Finite Group Databasebeta

← #28378010

Subgroups — #28378010

Order 13952.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#20295904C211yesmaximal, characteristic, complemented
2#20295870C211yesmaximal, characteristic, complemented
3#20294934C211yesmaximal, characteristic
4C2×C22⋊#89137—21no—
5C22⋊#11724786—21no—
6C22×C22⋊D109—21no—
7C2×C22⋊Dic109—21no—
8C2×#13182006C2211yescharacteristic
9#16812606C411yescharacteristic, complemented
10C22×D4×C109C411yescharacteristic, complemented
11C22×#89137—41no—
12C2×#11724786—41no—
13C22⋊#89137—22no—
14C22⋊#89137—41no—
15C23×D109D411yescharacteristic
16C2×C22⋊D109—42no—
17C2×C22⋊D109—42no—
18C2×C22⋊D109—41no—
19C2×C22⋊D109—41no—
20C22×Dic109—21no—
21C22×Dic109D411yescharacteristic
22C22⋊Dic109—42no—
23#13182006—41no—
24C24×C109—21no—
25C2×D4×C109—41no—
26C2×D4×C109—42no—
27C22×C4×C109C2×C411yescharacteristic
28C23×C109—22no—
29C23×C109—41no—
30C23×C109—41no—
31C23×C109—41no—
32C23×C109—41no—
33C23×C109—41no—
34C23×C109—41no—
35C23×C109C22⋊C411yescharacteristic
36C22×D109—21no—
37C22×D109—21no—
38C22×D109—41no—
39C22×D109—41no—
40C22×D109D811yescharacteristic
41C22×D109SD1611yescharacteristic
42C2×#89137—42no—
43C2×#89137—81no—
44C2×#89137—81no—
45D4×C109—42no—
46D4×C109—42no—
47C2×C4×C109—21no—
48C2×C4×C109—41no—
49C22⋊D109—44no—
50C22⋊D109—44no—
51C2×Dic109—22no—
52C2×Dic109—21no—
53C2×Dic109—41no—
54C2×Dic109—41no—
55C2×Dic109—41no—
56#11724786—81no—
57C22×C109—21no—
58C22×C109—21no—
59C22×C109—42no—
60C22×C109—42no—
61C22×C109—42no—
62C22×C109—81no—
63C22×C109—81no—
64C22×C109—81no—
65C22×C109—81no—
66C22×C109#9911yescharacteristic
67C22×C109#10211yescharacteristic
68C22×C109#10411yescharacteristic
69C2×D109—21no—
70C2×D109—21no—
71C2×D109—41no—
72C2×D109—41no—
73C2×D109—41no—
74C2×D109—41no—
75C2×D109—81no—
76#89137—82no—
77C4×C109—41no—
78Dic109—42no—
79Dic109—41no—
80C2×C109—21no—
81C2×C109—21no—
82C2×C109—82no—
83C2×C109#32711yescharacteristic
84C2×C109AΣL(1,𝔽16)11yescharacteristic
85C2×C109#35311yescharacteristic
86D109—41no—
87D109—41no—
88#1343—1091nomaximal, Sylow
89C109#134311yescharacteristic, complemented, Sylow
90#392—1091no—
91#342—1091no—
92#323—1091no—
93C22×D4—2181no—
94C22×D4#8913711yescharacteristic, complemented
95C2×C22⋊C4—1091no—
96C2×C22⋊C4—2181no—
97C2×C22⋊C4—2181no—
98C22⋊C8—2181no—
99#95—1091no—
100C24—21no—
101C24—1091no—
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—4362no—
105C2×D4—4361no—
106C2×D4—4361no—
107C2×D4—4362no—
108C22×C4—1091no—
109C22×C4—4361no—
110C22×C4—2181no—
111C22×C4C2×#8913711yescharacteristic
112C2×C8—4361no—
113C22⋊C4—4361no—
114C22⋊C4—4361no—
115C22⋊C4—4362no—
116C22⋊C4—2182no—
117C23—22no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—1091no—
125C23—1091no—
126C23—4361no—
127C23—4361no—
128C23—2181no—
129C23—2181no—
130C23C22⋊#8913711yescharacteristic
131D4—42no—
132D4—42no—
133D4—4364no—
134D4—4364no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—8721no—
138C2×C4—8721no—
139C2×C4—4362no—
140C2×C4—4361no—
141C2×C4—4361no—
142C2×C4—4361no—
143C2×C4—2182no—
144C2×C4—2181no—
145C8—8721no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—8721no—
156C22—4361no—
157C22—4361no—
158C22—4361no—
159C22—4361no—
160C22—2181no—
161C22—2181no—
162C22#1681275711yescharacteristic
163C22#1681276111yescharacteristic
164C22#1681276311yescharacteristic
165C4—41no—
166C4—8722no—
167C4—4362no—
168C4—4361no—
169C2—21no—
170C2—21no—
171C2—82no—
172C2—4361no—
173C2—4361no—
174C2#2029587711yescharacteristic
175C2#2029592611yescharacteristic
176C2#2029593011yescharacteristic
subgroupG/H
centerC22#16812757
commutatorC22×C4×C109C2×C4
FrattiniC22×C4C2×#89137
FittingC22×D4×C109C4
socleC22×C109#99
prime radical#20294934C2
cosocleC2×#13182006C22
hypercenterC22×D4#89137
hypocenterC109#1343
LCSG ▷ C22×C4×C109 ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20295904C2semidirect
2. #20295870C2semidirect
9. #16812606C4semidirect
10. C22×D4×C109C4semidirect
89. C109#1343semidirect
94. C22×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202959042
#202958702
#202949342
#1343109