Finite Group Databasebeta

← #49121704

Subgroups — #49121704

Order 36224.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22583538C212yesmaximal, complemented
3#31826429C211yesmaximal, characteristic, complemented
4#31826225C212yesmaximal, complemented
5C22×C42×C283C211yesmaximal, characteristic, complemented
6C2×#17985392C2211yescharacteristic
7C2×#17985376C2212yes—
8#22583593—21no—
9#22583589C412yescomplemented
10#22583584C412yescomplemented
11#22583579—21no—
12C4×C22⋊D283—22no—
13#22583569C2211yescharacteristic
14#22583538—24no—
15C22⋊(C283⋊C8)—22no—
16C23×C4×C283—21no—
17C23×C4×C283C2211yescharacteristic
18C2×C42×C283—21no—
19C2×C42×C283—24no—
20C2×C42×C283C2212yes—
21#17985392—22no—
22#17985392—22no—
23C2×Dic566C2×C411yescharacteristic, complemented
24C2×D1132C2×C411yescharacteristic, complemented
25C2×C22⋊D283—22no—
26C2×C22⋊D283—21no—
27C2×C4×D283—21no—
28#17985376—22no—
29#17985376—22no—
30C2×C283⋊C8—22no—
31C4⋊Dic283C2×C412yescomplemented
32Dic283⋊C4—22no—
33C22⋊Dic283—22no—
34C22⋊Dic283—21no—
35(C2×D283)⋊C4—22no—
36C4×Dic283—21no—
37C24×C283D411yescharacteristic
38C22×C4×C283—24no—
39C22×C4×C283—28no—
40C22×C4×C283—22no—
41C22×C4×C283—22no—
42C22×C4×C283—22no—
43C22×C4×C283C2×C412yes—
44C22×C4×C283D411yescharacteristic
45C22×C4×C283D412yes—
46C22×C4×C283C2311yescharacteristic
47C42×C283—24no—
48C42×C283—22no—
49C42×C283D414yescomplemented
50C22×D283—21no—
51Dic566—22no—
52D1132—22no—
53C22⋊D283—44no—
54C22⋊D283—41no—
55C22⋊D283—41no—
56C2×Dic283—22no—
57C2×Dic283—21no—
58C4×D283—42no—
59C283⋊C8—42no—
60C23×C283—24no—
61C23×C283—21no—
62C23×C283—21no—
63C23×C283C22⋊C412yes—
64C23×C283C2×D411yescharacteristic
65C2×C4×C283—216no—
66C2×C4×C283—28no—
67C2×C4×C283—21no—
68C2×C4×C283—24no—
69C2×C4×C283—21no—
70C2×C4×C283—24no—
71C2×C4×C283—24no—
72C2×C4×C283C22⋊C412yes—
73C2×C4×C283C22×C411yescharacteristic
74C2×C4×C283C2×D412yes—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283#4112yes—
77C22×C283—24no—
78C22×C283—24no—
79C22×C283—22no—
80C22×C283—22no—
81C22×C283—22no—
82C22×C283#10414yescomplemented
83C22×C283C2×C22⋊C411yescharacteristic
84C22×C283#12011yescharacteristic
85C22×C283#12311yescharacteristic
86C2×D283—41no—
87C2×D283—42no—
88C4×C283—28no—
89C4×C283—22no—
90C4×C283C4×D412yes—
91C4×C283#12112yes—
92Dic283—41no—
93Dic283—42no—
94C2×C283—21no—
95C2×C283—24no—
96C2×C283—21no—
97C2×C283#38611yescharacteristic
98C2×C283C2×#10412yes—
99D283—81no—
100C283#189611yescharacteristic, complemented, Sylow
101#1896—2831nomaximal, Sylow
102#525—2831no—
103C22×C42D28311yescharacteristic, complemented
104C2×#104—2832no—
105#407—2831no—
106#339—2832no—
107C2×#41—2831no—
108C23×C4—21no—
109C23×C4C2×D28311yescharacteristic
110C2×M16—2832no—
111#123—5661no—
112C22⋊Q8—2832no—
113#121—2832no—
114#120—5661no—
115C4×D4—5662no—
116#117—2831no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D28312yes—
120#104—5664no—
121C22⋊C8—5662no—
122C24C22⋊D28311yescharacteristic
123#41—5662no—
124#41—5662no—
125C2×Q8—2831no—
126C2×D4—2831no—
127C2×D4—5662no—
128C2×D4—5661no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—5661no—
135C22×C4C4×D28312yes—
136C22×C4C22⋊D28311yescharacteristic
137C22×C4D113212yes—
138C22×C4C22×D28311yescharacteristic
139M16—5662no—
140M16—5662no—
141C2×C8—5662no—
142C4⋊C4—2832no—
143C4⋊C4—5662no—
144C22⋊C4—5662no—
145C22⋊C4—5661no—
146C22⋊C4—5662no—
147C42—24no—
148C42—22no—
149C42—5661no—
150C42C22⋊D28314yescomplemented
151C23—21no—
152C23—21no—
153C23—24no—
154C23—5661no—
155C23(C2×D283)⋊C412yes—
156C23C2×C22⋊D28311yescharacteristic
157Q8—5662no—
158D4—5662no—
159D4—11321no—
160D4—11321no—
161D4—11324no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—5662no—
170C2×C4—5661no—
171C2×C4—11322no—
172C2×C4(C2×D283)⋊C412yes—
173C2×C4C2×C4×D28311yescharacteristic
174C2×C4C2×C22⋊D28312yes—
175C2×C4C2×D113211yescharacteristic
176C2×C4#1798539212yes—
177C8—11322no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—11322no—
184C22—11321no—
185C22#2258353814yescomplemented
186C22C2×(C2×D283)⋊C411yescharacteristic
187C22#2258357911yescharacteristic
188C22#2258359311yescharacteristic
189C4—28no—
190C4—22no—
191C4—11322no—
192C4—11321no—
193C4C4×C22⋊D28312yes—
194C4#2258358412yes—
195C2—21no—
196C2—21no—
197C2—24no—
198C2—22641no—
199C2#3182634411yescharacteristic
200C2C2×#2258353812yes—
subgroupG/H
centerC2×C4C2×D1132
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC22×C42×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826976C2
cosocleC22×C4×C283C23
hypercenterC22×C42D283
hypocenterC283#1896
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#22583538C2semidirect
3. #31826429C2semidirect
4. #31826225C2semidirect
5. C22×C42×C283C2semidirect
9. #22583589C4semidirect
10. #22583584C4semidirect
23. C2×Dic566C2×C4semidirect
24. C2×D1132C2×C4semidirect
31. C4⋊Dic283C2×C4semidirect
49. C42×C283D4semidirect
82. C22×C283#104semidirect
100. C283#1896semidirect
103. C22×C42D283semidirect
150. C42C22⋊D283semidirect
185. C22#22583538semidirect

Maximal subgroups

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

subgroupindex
#318269762
C2×#225835382
#318264292
#318262252
C22×C42×C2832
#1896283