Finite Group Databasebeta

← #20267985

Subgroups — #20267985

Order 6592.

140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C2×D824C211yesmaximal, characteristic, complemented
2C2×#13110090C211yesmaximal, characteristic, complemented
3#15693017C211yesmaximal, characteristic, complemented
4#15692983C211yesmaximal, characteristic, complemented
5Dic103⋊C8C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11C2×C22⋊D103—21no—
12C2×C4×D103—21no—
13D824—22no—
14#13110090—22no—
15C2×C103⋊C8C2211yescharacteristic
16(C2×D103)⋊C4—21no—
17C4×Dic103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C23×C103—21no—
22C22×D103—21no—
23C22×D103—21no—
24D4×C103—21no—
25D4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C22⋊D103—42no—
29C22⋊D103—42no—
30C2×Dic103D411yescharacteristic
31C2×Dic103D411yescharacteristic
32D412—21no—
33D412—21no—
34D412—21no—
35D412D412yescomplemented
36C4×D103—42no—
37C8×C103—21no—
38C103⋊C8—21no—
39C22×C103—41no—
40C22×C103—41no—
41C22×C103—41no—
42C22×C103C2×D411yescharacteristic
43C2×D103—22no—
44C2×D103—41no—
45C2×D103—41no—
46C2×D103—41no—
47C2×D103—41no—
48C2×D103—41no—
49C4×C103—41no—
50C4×C103C2×D411yescharacteristic
51C4×C103#4111yescharacteristic
52Dic103—21no—
53Dic103D812yescomplemented
54C2×C103—81no—
55C2×C103#12111yescharacteristic
56C2×C103C2×D811yescharacteristic
57C2×C103AGL(1,ℤ/8)11yescharacteristic
58D103—42no—
59D103—81no—
60C103#45911yescharacteristic, complemented, Sylow
61#459—1031nomaximal, Sylow
62C2×D8—1031no—
63C2×D8—1031no—
64#127—1031no—
65C4×D4—1031no—
66C4⋊C8—1031no—
67#102—1031no—
68#102D10311yescharacteristic, complemented
69C2×D4—1031no—
70C2×D4—1031no—
71C2×D4—2061no—
72C2×D4—2061no—
73C2×D4C2×D10311yescharacteristic
74C22×C4—2061no—
75D8—2062no—
76D8—2062no—
77C2×C8—1031no—
78C2×C8C2×D10311yescharacteristic
79C4⋊C4C2×D10311yescharacteristic
80C22⋊C4—2061no—
81C42—1031no—
82C23—21no—
83C23—2061no—
84C23—2061no—
85D4—21no—
86D4—21no—
87D4—1032no—
88D4—4122no—
89D4—4122no—
90D4—2061no—
91D4—2061no—
92D4—2061no—
93C2×C4—21no—
94C2×C4—1031no—
95C2×C4—1031no—
96C2×C4—4122no—
97C2×C4C22×D10311yescharacteristic
98C8—21no—
99C8—2061no—
100C22—41no—
101C22—41no—
102C22—41no—
103C22—4121no—
104C22—4121no—
105C22—4121no—
106C22—4121no—
107C22—4121no—
108C22—2062no—
109C22D4×D10311yescharacteristic
110C4—41no—
111C4—1032no—
112C4—2061no—
113C4D4×D10311yescharacteristic
114C4#1311010511yescharacteristic
115C2—81no—
116C2—8241no—
117C2—4122no—
118C2#1569299411yescharacteristic
119C2D8×D10311yescharacteristic
120C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#459
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D824C2semidirect
2. C2×#13110090C2semidirect
3. #15693017C2semidirect
4. #15692983C2semidirect
5. Dic103⋊C8C2semidirect
6. #15692941C2semidirect
7. #102×C103C2semidirect
35. D412D4semidirect
53. Dic103D8semidirect
60. C103#459semidirect
68. #102D103semidirect