Finite Group Databasebeta

← #49129892

Subgroups — #49129892

Order 36224.

484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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×C42×D283C211yesmaximal, characteristic
2#31826520C214yesmaximal, complemented
3#31826516C214yesmaximal, complemented
4#31826488C212yesmaximal, complemented
5#31826428C212yesmaximal
6C4×#17985376C211yesmaximal, characteristic, complemented
7C4×M16×C283C211yesmaximal, characteristic, complemented
8C22×C4×D283C412yes—
9C22×C4×D283C2211yescharacteristic
10C2×#17985376C2212yes—
11C2×C4×Dic283C412yes—
12C2×C4×Dic283C2211yescharacteristic
13C42×D283C412yes—
14C42×D283C412yes—
15C42×D283C2212yes—
16C42×D283C2212yes—
17Dic283⋊C8C2218yescomplemented
18(C2×D283)⋊C8C2218yes—
19#22583521C2212yescomplemented
20C4×C283⋊C8C2212yescomplemented
21C2×M16×C283C2212yes—
22C2×C42×C283C2211yescharacteristic
23#97×C283C2212yescomplemented
24C4×C8×C283C2212yescomplemented
25C23×D283C2×C411yescharacteristic
26C22×Dic283C2×C411yescharacteristic
27C22×Dic283C2×C412yes—
28C2×C4×D283—28no—
29C2×C4×D283—24no—
30C2×C4×D283C2×C412yes—
31C2×C4×D283C2×C412yes—
32C2×C4×D283C2×C412yes—
33C2×C4×D283C2×C412yes—
34C2×C4×D283C2×C412yes—
35C2×C4×D283C2312yes—
36#17985376—24no—
37C2×C283⋊C8C2314yes—
38C4×Dic283C2×C411yescharacteristic
39C4×Dic283C2×C411yescharacteristic
40C4×Dic283C2×C412yes—
41C4×Dic283C2×C412yes—
42C4×Dic283C2×C412yes—
43C4×Dic283C2×C412yes—
44C4×Dic283C2312yes—
45C22×C4×C283C2×C412yes—
46C22×C4×C283C2311yescharacteristic
47M16×C283—24no—
48C2×C8×C283C2314yes—
49C42×C283C2×C412yes—
50C42×C283C2311yescharacteristic
51C42×C283C2311yescharacteristic
52C22×D283—22no—
53C22×D283—24no—
54C22×D283C22×C412yes—
55C2×Dic283—22no—
56C2×Dic283—24no—
57C2×Dic283C22×C412yes—
58C2×Dic283C22×C412yes—
59C2×Dic283C22×C412yes—
60C4×D283—24no—
61C4×D283—24no—
62C4×D283—24no—
63C4×D283—24no—
64C4×D283—24no—
65C4×D283M1618yescomplemented
66C283⋊C8—24no—
67C23×C283C22×C411yescharacteristic
68C2×C4×C283—24no—
69C2×C4×C283C22×C412yes—
70C2×C4×C283C22×C411yescharacteristic
71C2×C4×C283C22×C412yes—
72C2×C4×C283#4114yes—
73C2×C4×C283C2411yescharacteristic
74C8×C283—24no—
75C22×C283—22no—
76C22×C283#11712yes—
77C22×C283C23×C411yescharacteristic
78C2×D283—28no—
79C2×D283—22no—
80C2×D283—22no—
81C2×D283C2×M1614yes—
82C4×C283—22no—
83C4×C283#11712yes—
84C4×C283C2×M1614yes—
85C4×C283C2×#4112yes—
86Dic283—22no—
87Dic283—22no—
88Dic283C2×M1614yes—
89C2×C283—22no—
90C2×C283C2×#11711yescharacteristic
91C2×C283C22×M1612yes—
92D283—24no—
93C283#292011yescharacteristic, complemented, Sylow
94#2920—2831nomaximal, Sylow
95C22×C42—2831no—
96#432—2834no—
97#431—2834no—
98#423—2832no—
99#407—2832no—
100C4×M16—2831no—
101C4×M16D28311yescharacteristic, complemented
102C23×C4—2832no—
103C23×C4—2831no—
104C2×M16—2832no—
105C2×M16C2×D28312yes—
106C2×C42—2832no—
107C2×C42—2831no—
108C2×C42—2832no—
109C2×C42—2832no—
110C2×C42—2832no—
111C2×C42—2832no—
112C2×C42C2×D28311yescharacteristic
113C4⋊C8—2838no—
114C22⋊C8—2838no—
115#97—2832no—
116#97C2×D28312yescomplemented
117C4×C8—2832no—
118C4×C8C2×D28312yescomplemented
119C24—2831no—
120C22×C4—2832no—
121C22×C4—2832no—
122C22×C4—2831no—
123C22×C4—2832no—
124C22×C4—2832no—
125C22×C4—2832no—
126C22×C4—2832no—
127C22×C4—2832no—
128C22×C4—5668no—
129C22×C4—5664no—
130C22×C4C4×D28312yes—
131C22×C4C22×D28311yescharacteristic
132M16—24no—
133M16—5664no—
134C2×C8—2834no—
135C2×C8C22×D28314yes—
136C42—2831no—
137C42—2832no—
138C42—2832no—
139C42—2832no—
140C42—2831no—
141C42—2832no—
142C42—2832no—
143C42C4×D28312yes—
144C42C22×D28311yescharacteristic
145C42C22×D28311yescharacteristic
146C23—2832no—
147C23—5664no—
148C23—5662no—
149C23C2×C4×D28311yescharacteristic
150C2×C4—24no—
151C2×C4—2832no—
152C2×C4—2838no—
153C2×C4—2832no—
154C2×C4—2832no—
155C2×C4—5664no—
156C2×C4—5664no—
157C2×C4—5664no—
158C2×C4—5662no—
159C2×C4—5664no—
160C2×C4—5664no—
161C2×C4—5664no—
162C2×C4C2×C4×D28312yes—
163C2×C4C2×C4×D28311yescharacteristic
164C2×C4C2×C4×D28312yes—
165C2×C4#1798539214yes—
166C2×C4C23×D28311yescharacteristic
167C8—24no—
168C8—5664no—
169C22—22no—
170C22—2834no—
171C22—5668no—
172C22—5662no—
173C22—5662no—
174C22#2258356712yes—
175C22C22×C4×D28311yescharacteristic
176C4—22no—
177C4—2834no—
178C4—5662no—
179C4—5662no—
180C4#2258356712yes—
181C4M16×D28314yes—
182C4C2×#1798539212yes—
183C2—22no—
184C2—5664no—
185C2C2×#2258356711yescharacteristic
186C2C2×M16×D28312yes—
subgroupG/H
centerC42C22×D283
commutator, socleC22×C283C23×C4
FrattiniC2×C4C23×D283
FittingC4×M16×C283C2
prime radicalC23×D283C2×C4
cosocleC2×C4×C283C24
hypercenterC4×M16D283
hypocenterC283#2920
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #31826520C2semidirect
3. #31826516C2semidirect
4. #31826488C2semidirect
6. C4×#17985376C2semidirect
7. C4×M16×C283C2semidirect
17. Dic283⋊C8C22semidirect
19. #22583521C22semidirect
20. C4×C283⋊C8C22semidirect
23. #97×C283C22semidirect
24. C4×C8×C283C22semidirect
65. C4×D283M16semidirect
93. C283#2920semidirect
101. C4×M16D283semidirect
116. #97C2×D283semidirect
118. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D2832
#318265202
#318265162
#318264882
#318264282
C4×#179853762
C4×M16×C2832
#2920283