Finite Group Databasebeta

← #44483055

Subgroups — #44483055

Order 30592.

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#29505322C211yesmaximal, characteristic
2#29504829C211yesmaximal, characteristic, complemented
3#29504505C214yesmaximal, complemented
4#376×C239C211yesmaximal, characteristic, complemented
5C2×#16838548—21no—
6#21439960C411yescharacteristic, complemented
7#21439957C411yescharacteristic, complemented
8#21439948—21no—
9#21439934—21no—
10#21439934C2212yes—
11C4×D956—21no—
12C4×D956C412yescomplemented
13C4⋊(C239⋊C8)—21no—
14C22⋊(C239⋊C8)C2212yes—
15#21439871—21no—
16C2×C42×C239—21no—
17C2×C42×C239C2211yescharacteristic
18#95×C239—21no—
19#95×C239C2212yes—
20#16838548—44no—
21C2×Dic478—21no—
22C2×D956—21no—
23C2×D956—21no—
24C2×D956C2×C412yes—
25C2×C22⋊D239—22no—
26C2×C4×D239—22no—
27C2×C239⋊C8—22no—
28C4⋊Dic239—21no—
29C4⋊Dic239C2×C412yes—
30(C2×D239)⋊C4—22no—
31(C2×D239)⋊C4—22no—
32C22×C4×C239—22no—
33C22×C4×C239D411yescharacteristic
34C22×C4×C239D411yescharacteristic
35C22×C4×C239C2311yescharacteristic
36C42×C239—24no—
37C42×C239C2×C411yescharacteristic
38C42×C239C2×C411yescharacteristic
39C42×C239D411yescharacteristic
40C42×C239D411yescharacteristic
41C22×D239—22no—
42Dic478—42no—
43D956—42no—
44D956—42no—
45D956—42no—
46C22⋊D239—44no—
47C2×Dic239—22no—
48C4×D239—44no—
49C239⋊C8—42no—
50C23×C239C2×D411yescharacteristic
51C2×C4×C239—22no—
52C2×C4×C239—22no—
53C2×C4×C239—24no—
54C2×C4×C239—41no—
55C2×C4×C239—42no—
56C2×C4×C239—42no—
57C2×C4×C239C22⋊C411yescharacteristic
58C2×C4×C239C22⋊C411yescharacteristic
59C2×C4×C239C22⋊C411yescharacteristic
60C2×C4×C239C22⋊C411yescharacteristic
61C2×C4×C239C22×C411yescharacteristic
62C2×C4×C239C2×D411yescharacteristic
63C22×C239—21no—
64C22×C239—21no—
65C22×C239C2×C22⋊C411yescharacteristic
66C22×C239AGL(1,ℤ/8)12yes—
67C2×D239—42no—
68C2×D239—42no—
69C2×D239—42no—
70C4×C239—21no—
71C4×C239—21no—
72C4×C239—21no—
73C4×C239—21no—
74C4×C239—21no—
75C4×C239—44no—
76C4×C239#10412yes—
77Dic239—42no—
78C2×C239—22no—
79C2×C239#41011yescharacteristic
80C2×C239#41811yescharacteristic
81C2×C239C2×#10411yescharacteristic
82D239—82no—
83C239#150511yescharacteristic, complemented, Sylow
84#1505—2391nomaximal, Sylow
85#532—2391no—
86#432—2391no—
87#376D23911yescharacteristic, complemented
88#327—2394no—
89C2×#41—4781no—
90C4⋊Q8—2391no—
91#127—2391no—
92#124—4781no—
93#121—4781no—
94#121—2392no—
95C4×D4—4781no—
96C4×D4—2392no—
97C2×C42—21no—
98C2×C42C2×D23911yescharacteristic
99C4⋊C8—4781no—
100C22⋊C8—2392no—
101#97—4781no—
102#95—21no—
103#95C2×D23912yes—
104#41—9564no—
105C2×Q8—4781no—
106C2×D4—4782no—
107C2×D4—4781no—
108C2×D4—4781no—
109C2×D4—2392no—
110C22×C4—22no—
111C22×C4—4782no—
112C22×C4C22⋊D23911yescharacteristic
113C22×C4C22⋊D23911yescharacteristic
114C22×C4C22×D23911yescharacteristic
115C2×C8—4782no—
116C4⋊C4—4781no—
117C4⋊C4—2392no—
118C22⋊C4—4782no—
119C22⋊C4—4782no—
120C42—24no—
121C42C4×D23911yescharacteristic
122C42C4×D23911yescharacteristic
123C42D95611yescharacteristic
124C42D95611yescharacteristic
125C23—4782no—
126C23C2×C22⋊D23911yescharacteristic
127Q8—9562no—
128D4—9562no—
129D4—9562no—
130D4—9564no—
131D4—9562no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—9564no—
139C2×C4—4782no—
140C2×C4(C2×D239)⋊C411yescharacteristic
141C2×C4(C2×D239)⋊C411yescharacteristic
142C2×C4(C2×D239)⋊C411yescharacteristic
143C2×C4(C2×D239)⋊C411yescharacteristic
144C2×C4C2×C4×D23911yescharacteristic
145C2×C4C2×D95611yescharacteristic
146C8—9562no—
147C22—21no—
148C22—21no—
149C22—9562no—
150C22—9562no—
151C22—9562no—
152C22C2×(C2×D239)⋊C411yescharacteristic
153C22#2143998512yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—9562no—
161C4#2143988812yes—
162C2—22no—
163C2—19122no—
164C2#2950474511yescharacteristic
165C2#2950477611yescharacteristic
166C2C2×#2143988811yescharacteristic
subgroupG/H
centerC22C2×(C2×D239)⋊C4
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#376×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505322C2
cosocleC22×C4×C239C23
hypercenter#376D239
hypocenterC239#1505
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #29504829C2semidirect
3. #29504505C2semidirect
4. #376×C239C2semidirect
6. #21439960C4semidirect
7. #21439957C4semidirect
12. C4×D956C4semidirect
83. C239#1505semidirect
87. #376D239semidirect

Maximal subgroups

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

subgroupindex
#295053222
#295048292
#295045052
#376×C2392
#1505239