Finite Group Databasebeta

← #27206009

Subgroups — #27206009

Order 13184.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268355C212yesmaximal, complemented
2#20268116C214yesmaximal, complemented
3#20268044C212yesmaximal, complemented
4#20268027C212yesmaximal, complemented
5#20267927C214yesmaximal, complemented
6#408×C103C211yesmaximal, characteristic, complemented
7C22×D412C2212yescomplemented
8C2×D824C2212yes—
9C2×D824C2212yes—
10#15693017—22no—
11#15693010—22no—
12#15692995C2214yes—
13#15692995C2214yescomplemented
14#15692989—22no—
15#15692989—22no—
16#15692980C2212yescomplemented
17#15692955C2212yescomplemented
18#15692953C2212yescomplemented
19#15692943C2214yescomplemented
20#15692943C2214yescomplemented
21C2×#41×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic, complemented
23C22×C8×C103C2211yescharacteristic, complemented
24C22⋊C8×C103C2214yescomplemented
25C23×D103—22no—
26C2×D412—22no—
27C2×D412—42no—
28C2×D412—42no—
29C2×D412C2314yes—
30C2×C22⋊D103—24no—
31C2×C22⋊D103—24no—
32D824—42no—
33D824—42no—
34C4⋊Dic103C2314yes—
35C22⋊Dic103—22no—
36(C2×D103)⋊C4—24no—
37(C2×D103)⋊C4—24no—
38C4×Dic103—22no—
39#41×C103—41no—
40#41×C103—41no—
41C2×Q8×C103D411yescharacteristic
42C2×D4×C103D411yescharacteristic
43C2×D4×C103D412yes—
44C22×C4×C103C2312yes—
45C22×C4×C103C2311yescharacteristic
46M16×C103—41no—
47C2×C8×C103—41no—
48C2×C8×C103C2312yes—
49C2×C8×C103C2312yes—
50C23×C103C2×D412yes—
51C23×C103C2×D411yescharacteristic
52C22×D103—24no—
53C22×D103—44no—
54C22×D103—84no—
55Q8×C103—41no—
56D4×C103—42no—
57D4×C103—41no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—22no—
61C2×C4×C103—22no—
62C2×C4×C103C2×D412yes—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2411yescharacteristic
65C22⋊D103—84no—
66C22⋊D103—84no—
67C2×Dic103—24no—
68D412—24no—
69D412—24no—
70D412—44no—
71C8×C103—22no—
72C8×C103—22no—
73C22×C103—22no—
74C22×C103—21no—
75C22×C103—22no—
76C22×C103—24no—
77C22×C103C22×D411yescharacteristic
78C2×D103—44no—
79C2×D103—44no—
80C2×D103—44no—
81C2×D103—88no—
82C4×C103—22no—
83C4×C103—21no—
84C4×C103H(5,𝔽2)11yescharacteristic
85C4×C103H(5,𝔽2)11yescharacteristic
86Dic103—44no—
87C2×C103—42no—
88C2×C103—41no—
89C2×C103#53411yescharacteristic
90C2×C103#57612yes—
91D103—84no—
92#3199—1031nomaximal, Sylow
93C103#319911yescharacteristic, complemented, Sylow
94#535—1032no—
95#482—1034no—
96#469—1032no—
97#466—1032no—
98#447—1034no—
99#408D10311yescharacteristic, complemented
100C2×#41C2×D10311yescharacteristic
101C22×D4—1032no—
102C2×D8—1032no—
103C2×D8—1032no—
104C2×M16C2×D10311yescharacteristic, complemented
105C22×C8C2×D10311yescharacteristic, complemented
106#127—2062no—
107#124—2062no—
108#121—1034no—
109#121—1034no—
110#120—2062no—
111#120—2062no—
112#117—1032no—
113#107—1032no—
114#106—1032no—
115#102—1034no—
116#102—1034no—
117C22⋊C8C2×D10314yescomplemented
118C24—2062no—
119#41—41no—
120#41—41no—
121C2×Q8D41211yescharacteristic
122C2×D4—1034no—
123C2×D4—4122no—
124C2×D4—4122no—
125C2×D4—2064no—
126C2×D4—2064no—
127C2×D4—2062no—
128C2×D4D41211yescharacteristic
129C2×D4D41212yes—
130C22×C4C22×D10312yes—
131C22×C4C22×D10311yescharacteristic
132D8—4122no—
133D8—4122no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D10312yes—
137C2×C8C22×D10312yes—
138C4⋊C4—1034no—
139C22⋊C4—2062no—
140C22⋊C4—2064no—
141C22⋊C4—2064no—
142C42—2062no—
143C23—8244no—
144C23—4124no—
145C23—2064no—
146C23C2×D41212yes—
147C23C2×D41211yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—8244no—
152D4—8244no—
153D4—4124no—
154D4—2064no—
155D4—2064no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—2064no—
161C2×C4C2×D41212yes—
162C2×C4C2×D41211yescharacteristic
163C2×C4C23×D10311yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—8248no—
171C22—4124no—
172C22—4124no—
173C22—4124no—
174C22C22×D41211yescharacteristic
175C4—22no—
176C4—21no—
177C4—4124no—
178C4#1569306611yescharacteristic
179C4#1569306611yescharacteristic
180C2—42no—
181C2—41no—
182C2—8244no—
183C2#2026835311yescharacteristic
184C2#2026859612yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#408×C103C2
socleC22×C103C22×D4
hypercenter#408D103
hypocenterC103#3199
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #20268355C2semidirect
2. #20268116C2semidirect
3. #20268044C2semidirect
4. #20268027C2semidirect
5. #20267927C2semidirect
6. #408×C103C2semidirect
7. C22×D412C22semidirect
13. #15692995C22semidirect
16. #15692980C22semidirect
17. #15692955C22semidirect
18. #15692953C22semidirect
19. #15692943C22semidirect
20. #15692943C22semidirect
22. C2×M16×C103C22semidirect
23. C22×C8×C103C22semidirect
24. C22⋊C8×C103C22semidirect
93. C103#3199semidirect
99. #408D103semidirect
104. C2×M16C2×D103semidirect
105. C22×C8C2×D103semidirect
117. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202681162
#202680442
#202680272
#202679272
#408×C1032
#3199103