Finite Group Databasebeta

← #49131650

Subgroups — #49131650

Order 36224.

400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583598C211yesmaximal, characteristic
2#31826827C214yesmaximal, complemented
3#31826822C214yesmaximal, complemented
4#31826473C212yesmaximal, complemented
5#31826469C212yesmaximal
6C4×#17985376C211yesmaximal, characteristic, complemented
7#533×C283C211yesmaximal, characteristic, complemented
8C22×Dic566C2211yescharacteristic
9C22×D1132C2211yescharacteristic
10C2×#17985376C2212yes—
11#22583598—22no—
12#22583598C2212yes—
13#22583598C2212yes—
14C2×(C2×D283)⋊C4—22no—
15#22583533C2218yescomplemented
16#22583530C2218yes—
17#22583521C2212yescomplemented
18C4×C283⋊C8C2212yescomplemented
19C4⋊Q8×C283C2212yescomplemented
20#125×C283C2212yescomplemented
21C22⋊Q8×C283—22no—
22C4×Q8×C283—22no—
23#117×C283C2212yes—
24C2×C42×C283C2211yescharacteristic
25C23×D283—21no—
26C2×Dic566—21no—
27C2×Dic566—24no—
28C2×Dic566C2312yes—
29C2×D1132—21no—
30C2×D1132—24no—
31C2×D1132C2312yes—
32C22×Dic283—21no—
33#17985376—24no—
34C2×C283⋊C8C2314yes—
35(C2×D283)⋊C4—24no—
36(C2×D283)⋊C4—24no—
37C2×Q8×C283—22no—
38C22×C4×C283D412yes—
39C22×C4×C283C2311yescharacteristic
40C4⋊C4×C283—24no—
41C4⋊C4×C283—22no—
42C4⋊C4×C283C2314yes—
43C22⋊C4×C283—22no—
44C42×C283—22no—
45C42×C283D412yes—
46C42×C283C2311yescharacteristic
47C42×C283C2311yescharacteristic
48C22×D283—22no—
49C22×D283—44no—
50C22×D283—42no—
51Dic566—24no—
52Dic566—42no—
53D1132—24no—
54D1132—42no—
55C2×Dic283—22no—
56C2×Dic283—42no—
57C283⋊C8—24no—
58C23×C283C2×D411yescharacteristic
59Q8×C283—44no—
60C2×C4×C283—24no—
61C2×C4×C283—42no—
62C2×C4×C283C2×D412yes—
63C2×C4×C283C2×D412yes—
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283#4114yes—
66C2×C4×C283C2411yescharacteristic
67C22×C283—22no—
68C22×C283#12412yes—
69C22×C283C22×D411yescharacteristic
70C2×D283—42no—
71C2×D283—44no—
72C2×D283—84no—
73C4×C283—22no—
74C4×C283—22no—
75C4×C283—44no—
76C4×C283#12412yes—
77C4×C283C2×#4112yes—
78Dic283—42no—
79C2×C283—22no—
80C2×C283C2×#12411yescharacteristic
81C2×C283#57512yes—
82D283—82no—
83C283#314011yescharacteristic, complemented, Sylow
84#3140—2831nomaximal, Sylow
85#533D28311yescharacteristic, complemented
86C2×#124—2831no—
87#489—2834no—
88#488—2834no—
89#419—2832no—
90#418—2832no—
91C4×M16—2831no—
92C22×Q8—2831no—
93C22×D4—2831no—
94C2×M16—2832no—
95C4⋊Q8C2×D28312yescomplemented
96#125C2×D28312yescomplemented
97#124—2832no—
98#124—2832no—
99#124—5662no—
100C22⋊Q8—22no—
101C4×Q8—22no—
102#117C2×D28312yes—
103C2×C22⋊C4—5662no—
104C2×C42C2×D28311yescharacteristic
105#103—2838no—
106#102—2838no—
107#97—2832no—
108C4×C8—2832no—
109C24—5661no—
110C2×Q8—22no—
111C2×Q8—2832no—
112C2×Q8—5661no—
113C2×Q8—5664no—
114C2×D4—2832no—
115C2×D4—5661no—
116C2×D4—5664no—
117C22×C4—5661no—
118C22×C4C22⋊D28312yes—
119C22×C4C22×D28311yescharacteristic
120M16—5664no—
121C2×C8—2834no—
122C4⋊C4—24no—
123C4⋊C4—22no—
124C4⋊C4C22×D28314yes—
125C22⋊C4—22no—
126C22⋊C4—5664no—
127C22⋊C4—5664no—
128C42—22no—
129C42C22⋊D28312yes—
130C42C22×D28311yescharacteristic
131C42C22×D28311yescharacteristic
132C23—5662no—
133C23—11324no—
134C23—11322no—
135C23C2×C22⋊D28311yescharacteristic
136Q8—44no—
137Q8—5664no—
138Q8—11322no—
139D4—5664no—
140D4—11322no—
141C2×C4—24no—
142C2×C4—42no—
143C2×C4—5662no—
144C2×C4—11322no—
145C2×C4C2×C22⋊D28312yes—
146C2×C4C2×C22⋊D28312yes—
147C2×C4C2×C22⋊D28311yescharacteristic
148C2×C4#1798539314yes—
149C2×C4C23×D28311yescharacteristic
150C8—5664no—
151C22—22no—
152C22—11322no—
153C22—11324no—
154C22—22644no—
155C22#2258359912yes—
156C22C22×C22⋊D28311yescharacteristic
157C4—22no—
158C4—22no—
159C4—44no—
160C4—11322no—
161C4#2258359912yes—
162C4C2×#1798539312yes—
163C2—22no—
164C2—22642no—
165C2C2×#2258359911yescharacteristic
166C2#3182726312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#533×C283C2
socleC22×C283C22×D4
prime radicalC22×D1132C22
hypercenter#533D283
hypocenterC283#3140
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #31826827C2semidirect
3. #31826822C2semidirect
4. #31826473C2semidirect
6. C4×#17985376C2semidirect
7. #533×C283C2semidirect
15. #22583533C22semidirect
17. #22583521C22semidirect
18. C4×C283⋊C8C22semidirect
19. C4⋊Q8×C283C22semidirect
20. #125×C283C22semidirect
83. C283#3140semidirect
85. #533D283semidirect
95. C4⋊Q8C2×D283semidirect
96. #125C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835982
#318268272
#318268222
#318264732
#318264692
C4×#179853762
#533×C2832
#3140283