Finite Group Databasebeta

← #49131663

Subgroups — #49131663

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#31827016C211yesmaximal, characteristic
2#125×D283C211yesmaximal, characteristic, complemented
3#31826833C211yesmaximal, characteristic, complemented
4#31826831C211yesmaximal, characteristic, complemented
5#31826830C211yesmaximal, characteristic, complemented
6#31826821C214yesmaximal, complemented
7#31826465C214yesmaximal, complemented
8#31826417C211yesmaximal, characteristic, complemented
9#491×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C2212yes—
11C2×#17985375C2212yes—
12#22583607C2211yescharacteristic
13#22583602C2211yescharacteristic
14#22583601C2212yes—
15#22583600—22no—
16#22583599C2212yes—
17#22583585—22no—
18#22583572—22no—
19C4⋊C4×D283—22no—
20C4⋊C4×D283C2212yes—
21C42×D283C2211yescharacteristic
22#22583534C2214yes—
23#22583532C2214yes—
24#22583530C2214yes—
25#22583521C2211yescharacteristic
26C8×Dic283C2212yes—
27C4⋊Q8×C283C2211yescharacteristic
28#125×C283C2211yescharacteristic
29#103×C283C2214yes—
30#97×C283C2211yescharacteristic
31#17985393—28no—
32C2×D1132—22no—
33C2×D1132—22no—
34C2×D1132C2312yes—
35C2×C4×D283—22no—
36C2×C4×D283—22no—
37C2×C4×D283D412yes—
38C2×C4×D283C2311yescharacteristic
39#17985375—24no—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283—22no—
42C4⋊Dic283C2312yes—
43Dic283⋊C4—22no—
44Dic283⋊C4—22no—
45Dic283⋊C4—22no—
46(C2×D283)⋊C4—24no—
47C4×Dic283D412yes—
48C4×Dic283C2311yescharacteristic
49C2×Q8×C283C2312yes—
50C2×C8×C283C2312yes—
51C4⋊C4×C283—22no—
52C4⋊C4×C283—22no—
53C4⋊C4×C283C2312yes—
54C42×C283C2311yescharacteristic
55C22×D283—22no—
56C22×D283C2×D411yescharacteristic
57D1132—24no—
58D1132—44no—
59D1132—44no—
60C2×Dic283—22no—
61C2×Dic283C2×D412yes—
62C2×Dic283C2×D411yescharacteristic
63C4×D283—42no—
64C4×D283—44no—
65C4×D283—44no—
66C4×D283#4114yes—
67C283⋊C8—22no—
68Q8×C283—24no—
69C2×C4×C283—22no—
70C2×C4×C283—22no—
71C2×C4×C283C2×D412yes—
72C2×C4×C283C2411yescharacteristic
73C8×C283—22no—
74C22×C283C22×D411yescharacteristic
75C2×D283—22no—
76C2×D283—42no—
77C2×D283—44no—
78C2×D283#12412yes—
79C4×C283—22no—
80C4×C283—42no—
81C4×C283—42no—
82C4×C283C2×#4112yes—
83Dic283—22no—
84Dic283—42no—
85Dic283#12412yes—
86C2×C283C2×#12411yescharacteristic
87C2×C283#57512yes—
88D283—22no—
89D283—82no—
90C283#314211yescharacteristic, complemented, Sylow
91#3142—2831nomaximal, Sylow
92#532—2831no—
93C2×#125—2831no—
94#491—2831no—
95#491D28311yescharacteristic, complemented
96#490—2831no—
97#490—2831no—
98#488—2834no—
99#417—2834no—
100C4×M16—2831no—
101C2×#41—2832no—
102C2×M16—2832no—
103C4⋊Q8C2×D28311yescharacteristic
104#127—2831no—
105#125—2832no—
106#125—2831no—
107#125—5662no—
108#125C2×D28311yescharacteristic
109#124—2832no—
110#121—5662no—
111C4×D4—5662no—
112C2×C4⋊C4—2832no—
113C2×C4⋊C4—5662no—
114C2×C42—2831no—
115#103—2834no—
116#103C2×D28314yes—
117#102—2834no—
118#102—2834no—
119#97—2831no—
120#97C2×D28311yescharacteristic
121C4×C8—2832no—
122#41—5668no—
123C2×Q8C22×D28312yes—
124C2×D4—2832no—
125C2×D4—5662no—
126C2×D4—5662no—
127C22×C4—2831no—
128C22×C4—2832no—
129C22×C4—5662no—
130C22×C4—5662no—
131M16—5664no—
132C2×C8—2832no—
133C2×C8C22×D28312yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—2832no—
137C4⋊C4—5662no—
138C4⋊C4—5662no—
139C4⋊C4—5662no—
140C4⋊C4—5662no—
141C4⋊C4C22×D28312yes—
142C22⋊C4—5664no—
143C42—2832no—
144C42—2831no—
145C42C22×D28311yescharacteristic
146C23—2831no—
147C23—5662no—
148Q8—24no—
149D4—5664no—
150D4—11324no—
151D4—11324no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—2831no—
155C2×C4—2834no—
156C2×C4—2832no—
157C2×C4—5662no—
158C2×C4—11322no—
159C2×C4—11324no—
160C2×C4—11324no—
161C2×C4D4×D28312yes—
162C2×C4C23×D28311yescharacteristic
163C8—22no—
164C8—5662no—
165C22—2832no—
166C22—5662no—
167C22—11322no—
168C22—11324no—
169C22C2×D4×D28311yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—2832no—
174C4—5662no—
175C4—11322no—
176C4#41×D28312yes—
177C2—5662no—
178C2—22642no—
179C2#124×D28311yescharacteristic
180C2#3182726412yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#491×C283C2
socleC22×C283C22×D4
prime radical#31827016C2
hypercenter#491D283
hypocenterC283#3142
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D283C2semidirect
3. #31826833C2semidirect
4. #31826831C2semidirect
5. #31826830C2semidirect
6. #31826821C2semidirect
7. #31826465C2semidirect
8. #31826417C2semidirect
9. #491×C283C2semidirect
90. C283#3142semidirect
95. #491D283semidirect

Maximal subgroups

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

subgroupindex
#318270162
#125×D2832
#318268332
#318268312
#318268302
#318268212
#318264652
#318264172
#491×C2832
#3142283