Finite Group Databasebeta

← #28378536

Subgroups — #28378536

Order 13952.

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

normal subgroups only

This group has 246 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#20296044C212yesmaximal, complemented
2#20295886C212yesmaximal, complemented
3#20295884C212yesmaximal, complemented
4#20295575C211yesmaximal, characteristic
5#16812766C2214yes—
6#16812756—22no—
7C4×#11724786—22no—
8C2×#13182030C411yescharacteristic
9C2×#13182028C411yescharacteristic
10#16812697C2211yescharacteristic
11#16812695C2211yescharacteristic
12#16812687C411yescharacteristic
13#16812672—22no—
14#16812659—22no—
15C42×D109C2211yescharacteristic
16#124×C109C411yescharacteristic
17C2×#11724786—24no—
18#13182030—42no—
19#13182028—42no—
20C2×Dic218C2×C411yescharacteristic
21C2×D436—21no—
22C2×D436C2×C411yescharacteristic
23C2×C22⋊D109—21no—
24C2×C22⋊D109—22no—
25C22×Dic109—21no—
26C2×C4×D109—21no—
27C2×C4×D109C2×C411yescharacteristic
28C2×C4×D109D412yes—
29#13182008—22no—
30#13182006—22no—
31C4×Dic109D412yes—
32C4×Dic109C2311yescharacteristic
33C2×Q8×C109C2×C411yescharacteristic
34C2×D4×C109C2×C411yescharacteristic
35C22⋊C4×C109—22no—
36C42×C109C2×C411yescharacteristic
37C23×C109—21no—
38C22×D109—21no—
39C22×D109C22⋊C411yescharacteristic
40Q8×C109—41no—
41D4×C109—41no—
42C2×C4×C109—21no—
43C2×C4×C109C22⋊C412yes—
44C2×C4×C109C22×C411yescharacteristic
45C22⋊D109—42no—
46C22⋊D109—44no—
47C2×Dic109—21no—
48C2×Dic109—42no—
49C2×Dic109C22⋊C411yescharacteristic
50C2×Dic109C2×D412yes—
51D436—41no—
52D436—42no—
53C4×D109—22no—
54C4×D109—24no—
55C4×D109—42no—
56Dic218—41no—
57#11724786—44no—
58C22×C109—41no—
59C22×C109—42no—
60C22×C109C2×C22⋊C411yescharacteristic
61C2×D109—21no—
62C2×D109—22no—
63C2×D109—41no—
64C2×D109—42no—
65C4×C109—21no—
66C4×C109—22no—
67C4×C109—41no—
68Dic109—41no—
69Dic109#10012yes—
70Dic109#13514yes—
71C2×C109—81no—
72C2×C109C2×#10011yescharacteristic
73C2×C109#41612yes—
74D109—41no—
75D109—81no—
76#1543—1091nomaximal, Sylow
77C109#154311yescharacteristic, complemented, Sylow
78#532—1091no—
79#431—1092no—
80#333—1092no—
81#331—1092no—
82C2×#41—1091no—
83C2×#41—1091no—
84C4⋊Q8—1091no—
85#127—1091no—
86#124—1091no—
87#124#8913711yescharacteristic
88#121—2182no—
89C4×D4—2182no—
90C2×C42—1091no—
91C4⋊C8—1094no—
92C22⋊C8—2182no—
93C4×C8—2182no—
94#41—4362no—
95#41—4362no—
96C2×Q8—1091no—
97C2×Q8C2×#8913711yescharacteristic
98C2×D4—1091no—
99C2×D4—2181no—
100C2×D4—2182no—
101C2×D4—2181no—
102C2×D4C2×#8913711yescharacteristic
103C22×C4—1092no—
104C22×C4—1091no—
105C22×C4—2181no—
106C22×C4—2181no—
107C2×C8—2184no—
108C4⋊C4—2182no—
109C22⋊C4—22no—
110C22⋊C4—2182no—
111C42—1092no—
112C42—1091no—
113C42C2×#8913711yescharacteristic
114C23—21no—
115C23—1091no—
116C23—2181no—
117Q8—41no—
118Q8—4361no—
119D4—41no—
120D4—4361no—
121D4—4362no—
122D4—4364no—
123D4—4362no—
124C2×C4—21no—
125C2×C4—1092no—
126C2×C4—1091no—
127C2×C4—4362no—
128C2×C4—4362no—
129C2×C4—2182no—
130C2×C4—2184no—
131C2×C4—2181no—
132C2×C4C22⋊#8913712yes—
133C2×C4C22×#8913711yescharacteristic
134C8—4364no—
135C22—41no—
136C22—42no—
137C22—4361no—
138C22—4362no—
139C22—2181no—
140C22—2182no—
141C22C2×C22⋊#8913711yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—1092no—
146C4—1094no—
147C4—4361no—
148C2—81no—
149C2—8721no—
150C2—4361no—
151C2D109⋊#10011yescharacteristic
152C2#2029601612yes—
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#1543
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. #20296044C2semidirect
2. #20295886C2semidirect
3. #20295884C2semidirect
77. C109#1543semidirect

Maximal subgroups

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

subgroupindex
#202960442
#202958862
#202958842
#202955752
#1543109