Finite Group Databasebeta

← #28378569

Subgroups — #28378569

Order 13952.

254 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 62 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#20296029C212yesmaximal, complemented
2#20295886C212yesmaximal, complemented
3#20295884C212yesmaximal, complemented
4#20295572C211yesmaximal, characteristic
5C2×#13182038—22no—
6#16812766C2214yes—
7C4⋊#11724786—22no—
8C2×#13182029C411yescharacteristic
9#16812697C2211yescharacteristic
10#16812695C2211yescharacteristic
11#16812688C411yescharacteristic
12#16812686C411yescharacteristic
13#16812671—22no—
14C4×C22⋊D109—22no—
15C2×C4×Dic109C2211yescharacteristic
16C2×#41×C109C411yescharacteristic
17#13182038—44no—
18C2×#11724786—24no—
19#13182029—42no—
20C2×Dic218C2×C411yescharacteristic
21C2×D436C2×C411yescharacteristic
22C2×C22⋊D109—21no—
23C2×C22⋊D109—22no—
24C22×Dic109D412yes—
25C2×C4×D109—21no—
26#13182008—22no—
27C22⋊Dic109—22no—
28#13182006—22no—
29C4×Dic109C2×C411yescharacteristic
30C4×Dic109D412yes—
31C4×Dic109C2311yescharacteristic
32#41×C109—42no—
33C2×Q8×C109C2×C411yescharacteristic
34C2×D4×C109—21no—
35C2×D4×C109C2×C411yescharacteristic
36C22×C4×C109—21no—
37C22×C4×C109C2×C411yescharacteristic
38C23×C109—21no—
39C23×C109C22⋊C411yescharacteristic
40C22×D109—21no—
41Q8×C109—41no—
42D4×C109—41no—
43D4×C109—42no—
44C2×C4×C109—22no—
45C2×C4×C109—21no—
46C2×C4×C109—42no—
47C2×C4×C109C22⋊C411yescharacteristic
48C2×C4×C109C22×C411yescharacteristic
49C22⋊D109—42no—
50C22⋊D109—42no—
51C22⋊D109—42no—
52C2×Dic109—22no—
53C2×Dic109—22no—
54C2×Dic109—21no—
55C2×Dic109C22⋊C412yes—
56C2×Dic109C2×D412yes—
57D436—41no—
58C4×D109—42no—
59Dic218—41no—
60#11724786—44no—
61C22×C109—21no—
62C22×C109—22no—
63C22×C109—41no—
64C22×C109—42no—
65C22×C109C2×C22⋊C411yescharacteristic
66C2×D109—41no—
67C2×D109—42no—
68C4×C109—21no—
69C4×C109—41no—
70C4×C109#10012yes—
71Dic109—22no—
72Dic109—41no—
73Dic109AGL(1,ℤ/8)12yes—
74Dic109#13712yes—
75C2×C109—41no—
76C2×C109—81no—
77C2×C109C2×#10011yescharacteristic
78C2×C109#41712yes—
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#8913711yescharacteristic
88C2×M16—2182no—
89C4⋊Q8—1091no—
90#127—1091no—
91#124—1091no—
92#124—1091no—
93#121—2182no—
94C4×D4—2182no—
95C2×C42—1091no—
96C4⋊C8—1094no—
97C4⋊C8—2182no—
98#41—42no—
99#41—4362no—
100C2×Q8—1091no—
101C2×Q8C2×#8913711yescharacteristic
102C2×D4—21no—
103C2×D4—1091no—
104C2×D4—2182no—
105C2×D4—2181no—
106C2×D4C2×#8913711yescharacteristic
107C22×C4—21no—
108C22×C4—1092no—
109C22×C4—2181no—
110C22×C4C2×#8913711yescharacteristic
111M16—4364no—
112C2×C8—2184no—
113C4⋊C4—2182no—
114C22⋊C4—2182no—
115C22⋊C4—2182no—
116C42—1092no—
117C42—1091no—
118C42—1091no—
119C23—21no—
120C23—2181no—
121C23C22⋊#8913711yescharacteristic
122Q8—41no—
123Q8—4361no—
124D4—41no—
125D4—42no—
126D4—4361no—
127D4—4362no—
128D4—4362no—
129D4—4362no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—42no—
133C2×C4—1092no—
134C2×C4—1092no—
135C2×C4—4362no—
136C2×C4—2182no—
137C2×C4—2182no—
138C2×C4—2181no—
139C2×C4C22⋊#8913711yescharacteristic
140C2×C4C22×#8913711yescharacteristic
141C8—4364no—
142C22—21no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—4361no—
147C22—4362no—
148C22C2×C22⋊#8913711yescharacteristic
149C4—21no—
150C4—41no—
151C4—1092no—
152C4—1092no—
153C4—4361no—
154C4—2182no—
155C4#1681275912yes—
156C2—41no—
157C2—81no—
158C2—8721no—
159C2C2×#1681275911yescharacteristic
160C2#2029601712yes—
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×#41×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295572C2
cosocleC4×Dic109C23
hypercenterC2×#41#89137
hypocenterC109#1560
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20296029C2semidirect
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
#202960292
#202958862
#202958842
#202955722
#1560109