Finite Group Databasebeta

← C2×#126×D29 #16832746

Subgroups — C2×#126×D29 #16832746

Order 3712.

1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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×#11745260C213yesmaximal, complemented
2C2×#11745238C211yesmaximal, characteristic, complemented
3C2×#11745241C213yesmaximal, complemented
4#126×D29C2116yesmaximal, direct product factor
5C2×C4⋊C4×D29C213yesmaximal, complemented
6C2×C22⋊C4×D29C213yesmaximal
7C2×C42×D29C211yesmaximal, characteristic, complemented
8C2×C29×#126C211yesmaximal, characteristic, complemented
9C24×D29C2211yescharacteristic
10C22×C4×D29C2213yes—
11C22×C4×D29C2213yes—
12C29×#126C2218yescomplemented
13C2×C4⋊C4×C29C2213yescomplemented
14C2×C22⋊C4×C29C2213yes—
15C2×C42×C29C2211yescharacteristic, complemented
16C2×C22⋊Dic29C2213yes—
17C2×#90781C2213yes—
18C2×#90781C2213yes—
19C2×C4⋊Dic29C2213yescomplemented
20C2×#90779C2213yescomplemented
21C2×#90779C2213yescomplemented
22C2×C4×Dic29C2213yescomplemented
23#11745260C22124yescomplemented
24C4⋊C4×D29C22124yescomplemented
25C22⋊C4×D29C22124yes—
26#11745241C22124yescomplemented
27#11745238C2218yescomplemented
28C42×D29C2218yescomplemented
29C24×C29C2311yescharacteristic
30C23×D29—212no—
31C23×D29C2311yescharacteristic
32C23×D29C2314yes—
33C23×D29C2311yescharacteristic
34C22×C4×C29C2313yes—
35C22×C4×C29C2313yes—
36C22×Dic29C2313yes—
37C22×Dic29C2313yes—
38C2×C4×D29—212no—
39C2×C4×D29—212no—
40C2×C4×D29C23112yes—
41C2×C4×D29C23112yes—
42C4⋊C4×C29C23112yescomplemented
43C22⋊C4×C29C23112yes—
44C42×C29C2314yescomplemented
45C22⋊Dic29C23112yes—
46#90781C23112yes—
47#90781C23112yes—
48C4⋊Dic29C23112yescomplemented
49#90779C23112yescomplemented
50#90779C23112yescomplemented
51C4×Dic29C23112yescomplemented
52C23×C29—26no—
53C23×C29C2412yes—
54C23×C29C2411yescharacteristic
55C22×D29—26no—
56C22×D29—224no—
57C22×D29—416no—
58C22×D29#41112yes—
59C22×D29C2412yes—
60C22×D29C2412yes—
61C2×C4×C29—26no—
62C2×C4×C29—26no—
63C2×C4×C29C2416yes—
64C2×C4×C29C2416yes—
65C2×Dic29—26no—
66C2×Dic29—26no—
67C2×Dic29C2416yes—
68C2×Dic29C2416yes—
69C4×D29—224no—
70C4×D29—224no—
71C22×#126—291nomaximal, Sylow
72C22×C29—26no—
73C22×C29—44no—
74C22×C29C2×#4116yes—
75C22×C29C2511yescharacteristic
76C2×D29—26no—
77C2×D29—44no—
78C2×D29—416no—
79C2×D29#126116yesdirect product factor
80C2×D29C2×#41112yes—
81C4×C29—26no—
82C4×C29—26no—
83Dic29—26no—
84Dic29—26no—
85C2×#126—2916no—
86C2×#126—293no—
87C2×#126—293no—
88C2×#126—291no—
89C2×#126D2911yescharacteristic, direct product factor
90C22×C4⋊C4—293no—
91C22×C22⋊C4—293no—
92C22×C42—291no—
93C2×C29—42no—
94C2×C29C2×#12614yescomplemented
95C2×C29C22×#4113yes—
96D29—42no—
97D29C2×#12618yesdirect product factor
98C25—291no—
99C23×C4—293no—
100C23×C4—293no—
101#126—2924no—
102#126—2924no—
103#126—298no—
104#126C2×D2918yesdirect product factor
105C2×C4⋊C4—293no—
106C2×C4⋊C4—293no—
107C2×C4⋊C4—293no—
108C2×C4⋊C4—2924no—
109C2×C4⋊C4C2×D2913yescomplemented
110C2×C22⋊C4—293no—
111C2×C22⋊C4—293no—
112C2×C22⋊C4—293no—
113C2×C22⋊C4—2924no—
114C2×C22⋊C4C2×D2913yes—
115C2×C42—293no—
116C2×C42—298no—
117C2×C42C2×D2911yescharacteristic, complemented
118C29C22×#12611yescharacteristic, complemented, Sylow
119C24—291no—
120C24—294no—
121C24—291no—
122C24—5812no—
123C24C22×D2911yescharacteristic
124C22×C4—293no—
125C22×C4—293no—
126C22×C4—2912no—
127C22×C4—2912no—
128C22×C4—5812no—
129C22×C4—5812no—
130C22×C4C22×D2913yes—
131C22×C4C22×D2913yes—
132C4⋊C4—2912no—
133C4⋊C4—2912no—
134C4⋊C4—2912no—
135C4⋊C4C22×D29112yescomplemented
136C22⋊C4—2912no—
137C22⋊C4—2912no—
138C22⋊C4—2912no—
139C22⋊C4C22×D29112yes—
140C42—2912no—
141C42C22×D2914yescomplemented
142C23—26no—
143C23—2912no—
144C23—292no—
145C23—292no—
146C23—5824no—
147C23—586no—
148C23—11616no—
149C23C23×D2912yes—
150C23C23×D2911yescharacteristic
151C2×C4—26no—
152C2×C4—26no—
153C2×C4—296no—
154C2×C4—296no—
155C2×C4—5824no—
156C2×C4—5824no—
157C2×C4—586no—
158C2×C4—586no—
159C2×C4C23×D2916yes—
160C2×C4C23×D2916yes—
161C22—26no—
162C22—44no—
163C22—2916no—
164C22—2912no—
165C22—586no—
166C22—11616no—
167C22—1164no—
168C22#41×D2916yes—
169C22C24×D2911yescharacteristic
170C4—26no—
171C4—26no—
172C4—586no—
173C4—586no—
174C2—42no—
175C2—298no—
176C2—1162no—
177C2#126×D2914yesdirect product factor
178C2C2×#41×D2913yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#126C2
socleC23×C29C24
prime radicalC24×D29C22
hypercenterC2×#126D29
hypocenterC29C22×#126
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#11745260C2semidirect
2. C2×#11745238C2semidirect
3. C2×#11745241C2semidirect
4. #126×D29C2direct (N × H)
5. C2×C4⋊C4×D29C2semidirect
7. C2×C42×D29C2semidirect
8. C2×C29×#126C2semidirect
12. C29×#126C22semidirect
13. C2×C4⋊C4×C29C22semidirect
15. C2×C42×C29C22semidirect
19. C2×C4⋊Dic29C22semidirect
20. C2×#90779C22semidirect
21. C2×#90779C22semidirect
22. C2×C4×Dic29C22semidirect
23. #11745260C22semidirect
24. C4⋊C4×D29C22semidirect
26. #11745241C22semidirect
27. #11745238C22semidirect
28. C42×D29C22semidirect
42. C4⋊C4×C29C23semidirect
44. C42×C29C23semidirect
48. C4⋊Dic29C23semidirect
49. #90779C23semidirect
50. #90779C23semidirect
51. C4×Dic29C23semidirect
79. C2×D29#126direct (N × H)
89. C2×#126D29direct (N × H)
94. C2×C29C2×#126semidirect
97. D29C2×#126direct (N × H)
104. #126C2×D29direct (N × H)
109. C2×C4⋊C4C2×D29semidirect
117. C2×C42C2×D29semidirect
118. C29C22×#126semidirect
135. C4⋊C4C22×D29semidirect
141. C42C22×D29semidirect
177. C2#126×D29direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117452602
C2×#117452382
C2×#117452412
#126×D292
C2×C4⋊C4×D292
C2×C22⋊C4×D292
C2×C42×D292
C2×C29×#1262
C22×#12629