Finite Group Databasebeta

← #20292798

Subgroups — #20292798

Order 6848.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#16812156C211yesmaximal, characteristic, complemented
2#16812135C211yesmaximal, characteristic, complemented
3#16812096C211yesmaximal, characteristic, complemented
4#16812036C211yesmaximal, characteristic, complemented
5#16812035C211yesmaximal, characteristic, complemented
6#16812027C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C107C211yesmaximal, characteristic, complemented
8#13133818—21no—
9#13133818C2211yescharacteristic
10#13133817—21no—
11#13133817—22no—
12C2×Dic214—21no—
13C2×Dic214C2211yescharacteristic
14Q8×D107—21no—
15#13133806—21no—
16#13133803—21no—
17#13133802C2211yescharacteristic
18C22⋊Dic107—22no—
19C4×Dic107C2211yescharacteristic
20#41×C107C2211yescharacteristic
21C2×D4×C107C2211yescharacteristic
22SD16×C107—21no—
23D8×C107—21no—
24M16×C107C2211yescharacteristic
25C23×C107—21no—
26Q8×C107D411yescharacteristic
27D4×C107—21no—
28D4×C107—21no—
29D4×C107—21no—
30D4×C107D411yescharacteristic
31C2×C4×C107—21no—
32C2×C4×C107C2311yescharacteristic
33C22⋊D107—22no—
34C22⋊D107—21no—
35C2×Dic107—22no—
36C2×Dic107—21no—
37C2×Dic107D412yes—
38D428D411yescharacteristic
39C4×D107—22no—
40C4×D107—21no—
41Dic214—22no—
42Dic214—21no—
43Dic214—21no—
44Dic214D411yescharacteristic
45C8×C107—21no—
46C107⋊C8—21no—
47C22×C107—21no—
48C22×C107—42no—
49C22×C107—41no—
50C22×C107C2×D411yescharacteristic
51C2×D107—21no—
52C4×C107—21no—
53C4×C107C2×D411yescharacteristic
54C4×C107C2×D411yescharacteristic
55Dic107—22no—
56Dic107—21no—
57Dic107—41no—
58C2×C107—21no—
59C2×C107—41no—
60C2×C107—81no—
61C2×C107#12011yescharacteristic
62D107—41no—
63C107#45411yescharacteristic, complemented, Sylow
64#454—1071nomaximal, Sylow
652−1+4—1071no—
66AGL(1,ℤ/8)—1071no—
67AGL(1,ℤ/8)D10711yescharacteristic, complemented
68#124—1071no—
69#104—1071no—
70#104—1071no—
71#101—1071no—
72#41—1071no—
73#41—2141no—
74#41—2142no—
75#41—2141no—
76#41C2×D10711yescharacteristic
77C2×Q8—1071no—
78C2×Q8—2141no—
79C2×Q8—2141no—
80C2×D4C2×D10711yescharacteristic
81SD16—21no—
82SD16—2141no—
83D8—21no—
84D8—2141no—
85M16—1071no—
86M16C2×D10711yescharacteristic
87C22⋊C4—2142no—
88C42—1071no—
89C23—21no—
90Q8—1071no—
91Q8—2142no—
92Q8—2141no—
93Q8—2141no—
94Q8C22⋊D10711yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—1071no—
99D4—2142no—
100D4—2141no—
101D4C22⋊D10711yescharacteristic
102C2×C4—21no—
103C2×C4—1072no—
104C2×C4—2142no—
105C2×C4—2141no—
106C2×C4—2142no—
107C2×C4—2141no—
108C2×C4C22×D10711yescharacteristic
109C8—21no—
110C8—2141no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—2141no—
115C22D4×D10711yescharacteristic
116C4—21no—
117C4—4281no—
118C4—2142no—
119C4—2141no—
120C4D4×D10711yescharacteristic
121C4C2×C22⋊D10711yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—4281no—
126C2#1681207711yescharacteristic
subgroupG/H
centerC2#16812077
commutatorC2×C4×C107C23
FrattiniC2×C4C22×D107
FittingAGL(1,ℤ/8)×C107C2
socleC2×C107#120
hypercenterAGL(1,ℤ/8)D107
hypocenterC107#454
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16812156C2semidirect
2. #16812135C2semidirect
3. #16812096C2semidirect
4. #16812036C2semidirect
5. #16812035C2semidirect
6. #16812027C2semidirect
7. AGL(1,ℤ/8)×C107C2semidirect
63. C107#454semidirect
67. AGL(1,ℤ/8)D107semidirect