Finite Group Databasebeta

← #49094344

Subgroups — #49094344

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#31823798C212yesmaximal
3#31823199C212yesmaximal
4#31823189C211yesmaximal, characteristic
5#400×C281C211yesmaximal, characteristic
6#22582878—22no—
7#22582870—22no—
8#22582858—21no—
9#22582858C2212yes—
10#22582838—21no—
11#22582812—22no—
12#22582802—22no—
13C22⋊#14555886C2212yes—
14C2×C4⋊C4×C281C2211yescharacteristic
15C2×C4⋊C4×C281C2211yescharacteristic
16#95×C281—21no—
17#95×C281—21no—
18#95×C281C2211yescharacteristic
19C2×Dic562—21no—
20C2×Dic562D412yes—
21C2×#14555886—22no—
22C4⋊Dic281—21no—
23C4⋊Dic281—21no—
24C4⋊Dic281—21no—
25C4⋊Dic281D412yes—
26#17985117—22no—
27#17985117—22no—
28C22⋊Dic281—22no—
29C4×Dic281—22no—
30C22×C4×C281—21no—
31C22×C4×C281—21no—
32C22×C4×C281D411yescharacteristic
33C22×C4×C281D411yescharacteristic
34C22×C4×C281C2311yescharacteristic
35C4⋊C4×C281—22no—
36C4⋊C4×C281—22no—
37Dic562—42no—
38Dic562—81no—
39C2×Dic281—22no—
40C2×Dic281—22no—
41#14555886—42no—
42C23×C281C2×D411yescharacteristic
43C2×C4×C281—21no—
44C2×C4×C281—21no—
45C2×C4×C281—21no—
46C2×C4×C281—41no—
47C2×C4×C281—41no—
48C2×C4×C281—41no—
49C2×C4×C281—41no—
50C2×C4×C281—42no—
51C2×C4×C281—41no—
52C2×C4×C281—41no—
53C2×C4×C281Q1612yes—
54C2×C4×C281C2×D412yes—
55C22×C281—21no—
56C22×C281—21no—
57C22×C281#12011yescharacteristic
58C22×C281C2×Q1611yescharacteristic
59C22×C281#13711yescharacteristic
60C4×C281—22no—
61C4×C281—22no—
62C4×C281—41no—
63C4×C281—81no—
64C4×C281—81no—
65Dic281—42no—
66Dic281—42no—
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#400D28111yescharacteristic
77#328—2812no—
78#324—2811no—
79C4⋊Q8—5622no—
80#125—5622no—
81C22⋊Q8—2812no—
82C22⋊Q8—5621no—
83#117—5621no—
84C2×C4⋊C4C2×D28111yescharacteristic
85C2×C4⋊C4C2×D28111yescharacteristic
86#107—5622no—
87#103—5622no—
88C22⋊C8—2812no—
89#95—21no—
90#95—21no—
91#95C2×D28111yescharacteristic
92C2×Q8—2812no—
93C2×Q8—5621no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D28111yescharacteristic
97C22×C4C22⋊D28111yescharacteristic
98C22×C4C22×D28111yescharacteristic
99C2×C8—5622no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—2812no—
103C4⋊C4—5622no—
104C4⋊C4—5621no—
105C4⋊C4—5621no—
106C4⋊C4—5621no—
107C4⋊C4—5622no—
108C22⋊C4—5622no—
109C42—5622no—
110C23C2×C22⋊D28111yescharacteristic
111Q8—11242no—
112Q8—22481no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—5622no—
124C2×C4—5622no—
125C2×C4#1798512812yes—
126C2×C4D4×D28112yes—
127C8—11242no—
128C22—21no—
129C22—21no—
130C22#2258284711yescharacteristic
131C22C2×#1798512811yescharacteristic
132C22#2258290911yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—11242no—
139C4—11242no—
140C2—21no—
141C2—21no—
142C2#3182361811yescharacteristic
143C2#3182363511yescharacteristic
144C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#400×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
hypercenter#400D281
hypocenterC281#1617
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

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
#318237982
#318231992
#318231892
#400×C2812
#1617281