Finite Group Databasebeta

← #49120237

Subgroups — #49120237

Order 36224.

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

normal subgroups only

This group has 238 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#31826623C212yesmaximal
3#31826385C211yesmaximal, characteristic
4#31826203C212yesmaximal
5#324×C283C211yesmaximal, characteristic
6C22×Dic566C2211yescharacteristic
7C2×Dic1132—22no—
8#22583609—22no—
9#22583601—22no—
10#22583589—21no—
11#22583589C2212yes—
12#22583569—21no—
13C2×Dic283⋊C4—21no—
14#22583535—22no—
15C283⋊#95—21no—
16C283⋊#95C2211yescharacteristic
17C2×C4⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C2×Dic566—21no—
20C2×Dic566—22no—
21C2×Dic566—42no—
22C2×Dic566D412yes—
23C22×Dic283—21no—
24C22×Dic283—21no—
25Dic1132—44no—
26C4⋊Dic283—21no—
27C4⋊Dic283—21no—
28C4⋊Dic283—21no—
29C4⋊Dic283D412yes—
30Dic283⋊C4—22no—
31Dic283⋊C4—22no—
32Dic283⋊C4—42no—
33C22⋊Dic283—22no—
34C4×Dic283—22no—
35C22×C4×C283D411yescharacteristic
36C22×C4×C283D411yescharacteristic
37C22×C4×C283C2311yescharacteristic
38C2×C8×C283—22no—
39C4⋊C4×C283—22no—
40Dic566—24no—
41Dic566—42no—
42Dic566—42no—
43Dic566—81no—
44C2×Dic283—22no—
45C2×Dic283—22no—
46C2×Dic283—22no—
47C2×Dic283—22no—
48C2×Dic283—41no—
49C2×Dic283—41no—
50C2×Dic283—41no—
51C2×Dic283—41no—
52C23×C283C2×D411yescharacteristic
53C2×C4×C283—21no—
54C2×C4×C283—21no—
55C2×C4×C283—21no—
56C2×C4×C283—41no—
57C2×C4×C283—41no—
58C2×C4×C283Q1612yescomplemented
59C2×C4×C283C2×D412yes—
60C8×C283—42no—
61C22×C283—21no—
62C22×C283—21no—
63C22×C283#12011yescharacteristic
64C22×C283C2×Q1611yescharacteristic
65C22×C283#13711yescharacteristic
66C4×C283—22no—
67C4×C283—22no—
68C4×C283—41no—
69Dic283—42no—
70Dic283—42no—
71Dic283—42no—
72Dic283—42no—
73C2×C283—21no—
74C2×C283—21no—
75C2×C283#45111yescharacteristic
76C2×C283#45611yescharacteristic
77C2×C283B(4,𝔽2)11yescharacteristic
78C283#160511yescharacteristic, complemented, Sylow
79#1605—2831nomaximal, Sylow
80#544—2831no—
81#451—2832no—
82#395—2831no—
83#328—2832no—
84#324D28311yescharacteristic
85C22×Q8—2831no—
86C2×Q16—5662no—
87C4⋊Q8—5662no—
88#125—5662no—
89C22⋊Q8—2832no—
90C22⋊Q8—5661no—
91#117—5661no—
92C2×C4⋊C4—5661no—
93C2×C4⋊C4C2×D28311yescharacteristic
94#103—5662no—
95C22⋊C8C2×D28312yes—
96#95—2831no—
97#95—5661no—
98C2×Q8—2832no—
99C2×Q8—5661no—
100C2×Q8—5662no—
101C2×Q8—11322no—
102C22×C4—5661no—
103C22×C4—5661no—
104C22×C4D113211yescharacteristic
105C22×C4D113211yescharacteristic
106C22×C4C22×D28311yescharacteristic
107Q16—11324no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—2832no—
111C4⋊C4—5662no—
112C4⋊C4—5661no—
113C4⋊C4—5661no—
114C4⋊C4—5661no—
115C4⋊C4—5662no—
116C4⋊C4—11322no—
117C22⋊C4—5662no—
118C42—5662no—
119C23C2×D113211yescharacteristic
120Q8—5664no—
121Q8—11322no—
122Q8—11322no—
123Q8—22641no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—5662no—
130C2×C4—5662no—
131C2×C4—5662no—
132C2×C4—5662no—
133C2×C4—11321no—
134C2×C4—11321no—
135C2×C4—11321no—
136C2×C4—11321no—
137C2×C4Dic113212yescomplemented
138C2×C4D4×D28312yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#2258358011yescharacteristic
143C22C2×Dic113211yescharacteristic
144C22#2258364311yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—11322no—
149C4—11322no—
150C4—11322no—
151C4—11322no—
152C2—21no—
153C2—21no—
154C2#3182662311yescharacteristic
155C2#3182665011yescharacteristic
156C2#3182665311yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#324×C283C2
socleC22×C283#120
prime radicalC23×C283C2×D4
hypercenter#324D283
hypocenterC283#1605
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
58. C2×C4×C283Q16semidirect
78. C283#1605semidirect
137. C2×C4Dic1132semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318266232
#318263852
#318262032
#324×C2832
#1605283