Finite Group Databasebeta

← C47×#62652 #26102350

Subgroups — C47×#62652 #26102350

Order 12032.

11674 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×H(5,𝔽2)×C47C211yesmaximal, characteristic
2C4×H(5,𝔽2)×C47C2132yesmaximal, complemented
3C47×#3428C2112yesmaximal, complemented
4C2×C47×#518C2118yesmaximal, complemented
5C2×H(5,𝔽2)×C47C4132yescomplemented
6C2×H(5,𝔽2)×C47C22116yes—
7C22×#41×C47C2216yes—
8C23×D4×C47C2219yes—
9C47×#520C22196yescomplemented
10C47×#519C2218yescomplemented
11C47×#518C22172yescomplemented
12C47×#518C221144yescomplemented
13C4×#41×C47C22196yescomplemented
14C2×C4×D4×C47C221144yescomplemented
15C2×#117×C47C22136yescomplemented
16C22×C22⋊C4×C47C22124yescomplemented
17C25×C47C2316yes—
18H(5,𝔽2)×C47C2×C41256yescomplemented
19C2×#41×C47C2×C4196yescomplemented
20C2×#41×C47C23148yes—
21C22×Q8×C47C2312yes—
22C22×D4×C47C2×C41144yescomplemented
23C22×D4×C47C23172yes—
24C22×D4×C47C23118yes—
25C23×C4×C47C2319yes—
26C23×C4×C47C23148yescomplemented
27C4×Q8×C47C23164yescomplemented
28C4×D4×C47C231576yescomplemented
29#117×C47C23148yes—
30#117×C47C231144yescomplemented
31C2×C4⋊C4×C47C23172yescomplemented
32C2×C22⋊C4×C47C23172yes—
33C2×C22⋊C4×C47C231144yescomplemented
34C2×C42×C47C23172yescomplemented
35C24×C47—812no—
36C24×C47C22×C4148yescomplemented
37C24×C47C2419yes—
38C24×C47C24124yes—
39#41×C47C22×C41384yescomplemented
40C2×Q8×C47C22×C4116yescomplemented
41C2×Q8×C47C2418yes—
42C2×D4×C47C22×C41144yescomplemented
43C2×D4×C47C22×C41576yescomplemented
44C2×D4×C47C24172yes—
45C22×C4×C47—848no—
46C22×C4×C47C22×C4172yescomplemented
47C22×C4×C47C241144yes—
48C22×C4×C47C24136yes—
49C22×C4×C47C2416yes—
50C4⋊C4×C47C24196yes—
51C22⋊C4×C47C24116yes—
52C22⋊C4×C47C241144yes—
53C42×C47C24196yes—
54C23×C47—448no—
55C23×C47—418no—
56C23×C47—848no—
57C23×C47C23×C4136yes—
58C23×C47C23×C4196yes—
59C23×C47C2511yescharacteristic
60C23×C47C25118yes—
61Q8×C47C23×C4132yes—
62D4×C47C23×C41288yes—
63C2×C4×C47—4144no—
64C2×C4×C47C23×C4124yes—
65C2×C4×C47C23×C41144yes—
66C2×C4×C47C25132yes—
67C2×C4×C47C25112yes—
68#62652C4711yesmaximal, characteristic, direct product factor, Sylow
69C22×C47—236no—
70C22×C47—22no—
71C22×C47—436no—
72C22×C47—496no—
73C22×C47C24×C412yes—
74C22×C47C24×C4136yes—
75C22×C47C2611yescharacteristic
76C4×C47—232no—
77C4×C47C24×C4124yes—
78C22×H(5,𝔽2)C2×C4711yescharacteristic
79C4×H(5,𝔽2)C2×C47132yescomplemented
80#3428C2×C47112yescomplemented
81C2×#518C2×C47118yescomplemented
82C2×C47—22no—
83C2×C47—236no—
84C2×C47C25×C411yescharacteristic
85C2×C47H(7,𝔽2)12yes—
86C2×H(5,𝔽2)C4×C47132yescomplemented
87C2×H(5,𝔽2)C22×C47116yes—
88C22×#41C22×C4716yes—
89C23×D4C22×C4719yes—
90#520C22×C47196yescomplemented
91#519C22×C4718yescomplemented
92#518C22×C47172yescomplemented
93#518C22×C471144yescomplemented
94C4×#41C22×C47196yescomplemented
95C2×C4×D4C22×C471144yescomplemented
96C2×#117C22×C47136yescomplemented
97C22×C22⋊C4C22×C47124yescomplemented
98C47#6265211yescharacteristic, direct product factor, Sylow
99C25C23×C4716yes—
100H(5,𝔽2)C2×C4×C471256yescomplemented
101C2×#41C2×C4×C47196yescomplemented
102C2×#41C23×C47148yes—
103C22×Q8C23×C4712yes—
104C22×D4C2×C4×C471144yescomplemented
105C22×D4C23×C47172yes—
106C22×D4C23×C47118yes—
107C23×C4C23×C4719yes—
108C23×C4C23×C47148yescomplemented
109C4×Q8C23×C47164yescomplemented
110C4×D4C23×C471576yescomplemented
111#117C23×C47148yes—
112#117C23×C471144yescomplemented
113C2×C4⋊C4C23×C47172yescomplemented
114C2×C22⋊C4C23×C47172yes—
115C2×C22⋊C4C23×C471144yescomplemented
116C2×C42C23×C47172yescomplemented
117C24—812no—
118C24C22×C4×C47148yescomplemented
119C24C24×C4719yes—
120C24C24×C47124yes—
121#41C22×C4×C471384yescomplemented
122C2×Q8C22×C4×C47116yescomplemented
123C2×Q8C24×C4718yes—
124C2×D4C22×C4×C471144yescomplemented
125C2×D4C22×C4×C471576yescomplemented
126C2×D4C24×C47172yes—
127C22×C4—848no—
128C22×C4C22×C4×C47172yescomplemented
129C22×C4C24×C471144yes—
130C22×C4C24×C47136yes—
131C22×C4C24×C4716yes—
132C4⋊C4C24×C47196yes—
133C22⋊C4C24×C47116yes—
134C22⋊C4C24×C471144yes—
135C42C24×C47196yes—
136C23—448no—
137C23—418no—
138C23—848no—
139C23C23×C4×C47136yes—
140C23C23×C4×C47196yes—
141C23C25×C4711yescharacteristic
142C23C25×C47118yes—
143Q8C23×C4×C47132yes—
144D4C23×C4×C471288yes—
145C2×C4—4144no—
146C2×C4C23×C4×C47124yes—
147C2×C4C23×C4×C471144yes—
148C2×C4C25×C47132yes—
149C2×C4C25×C47112yes—
150C22—236no—
151C22—22no—
152C22—436no—
153C22—496no—
154C22C24×C4×C4712yes—
155C22C24×C4×C47136yes—
156C22C26×C4711yescharacteristic
157C4—232no—
158C4C24×C4×C47124yes—
159C2—22no—
160C2—236no—
161C2C25×C4×C4711yescharacteristic
162C2C47×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C47C26
commutatorC2C25×C4×C47
Frattini, cosocleC22C26×C47
prime radicalC22×H(5,𝔽2)×C47C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×H(5,𝔽2)×C47C2semidirect
3. C47×#3428C2semidirect
4. C2×C47×#518C2semidirect
5. C2×H(5,𝔽2)×C47C4semidirect
9. C47×#520C22semidirect
10. C47×#519C22semidirect
11. C47×#518C22semidirect
12. C47×#518C22semidirect
13. C4×#41×C47C22semidirect
14. C2×C4×D4×C47C22semidirect
15. C2×#117×C47C22semidirect
16. C22×C22⋊C4×C47C22semidirect
18. H(5,𝔽2)×C47C2×C4semidirect
19. C2×#41×C47C2×C4semidirect
22. C22×D4×C47C2×C4semidirect
26. C23×C4×C47C23semidirect
27. C4×Q8×C47C23semidirect
28. C4×D4×C47C23semidirect
30. #117×C47C23semidirect
31. C2×C4⋊C4×C47C23semidirect
33. C2×C22⋊C4×C47C23semidirect
34. C2×C42×C47C23semidirect
36. C24×C47C22×C4semidirect
39. #41×C47C22×C4semidirect
40. C2×Q8×C47C22×C4semidirect
42. C2×D4×C47C22×C4semidirect
43. C2×D4×C47C22×C4semidirect
46. C22×C4×C47C22×C4semidirect
68. #62652C47direct (N × H)
79. C4×H(5,𝔽2)C2×C47semidirect
80. #3428C2×C47semidirect
81. C2×#518C2×C47semidirect
86. C2×H(5,𝔽2)C4×C47semidirect
90. #520C22×C47semidirect
91. #519C22×C47semidirect
92. #518C22×C47semidirect
93. #518C22×C47semidirect
94. C4×#41C22×C47semidirect
95. C2×C4×D4C22×C47semidirect
96. C2×#117C22×C47semidirect
97. C22×C22⋊C4C22×C47semidirect
98. C47#62652direct (N × H)
100. H(5,𝔽2)C2×C4×C47semidirect
101. C2×#41C2×C4×C47semidirect
104. C22×D4C2×C4×C47semidirect
108. C23×C4C23×C47semidirect
109. C4×Q8C23×C47semidirect
110. C4×D4C23×C47semidirect
112. #117C23×C47semidirect
113. C2×C4⋊C4C23×C47semidirect
115. C2×C22⋊C4C23×C47semidirect
116. C2×C42C23×C47semidirect
118. C24C22×C4×C47semidirect
121. #41C22×C4×C47semidirect
122. C2×Q8C22×C4×C47semidirect
124. C2×D4C22×C4×C47semidirect
125. C2×D4C22×C4×C47semidirect
128. C22×C4C22×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C22×H(5,𝔽2)×C472
C4×H(5,𝔽2)×C472
C47×#34282
C2×C47×#5182
#6265247