Finite Group Databasebeta

← #28378570

Subgroups — #28378570

Order 13952.

254 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 60 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#20296031C212yesmaximal, complemented
2#20295886C212yesmaximal, complemented
3#20295884C212yesmaximal, complemented
4#20295575C211yesmaximal, characteristic
5C2×#13182039—22no—
6#16812766—22no—
7#16812766C2214yes—
8C2×#13182030C411yescharacteristic
9C2×#13182028C411yescharacteristic
10#16812697C2211yescharacteristic
11#16812695C2211yescharacteristic
12#16812687C411yescharacteristic
13#16812672—22no—
14#16812659—22no—
15C42×D109C2211yescharacteristic
16#124×C109C411yescharacteristic
17#13182039—44no—
18C2×#11724786—24no—
19#13182030—42no—
20#13182028—42no—
21C2×Dic218C2×C411yescharacteristic
22C2×D436—21no—
23C2×D436C2×C411yescharacteristic
24C2×C22⋊D109—21no—
25C2×C22⋊D109—22no—
26C22×Dic109—21no—
27C2×C4×D109—21no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D412yes—
30#13182008—22no—
31#13182006—22no—
32C4×Dic109D412yes—
33C4×Dic109C2311yescharacteristic
34C2×Q8×C109C2×C411yescharacteristic
35C2×D4×C109C2×C411yescharacteristic
36C22⋊C4×C109—22no—
37C42×C109C2×C411yescharacteristic
38C23×C109—21no—
39C22×D109—21no—
40C22×D109C22⋊C411yescharacteristic
41Q8×C109—41no—
42D4×C109—41no—
43C2×C4×C109—21no—
44C2×C4×C109C22⋊C412yes—
45C2×C4×C109C22×C411yescharacteristic
46C22⋊D109—42no—
47C22⋊D109—42no—
48C22⋊D109—42no—
49C2×Dic109—21no—
50C2×Dic109—42no—
51C2×Dic109C22⋊C411yescharacteristic
52C2×Dic109C2×D412yes—
53D436—41no—
54D436—42no—
55C4×D109—22no—
56C4×D109—22no—
57C4×D109—22no—
58C4×D109—42no—
59Dic218—41no—
60#11724786—44no—
61C22×C109—41no—
62C22×C109—42no—
63C22×C109C2×C22⋊C411yescharacteristic
64C2×D109—21no—
65C2×D109—22no—
66C2×D109—41no—
67C2×D109—42no—
68C4×C109—21no—
69C4×C109—22no—
70C4×C109—41no—
71Dic109—41no—
72Dic109#10012yes—
73Dic109AGL(1,ℤ/8)12yes—
74Dic109#13712yes—
75C2×C109—81no—
76C2×C109C2×#10011yescharacteristic
77C2×C109#41712yes—
78D109—41no—
79D109—81no—
80#1560—1091nomaximal, Sylow
81C109#156011yescharacteristic, complemented, Sylow
82#532—1091no—
83#423—1092no—
84#333—1092no—
85#331—1092no—
86C2×#41—1091no—
87C2×#41—1091no—
88C2×M16—2182no—
89C4⋊Q8—1091no—
90#127—1091no—
91#124—1091no—
92#124#8913711yescharacteristic
93#121—2182no—
94C4×D4—2182no—
95C2×C42—1091no—
96C4⋊C8—1094no—
97C4⋊C8—2182no—
98#41—4362no—
99#41—4362no—
100C2×Q8—1091no—
101C2×Q8C2×#8913711yescharacteristic
102C2×D4—1091no—
103C2×D4—2181no—
104C2×D4—2182no—
105C2×D4—2181no—
106C2×D4C2×#8913711yescharacteristic
107C22×C4—1092no—
108C22×C4—1091no—
109C22×C4—2181no—
110C22×C4—2181no—
111M16—4364no—
112C2×C8—2184no—
113C4⋊C4—2182no—
114C22⋊C4—22no—
115C22⋊C4—2182no—
116C42—1092no—
117C42—1091no—
118C42C2×#8913711yescharacteristic
119C23—21no—
120C23—1091no—
121C23—2181no—
122Q8—41no—
123Q8—4361no—
124D4—41no—
125D4—4361no—
126D4—4362no—
127D4—4362no—
128D4—4362no—
129D4—4362no—
130C2×C4—21no—
131C2×C4—1092no—
132C2×C4—1091no—
133C2×C4—4362no—
134C2×C4—4362no—
135C2×C4—2182no—
136C2×C4—2182no—
137C2×C4—2182no—
138C2×C4—2181no—
139C2×C4C22⋊#8913712yes—
140C2×C4C22×#8913711yescharacteristic
141C8—4364no—
142C22—41no—
143C22—42no—
144C22—4361no—
145C22—4362no—
146C22—2181no—
147C22—2182no—
148C22C2×C22⋊#8913711yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—1092no—
153C4—1092no—
154C4—1092no—
155C4—4361no—
156C2—81no—
157C2—8721no—
158C2—4361no—
159C2D109⋊#10011yescharacteristic
160C2#2029601712yes—
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295575C2
cosocleC4×Dic109C23
hypercenter#124#89137
hypocenterC109#1560
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296031C2semidirect
2. #20295886C2semidirect
3. #20295884C2semidirect
81. C109#1560semidirect

Maximal subgroups

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

subgroupindex
#202960312
#202958862
#202958842
#202955752
#1560109