Finite Group Databasebeta

← #28335054

Subgroups — #28335054

Order 13696.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#20293183C211yesmaximal, characteristic
2#20292579C212yesmaximal
3#20292369C211yesmaximal, characteristic, complemented
4#20292368C212yesmaximal, complemented
5#330×C107C211yesmaximal, characteristic, complemented
6C2×#13133801—22no—
7#16812108C412yes—
8#16812101C2211yescharacteristic
9#16812087—22no—
10#16812074—22no—
11#16812067C412yes—
12C42×D107C2211yescharacteristic
13#16812020C2212yes—
14C8×Dic107—22no—
15#125×C107C2211yescharacteristic
16#97×C107C2212yes—
17C2×Dic214—22no—
18C2×C4×D107C2×C411yescharacteristic
19C2×C4×D107D412yes—
20#13133801—28no—
21C2×C107⋊C8—22no—
22C4⋊Dic107C2×C412yes—
23Dic107⋊C4—22no—
24Dic107⋊C4—22no—
25(C2×D107)⋊C4—22no—
26C4×Dic107—22no—
27C4×Dic107C2×C411yescharacteristic
28C4×Dic107D412yes—
29C2×C8×C107—22no—
30C4⋊C4×C107—22no—
31C4⋊C4×C107C2×C412yes—
32C42×C107C2311yescharacteristic
33C22×D107C22⋊C411yescharacteristic
34C2×C4×C107—22no—
35C2×C4×C107C22×C411yescharacteristic
36C2×C4×C107C2×D412yes—
37C2×Dic107—22no—
38C2×Dic107C22⋊C411yescharacteristic
39C2×Dic107C22⋊C412yes—
40C4×D107—22no—
41C4×D107—24no—
42Dic214—44no—
43C8×C107—24no—
44C107⋊C8—24no—
45C22×C107C2×C22⋊C411yescharacteristic
46C2×D107—21no—
47C2×D107—22no—
48C4×C107—21no—
49C4×C107—22no—
50C4×C107—42no—
51Dic107—42no—
52Dic107#10112yes—
53Dic107#10414yes—
54C2×C107C2×#10111yescharacteristic
55C2×C107C2×#10412yes—
56D107—41no—
57#1526—1071nomaximal, Sylow
58C107#152611yescharacteristic, complemented, Sylow
59#533—1071no—
60C4×M16—1072no—
61#330—1071no—
62#330—1072no—
63#330D10711yescharacteristic, complemented
64C2×M16—2142no—
65C4⋊Q8—1072no—
66#125—1071no—
67#125C2×D10711yescharacteristic
68C22⋊Q8—2142no—
69C4×Q8—2142no—
70#117—1072no—
71C2×C42—1071no—
72#97—1072no—
73#97C2×D10712yes—
74C4×C8—2142no—
75C2×Q8—2142no—
76C22×C4—1071no—
77C22×C4—1072no—
78M16—2148no—
79C2×C8—22no—
80C2×C8—2142no—
81C4⋊C4—22no—
82C4⋊C4—1072no—
83C4⋊C4—2142no—
84C4⋊C4—2142no—
85C4⋊C4C4×D10712yes—
86C22⋊C4—2142no—
87C42—1071no—
88C42—1072no—
89C42—2142no—
90C42C22×D10711yescharacteristic
91C23—1071no—
92Q8—4284no—
93C2×C4—22no—
94C2×C4—1071no—
95C2×C4—1072no—
96C2×C4—2144no—
97C2×C4—2142no—
98C2×C4—2142no—
99C2×C4C2×C4×D10711yescharacteristic
100C2×C4D4×D10712yes—
101C8—24no—
102C8—2144no—
103C22—2142no—
104C22—2141no—
105C22C22⋊C4×D10711yescharacteristic
106C4—22no—
107C4—21no—
108C4—42no—
109C4—1074no—
110C4—1072no—
111C4—4282no—
112C2—4281no—
113C2#101×D10711yescharacteristic
114C2#104×D10712yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×D107C22⋊C4
cosocleC42×C107C23
hypercenter#330D107
hypocenterC107#1526
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20292369C2semidirect
4. #20292368C2semidirect
5. #330×C107C2semidirect
58. C107#1526semidirect
63. #330D107semidirect

Maximal subgroups

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

subgroupindex
#202931832
#202925792
#202923692
#202923682
#330×C1072
#1526107