Finite Group Databasebeta

← #28362356

Subgroups — #28362356

Order 13952.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#20295774C211yesmaximal, characteristic
2#20295396C211yesmaximal, characteristic, complemented
3#20295386C212yesmaximal, complemented
4#20294765C212yesmaximal, complemented
5#330×C109C211yesmaximal, characteristic, complemented
6#16812699C2211yescharacteristic
7#16812687C2212yes—
8#16812684—22no—
9#16812677—22no—
10#16812674—22no—
11#16812624—22no—
12#16812622—22no—
13#16812621—22no—
14#16812610C2211yescharacteristic
15#125×C109C2211yescharacteristic
16#97×C109C2212yes—
17C2×Dic218—21no—
18C2×Dic218D412yes—
19C2×D436—22no—
20C2×D436D412yes—
21C2×C4×D109—22no—
22C2×#11724784—21no—
23C4⋊Dic109—22no—
24#13182008—22no—
25#13182006—22no—
26#13182006—22no—
27#13182006—22no—
28C2×C8×C109—22no—
29C4⋊C4×C109—22no—
30C4⋊C4×C109D412yes—
31C42×C109C2311yescharacteristic
32C22×D109—22no—
33C2×C4×C109—22no—
34C2×C4×C109C2×D412yes—
35C2×C4×C109C2×D411yescharacteristic
36C2×Dic109—22no—
37C2×Dic109—41no—
38D436—42no—
39D436—82no—
40C4×D109—82no—
41Dic218—42no—
42Dic218—42no—
43C8×C109—42no—
44#11724784—41no—
45C22×C109#12011yescharacteristic
46C2×D109—42no—
47C2×D109—42no—
48C2×D109—42no—
49C4×C109—21no—
50C4×C109—22no—
51C4×C109—42no—
52Dic109—42no—
53Dic109—81no—
54C2×C109#45411yescharacteristic
55C2×C109#45512yes—
56D109—82no—
57#1662—1091nomaximal, Sylow
58C109#166211yescharacteristic, complemented, Sylow
59#562—1091no—
60#491—1091no—
61#489—1092no—
62#330D10911yescharacteristic, complemented
63#329—1092no—
64C4⋊Q8—1091no—
65#125C2×D10911yescharacteristic
66#124—1092no—
67#123—2182no—
68C22⋊Q8—2182no—
69#121—2182no—
70#103—2182no—
71#103—2182no—
72#102—2182no—
73#97—1091no—
74#97C2×D10912yes—
75C2×Q8—1092no—
76C2×Q8—2181no—
77C2×D4—1092no—
78C2×D4—2182no—
79C22×C4—2182no—
80C2×C8—22no—
81C2×C8—2181no—
82C4⋊C4—22no—
83C4⋊C4—2182no—
84C4⋊C4—2182no—
85C4⋊C4D43612yes—
86C22⋊C4—2182no—
87C22⋊C4—2182no—
88C22⋊C4—2182no—
89C42C22×D10911yescharacteristic
90C23—2182no—
91Q8—4362no—
92Q8—4362no—
93D4—8722no—
94D4—4362no—
95C2×C4—22no—
96C2×C4—8722no—
97C2×C4—4361no—
98C2×C4—2182no—
99C2×C4D4×D10912yes—
100C2×C4C2×D43611yescharacteristic
101C8—42no—
102C8—4361no—
103C22—4362no—
104C22—4362no—
105C22—4362no—
106C22#1681266911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—8721no—
111C4—4362no—
112C2—8722no—
113C2#2029520111yescharacteristic
114C2#2029520512yes—
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#330×C109C2
socleC22×C109#120
prime radical#20295774C2
hypercenter#330D109
hypocenterC109#1662
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20295396C2semidirect
3. #20295386C2semidirect
4. #20294765C2semidirect
5. #330×C109C2semidirect
58. C109#1662semidirect
62. #330D109semidirect

Maximal subgroups

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

subgroupindex
#202957742
#202953962
#202953862
#202947652
#330×C1092
#1662109