Finite Group Databasebeta

← #44548872

Subgroups — #44548872

Order 32128.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#30632237C211yesmaximal, characteristic
2#30631744C211yesmaximal, characteristic, complemented
3#30631420C214yesmaximal, complemented
4#376×C251C211yesmaximal, characteristic, complemented
5C2×#16860810—21no—
6#22548715C411yescharacteristic, complemented
7#22548712C411yescharacteristic, complemented
8#22548703—21no—
9#22548689—21no—
10#22548689C2212yes—
11C4×D1004—21no—
12C4×D1004C412yescomplemented
13C4⋊(C251⋊C8)—21no—
14C22⋊(C251⋊C8)C2212yes—
15#22548626—21no—
16C2×C42×C251—21no—
17C2×C42×C251C2211yescharacteristic
18#95×C251—21no—
19#95×C251C2212yes—
20#16860810—44no—
21C2×Dic502—21no—
22C2×D1004—21no—
23C2×D1004—21no—
24C2×D1004C2×C412yes—
25C2×C22⋊D251—22no—
26C2×C4×D251—22no—
27C2×C251⋊C8—22no—
28C4⋊Dic251—21no—
29C4⋊Dic251C2×C412yes—
30(C2×D251)⋊C4—22no—
31(C2×D251)⋊C4—22no—
32C22×C4×C251—22no—
33C22×C4×C251D411yescharacteristic
34C22×C4×C251D411yescharacteristic
35C22×C4×C251C2311yescharacteristic
36C42×C251—24no—
37C42×C251C2×C411yescharacteristic
38C42×C251C2×C411yescharacteristic
39C42×C251D411yescharacteristic
40C42×C251D411yescharacteristic
41C22×D251—22no—
42Dic502—42no—
43D1004—42no—
44D1004—42no—
45D1004—42no—
46C22⋊D251—44no—
47C2×Dic251—22no—
48C4×D251—44no—
49C251⋊C8—42no—
50C23×C251C2×D411yescharacteristic
51C2×C4×C251—22no—
52C2×C4×C251—22no—
53C2×C4×C251—24no—
54C2×C4×C251—41no—
55C2×C4×C251—42no—
56C2×C4×C251—42no—
57C2×C4×C251C22⋊C411yescharacteristic
58C2×C4×C251C22⋊C411yescharacteristic
59C2×C4×C251C22⋊C411yescharacteristic
60C2×C4×C251C22⋊C411yescharacteristic
61C2×C4×C251C22×C411yescharacteristic
62C2×C4×C251C2×D411yescharacteristic
63C22×C251—21no—
64C22×C251—21no—
65C22×C251C2×C22⋊C411yescharacteristic
66C22×C251AGL(1,ℤ/8)12yes—
67C2×D251—42no—
68C2×D251—42no—
69C2×D251—42no—
70C4×C251—21no—
71C4×C251—21no—
72C4×C251—21no—
73C4×C251—21no—
74C4×C251—21no—
75C4×C251—44no—
76C4×C251#10412yes—
77Dic251—42no—
78C2×C251—22no—
79C2×C251#41011yescharacteristic
80C2×C251#41811yescharacteristic
81C2×C251C2×#10411yescharacteristic
82D251—82no—
83C251#150511yescharacteristic, complemented, Sylow
84#1505—2511nomaximal, Sylow
85#532—2511no—
86#432—2511no—
87#376D25111yescharacteristic, complemented
88#327—2514no—
89C2×#41—5021no—
90C4⋊Q8—2511no—
91#127—2511no—
92#124—5021no—
93#121—5021no—
94#121—2512no—
95C4×D4—5021no—
96C4×D4—2512no—
97C2×C42—21no—
98C2×C42C2×D25111yescharacteristic
99C4⋊C8—5021no—
100C22⋊C8—2512no—
101#97—5021no—
102#95—21no—
103#95C2×D25112yes—
104#41—10044no—
105C2×Q8—5021no—
106C2×D4—5022no—
107C2×D4—5021no—
108C2×D4—5021no—
109C2×D4—2512no—
110C22×C4—22no—
111C22×C4—5022no—
112C22×C4C22⋊D25111yescharacteristic
113C22×C4C22⋊D25111yescharacteristic
114C22×C4C22×D25111yescharacteristic
115C2×C8—5022no—
116C4⋊C4—5021no—
117C4⋊C4—2512no—
118C22⋊C4—5022no—
119C22⋊C4—5022no—
120C42—24no—
121C42C4×D25111yescharacteristic
122C42C4×D25111yescharacteristic
123C42D100411yescharacteristic
124C42D100411yescharacteristic
125C23—5022no—
126C23C2×C22⋊D25111yescharacteristic
127Q8—10042no—
128D4—10042no—
129D4—10042no—
130D4—10044no—
131D4—10042no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—10044no—
139C2×C4—5022no—
140C2×C4(C2×D251)⋊C411yescharacteristic
141C2×C4(C2×D251)⋊C411yescharacteristic
142C2×C4(C2×D251)⋊C411yescharacteristic
143C2×C4(C2×D251)⋊C411yescharacteristic
144C2×C4C2×C4×D25111yescharacteristic
145C2×C4C2×D100411yescharacteristic
146C8—10042no—
147C22—21no—
148C22—21no—
149C22—10042no—
150C22—10042no—
151C22—10042no—
152C22C2×(C2×D251)⋊C411yescharacteristic
153C22#2254874012yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—10042no—
161C4#2254864312yes—
162C2—22no—
163C2—20082no—
164C2#3063166011yescharacteristic
165C2#3063169111yescharacteristic
166C2C2×#2254864311yescharacteristic
subgroupG/H
centerC22C2×(C2×D251)⋊C4
commutatorC2×C4×C251C22×C4
FrattiniC22×C4C22×D251
Fitting#376×C251C2
socleC22×C251C2×C22⋊C4
prime radical#30632237C2
cosocleC22×C4×C251C23
hypercenter#376D251
hypocenterC251#1505
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #30631744C2semidirect
3. #30631420C2semidirect
4. #376×C251C2semidirect
6. #22548715C4semidirect
7. #22548712C4semidirect
12. C4×D1004C4semidirect
83. C251#1505semidirect
87. #376D251semidirect

Maximal subgroups

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

subgroupindex
#306322372
#306317442
#306314202
#376×C2512
#1505251