Finite Group Databasebeta

← #49131194

Subgroups — #49131194

Order 36224.

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

normal subgroups only

This group has 414 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
1#31826976C211yesmaximal, characteristic
2C2×#22583569C211yesmaximal, characteristic, complemented
3#31826807C214yesmaximal, complemented
4#31826790C214yesmaximal, complemented
5#31826507C212yesmaximal, complemented
6#31826467C212yesmaximal, complemented
7#407×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583593—21no—
10#22583589C2212yes—
11#22583584C2212yes—
12#22583579—21no—
13C4×C22⋊D283—22no—
14#22583569—22no—
15#22583569C2211yescharacteristic
16#22583569C2214yes—
17C2×C4⋊Dic283C2212yes—
18C2×C22⋊Dic283—21no—
19C2×C4×Dic283—21no—
20#22583544C2214yescomplemented
21#22583542C2214yescomplemented
22#22583535C2214yescomplemented
23#22583532C2214yescomplemented
24C23×C4×C283C2211yescharacteristic
25C2×M16×C283C2212yes—
26C22⋊C8×C283C2214yes—
27#17985392—24no—
28C2×Dic566C2311yescharacteristic
29C2×D1132C2311yescharacteristic
30C2×C22⋊D283—22no—
31C2×C22⋊D283—21no—
32C22×Dic283—22no—
33C2×C4×D283—21no—
34C4⋊Dic283—22no—
35C4⋊Dic283C2314yes—
36C4⋊Dic283C2312yes—
37Dic283⋊C4—22no—
38C22⋊Dic283—24no—
39C22⋊Dic283—21no—
40C22⋊Dic283—22no—
41(C2×D283)⋊C4—22no—
42C4×Dic283—24no—
43C4×Dic283—21no—
44C24×C283D411yescharacteristic
45C22×C4×C283—24no—
46C22×C4×C283D411yescharacteristic
47C22×C4×C283D412yes—
48C22×C4×C283C2312yes—
49C22×C4×C283C2311yescharacteristic
50M16×C283—24no—
51C2×C8×C283C2314yes—
52C22×D283—21no—
53Dic566—22no—
54D1132—22no—
55C22⋊D283—44no—
56C22⋊D283—42no—
57C2×Dic283—24no—
58C2×Dic283—22no—
59C2×Dic283—21no—
60C2×Dic283—44no—
61C4×D283—42no—
62C23×C283—22no—
63C23×C283—42no—
64C23×C283C2×D412yes—
65C23×C283C2×D411yescharacteristic
66C2×C4×C283—22no—
67C2×C4×C283—24no—
68C2×C4×C283—24no—
69C2×C4×C283C2×D412yes—
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283#4114yes—
72C2×C4×C283C2411yescharacteristic
73C8×C283—24no—
74C22×C283—22no—
75C22×C283—22no—
76C22×C283—22no—
77C22×C283—22no—
78C22×C283—44no—
79C22×C283#12312yes—
80C22×C283C22×D411yescharacteristic
81C2×D283—41no—
82C2×D283—42no—
83C4×C283—22no—
84C4×C283#12312yes—
85C4×C283C2×#4112yes—
86Dic283—41no—
87Dic283—44no—
88Dic283—42no—
89C2×C283—22no—
90C2×C283—42no—
91C2×C283C2×#12311yescharacteristic
92C2×C283#57512yes—
93D283—81no—
94C283#309311yescharacteristic, complemented, Sylow
95#3093—2831nomaximal, Sylow
96#525—2831no—
97C2×#117—2831no—
98#485—2834no—
99#482—2834no—
100#428—2832no—
101#417—2832no—
102#407D28311yescharacteristic, complemented
103C2×#41—2831no—
104C23×C4C2×D28311yescharacteristic
105C2×M16C2×D28312yes—
106#123—5661no—
107C22⋊Q8—2832no—
108#121—2832no—
109#120—5661no—
110C4×D4—5662no—
111#117—2834no—
112#117—2831no—
113#117—5662no—
114C2×C4⋊C4—2832no—
115C2×C22⋊C4—5661no—
116C2×C42—5661no—
117#107—2834no—
118#106—2834no—
119#103—2834no—
120#102—2834no—
121C22⋊C8C2×D28314yes—
122C24D113211yescharacteristic
123#41—5664no—
124C2×Q8—2831no—
125C2×D4—2831no—
126C2×D4—5662no—
127C2×D4—5661no—
128C22×C4—24no—
129C22×C4—5662no—
130C22×C4—5661no—
131C22×C4D113211yescharacteristic
132C22×C4D113212yes—
133C22×C4C22×D28312yes—
134C22×C4C22×D28311yescharacteristic
135M16—24no—
136C2×C8C22×D28314yes—
137C4⋊C4—2834no—
138C4⋊C4—2832no—
139C4⋊C4—5662no—
140C4⋊C4—5662no—
141C22⋊C4—5664no—
142C22⋊C4—5661no—
143C22⋊C4—5662no—
144C22⋊C4—5662no—
145C42—5664no—
146C42—5661no—
147C23—22no—
148C23—42no—
149C23—5661no—
150C23C2×D113212yes—
151C23C2×D113211yescharacteristic
152Q8—5662no—
153D4—5662no—
154D4—11324no—
155D4—11322no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—5664no—
160C2×C4—5662no—
161C2×C4—5661no—
162C2×C4—11324no—
163C2×C4—11322no—
164C2×C4C2×D113212yes—
165C2×C4C2×D113211yescharacteristic
166C2×C4#1798539114yes—
167C2×C4C23×D28311yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—11321no—
175C22—11322no—
176C22#2258359412yes—
177C22C22×D113211yescharacteristic
178C4—22no—
179C4—11321no—
180C4—11324no—
181C4—11322no—
182C4#2258359412yes—
183C4C2×#1798539112yes—
184C2—22no—
185C2—42no—
186C2—22641no—
187C2C2×#2258359411yescharacteristic
188C2#3182726512yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#407×C283C2
socleC22×C283C22×D4
prime radical#31826976C2
hypercenter#407D283
hypocenterC283#3093
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#22583569C2semidirect
3. #31826807C2semidirect
4. #31826790C2semidirect
5. #31826507C2semidirect
6. #31826467C2semidirect
7. #407×C283C2semidirect
20. #22583544C22semidirect
21. #22583542C22semidirect
22. #22583535C22semidirect
23. #22583532C22semidirect
94. C283#3093semidirect
102. #407D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
C2×#225835692
#318268072
#318267902
#318265072
#318264672
#407×C2832
#3093283