Finite Group Databasebeta

← #28361668

Subgroups — #28361668

Order 13952.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#20295582C211yesmaximal, characteristic
2#20295081C212yesmaximal
3#20294768C211yesmaximal, characteristic, complemented
4#20294767C212yesmaximal, complemented
5#330×C109C211yesmaximal, characteristic, complemented
6#16812698C412yes—
7#16812691C2211yescharacteristic
8#16812677—22no—
9#16812664—22no—
10#16812657C412yes—
11C42×D109C2211yescharacteristic
12#16812628—22no—
13#16812611—22no—
14#16812610C2212yes—
15#125×C109C2211yescharacteristic
16#97×C109C2212yes—
17C2×Dic218—22no—
18C2×C4×D109C2×C411yescharacteristic
19C2×C4×D109D412yes—
20C2×#11724784—22no—
21C4⋊Dic109C2×C412yes—
22#13182008—22no—
23#13182008—22no—
24#13182006—22no—
25C4×Dic109—22no—
26C4×Dic109C2×C411yescharacteristic
27C4×Dic109D412yes—
28C2×C8×C109—22no—
29C4⋊C4×C109—22no—
30C4⋊C4×C109C2×C412yes—
31C42×C109C2311yescharacteristic
32C22×D109C22⋊C411yescharacteristic
33C2×C4×C109—22no—
34C2×C4×C109C22×C411yescharacteristic
35C2×C4×C109C2×D412yes—
36C2×Dic109—22no—
37C2×Dic109C22⋊C412yes—
38C2×Dic109C22⋊C411yescharacteristic
39C4×D109—22no—
40C4×D109—42no—
41Dic218—44no—
42C8×C109—42no—
43#11724784—42no—
44C22×C109C2×C22⋊C411yescharacteristic
45C2×D109—21no—
46C2×D109—22no—
47C4×C109—21no—
48C4×C109—22no—
49C4×C109—42no—
50Dic109—22no—
51Dic109—42no—
52Dic109#10112yes—
53C2×C109C2×#10111yescharacteristic
54C2×C109#42112yes—
55D109—41no—
56#1537—1091nomaximal, Sylow
57C109#153711yescharacteristic, complemented, Sylow
58#533—1091no—
59#432—1092no—
60#330—1091no—
61#330—1092no—
62#330D10911yescharacteristic, complemented
63C4⋊Q8—1092no—
64#125—1091no—
65#125C2×D10911yescharacteristic
66C22⋊Q8—2182no—
67C4×Q8—2182no—
68#117—1092no—
69C2×C42—1091no—
70C4⋊C8—2182no—
71C22⋊C8—2182no—
72#97—1092no—
73#97C2×D10912yes—
74C2×Q8—2182no—
75C22×C4—1092no—
76C22×C4—1091no—
77C2×C8—22no—
78C2×C8—2182no—
79C4⋊C4—22no—
80C4⋊C4—1092no—
81C4⋊C4—2182no—
82C4⋊C4—2182no—
83C4⋊C4C4×D10912yes—
84C22⋊C4—2182no—
85C42—1091no—
86C42—1092no—
87C42—2182no—
88C42C22×D10911yescharacteristic
89C23—1091no—
90Q8—4364no—
91C2×C4—22no—
92C2×C4—1091no—
93C2×C4—1092no—
94C2×C4—4362no—
95C2×C4—2182no—
96C2×C4—2182no—
97C2×C4C2×C4×D10911yescharacteristic
98C2×C4D4×D10912yes—
99C8—42no—
100C8—4362no—
101C22—2181no—
102C22—2182no—
103C22C22⋊C4×D10911yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—1092no—
108C4—4362no—
109C4—2182no—
110C2—4361no—
111C2#101×D10911yescharacteristic
112C2#2029504112yes—
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC42C22×D109
Fitting#330×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C22⋊C4
cosocleC42×C109C23
hypercenter#330D109
hypocenterC109#1537
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20294768C2semidirect
4. #20294767C2semidirect
5. #330×C109C2semidirect
57. C109#1537semidirect
62. #330D109semidirect

Maximal subgroups

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

subgroupindex
#202955822
#202950812
#202947682
#202947672
#330×C1092
#1537109