Finite Group Databasebeta

← C2×C29×#466 #16816762

Subgroups — C2×C29×#466 #16816762

Order 3712.

616 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 232 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
1C22×D8×C29C211yesmaximal, characteristic, complemented
2C23×C8×C29C211yesmaximal, characteristic, complemented
3C2×C29×#121C212yesmaximal, complemented
4C29×#466C218yesmaximal, direct product factor
5C2×C29×#107C211yesmaximal, characteristic, complemented
6C2×C29×#102C212yesmaximal, complemented
7C22×D4×C29—22no—
8C22×D4×C29C2212yes—
9C23×C4×C29C2211yescharacteristic
10C2×D8×C29—24no—
11C2×D8×C29C2214yescomplemented
12C22×C8×C29—24no—
13C22×C8×C29C2211yescharacteristic
14C22×C8×C29C2211yescharacteristic
15C22×C8×C29C2214yescomplemented
16C29×#121—24no—
17C29×#121C2218yescomplemented
18C2×C4⋊C4×C29C2212yes—
19C2×C22⋊C4×C29—22no—
20C29×#107C2214yescomplemented
21C29×#102C2218yescomplemented
22C24×C29—22no—
23C24×C29D411yescharacteristic
24C2×D4×C29—28no—
25C2×D4×C29—24no—
26C2×D4×C29—22no—
27C2×D4×C29—24no—
28C2×D4×C29—48no—
29C2×D4×C29C2314yes—
30C22×C4×C29—22no—
31C22×C4×C29—22no—
32C22×C4×C29—22no—
33C22×C4×C29D412yes—
34C22×C4×C29D411yescharacteristic
35C22×C4×C29C2312yes—
36C22×C4×C29C2311yescharacteristic
37D8×C29—28no—
38C2×C8×C29—22no—
39C2×C8×C29—28no—
40C2×C8×C29D414yescomplemented
41C2×C8×C29C2312yes—
42C2×C8×C29C2312yes—
43C4⋊C4×C29—22no—
44C4⋊C4×C29C2314yes—
45C22⋊C4×C29—28no—
46C23×C29—22no—
47C23×C29—22no—
48C23×C29—24no—
49C23×C29—44no—
50C23×C29—44no—
51C23×C29—44no—
52C23×C29D814yescomplemented
53C23×C29C2×D412yes—
54C23×C29C2×D411yescharacteristic
55D4×C29—24no—
56D4×C29—24no—
57D4×C29—416no—
58D4×C29—44no—
59C2×C4×C29—22no—
60C2×C4×C29—24no—
61C2×C4×C29—22no—
62C2×C4×C29—22no—
63C2×C4×C29—24no—
64C2×C4×C29—44no—
65C2×C4×C29C2×D412yes—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D412yes—
68C2×C4×C29#4112yes—
69C2×C4×C29C2411yescharacteristic
70C8×C29—22no—
71C8×C29C2×D414yescomplemented
72C2×#466C2911yesmaximal, characteristic, direct product factor, Sylow
73C22×C29—22no—
74C22×C29—22no—
75C22×C29—28no—
76C22×C29—44no—
77C22×C29—44no—
78C22×C29—44no—
79C22×C29—88no—
80C22×C29#12112yes—
81C22×C29C2×D812yes—
82C22×C29C2×D814yescomplemented
83C22×C29#13512yes—
84C22×C29C22×D411yescharacteristic
85C4×C29—22no—
86C4×C29—44no—
87C4×C29#12112yes—
88C4×C29C22×D411yescharacteristic
89C4×C29C2×#4111yescharacteristic
90C22×D8C2×C2911yescharacteristic, complemented
91C23×C8C2×C2911yescharacteristic, complemented
92C2×#121C2×C2912yescomplemented
93#466C2×C2918yesdirect product factor
94C2×#107C2×C2911yescharacteristic, complemented
95C2×#102C2×C2912yescomplemented
96C2×C29—24no—
97C2×C29—84no—
98C2×C29#46614yesdirect product factor
99C2×C29C2×#12111yescharacteristic
100C2×C29C22×D811yescharacteristic
101C2×C29C2×#13511yescharacteristic
102C22×D4—22no—
103C22×D4C22×C2912yes—
104C23×C4C22×C2911yescharacteristic
105C2×D8—24no—
106C2×D8C22×C2914yescomplemented
107C22×C8—24no—
108C22×C8C22×C2911yescharacteristic
109C22×C8C22×C2911yescharacteristic
110C22×C8C22×C2914yescomplemented
111#121—24no—
112#121C22×C2918yescomplemented
113C2×C4⋊C4C22×C2912yes—
114C2×C22⋊C4—22no—
115#107C22×C2914yescomplemented
116#102C22×C2918yescomplemented
117C29C2×#46611yescharacteristic, direct product factor, Sylow
118C24—22no—
119C24D4×C2911yescharacteristic
120C2×D4—28no—
121C2×D4—24no—
122C2×D4—22no—
123C2×D4—24no—
124C2×D4—48no—
125C2×D4C23×C2914yes—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4D4×C2911yescharacteristic
130C22×C4D4×C2912yes—
131C22×C4C23×C2912yes—
132C22×C4C23×C2911yescharacteristic
133D8—28no—
134C2×C8—22no—
135C2×C8—28no—
136C2×C8D4×C2914yescomplemented
137C2×C8C23×C2912yes—
138C2×C8C23×C2912yes—
139C4⋊C4—22no—
140C4⋊C4C23×C2914yes—
141C22⋊C4—28no—
142C23—22no—
143C23—22no—
144C23—24no—
145C23—44no—
146C23—44no—
147C23—44no—
148C23D8×C2914yescomplemented
149C23C2×D4×C2912yes—
150C23C2×D4×C2911yescharacteristic
151D4—24no—
152D4—24no—
153D4—416no—
154D4—44no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4C2×D4×C2912yes—
162C2×C4C2×D4×C2911yescharacteristic
163C2×C4C2×D4×C2912yes—
164C2×C4#41×C2912yes—
165C2×C4C24×C2911yescharacteristic
166C8—22no—
167C8C2×D4×C2914yescomplemented
168C22—28no—
169C22—22no—
170C22—22no—
171C22—44no—
172C22—44no—
173C22—44no—
174C22—88no—
175C22C29×#12112yes—
176C22C2×D8×C2912yes—
177C22C2×D8×C2914yescomplemented
178C22C29×#13512yes—
179C22C22×D4×C2911yescharacteristic
180C4—22no—
181C4—44no—
182C4C29×#12112yes—
183C4C22×D4×C2911yescharacteristic
184C4C2×#41×C2911yescharacteristic
185C2—24no—
186C2—84no—
187C2C29×#46614yesdirect product factor
188C2C2×C29×#12111yescharacteristic
189C2C22×D8×C2911yescharacteristic
190C2C2×C29×#13511yescharacteristic
subgroupG/H
center, socleC23×C29C2×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D8×C29C2semidirect
2. C23×C8×C29C2semidirect
3. C2×C29×#121C2semidirect
4. C29×#466C2direct (N × H)
5. C2×C29×#107C2semidirect
6. C2×C29×#102C2semidirect
11. C2×D8×C29C22semidirect
15. C22×C8×C29C22semidirect
17. C29×#121C22semidirect
20. C29×#107C22semidirect
21. C29×#102C22semidirect
40. C2×C8×C29D4semidirect
52. C23×C29D8semidirect
71. C8×C29C2×D4semidirect
72. C2×#466C29direct (N × H)
82. C22×C29C2×D8semidirect
90. C22×D8C2×C29semidirect
91. C23×C8C2×C29semidirect
92. C2×#121C2×C29semidirect
93. #466C2×C29direct (N × H)
94. C2×#107C2×C29semidirect
95. C2×#102C2×C29semidirect
98. C2×C29#466direct (N × H)
106. C2×D8C22×C29semidirect
110. C22×C8C22×C29semidirect
112. #121C22×C29semidirect
115. #107C22×C29semidirect
116. #102C22×C29semidirect
117. C29C2×#466direct (N × H)
136. C2×C8D4×C29semidirect
148. C23D8×C29semidirect
167. C8C2×D4×C29semidirect
177. C22C2×D8×C29semidirect
187. C2C29×#466direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D8×C292
C23×C8×C292
C2×C29×#1212
C29×#4662
C2×C29×#1072
C2×C29×#1022
C2×#46629