Finite Group Databasebeta

← #49120303

Subgroups — #49120303

Order 36224.

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

normal subgroups only

This group has 202 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#31826798C212yesmaximal
2#31826404C211yesmaximal, characteristic
3#31826202C212yesmaximal
4#31826191C211yesmaximal, characteristic
5#544×C283C211yesmaximal, characteristic
6C2×C4⋊Dic283C2211yescharacteristic
7#22583543—22no—
8#22583534—22no—
9C22⋊(C283⋊C8)C2212yes—
10C283⋊#95—21no—
11C283⋊#95—21no—
12C283⋊#95C2211yescharacteristic
13C4⋊Q8×C283—22no—
14#125×C283—22no—
15C22⋊Q8×C283—21no—
16C22⋊Q8×C283C2212yes—
17#117×C283—21no—
18C2×C4⋊C4×C283C2211yescharacteristic
19C22×Dic283—21no—
20C22×Dic283—21no—
21C2×C283⋊C8—22no—
22C4⋊Dic283—22no—
23C2×Q8×C283—21no—
24C2×Q8×C283D412yes—
25C22×C4×C283D411yescharacteristic
26C22×C4×C283D411yescharacteristic
27C22×C4×C283C2311yescharacteristic
28C4⋊C4×C283—21no—
29C4⋊C4×C283—21no—
30C4⋊C4×C283—21no—
31C4⋊C4×C283—22no—
32C4⋊C4×C283—22no—
33C4⋊C4×C283—22no—
34C4⋊C4×C283D412yes—
35C22⋊C4×C283—22no—
36C42×C283—22no—
37C2×Dic283—41no—
38C2×Dic283—41no—
39C2×Dic283—42no—
40C2×Dic283—41no—
41C2×Dic283—41no—
42C283⋊C8—42no—
43C23×C283C2×D411yescharacteristic
44Q8×C283—42no—
45Q8×C283—81no—
46C2×C4×C283—21no—
47C2×C4×C283—21no—
48C2×C4×C283—22no—
49C2×C4×C283—22no—
50C2×C4×C283—21no—
51C2×C4×C283—41no—
52C2×C4×C283—41no—
53C2×C4×C283Q1612yes—
54C2×C4×C283C2×D412yes—
55C22×C283—21no—
56C22×C283—21no—
57C22×C283#12011yescharacteristic
58C22×C283C2×Q1611yescharacteristic
59C22×C283#13711yescharacteristic
60C4×C283—22no—
61C4×C283—22no—
62C4×C283—42no—
63C4×C283—41no—
64C4×C283—42no—
65Dic283—81no—
66Dic283—81no—
67C2×C283—21no—
68C2×C283—21no—
69C2×C283#45111yescharacteristic
70C2×C283#45411yescharacteristic
71C2×C283#45811yescharacteristic
72C283#161711yescharacteristic, complemented, Sylow
73#1617—2831nomaximal, Sylow
74#544D28311yescharacteristic
75#484—2832no—
76#400—2831no—
77#328—2832no—
78#324—2831no—
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D28312yes—
83#117—21no—
84C2×C4⋊C4—2831no—
85C2×C4⋊C4C2×D28311yescharacteristic
86#107—5662no—
87#103—5662no—
88C22⋊C8—2832no—
89#95—2831no—
90#95—5661no—
91#95—5661no—
92C2×Q8—21no—
93C2×Q8C22⋊D28312yes—
94C22×C4—5661no—
95C22×C4—5661no—
96C22×C4C22⋊D28311yescharacteristic
97C22×C4C22⋊D28311yescharacteristic
98C22×C4C22×D28311yescharacteristic
99C2×C8—5662no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—5662no—
107C4⋊C4C22⋊D28312yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D28311yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—11321no—
121C2×C4—11321no—
122C2×C4—11322no—
123C2×C4—11321no—
124C2×C4—11321no—
125C2×C4#1798538212yes—
126C2×C4C2×C22⋊D28312yes—
127C8—11322no—
128C22—21no—
129C22—21no—
130C22#2258357911yescharacteristic
131C22C2×#1798538211yescharacteristic
132C22#2258364111yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—22641no—
139C4—22641no—
140C2—21no—
141C2—21no—
142C2#3182662111yescharacteristic
143C2#3182663811yescharacteristic
144C2#3182665511yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#544×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#544D283
hypocenterC283#1617
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
72. C283#1617semidirect

Maximal subgroups

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

subgroupindex
#318267982
#318264042
#318262022
#318261912
#544×C2832
#1617283