Finite Group Databasebeta

← #49119592

Subgroups — #49119592

Order 36224.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#22583566C211yesmaximal, characteristic
2#31826519C212yesmaximal, complemented
3#31826190C212yesmaximal, complemented
4#31826189C211yesmaximal, characteristic
5#323×C283C211yesmaximal, characteristic
6C23×Dic283C411yescharacteristic
7#22583566—22no—
8#22583566—22no—
9C2×Dic283⋊C4C411yescharacteristic
10C2×Dic283⋊C4C2211yescharacteristic
11C2×C22⋊Dic283C411yescharacteristic
12C2×C4×Dic283C411yescharacteristic
13C2×C4×Dic283C2211yescharacteristic
14Dic283⋊C8—22no—
15C22⋊(C283⋊C8)C2212yes—
16#22583520—22no—
17C2×C22⋊C4×C283C2211yescharacteristic
18C22⋊C8×C283C2212yes—
19C22×Dic283—21no—
20C22×Dic283—21no—
21C22×Dic283—22no—
22C22×Dic283—22no—
23C22×Dic283C2×C411yescharacteristic
24C22×Dic283C2×C411yescharacteristic
25C22×Dic283C2×C411yescharacteristic
26C22×Dic283C2×C411yescharacteristic
27C2×C283⋊C8—22no—
28Dic283⋊C4—22no—
29Dic283⋊C4—22no—
30C22⋊Dic283—22no—
31C4×Dic283—21no—
32C4×Dic283—21no—
33C4×Dic283D412yes—
34C4×Dic283D412yes—
35C24×C283C2×C411yescharacteristic
36C22×C4×C283C2×C411yescharacteristic
37C22×C4×C283C2311yescharacteristic
38C2×C8×C283—22no—
39C22⋊C4×C283—22no—
40C2×Dic283—24no—
41C2×Dic283—24no—
42C2×Dic283—21no—
43C2×Dic283—21no—
44C2×Dic283—21no—
45C2×Dic283—21no—
46C2×Dic283—21no—
47C2×Dic283—41no—
48C2×Dic283—41no—
49C2×Dic283C22⋊C411yescharacteristic
50C2×Dic283C22⋊C411yescharacteristic
51C2×Dic283C22⋊C412yes—
52C2×Dic283M1612yes—
53C283⋊C8—42no—
54C23×C283—21no—
55C23×C283—21no—
56C23×C283—41no—
57C23×C283—41no—
58C23×C283M1612yes—
59C23×C283C22×C411yescharacteristic
60C2×C4×C283—21no—
61C2×C4×C283—41no—
62C2×C4×C283—41no—
63C2×C4×C283C2×D412yes—
64C8×C283—42no—
65C22×C283—21no—
66C22×C283—21no—
67C22×C283—22no—
68C22×C283—42no—
69C22×C283—42no—
70C22×C283—41no—
71C22×C283—41no—
72C22×C283C2×C22⋊C411yescharacteristic
73C22×C283C2×M1611yescharacteristic
74C22×C283C2×M1611yescharacteristic
75C4×C283—22no—
76C4×C283—41no—
77Dic283—21no—
78Dic283—21no—
79Dic283—22no—
80Dic283—22no—
81Dic283—41no—
82C2×C283—21no—
83C2×C283—21no—
84C2×C283—42no—
85C2×C283#40711yescharacteristic
86C2×C283#41011yescharacteristic
87C2×C283#41311yescharacteristic
88C283#146411yescharacteristic, complemented, Sylow
89#1464—2831nomaximal, Sylow
90C2×#117—2831no—
91#432—2832no—
92#324—2832no—
93#323—2831no—
94#323D28311yescharacteristic
95C23×C4—2831no—
96#117—5662no—
97#117—5662no—
98C2×C4⋊C4—2831no—
99C2×C4⋊C4—2831no—
100C2×C22⋊C4—2831no—
101C2×C22⋊C4C2×D28311yescharacteristic
102C2×C42—2831no—
103C2×C42—2831no—
104C4⋊C8—5662no—
105C22⋊C8—2832no—
106C22⋊C8C2×D28312yes—
107#97—5662no—
108C24C4×D28311yescharacteristic
109C22×C4—2831no—
110C22×C4—2831no—
111C22×C4—2831no—
112C22×C4—2831no—
113C22×C4—5661no—
114C22×C4—5661no—
115C22×C4—5662no—
116C22×C4—5662no—
117C22×C4C4×D28311yescharacteristic
118C22×C4C22×D28311yescharacteristic
119C2×C8—22no—
120C2×C8—5662no—
121C4⋊C4—5662no—
122C4⋊C4—5662no—
123C22⋊C4—22no—
124C22⋊C4—5662no—
125C42—2832no—
126C42—2832no—
127C42—5661no—
128C42—5661no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23#1798537512yes—
134C23C2×C4×D28311yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—2831no—
139C2×C4—2831no—
140C2×C4—2832no—
141C2×C4—2832no—
142C2×C4—5664no—
143C2×C4—5664no—
144C2×C4—5661no—
145C2×C4—5661no—
146C2×C4—5661no—
147C2×C4—5661no—
148C2×C4—5661no—
149C2×C4—11321no—
150C2×C4—11321no—
151C2×C4D4×D28312yes—
152C8—42no—
153C8—11322no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D28311yescharacteristic
162C22M16×D28311yescharacteristic
163C22C2×#1798537511yescharacteristic
164C4—22no—
165C4—41no—
166C4—5662no—
167C4—5661no—
168C4—5661no—
169C4—5662no—
170C4—11321no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2#3182642711yescharacteristic
175C2#3182643711yescharacteristic
176C2#3182644611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#323×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC24×C283C2×C4
cosocleC22×C4×C283C23
hypercenter#323D283
hypocenterC283#1464
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31826519C2semidirect
3. #31826190C2semidirect
88. C283#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#225835662
#318265192
#318261902
#318261892
#323×C2832
#1464283