⋊C8—2811no—
104C4⋊C8—2811no—
105#103—22no—
106#103—5621no—
107#103—5621no—
108C4×C8C2×D28111yescharacteristic
109C2×Q8—21no—
110C2×Q8—2811no—
111C2×Q8—2811no—
112C2×Q8—5622no—
113C2×Q8C22⋊D28112yes—
114Q16—11242no—
115C2×C8—21no—
116C2×C8—5621no—
117C2×C8—5621no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2811no—
123C4⋊C4—2811no—
124C4⋊C4—5622no—
125C4⋊C4—5622no—
126C4⋊C4—5621no—
127C4⋊C4—5621no—
128C42—5622no—
129C42—5621no—
130C42—5621no—
131C42C22×D28111yescharacteristic
132Q8—42no—
133Q8—41no—
134Q8—41no—
135Q8—2812no—
136Q8—2812no—
137Q8—5621no—
138Q8—5621no—
139Q8—22482no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—5621no—
143C2×C4—5621no—
144C2×C4—5621no—
145C2×C4—5621no—
146C2×C4D4×D28111yescharacteristic
147C2×C4D4×D28111yescharacteristic
148C2×C4C2×C22⋊D28111yescharacteristic
149C8—41no—
150C8—11241no—
151C8—11241no—
152C22#2258284711yescharacteristic
153C4—21no—
154C4—42no—
155C4—81no—
156C4—5622no—
157C4—5622no—
158C4—11241no—
159C4—11241no—
160C4SD16×D28111yescharacteristic
161C4Q16×D28111yescharacteristic
162C4#2258290811yescharacteristic
163C4#2258291111yescharacteristic
164C2#3182360011yescharacteristic
165C2#3182361711yescharacteristic
166C2#3182364011yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#487×C281C2
socle, prime radicalC22×C281#120
hypercenter#487D281
hypocenterC281#1645
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
52. Dic562Q16semidirect
83. C281#1645semidirect

Maximal subgroups

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

subgroupindex
#318241932
#318237452
#318236702
#318232122
#318231952
#487×C2812
#1645281