Finite Group Databasebeta

← #49131605

Subgroups — #49131605

Order 36224.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827021C211yesmaximal, characteristic, complemented
2#31827013C211yesmaximal, characteristic
3#31826835C211yesmaximal, characteristic, complemented
4#31826834C211yesmaximal, characteristic, complemented
5#31826829C211yesmaximal, characteristic, complemented
6#31826823C214yesmaximal, complemented
7#31826458C214yesmaximal, complemented
8#97×D283C211yesmaximal, characteristic, complemented
9#490×C283C211yesmaximal, characteristic, complemented
10C2×#17985391C2212yes—
11C2×C8×D283C2212yes—
12#22583610C2211yescharacteristic
13#22583609C2212yes—
14#22583602C2211yescharacteristic
15#22583597C2212yes—
16#22583588—22no—
17#22583581—22no—
18#22583575—22no—
19D4×Dic283—22no—
20#22583568C2212yes—
21C42×D283C2211yescharacteristic
22#22583535C2214yes—
23#22583533C2214yes—
24#22583531C2214yes—
25#22583521C2211yescharacteristic
26#22583520C2212yes—
27#127×C283C2211yescharacteristic
28#125×C283C2211yescharacteristic
29#102×C283C2214yes—
30#97×C283C2211yescharacteristic
31#17985391—28no—
32C2×Dic566—22no—
33C2×Dic566C2312yes—
34C2×C22⋊D283—22no—
35C22×Dic283—22no—
36C2×C4×D283D412yes—
37C2×C4×D283C2311yescharacteristic
38C2×C283⋊C8C2312yes—
39C8×D283—24no—
40C4⋊Dic283—22no—
41C4⋊Dic283C2312yes—
42Dic283⋊C4—22no—
43Dic283⋊C4—22no—
44C22⋊Dic283—24no—
45(C2×D283)⋊C4—22no—
46C4×Dic283—22no—
47C4×Dic283D412yes—
48C4×Dic283C2311yescharacteristic
49C2×D4×C283—22no—
50C2×D4×C283C2312yes—
51C2×C8×C283C2312yes—
52C4⋊C4×C283—22no—
53C4⋊C4×C283C2312yes—
54C42×C283C2311yescharacteristic
55C22×D283C2×D411yescharacteristic
56Dic566—24no—
57Dic566—44no—
58C22⋊D283—44no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—44no—
62C2×Dic283C2×D412yes—
63C2×Dic283C2×D411yescharacteristic
64C4×D283—42no—
65C4×D283#4114yes—
66C283⋊C8—22no—
67C23×C283—22no—
68D4×C283—24no—
69D4×C283—44no—
70C2×C4×C283—22no—
71C2×C4×C283C2×D412yes—
72C2×C4×C283C2411yescharacteristic
73C8×C283—22no—
74C22×C283—42no—
75C22×C283—44no—
76C22×C283C22×D411yescharacteristic
77C2×D283—22no—
78C2×D283#12412yes—
79C4×C283—22no—
80C4×C283—42no—
81C4×C283C2×#4112yes—
82Dic283—22no—
83Dic283—42no—
84Dic283—42no—
85Dic283#12412yes—
86C2×C283—82no—
87C2×C283C2×#12411yescharacteristic
88C2×C283#57512yes—
89D283—22no—
90C283#313511yescharacteristic, complemented, Sylow
91#3135—2831nomaximal, Sylow
92#533—2831no—
93#532—2831no—
94#491—2831no—
95#491—2831no—
96#490—2831no—
97#490D28311yescharacteristic, complemented
98#489—2834no—
99#416—2834no—
100C2×#97—2831no—
101C2×#41—2832no—
102C22×C8—2832no—
103C4⋊Q8—2832no—
104C4⋊Q8—2831no—
105#127C2×D28311yescharacteristic
106#125—2831no—
107#125C2×D28311yescharacteristic
108#124—2832no—
109C22⋊Q8—5662no—
110#121—5662no—
111C4×Q8—5662no—
112C4×D4—5662no—
113#117—2832no—
114C2×C42—2831no—
115#103—2834no—
116#103—2834no—
117#102—2834no—
118#102C2×D28314yes—
119#97—2832no—
120#97—2831no—
121#97C2×D28311yescharacteristic
122#41—5668no—
123C2×Q8—2832no—
124C2×Q8—5662no—
125C2×D4—22no—
126C2×D4—5662no—
127C2×D4C22×D28312yes—
128C22×C4—2831no—
129C22×C4—2832no—
130C22×C4—5662no—
131C2×C8—2832no—
132C2×C8—5664no—
133C2×C8C22×D28312yes—
134C4⋊C4—22no—
135C4⋊C4—2832no—
136C4⋊C4—5662no—
137C4⋊C4—5662no—
138C4⋊C4—5662no—
139C4⋊C4C22×D28312yes—
140C22⋊C4—5662no—
141C22⋊C4—5664no—
142C42—2832no—
143C42—2831no—
144C42—5662no—
145C42C22×D28311yescharacteristic
146C23—22no—
147C23—2831no—
148Q8—5664no—
149Q8—11324no—
150D4—24no—
151D4—44no—
152D4—11324no—
153C2×C4—22no—
154C2×C4—2831no—
155C2×C4—2834no—
156C2×C4—2832no—
157C2×C4—5662no—
158C2×C4—5662no—
159C2×C4—11322no—
160C2×C4—11324no—
161C2×C4D4×D28312yes—
162C2×C4C23×D28311yescharacteristic
163C8—22no—
164C8—5662no—
165C22—42no—
166C22—44no—
167C22—2832no—
168C22—5662no—
169C22C2×D4×D28311yescharacteristic
170C4—22no—
171C4—42no—
172C4—2832no—
173C4—5662no—
174C4—11322no—
175C4—11322no—
176C4#41×D28312yes—
177C2—82no—
178C2—5662no—
179C2#124×D28311yescharacteristic
180C2#3182726112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#490×C283C2
socleC22×C283C22×D4
prime radical#31827013C2
hypercenter#490D283
hypocenterC283#3135
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31827021C2semidirect
3. #31826835C2semidirect
4. #31826834C2semidirect
5. #31826829C2semidirect
6. #31826823C2semidirect
7. #31826458C2semidirect
8. #97×D283C2semidirect
9. #490×C283C2semidirect
90. C283#3135semidirect
97. #490D283semidirect

Maximal subgroups

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

subgroupindex
#318270212
#318270132
#318268352
#318268342
#318268292
#318268232
#318264582
#97×D2832
#490×C2832
#3135283