Finite Group Databasebeta

← #49094347

Subgroups — #49094347

Order 35968.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824094C211yesmaximal, characteristic
2#31823799C212yesmaximal
3#31823402C211yesmaximal, characteristic
4#31823201C212yesmaximal
5#324×C281C211yesmaximal, characteristic
6#22582878—22no—
7#22582870—22no—
8#22582858—21no—
9#22582858C2212yes—
10#22582838—21no—
11C2×C4⋊Dic281C2211yescharacteristic
12#22582813—22no—
13#22582804—22no—
14#22582786—21no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562D412yes—
21C22×Dic281—21no—
22C22×Dic281—21no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281—22no—
27C4⋊Dic281D412yes—
28#17985117—22no—
29#17985117—22no—
30C22⋊Dic281—22no—
31C4×Dic281—22no—
32C22×C4×C281D411yescharacteristic
33C22×C4×C281D411yescharacteristic
34C22×C4×C281C2311yescharacteristic
35C2×C8×C281—22no—
36C4⋊C4×C281—22no—
37Dic562—42no—
38Dic562—81no—
39C2×Dic281—22no—
40C2×Dic281—22no—
41C2×Dic281—41no—
42C2×Dic281—41no—
43C2×Dic281—42no—
44C2×Dic281—41no—
45C2×Dic281—41no—
46C23×C281C2×D411yescharacteristic
47C2×C4×C281—21no—
48C2×C4×C281—21no—
49C2×C4×C281—21no—
50C2×C4×C281—41no—
51C2×C4×C281—41no—
52C2×C4×C281Q1612yes—
53C2×C4×C281C2×D412yes—
54C8×C281—42no—
55C22×C281—21no—
56C22×C281—21no—
57C22×C281#12011yescharacteristic
58C22×C281C2×Q1611yescharacteristic
59C22×C281#13711yescharacteristic
60C4×C281—22no—
61C4×C281—22no—
62C4×C281—41no—
63Dic281—42no—
64Dic281—42no—
65Dic281—81no—
66Dic281—81no—
67C2×C281—21no—
68C2×C281—21no—
69C2×C281#45111yescharacteristic
70C2×C281#45411yescharacteristic
71C2×C281#45811yescharacteristic
72C281#161711yescharacteristic, complemented, Sylow
73#1617—2811nomaximal, Sylow
74#544—2811no—
75#484—2812no—
76#400—2811no—
77#328—2812no—
78#324D28111yescharacteristic
79C4⋊Q8—5622no—
80#125—5622no—
81C22⋊Q8—2812no—
82C22⋊Q8—5621no—
83#117—5621no—
84C2×C4⋊C4—2811no—
85C2×C4⋊C4C2×D28111yescharacteristic
86#107—5622no—
87#103—5622no—
88C22⋊C8C2×D28112yes—
89#95—2811no—
90#95—5621no—
91#95—5621no—
92C2×Q8—2812no—
93C2×Q8—5621no—
94C22×C4—5621no—
95C22×C4—5621no—
96C22×C4D112411yescharacteristic
97C22×C4D112411yescharacteristic
98C22×C4C22×D28111yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2812no—
102C4⋊C4—5622no—
103C4⋊C4—5621no—
104C4⋊C4—5621no—
105C4⋊C4—5621no—
106C4⋊C4—5622no—
107C4⋊C4—5622no—
108C22⋊C4—5622no—
109C42—5622no—
110C23C2×D112411yescharacteristic
111Q8—11242no—
112Q8—22481no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—5622no—
119C2×C4—5622no—
120C2×C4—11241no—
121C2×C4—11241no—
122C2×C4—11242no—
123C2×C4—11241no—
124C2×C4—11241no—
125C2×C4Dic112412yes—
126C2×C4D4×D28112yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2258284911yescharacteristic
131C22C2×Dic112411yescharacteristic
132C22#2258291211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—11242no—
137C4—11242no—
138C4—22481no—
139C4—22481no—
140C2—21no—
141C2—21no—
142C2#3182362111yescharacteristic
143C2#3182363811yescharacteristic
144C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#324D281
hypocenterC281#1617
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C281#1617semidirect

Maximal subgroups

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

subgroupindex
#318240942
#318237992
#318234022
#318232012
#324×C2812
#1617281