Finite Group Databasebeta

← #49120305

Subgroups — #49120305

Order 36224.

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#31827096C211yesmaximal, characteristic
2#31826801C212yesmaximal
3#31826404C211yesmaximal, characteristic
4#31826203C212yesmaximal
5#324×C283C211yesmaximal, characteristic
6#22583609—22no—
7#22583601—22no—
8#22583589—21no—
9#22583589C2212yes—
10#22583569—21no—
11C2×C4⋊Dic283C2211yescharacteristic
12#22583544—22no—
13#22583535—22no—
14C283⋊#95—21no—
15C283⋊#95—21no—
16C283⋊#95C2211yescharacteristic
17C2×C4⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C2×Dic566—21no—
20C2×Dic566D412yes—
21C22×Dic283—21no—
22C22×Dic283—21no—
23C4⋊Dic283—21no—
24C4⋊Dic283—21no—
25C4⋊Dic283—21no—
26C4⋊Dic283—22no—
27C4⋊Dic283D412yes—
28Dic283⋊C4—22no—
29Dic283⋊C4—22no—
30C22⋊Dic283—22no—
31C4×Dic283—22no—
32C22×C4×C283D411yescharacteristic
33C22×C4×C283D411yescharacteristic
34C22×C4×C283C2311yescharacteristic
35C2×C8×C283—22no—
36C4⋊C4×C283—22no—
37Dic566—42no—
38Dic566—81no—
39C2×Dic283—22no—
40C2×Dic283—22no—
41C2×Dic283—41no—
42C2×Dic283—41no—
43C2×Dic283—42no—
44C2×Dic283—41no—
45C2×Dic283—41no—
46C23×C283C2×D411yescharacteristic
47C2×C4×C283—21no—
48C2×C4×C283—21no—
49C2×C4×C283—21no—
50C2×C4×C283—41no—
51C2×C4×C283—41no—
52C2×C4×C283Q1612yes—
53C2×C4×C283C2×D412yes—
54C8×C283—42no—
55C22×C283—21no—
56C22×C283—21no—
57C22×C283#12011yescharacteristic
58C22×C283C2×Q1611yescharacteristic
59C22×C283#13711yescharacteristic
60C4×C283—22no—
61C4×C283—22no—
62C4×C283—41no—
63Dic283—42no—
64Dic283—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#544—2831no—
75#484—2832no—
76#400—2831no—
77#328—2832no—
78#324D28311yescharacteristic
79C4⋊Q8—5662no—
80#125—5662no—
81C22⋊Q8—2832no—
82C22⋊Q8—5661no—
83#117—5661no—
84C2×C4⋊C4—2831no—
85C2×C4⋊C4C2×D28311yescharacteristic
86#107—5662no—
87#103—5662no—
88C22⋊C8C2×D28312yes—
89#95—2831no—
90#95—5661no—
91#95—5661no—
92C2×Q8—2832no—
93C2×Q8—5661no—
94C22×C4—5661no—
95C22×C4—5661no—
96C22×C4D113211yescharacteristic
97C22×C4D113211yescharacteristic
98C22×C4C22×D28311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—2832no—
102C4⋊C4—5662no—
103C4⋊C4—5661no—
104C4⋊C4—5661no—
105C4⋊C4—5661no—
106C4⋊C4—5662no—
107C4⋊C4—5662no—
108C22⋊C4—5662no—
109C42—5662no—
110C23C2×D113211yescharacteristic
111Q8—11322no—
112Q8—22641no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—5662no—
119C2×C4—5662no—
120C2×C4—11321no—
121C2×C4—11321no—
122C2×C4—11322no—
123C2×C4—11321no—
124C2×C4—11321no—
125C2×C4Dic113212yes—
126C2×C4D4×D28312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2258358011yescharacteristic
131C22C2×Dic113211yescharacteristic
132C22#2258364311yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—11322no—
137C4—11322no—
138C4—22641no—
139C4—22641no—
140C2—21no—
141C2—21no—
142C2#3182662311yescharacteristic
143C2#3182664011yescharacteristic
144C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#324D283
hypocenterC283#1617
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

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
#318270962
#318268012
#318264042
#318262032
#324×C2832
#1617283