Finite Group Databasebeta

← #49119809

Subgroups — #49119809

Order 36224.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#31827015C211yesmaximal, characteristic
2#31826333C211yesmaximal, characteristic, complemented
3#31826200C214yesmaximal, complemented
4#432×C283C211yesmaximal, characteristic, complemented
5C2×#17985392—21no—
6#22583610C411yescharacteristic, complemented
7#22583607C411yescharacteristic, complemented
8#22583598—21no—
9#22583584—21no—
10#22583584C2212yes—
11C4×D1132—21no—
12C4×D1132C412yescomplemented
13C283⋊#95—21no—
14C283⋊#95—21no—
15C283⋊#95C2212yes—
16C2×C42×C283C2211yescharacteristic
17C4⋊C8×C283—21no—
18C22⋊C8×C283C2212yes—
19#97×C283—21no—
20#17985392—44no—
21C2×Dic566—21no—
22C2×D1132—21no—
23C2×D1132—21no—
24C2×D1132C2×C412yes—
25C2×C22⋊D283—22no—
26C22×Dic283—22no—
27C2×C4×D283—22no—
28C4⋊Dic283—21no—
29C4⋊Dic283C2×C412yes—
30(C2×D283)⋊C4—22no—
31(C2×D283)⋊C4—22no—
32C22×C4×C283D411yescharacteristic
33C22×C4×C283D411yescharacteristic
34C22×C4×C283C2311yescharacteristic
35C2×C8×C283—22no—
36C42×C283C2×C411yescharacteristic
37C42×C283C2×C411yescharacteristic
38C42×C283D411yescharacteristic
39C42×C283D411yescharacteristic
40C22×D283—22no—
41Dic566—42no—
42D1132—42no—
43D1132—42no—
44D1132—42no—
45C22⋊D283—44no—
46C2×Dic283—22no—
47C2×Dic283—42no—
48C2×Dic283—42no—
49C2×Dic283—42no—
50C4×D283—44no—
51C23×C283C2×D411yescharacteristic
52C2×C4×C283—22no—
53C2×C4×C283—41no—
54C2×C4×C283—41no—
55C2×C4×C283C22⋊C411yescharacteristic
56C2×C4×C283C22⋊C411yescharacteristic
57C2×C4×C283C22⋊C411yescharacteristic
58C2×C4×C283C22⋊C411yescharacteristic
59C2×C4×C283C22×C411yescharacteristic
60C2×C4×C283C2×D411yescharacteristic
61C8×C283—42no—
62C22×C283—21no—
63C22×C283—21no—
64C22×C283C2×C22⋊C411yescharacteristic
65C22×C283AGL(1,ℤ/8)12yes—
66C2×D283—42no—
67C2×D283—42no—
68C2×D283—42no—
69C4×C283—21no—
70C4×C283—21no—
71C4×C283—21no—
72C4×C283—21no—
73C4×C283—21no—
74C4×C283—21no—
75Dic283—42no—
76Dic283—82no—
77C2×C283—22no—
78C2×C283#41011yescharacteristic
79C2×C283#41811yescharacteristic
80C2×C283#42111yescharacteristic
81D283—82no—
82C283#151411yescharacteristic, complemented, Sylow
83#1514—2831nomaximal, Sylow
84#532—2831no—
85#432D28311yescharacteristic, complemented
86#383—2831no—
87#327—2834no—
88C2×#41—5661no—
89C4⋊Q8—2831no—
90#127—2831no—
91#124—5661no—
92#121—2832no—
93#121—5661no—
94C4×D4—2832no—
95C4×D4—5661no—
96C2×C42C2×D28311yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D28312yes—
99#97—21no—
100#95—2832no—
101#95—5661no—
102#95—5661no—
103#41—11324no—
104C2×Q8—5661no—
105C2×D4—2832no—
106C2×D4—5662no—
107C2×D4—5661no—
108C2×D4—5661no—
109C22×C4—5662no—
110C22×C4—5662no—
111C22×C4D113211yescharacteristic
112C22×C4D113211yescharacteristic
113C22×C4C22×D28311yescharacteristic
114C2×C8—22no—
115C4⋊C4—2832no—
116C4⋊C4—5661no—
117C22⋊C4—5662no—
118C22⋊C4—5662no—
119C42C4×D28311yescharacteristic
120C42C4×D28311yescharacteristic
121C42C22⋊D28311yescharacteristic
122C42C22⋊D28311yescharacteristic
123C23—5662no—
124C23C2×D113211yescharacteristic
125Q8—11322no—
126D4—11322no—
127D4—11322no—
128D4—11322no—
129D4—11324no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—5662no—
134C2×C4—11324no—
135C2×C4—11322no—
136C2×C4—11322no—
137C2×C4—11322no—
138C2×C4(C2×D283)⋊C411yescharacteristic
139C2×C4(C2×D283)⋊C411yescharacteristic
140C2×C4(C2×D283)⋊C411yescharacteristic
141C2×C4(C2×D283)⋊C411yescharacteristic
142C2×C4C2×C4×D28311yescharacteristic
143C2×C4C2×C22⋊D28311yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—11322no—
148C22—11322no—
149C22—11322no—
150C22C2×(C2×D283)⋊C411yescharacteristic
151C22#2258363812yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—11322no—
159C4—22642no—
160C2—22no—
161C2—22642no—
162C2#3182643811yescharacteristic
163C2#3182647111yescharacteristic
164C2#3182648111yescharacteristic
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#432×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31827015C2
cosocleC22×C4×C283C23
hypercenter#432D283
hypocenterC283#1514
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #31826333C2semidirect
3. #31826200C2semidirect
4. #432×C283C2semidirect
6. #22583610C4semidirect
7. #22583607C4semidirect
12. C4×D1132C4semidirect
82. C283#1514semidirect
85. #432D283semidirect

Maximal subgroups

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

subgroupindex
#318270152
#318263332
#318262002
#432×C2832
#1514283