Finite Group Databasebeta

← C29×#3199 #16816913

Subgroups — C29×#3199 #16816913

Order 3712.

442 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C29×#535C212yesmaximal, complemented
2C29×#482C214yesmaximal, complemented
3C29×#469C212yesmaximal, complemented
4C29×#466C212yesmaximal, complemented
5C29×#447C214yesmaximal, complemented
6C29×#408C211yesmaximal, characteristic, complemented
7C2×#41×C29C2211yescharacteristic
8C22×D4×C29C2212yescomplemented
9C2×D8×C29C2212yes—
10C2×D8×C29C2212yes—
11C2×M16×C29C2211yescharacteristic, complemented
12C22×C8×C29C2211yescharacteristic, complemented
13C29×#127—22no—
14C29×#124—22no—
15C29×#121C2214yes—
16C29×#121C2214yescomplemented
17C29×#120—22no—
18C29×#120—22no—
19C29×#117C2212yescomplemented
20C29×#107C2212yescomplemented
21C29×#106C2212yescomplemented
22C29×#102C2214yescomplemented
23C29×#102C2214yescomplemented
24C29×C22⋊C8C2214yescomplemented
25C24×C29—22no—
26#41×C29—41no—
27#41×C29—41no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—24no—
30C2×D4×C29—24no—
31C2×D4×C29—22no—
32C2×D4×C29—42no—
33C2×D4×C29—42no—
34C2×D4×C29D411yescharacteristic
35C2×D4×C29D412yes—
36C2×D4×C29C2314yes—
37C22×C4×C29C2312yes—
38C22×C4×C29C2311yescharacteristic
39D8×C29—42no—
40D8×C29—42no—
41M16×C29—41no—
42C2×C8×C29—41no—
43C2×C8×C29C2312yes—
44C2×C8×C29C2312yes—
45C4⋊C4×C29C2314yes—
46C22⋊C4×C29—22no—
47C22⋊C4×C29—24no—
48C22⋊C4×C29—24no—
49C42×C29—22no—
50C23×C29—24no—
51C23×C29—44no—
52C23×C29—84no—
53C23×C29C2×D412yes—
54C23×C29C2×D411yescharacteristic
55Q8×C29—41no—
56D4×C29—24no—
57D4×C29—24no—
58D4×C29—42no—
59D4×C29—41no—
60D4×C29—44no—
61D4×C29—84no—
62D4×C29—84no—
63C2×C4×C29—21no—
64C2×C4×C29—21no—
65C2×C4×C29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—24no—
68C2×C4×C29C2×D412yes—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2411yescharacteristic
71C8×C29—22no—
72C8×C29—22no—
73#3199C2911yesmaximal, characteristic, direct product factor, Sylow
74C22×C29—22no—
75C22×C29—21no—
76C22×C29—22no—
77C22×C29—24no—
78C22×C29—44no—
79C22×C29—44no—
80C22×C29—44no—
81C22×C29—88no—
82C22×C29C22×D411yescharacteristic
83C4×C29—22no—
84C4×C29—21no—
85C4×C29—44no—
86C4×C29H(5,𝔽2)11yescharacteristic
87C4×C29H(5,𝔽2)11yescharacteristic
88#535C2×C2912yescomplemented
89#482C2×C2914yescomplemented
90#469C2×C2912yescomplemented
91#466C2×C2912yescomplemented
92#447C2×C2914yescomplemented
93#408C2×C2911yescharacteristic, complemented
94C2×C29—41no—
95C2×C29—42no—
96C2×C29—84no—
97C2×C29#53411yescharacteristic
98C2×C29#57612yes—
99C2×#41C22×C2911yescharacteristic
100C22×D4C22×C2912yescomplemented
101C2×D8C22×C2912yes—
102C2×D8C22×C2912yes—
103C2×M16C22×C2911yescharacteristic, complemented
104C22×C8C22×C2911yescharacteristic, complemented
105#127—22no—
106#124—22no—
107#121C22×C2914yes—
108#121C22×C2914yescomplemented
109#120—22no—
110#120—22no—
111#117C22×C2912yescomplemented
112#107C22×C2912yescomplemented
113#106C22×C2912yescomplemented
114#102C22×C2914yescomplemented
115#102C22×C2914yescomplemented
116C22⋊C8C22×C2914yescomplemented
117C29#319911yescharacteristic, direct product factor, Sylow
118C24—22no—
119#41—41no—
120#41—41no—
121C2×Q8D4×C2911yescharacteristic
122C2×D4—24no—
123C2×D4—24no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4D4×C2911yescharacteristic
128C2×D4D4×C2912yes—
129C2×D4C23×C2914yes—
130C22×C4C23×C2912yes—
131C22×C4C23×C2911yescharacteristic
132D8—42no—
133D8—42no—
134M16—41no—
135C2×C8—41no—
136C2×C8C23×C2912yes—
137C2×C8C23×C2912yes—
138C4⋊C4C23×C2914yes—
139C22⋊C4—22no—
140C22⋊C4—24no—
141C22⋊C4—24no—
142C42—22no—
143C23—24no—
144C23—44no—
145C23—84no—
146C23C2×D4×C2912yes—
147C23C2×D4×C2911yescharacteristic
148Q8—41no—
149D4—24no—
150D4—24no—
151D4—42no—
152D4—41no—
153D4—44no—
154D4—84no—
155D4—84no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4C2×D4×C2912yes—
162C2×C4C2×D4×C2911yescharacteristic
163C2×C4C24×C2911yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—21no—
168C22—22no—
169C22—24no—
170C22—44no—
171C22—44no—
172C22—44no—
173C22—88no—
174C22C22×D4×C2911yescharacteristic
175C4—22no—
176C4—21no—
177C4—44no—
178C4C29×H(5,𝔽2)11yescharacteristic
179C4C29×H(5,𝔽2)11yescharacteristic
180C2—42no—
181C2—41no—
182C2—84no—
183C2C29×#53411yescharacteristic
184C2C29×#57612yes—
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#535C2semidirect
2. C29×#482C2semidirect
3. C29×#469C2semidirect
4. C29×#466C2semidirect
5. C29×#447C2semidirect
6. C29×#408C2semidirect
8. C22×D4×C29C22semidirect
11. C2×M16×C29C22semidirect
12. C22×C8×C29C22semidirect
16. C29×#121C22semidirect
19. C29×#117C22semidirect
20. C29×#107C22semidirect
21. C29×#106C22semidirect
22. C29×#102C22semidirect
23. C29×#102C22semidirect
24. C29×C22⋊C8C22semidirect
73. #3199C29direct (N × H)
88. #535C2×C29semidirect
89. #482C2×C29semidirect
90. #469C2×C29semidirect
91. #466C2×C29semidirect
92. #447C2×C29semidirect
93. #408C2×C29semidirect
100. C22×D4C22×C29semidirect
103. C2×M16C22×C29semidirect
104. C22×C8C22×C29semidirect
108. #121C22×C29semidirect
111. #117C22×C29semidirect
112. #107C22×C29semidirect
113. #106C22×C29semidirect
114. #102C22×C29semidirect
115. #102C22×C29semidirect
116. C22⋊C8C22×C29semidirect
117. C29#3199direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5352
C29×#4822
C29×#4692
C29×#4662
C29×#4472
C29×#4082
#319929