Finite Group Databasebeta

← #28361365

Subgroups — #28361365

Order 13952.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#16812657C211yesmaximal, characteristic
2#20295080C212yesmaximal, complemented
3#20294752C211yesmaximal, characteristic, complemented
4#20294749C212yesmaximal
5#324×C109C211yesmaximal, characteristic, complemented
6C22×C4×D109C411yescharacteristic
7#16812657—22no—
8#16812657—22no—
9C2×C4⋊Dic109C411yescharacteristic
10C2×#13182006C411yescharacteristic
11C2×#13182006C2211yescharacteristic
12C2×C4×Dic109C411yescharacteristic
13C2×C4×Dic109C2211yescharacteristic
14#16812628—22no—
15C22⋊#11724784C2212yes—
16#16812609—22no—
17C2×C4⋊C4×C109C2211yescharacteristic
18C22⋊C8×C109C2212yes—
19C23×D109C2×C411yescharacteristic
20C22×Dic109C2×C411yescharacteristic
21C22×Dic109C2×C411yescharacteristic
22C22×Dic109C2×C411yescharacteristic
23C2×C4×D109—22no—
24C2×C4×D109—22no—
25C2×C4×D109—21no—
26C2×C4×D109—21no—
27C2×#11724784—22no—
28C4⋊Dic109—22no—
29#13182006—22no—
30#13182006—22no—
31C4×Dic109—21no—
32C4×Dic109—21no—
33C4×Dic109D412yes—
34C4×Dic109D412yes—
35C22×C4×C109C2×C411yescharacteristic
36C22×C4×C109C2×C411yescharacteristic
37C22×C4×C109C2311yescharacteristic
38C2×C8×C109—22no—
39C4⋊C4×C109—22no—
40C23×C109C22×C411yescharacteristic
41C22×D109—21no—
42C22×D109—21no—
43C22×D109—41no—
44C22×D109—41no—
45C22×D109M1612yes—
46C2×C4×C109—21no—
47C2×C4×C109—21no—
48C2×C4×C109—21no—
49C2×C4×C109—41no—
50C2×C4×C109—41no—
51C2×C4×C109M1612yes—
52C2×C4×C109C2×D412yes—
53C2×Dic109—21no—
54C2×Dic109—21no—
55C2×Dic109—21no—
56C2×Dic109—41no—
57C2×Dic109—41no—
58C2×Dic109C22⋊C411yescharacteristic
59C2×Dic109C22⋊C411yescharacteristic
60C2×Dic109C22⋊C412yes—
61C4×D109—24no—
62C4×D109—24no—
63C8×C109—42no—
64#11724784—42no—
65C22×C109—21no—
66C22×C109—21no—
67C22×C109C2×C22⋊C411yescharacteristic
68C22×C109C2×M1611yescharacteristic
69C22×C109C2×M1611yescharacteristic
70C2×D109—22no—
71C2×D109—42no—
72C2×D109—41no—
73C2×D109—41no—
74C2×D109—42no—
75C4×C109—22no—
76C4×C109—22no—
77C4×C109—41no—
78Dic109—21no—
79Dic109—21no—
80Dic109—22no—
81Dic109—41no—
82C2×C109—21no—
83C2×C109—21no—
84C2×C109#40711yescharacteristic
85C2×C109#41011yescharacteristic
86C2×C109#41311yescharacteristic
87D109—42no—
88#1464—1091nomaximal, Sylow
89C109#146411yescharacteristic, complemented, Sylow
90C2×#117—1091no—
91#432—1092no—
92#324—1091no—
93#324D10911yescharacteristic, complemented
94#323—1092no—
95C23×C4—1091no—
96#117—2182no—
97#117—2182no—
98C2×C4⋊C4—1091no—
99C2×C4⋊C4C2×D10911yescharacteristic
100C2×C22⋊C4—1091no—
101C2×C22⋊C4—1091no—
102C2×C42—1091no—
103C2×C42—1091no—
104C4⋊C8—2182no—
105C22⋊C8—1092no—
106C22⋊C8C2×D10912yes—
107#97—2182no—
108C24—1091no—
109C22×C4—1091no—
110C22×C4—1091no—
111C22×C4—1091no—
112C22×C4—2181no—
113C22×C4—2181no—
114C22×C4—2182no—
115C22×C4—2182no—
116C22×C4C4×D10911yescharacteristic
117C22×C4C4×D10911yescharacteristic
118C22×C4C22×D10911yescharacteristic
119C2×C8—22no—
120C2×C8—2182no—
121C4⋊C4—22no—
122C4⋊C4—2182no—
123C22⋊C4—2182no—
124C22⋊C4—2182no—
125C42—1092no—
126C42—1092no—
127C42—2181no—
128C42—2181no—
129C23—1092no—
130C23—4361no—
131C23—4361no—
132C23—2181no—
133C23—2181no—
134C23C2×C4×D10911yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—1091no—
141C2×C4—1091no—
142C2×C4—1092no—
143C2×C4—4361no—
144C2×C4—4361no—
145C2×C4—2184no—
146C2×C4—2184no—
147C2×C4—2181no—
148C2×C4—2181no—
149C2×C4—2181no—
150C2×C4#1318201212yes—
151C2×C4D4×D10912yes—
152C8—42no—
153C8—4362no—
154C22—21no—
155C22—21no—
156C22—4362no—
157C22—4362no—
158C22—4361no—
159C22—4361no—
160C22—2182no—
161C22C22⋊C4×D10911yescharacteristic
162C22M16×D10911yescharacteristic
163C22C2×#1318201211yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—4361no—
168C4—2181no—
169C4—2181no—
170C4—2182no—
171C2—21no—
172C2—21no—
173C2—4362no—
174C2#2029498811yescharacteristic
175C2#2029499811yescharacteristic
176C2#2029500911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#324×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC23×D109C2×C4
cosocleC22×C4×C109C23
hypercenter#324D109
hypocenterC109#1464
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20295080C2semidirect
3. #20294752C2semidirect
5. #324×C109C2semidirect
89. C109#1464semidirect
93. #324D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126572
#202950802
#202947522
#202947492
#324×C1092
#1464109