Finite Group Databasebeta

← #28363560

Subgroups — #28363560

Order 13952.

344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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#20295793C211yesmaximal, characteristic, complemented
2#20295031C212yesmaximal, complemented
3#20295000C211yesmaximal, characteristic, complemented
4#20294782C212yesmaximal, complemented
5#535×C109C211yesmaximal, characteristic
6#16812706—24no—
7C2×#13182013—22no—
8C2×#13182013C2212yes—
9#16812658C2212yes—
10#16812620—24no—
11#16812614—22no—
12C2×#41×C109C2211yescharacteristic
13C22×D4×C109C2211yescharacteristic
14#127×C109C412yescomplemented
15#124×C109C412yescomplemented
16#121×C109—22no—
17#120×C109—22no—
18#117×C109C2211yescharacteristic
19#13182013—24no—
20#13182013—22no—
21#13182013—22no—
22C2×#11724784—24no—
23C2×#11724784D414yescomplemented
24C4⋊Dic109—22no—
25C22⋊Dic109—22no—
26C4×Dic109—22no—
27C24×C109—21no—
28#41×C109—22no—
29#41×C109—22no—
30C2×Q8×C109C2×C411yescharacteristic
31C2×D4×C109—24no—
32C2×D4×C109—22no—
33C2×D4×C109—21no—
34C2×D4×C109—22no—
35C2×D4×C109C2×C412yes—
36C2×D4×C109C2×C411yescharacteristic
37C2×D4×C109D412yes—
38C22×C4×C109D412yes—
39C22×C4×C109C2311yescharacteristic
40C4⋊C4×C109—21no—
41C22⋊C4×C109—21no—
42C22⋊C4×C109—24no—
43C42×C109C2×C412yes—
44C23×C109—22no—
45C23×C109—42no—
46C23×C109—82no—
47C23×C109C22⋊C412yes—
48C23×C109C2×D411yescharacteristic
49Q8×C109—22no—
50D4×C109—24no—
51D4×C109—22no—
52D4×C109—24no—
53D4×C109—41no—
54D4×C109—41no—
55D4×C109—84no—
56C2×C4×C109—22no—
57C2×C4×C109—22no—
58C2×C4×C109—22no—
59C2×C4×C109C22⋊C412yes—
60C2×C4×C109C22×C411yescharacteristic
61C2×C4×C109C2×D412yes—
62C2×C4×C109C2×D411yescharacteristic
63C2×C4×C109#4112yes—
64C2×Dic109—42no—
65#11724784—24no—
66C22×C109—22no—
67C22×C109—41no—
68C22×C109—42no—
69C22×C109—44no—
70C22×C109—42no—
71C22×C109—84no—
72C22×C109C2×C22⋊C411yescharacteristic
73C22×C109#12112yes—
74C4×C109—22no—
75C4×C109—42no—
76C4×C109C4×D412yes—
77C4×C109#12011yescharacteristic
78C4×C109#12311yescharacteristic
79Dic109—82no—
80C2×C109—22no—
81C2×C109—21no—
82C2×C109—42no—
83C2×C109—82no—
84C2×C109#38611yescharacteristic
85#1910—1091nomaximal, Sylow
86C109#191011yescharacteristic, complemented, Sylow
87#568—1091no—
88#535D10911yescharacteristic
89#418—1092no—
90#410—1091no—
91H(3,ℤ/4)—1092no—
92C2×#41C2×D10911yescharacteristic
93C22×D4C2×D10911yescharacteristic
94#131—2184no—
95C2×M16—1092no—
96C2×M16—2182no—
97#127Dic10912yescomplemented
98#124Dic10912yescomplemented
99#121—22no—
100#120—22no—
101#117—1092no—
102#117C2×D10911yescharacteristic
103#102—2184no—
104#99—2182no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic10911yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic10912yes—
114C2×D4C2×Dic10911yescharacteristic
115C2×D4C22⋊D10912yes—
116C22×C4C22⋊D10912yes—
117C22×C4C22×D10911yescharacteristic
118M16—2184no—
119M16—2182no—
120M16—2182no—
121C2×C8—1094no—
122C2×C8—2184no—
123C4⋊C4—21no—
124C4⋊C4—2182no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—2182no—
128C42—2182no—
129C42C2×Dic10912yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic10912yes—
134C23C2×C22⋊D10911yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—4362no—
146C2×C4C22⋊Dic10912yes—
147C2×C4C22×Dic10911yescharacteristic
148C2×C4D4×D10912yes—
149C2×C4C2×C22⋊D10911yescharacteristic
150C2×C4#1318202812yes—
151C8—2184no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic10911yescharacteristic
159C22#1681267112yes—
160C4—22no—
161C4—42no—
162C4—8722no—
163C4D4×Dic10912yes—
164C4#1681266711yescharacteristic
165C4#1681268011yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2029490611yescharacteristic
subgroupG/H
centerC2#20294906
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting, prime radical#535×C109C2
socleC2×C109#386
cosocleC22×C4×C109C23
hypercenter#535D109
hypocenterC109#1910
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20295793C2semidirect
2. #20295031C2semidirect
3. #20295000C2semidirect
4. #20294782C2semidirect
14. #127×C109C4semidirect
15. #124×C109C4semidirect
23. C2×#11724784D4semidirect
86. C109#1910semidirect
97. #127Dic109semidirect
98. #124Dic109semidirect

Maximal subgroups

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

subgroupindex
#202957932
#202950312
#202950002
#202947822
#535×C1092
#1910109