Finite Group Databasebeta

← #28362344

Subgroups — #28362344

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#20295776C211yesmaximal, characteristic
2#20295435C212yesmaximal, complemented
3#20295421C211yesmaximal, characteristic
4#20294767C212yesmaximal, complemented
5#329×C109C211yesmaximal, characteristic
6C2×#13182019—21no—
7C2×#13182017—21no—
8#16812699C2211yescharacteristic
9#16812697—21no—
10#16812692—22no—
11#16812691C2212yes—
12#16812680—21no—
13#16812676—22no—
14#16812633—22no—
15#16812631—22no—
16#16812610C2211yescharacteristic
17#124×C109C2211yescharacteristic
18#97×C109C2212yes—
19C2×Dic218—21no—
20C2×Dic218—21no—
21C22×Dic109—21no—
22#13182019—42no—
23#13182017—42no—
24C2×#11724784—21no—
25C4⋊Dic109—22no—
26C4⋊Dic109D412yes—
27C4⋊Dic109D412yes—
28#13182008—22no—
29#13182008—22no—
30#13182008—22no—
31C22⋊Dic109—22no—
32C22⋊Dic109—21no—
33C4×Dic109—21no—
34C2×Q8×C109D411yescharacteristic
35C2×D4×C109D411yescharacteristic
36C2×C8×C109—22no—
37C22⋊C4×C109—22no—
38C42×C109C2311yescharacteristic
39C23×C109—21no—
40Q8×C109—41no—
41D4×C109—41no—
42C2×C4×C109—21no—
43C2×C4×C109C2×D412yes—
44C2×C4×C109C2×D411yescharacteristic
45C2×Dic109—22no—
46C2×Dic109—22no—
47C2×Dic109—41no—
48C2×Dic109—81no—
49Dic218—41no—
50Dic218—41no—
51Dic218—81no—
52C8×C109—24no—
53#11724784—22no—
54C22×C109—41no—
55C22×C109—42no—
56C22×C109#12011yescharacteristic
57C4×C109—21no—
58C4×C109—22no—
59C4×C109—41no—
60Dic109—42no—
61Dic109—42no—
62Dic109—81no—
63C2×C109—81no—
64C2×C109#45311yescharacteristic
65C2×C109#45612yes—
66#1660—1091nomaximal, Sylow
67C109#166011yescharacteristic, complemented, Sylow
68#563—1091no—
69#501—1092no—
70#497—1091no—
71#330—1092no—
72#329D10911yescharacteristic
73C2×Q16—2181no—
74C2×SD16—2181no—
75C4⋊Q8—1091no—
76C4⋊Q8—2181no—
77#126—2182no—
78#125—1092no—
79#124C2×D10911yescharacteristic
80#123—2181no—
81C22⋊Q8—2182no—
82#107—2182no—
83#106—2182no—
84#97—1091no—
85#97C2×D10912yes—
86C2×Q8—2181no—
87C2×Q8—2181no—
88C2×Q8D43611yescharacteristic
89C2×D4D43611yescharacteristic
90C22×C4—2181no—
91Q16—4362no—
92SD16—4362no—
93C2×C8—22no—
94C2×C8—2181no—
95C4⋊C4—1092no—
96C4⋊C4—1092no—
97C4⋊C4—2182no—
98C4⋊C4—2182no—
99C4⋊C4—2182no—
100C4⋊C4—2182no—
101C22⋊C4—22no—
102C22⋊C4—2182no—
103C22⋊C4—2181no—
104C42—2181no—
105C42C22×D10911yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—8721no—
109Q8—4361no—
110Q8—4361no—
111D4—41no—
112C2×C4—21no—
113C2×C4—8721no—
114C2×C4—4361no—
115C2×C4—2182no—
116C2×C4—2182no—
117C2×C4D4×D10912yes—
118C2×C4C2×D43611yescharacteristic
119C8—24no—
120C8—2182no—
121C22—41no—
122C22—42no—
123C22#1681266911yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—8721no—
128C4—4362no—
129C4—4362no—
130C2—81no—
131C2#2029519611yescharacteristic
132C2#2029521012yes—
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#329×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenter#329D109
hypocenterC109#1660
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20295435C2semidirect
4. #20294767C2semidirect
67. C109#1660semidirect

Maximal subgroups

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

subgroupindex
#202957762
#202954352
#202954212
#202947672
#329×C1092
#1660109